analysis of plate straightening approaches

Eindhoven University of Technology Master Internship

Analysis of plate straightening approaches

[MT 07.10] Thijs Romans, BEng.

Eindhoven University of Technology

Master Internship

Analysis of plate straightening

approaches

Thijs Romans, BEng. External Supervisor: TU/e Supervisor: Christopher Bayley, PhD. PEng prof. dr. ir. Marc Geers DRDC Atlantic, Eindhoven University of Dockyard Laboratory Pacific Technology CFB Esquimalt, Victoria, BC Eindhoven, Noord-Brabant Canada The Netherlands Esquimalt, 15 February 2007

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Table of contents Table of contents................................................................................................................. ii Acknowledgements............................................................................................................ iii Abstract ............................................................................................................................... 1 Summary............................................................................................................................. 2 1. The Victoria class submarine.......................................................................................... 3 2. Geometry......................................................................................................................... 5 3. Material ........................................................................................................................... 7

3.1. Mechanical material properties................................................................................ 7 3.1.1. Tensile experiments .......................................................................................... 8 3.1.2. Tensile experiments results............................................................................... 9 3.1.3. Indentation experiments.................................................................................. 11 3.1.4. Indentation experiments results ...................................................................... 12

3.2. Thermal material properties................................................................................... 13 4. Mechanical straightening .............................................................................................. 15

4.1. Experiments ........................................................................................................... 15 4.1.1. Set-up .............................................................................................................. 15 4.1.2. Results............................................................................................................. 17

4.2. Simulations ............................................................................................................ 18 4.2.1. LS-DYNA input keyword file (mechanical)................................................... 18 4.2.2. Results............................................................................................................. 19 4.2.3. Influence of constraint and incorporation of weld residual stresses ............... 23

5. Flame straightening....................................................................................................... 25 5.1. Experiments ........................................................................................................... 25 5.2 Thermo-mechanical simulations............................................................................. 26

5.2.1 LS-DYNA input keyword file (thermal).......................................................... 26 5.2.2 Results.............................................................................................................. 27

Conclusion ........................................................................................................................ 30 Literature list ..................................................................................................................... 31 Appendix A: Submarines names and dates....................................................................... 33 Appendix B: Final_bar_geomerty.sce .............................................................................. 34 Appendix C: Tensile experiments results ......................................................................... 41 Appendix D: Stress and strain formulas ........................................................................... 46 Appendix E: Vickers Hardness formulas.......................................................................... 47 Appendix F: Temperature dependency............................................................................. 48 Appendix G: Bending formulas ........................................................................................ 49 Appendix H: SB02DOF keyword file............................................................................... 50 Appendix I: Scilab mechanical straightening m-files....................................................... 63 Appendix J: Plots of finite element variations.................................................................. 79 Appendix K: Compressed heat transfer keyword file....................................................... 81 Appendix L: Flame_straightening.sce .............................................................................. 84

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Acknowledgements I would like to gratefully acknowledge the following individuals and organizations for their help and support through the completion of this internship:

Dr. Christopher Bayley for his constant guidance and support and for constantly challenging me to expand my knowledge and improve this work; Prof. dr. ir. Marc Geers for providing me with this opportunity and for being my supervisor at the TU/e Eindhoven in this foreign internship All my co-workers at Dockyard Laboratory Pacific for offering assistance and feedback on a regular basis, and for making me feel home in another country And most importantly, my parents Jean & Hannie Romans for their years of support and interest, through which I had the opportunity to develop and educated myself

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Abstract

This report examines two approaches to resolve a geometrical imperfection of a high tensile steel plate. Two different procedures are examined; mechanical straightening and flame straightening. The report summarizes the results from the experiments and numerical simulations using FEM (LS-DYNA). With the aid of the experimental and numerical results, a comparison between these two straightening methods is made. Keywords: NQ1 high tensile steel, mechanical straightening, flame straightening, thermo-mechanical simulations, LS-DYNA

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Summary

This report covers the research performed by a mechanical engineering student during a three months internship at Dockyard Laboratory Pacific (DL(P)). DL(P) is part of Defence Research and Development Canada. A foreign internship is a requirement of the mechanical engineer master’s diploma at the Eindhoven University of Technology (TU/e).

The report tries to find a solution for a geometrical imperfection found in a NQ1 high tensile steel plate. The height of this deviation lies between 5 and 8 mm while the relevant standard limits such undulations to only 3 mm. Therefore procedures and methods are investigated to straighten the metal plate.

Two different types of straightening will be compared; mechanical and flame straightening. Mechanical straightening applies a force which deforms the material plastically. The other procedure examined is flame straightening. This procedure relies on the difference in thermal expansion to flatten out the material by applying heat to predefined spots on the metal plate.

To experimentally characterize these procedures two specimens have been extracted from the metal plate. These specimens take the shape of beams and are physically tested by the use of appropriate experiments. Subsequently virtual counter parts will be examined by using the non-linear finite element analysis program, LS-DYNA. By comparing these two approaches, a well grounded conclusion can be made, about which procedure is most suitable for straightening the metal plate.

The report layout follows the following progression. First the Victoria class submarine is examined and discussed in chapter 1. In chapter 2 and 3 the shape and material properties of the specimens, used in the experiments and finite element models, are described. Chapter 4 and 5 cover the mechanical straightening and flame straightening procedures.

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1. The Victoria class submarine

The Victoria class submarines, formerly know as the Upholder class submarines or the Type 2400 patrol class submarines, are diesel-electric hunter-killer submarines. The name, Type 2400, comes from their 2400t water displacement. This type of submarine was designed in the late 1970s to supplement the UK’s nuclear submarine force.

The English company Vickers Shipbuilding and Engineering Ltd or VSEL, developed the Upholder class. The first vessel ordered by the UK royal navy in 1983 was commissioned in 1990 as the HMS UPHOLDER. Three other vessels (ordered in 1986) followed; HMS UNSEEN, HMS URSULA and the HMS UNICORN. These were commissioned between 1991 and 1993. The submarines only saw brief service before being mothballed, following a defensive review by the UK government in 1994, which was in favour for an all nuclear force. Canada purchased the submarines in 1998 and BAE Systems (formerly VSEL) at Barrow were contracted to refit the submarines. The submarines were later transferred to Halifax, Canada for commissioning. [1]

One submarine, the HMCS VICTORIA [876] (ex-HMS UNSEEN), operates in the Maritime Forces Pacific fleet, which has a base in Esquimalt near Victoria in British Columbia. The three other submarines renamed HMCS WINDSOR [877], HMCS CORNER BROOK [878] & HMCS CHICOUTIMI [879] (ex-HMS Unicorn, Ursula and Upholder, respectively) operate within the Maritime Forces Atlantic Fleet based in Halifax. [2] For further information see Appendix A.

During the mothballed period between the years 1994 and 1998 the condition of each submarine deteriorated. There have been much arguments over the quality of the submarines, but one must not forget that these submarines are packed with technology generally found only on nuclear-power submarines and so they are still widely regarded as being among the best diesel-electric submarines in the world. These boats are quieter and more manoeuvrable than there nuclear brothers, but sub sequentially have a far shorter range.

Figure 1.1: Type 2400 patrol class submarine (Corvus Publising Ltd./Canada’s Navy)

Figure 1.2: The Victoria class submarine in dry-dock; HMCS VICTORIA [876] (DND)

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Figure 1.3: The Victoria class submarine; HMCS Victoria [876] (US Navy, Ray F. Longaker, Jr.)

The design of the submarine features a single skin hull stiffened by circular

internal frames and constructed out of NQ1 high tensile steel, which is similar to the American designated HY-80 steel and broadly used for military applications. The skin of the submarine is fitted with about 22,000 elastomeric acoustic tiles to reduce the submarine’s acoustic signature. The hull is a teardrop shape design, 70.3m in length by 7.6m in width and with a hull depth of 5.5m. This shape is normally used only with nuclear submarines. [3]

The diving depth of the submarine is 200 m. Speed above water is KNOTS (22 km/h) and below KNOTS (37 km/h). Patrol endurance can go up to 56 days with a range of 13 000 km and has a crew of 48 sailors. [4]

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Figure 2.2: Close-up from the weld

2. Geometry In this internship a metal

plate with a geometrical imperfection is being investigated. The plate is made from 2 pieces of NQ1 high tensile steel which have been butt welded together. The geometric imperfection developed on either side of a butt weld, and on the upper surface of the plate. The peak deviation is 8 mm. To analyse this excursion in greater detail, three smaller sections have been cut out of the plate. Two, of these three bars, are depicted in figure 2.1. On one of these two bars, strain gages with cables have been attached. This bar will be used for mechanical straightening, discussed in chapter 4, while the other longer bar in the background, will serve as a specimen for

flame straightening. The curved-shape of the surface deviation is clearly visible on this longer bar.

By examining one of these bars in closer proximity, the butt weld can be distinguished. A close-up of the weld is shown in figure 2.2. In the sketch of figure 2.3 three welding zones can be distinguished. Here the black represents the weld or fusion zone, the medium gray the heated-effected

zone (HAZ) and the lightest gray the base material. The metal in the HAZ has different material characteristics than the fusion zone or base material and relates to the influence of the thermal cycle on the microstructure [5]

The geometry of the bars; their exact dimension and also the position of the weld are measured by the use of a laser-scanner. For distances in the micron to millimetre

range the laser-scanner is very accurate and knowledge of the exact geometry of the bars is an essential input to the numerical simulations. To measure the bars, the laser-scanner was slid along a cylindrical rod and the distance between the laser-scanner and the position along the rod was simultaneously recorded by a computer and written into text-files. The laser-scanner and positions data were recorded in volts and was

converted to distance through calibrations. This is done within a program called Scilab 4.0, [6], [7], [8], [9], [10] a freely available Matlab-like application. Key feature of Scilab is its ability to handle matrices.

Figure 2.1: Two bar specimens

Figure 2.3: Geometry before and after welding

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Appendix B contains the script files used to determine the surface deviations, while the interpolated curves of the upper surface deviations of both bars are plotted in figure 2.4.

Figure 2.4: Surface deviation of a) flame (P1) and b) mechanical straightening (P2) bars

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3. Material

The material of concern in this research project is NQ1 high tensile steel. NQ1 high tensile steel has a tempered Martensite crystal structure. Martensite most commonly refers to a form of ferrite supersaturated with carbon, found in very hard steels. Martensite is formed by rapid cooling (quenching) of Austenite, which traps carbon atoms that do not have time to diffuse out of the crystal structure. When viewed in cross-section, the lens-shaped crystal grains appear needle-shaped. This can be viewed in figure 3.1. [11]

3.1. Mechanical material properties

For computer simulation or simple analyses on the excursion, material properties for the NQ1 high tensile steel have to be known. Due to the similarity between NQ1 and the American grade HY-80 steel, many of the mechanical properties of NQ1 have been assumed similar to the more readily available HY-80 properties.

HY80 steel is used primarily for military applications. It has a minimum high yield strength of 80 ksi (550 MPa), and is considered to be a low carbon, low alloy steel with nickel, molybdenum and chromium additions. It has good weld ability and notch toughness along with good ductility even in welded sections. Typical mechanical material properties at 293K are presented in table 3.1.

Table 3.1: Typical mechanical material properties of HY80 at 293 K [12], [13], [14], [15]

Mechanical material properties Value Density 7830 [kg/m3]

Yield limit 550 [MPa] Modulus of elasticity (tension) 207 [GPa]

Poisson Ratio 0.28 Hardening modulus 30 [GPa]

Figure 3.1: Martensite crystal structure (Nayang Tech. University)

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Figure 3.3: Geometry of the tensile specimens

3.1.1. Tensile experiments

Tensile experiments were done to find and compare the material properties of the metal plate, to those found in the literature and reported in Table 3.1. And to establish whether mechanical properties of the weld metal were different from the base material.

Cylindrical tensile bars were extracted from a section of the metal plate. A sketch of this section, which has the geometry of a bar, can be seen in figure 3.2. Three sample locations can be distinguished. The first type of tensile specimens is designated L. These specimens are extracted from the base material and have a longitudinal orientation, while specimens taken from section W and C have a tangential orientation. Furthermore, the difference between W- and C-locations

is that C-specimens were obtained from the base material while location W specimens were taken from the butt weld.

The geometry of a tensile specimen can be seen in figure 3.3. The cross-section of each specimen is on average 32e-6 mm2 and has a gage length of 19 mm. Unfortunately a manufacturing error resulted in the wrong thread pitch being machined and the tensile specimens could not tested in the intended grips. Instead, a sleeve was manufactured to accommodate the misthreaded specimens and inserted into a pair of hydraulic grips. A photograph of the material

testing system and the extensometer used in the tensile specimens is seen in figure 3.4.

During each test both the displacement and force were recorded. The displacement was measured by both an extensometer attached to the tensile specimens and the actuator movement. The extensometer measured the elongation of the gage region of the tensile specimens over a distance of 10 mm while the actuator displacement (in this case the lower part of the testing system) measures the displacement of the cross head. However, this value is less accurate, due to machine compliance and slippage within the hydraulic clamps.

Figure 3.2: Three tensile specimen locations

Figure 3.4: Tensile experiments set-up

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[W3] Stress-strain curves

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-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Strain [-]

Str

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[1] True stress vs. strain [1] Engineering stress vs. strain

[2] True stress vs. strain (extensometer) [2] Engineering stress vs. strain (extensometer)

3.1.2. Tensile experiments results

The complete set of results for all the tensile experiments (specimens; C1, C4, L1, L2, W2 and W3) can be found in Appendix C. In this chapter only the results of one of the weld metal specimens (W3) is presented in figure 3.5.

Data obtained from the tensile experiments was converted into engineering stress

engineering strain and in true stress and true strain. The formulas used for these calculations can be found in Appendix D. [16]

In figure 3.5 four lines can be distinguished. Two lines are drawn by using the data obtained by the extensometer, while the other two other lines are calculated by using the measured displacement of the actuator. The extensometer data stops at a 0.2 engineering strain, because the extensometer was limited to a range of only ±2 mm elongation

Figure 3.5: Stress-strain curves for one of the weld only tensile specimen (W3) showing the difference s between true-stress and engineering stress, along with the influence of the different displacement measurement systems

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Although the actuator displacement has a greater range, a comparison of the elastic portion of the stress strain curves shown in figure 3.6 reveals that it is less accurate.

[W3] Elastic behavior

y = 154817x + 1095.2 y = 23368x - 1.4389

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-0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

Strain [-]

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[2] True stress vs. strain (extensometer) [1] True stress vs. strain

Linear ([2] True stress vs. strain (extensometer)) Linear ([1] True stress vs. strain)

Figure 3.6: Modulus of elasticity comparison for tensile specimen depending on whether the strain is determined from either the cross head or extensometer

In figure 3.6 trend lines have been drawn in the elastic region of tensile behaviour.

The best-fit lines show that the computed modulus of elasticity is 154 GPa for the extensometer, which is much closer to the published value of 207 GPa, than the 23 GPa calculated by the displacement of the actuator. The larger error in the actuator derived modulus is the result of slippage within the load train which is included in the actuator measurement, but not present within the gage length of the specimen. The significant error in the extensometer derived modulus may be attributed to the use of elastic bands to attach it to the specimen.

Overall it can be concluded that the extensometer gives more accurate values, however over a shorter range. Conclusions drawn between the different specimen locations can still be made, because they all experience the same experimental approach.

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In figure 3.7 the true stress-strain curves (based on the extensometer) for all the sampling locations are presented. From the similarity in the results of base metal results in the longitudinal and transverse directions (i.e., samples L1, L2, C1and C4), differences in the stress-strain behaviour due to the specimen orientation can be neglected. This leads to the conclusion that there is no difference between the axial and tangential orientation in the base material and the base material behaviour thus can be viewed as isotropic. [17]

Figure 3.7: True-stress curves for all locations

There is however a slight difference between the weld material and the base

material due in part to the micro-structural changes of the material during welding. [5] To investigate this difference in behaviour, indentation measurements were taken across the weld to confirm the trends observed in the tensile test.

3.1.3. Indentation experiments

To verify whether the increased yield behaviour of tensile specimen W2 is an experimental error or a result of different material properties of the weld, indentation experiments were performed.

Micro Vickers indentations were taken on a cross section of the metal plate. Indentations were taken along three parallel lines located at the quarter, middle and three quarter through-thickness positions. The sampling location set-up can be viewed in figure 3.8.

[2] Calculation by extensometer

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[C1] True stress vs. strain [C4] True stress vs. strain [L1] True stress vs. strain

[L2] True stress vs. strain [W2] True stress vs. strain [W3] True stress vs. strain

Figure 3.8: Indentation set-up

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The Vickers Hardness test uses a diamond shaped indenter. [18] In figure 3.9 the indentation testing system along with the specimen is depicted. The weld is located in the exact middle of the bar and taken as the zero position. When the indenter is placed on the surface with an applied load of 0.2 kg, the average indentation surface area is 8.5e+2 µm2.

3.1.4. Indentation experiments results

The indentation results are presented in figure 3.10. As sketched in Figure 3.8, the left and right most indentations are located in the base material. These base material indentations have an average Vickers Hardness of 230 Hv, which is equivalent to a maximum tensile strength of 736 MPa (See Appendix E for calculation details). [19] This

Figure 3.9: Indentation testing system

Figure 3.10: Vickers hardness values found for three different drawn lines on the metal bar

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corresponds well with the true stress-strain curves for base metal tensile results (i.e. C1, C4, L1 and L2).

Between the base material points, peaks in the indentation values correspond with the heat affected zones and between each peak lies the weld metal. The relative location of the peaks from each of the three sampling locations is explained by viewing the weld geometry, which has an hourglass-shape: The weld zone is much smaller at the mid point than at the ¼ and ¾ through-thickness locations.

Apart from the clearly discernable HAZ boundaries, the hardness profiles confirm that the weld and base materials have similar tensile properties. The difference between the tensile behaviour of two weld only specimens W2 and W3 cannot be explained with the indentations since weld hardness values at all three indentation sampling locations appear to be similar. The premature failure and behaviour of W2 during the tensile experiments must be declared as an experimental error and for the purposes of the numerical simulations there lays insufficient evidence to differentiate the mechanical behaviour of the base and weld metals. Therefore they will be treated as isotropic and uniform along the length of the bar.

3.2. Thermal material properties

Published thermal properties of HY80 steel (NQ1 high tensile steel, respectively) are limited. For the thermo-mechanical simulations the material’s thermal conductivity, thermal expansion and specific heat needs to be defined over the temperature range of interest. For NQ1 steel, these properties are typically reported at room temperature, but are known to be temperature dependent. Not only are the thermal properties temperature dependent, but also the yield limit, elastic modulus and hardening modulus. Unfortunately ascertaining the temperature dependence of all these properties is difficult and frequently not given in the literature. To resolve this, the thermal dependence of the thermal and mechanical behaviour is estimated from three sources Borjessen (2001) [20], Fuerschbach (2002) [21] and Goldak (1985) [22].

For the temperature dependent thermal properties of heat capacity, thermal expansion and conductivity, the values of conventional Martensitic steel listed in Borjessen (2001) are partially adopted and listed in Table 3.2. (See Appendix F) However, for the thermal conductivity, Fuerschbach (2002) suggests a constant value of 44 W/moC for NQ1 steel. To examine the influence of these two different thermal conductivity values, separate simulations are run and compared.

Table 3.2: Temperature dependent thermal material properties for NQ1 high tensile steel [20], [21]

Temperature [oC] 20 125 250 375 500 600 Heat capacity [J/kg oC] 456 500 556 600 652 733 Conductivity [W/m oC] (MAR) [20] 25 25 26 26 27 27 Conductivity [W/m oC] (44C) [21] 44 44 44 44 44 44 Thermal expansion coefficient [1/ oC] 1.1 1.3 1.5 1.7 1.9 2.1

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Yield limit vs. temperature

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304 Stainless steel 23% Carbon Steel Fine grain steel HY80 steel estimate

Table 3.3: Temperature dependent mechanical material properties for NQ1 high tensile steel [20], [22]

Temperature [oC] 20 125 250 375 500 600 Modulus of elasticity [GPa] 210 204 196 185 170 158 Yield limit [MPa] [20], [22] 550 482 415 348 280 221 Hardening modulus [GPa] 30 30 30 30 30 30

Goldak (1985) presents a temperature dependence of the yield stress for a low carbon steel, stainless steel and micro-alloy fine grained steel. From these values it is possible to approximate the temperature dependence of the yield strength of NQ1 steel, by scaling the fine grained yield properties, to the room temperature yield strength of NQ1 steel. The results of this interpolation are plotted in figure 3.11. For the remaining temperature dependent mechanical material properties, the values suggested by Borjesson (2001) for a Martensitic structure are used. This includes the modulus of elasticity and hardening modulus. The data can be viewed in table 3.3 where the values at six different temperature points are defined.

Figure 3.11: Interpolation of yield limit vs. temperature for HY80 steel by scaling the room temperature yield strength from Goldak (1985) [22]

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Figure 4.1: Mechanical Straightening set-up

4. Mechanical straightening

In chapter 2 a surface deviation was reported for the bar specimens. For the bar tested in the mechanical straightening procedure this deviation has a peak value of 5 mm. The goal set out in this research project is to determine a method to flatten the plate which will introduce the least amount of residual stresses within the straightened bar.

4.1. Experiments

Mechanical straightening experiments are performed on metal bar P2. The data collected from these experiments will establish a baseline and verification for the numerical models, described in chapter 4.2. It also serves to validate the assumptions that the bar behaves isotropically and has uniform material properties along its length.

4.1.1. Set-up

Prior to starting the mechanical straightening set-up the peak forces necessary to plastically deform the metal bar is predicted. This peak force is determined using the formulas of “moment of inertia of rectangle area” [23] and the “Euler-Bernoulli beam equation” [24], both described in Appendix G. Based on these calculations, it is concluded that a load of 45 kN is required to yield the bar For flattening the deviation, the force applied during the experiments should thus be in the range of 45 to 90 kN.

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The set-up for the experiments can be seen in figure 4.1. Figure 4.2 sketches the metal bar along with the location of the strain gauge, reaction and loading points. The force is applied at the peak deviation with a cylindrical-shaped rod mounted on a 250 kN load-cell. This force applied is measured and recorded by a computer. The voltage output of five attached strain gages is also being recorded. These strain gages are Vishay’s “general purpose” strain gages (Item code 17059) and have a range up to 30,000 micro-strain and a gage length of 3.5 mm. Their positions are chosen as follows. Strain gages A, B and C are mounted on the bottom surface while gages U and V are attached to top surface. All of the gages are oriented so that they measure along the beam length. Gages A and U are located on the opposite sides of the beam within the weld metal. The gages are located 18 and 20 mm (A and U, respectively) away from the loading point, while gages C and V are located in the base material 24 and 25 mm, respectively, away from the loading point. Gage B is positioned directly below the applied force and is located where the maximum x-strain is anticipated to occur during the experiment. The strain gages are set-up in a quarter-bridge configuration using an internal dummy which is described in the signal conditioning amplifier manual (1993). [25] To calibrate the gages, a shunt method is used which increases the resistance of the active gauge by a known amount and then related to the voltage output.

The bar itself is supported by two cylindrical polished rods spanning the peak deviation. The beam is able to move along the rods which are rigidly clamped to a large I-shaped beam and thus any deformation within the restraints can be neglected.

The beam is incrementally deformed with increasingly greater depths. The initial cycles start with only a minimal force well within the elastic behaviour of the material. After each load cycle, the load is removed and the flatness of the beam determined. Incrementally adding the force allows more control, especially since the required depth to flatten the beam was initially unknown. Furthermore, the initial elastic deformations conditions the strain gages reducing the magnitude of the hysterisis effect.

Figure 4.2: Close-up sketch of the metal bar in mechanical straightening

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4.1.2. Results

In figure 4.3 a subplot of the strain versus force and displacement versus force

collected during the mechanical straightening experiment is presented. In this figure the bottom row of plots correspond to strain gages A, B and C, while the upper left and right subplots display the results from gages U and V, respectively. The center plot on the upper row plots the load as a function of the cross head displacement.

Starting with the cross head displacement vs. force plot several things can be concluded. Clearly visible is the procedure of incrementally increasing the displacement. The peak displacement is 7.0 mm, penetrates well beyond the initial surface deviation of only 5.3 mm. After unloading, the actuator displacement measures 3.2 mm of springback. At this point the beam is still not straight, but within the acceptable tolerances of ±3.0 mm. The maximum force to achieve this displacement is 82 kN while initial yielding occurs slightly above the analytically calculated value of 45 kN thus validating theoretical approximations

The remaining figures plot the strain history of the gages. The gages on the upper row display compressive values, while those on the bottom side are in tension. As expected, gage B is located at the location of greatest strain, and fails beyond 25,000 µε, close to the manufacture’s limit of 30,000 µε. Strain gages A and U, located in the weld metal record less strain than gages C and V located in the base metal. Microstructural

Figure 4.3: Strain vs force and displacement vs force during the mechanical straightening experiment. The gages locations are shown in Figure 4.2

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Figure 4.4: The largest element mesh (25x2x2) for the metal bar

heterogeneity, presence of residual stresses, relative position of the gage with respect to the loading point and the original shape of the deformed beam all contribute to the strain gage readings. In order to examine in detail the geometrical rather than microstructural related factors contributing to the difference in strain gauge readings, a detailed finite element model of the straightening procedure was developed.

4.2. Simulations

With the knowledge and the results from the mechanical straightening experiments, described in chapter 4.1, a numerical simulation is compared to the experimental data. The model serves two main purposes; it allows a detailed understanding of the geometrical influence on the resultant residual stresses, and also as an experimentally validated benchmark for future parametric studies.

4.2.1. LS-DYNA input keyword file (mechanical)

Once calibrated, the finite element model allows the influence of boundary conditions to be studied, the so-called constrained set-up, which would be near impossible to achieve experimentally. This constrained set-up is motivated by the fact the surface deviation exists in a large plate rather than a metal bar. Examining the influence of the boundary conditions helps in getting a better understanding of what is necessary to flatten the deviation on the metal plate, and the ensuing residual stresses which develop during springback.

In this research project LS-DYNA is used. It is a non-linear finite element analysis program capable of simulating complex real world problems. Another program in use is LS-PrePost, an advanced interactive program for preparing input data for LS-DYNA and post processing the results. [26] The last program used in creating a finite element model is NEdit. NEdit stand for Nirvana Editor and is a popular text and source code editor. [27]

In figure 4.4 the simplest mesh for the metal bar is depicted. This particular one consists of 100 elements. It will be named “SolidBeam02DOF” or “SB02DOF”. “02”

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stands for 2 elements in the z-direction. (This is the width of the bar) “DOF” stands for “degree of freedom”. In the mechanical straightening experiments the bar was simply supported and mimics the loadings and restraints imposed during the mechanical straightening experiments. Other variations (the constrained for instance) will be discussed in chapter 4.2.3. A convergence study to study the influence of the mesh size is also performed on models with 800, 6400 and 12800 elements and discussed in chapter 4.2.2, it defines the preferred mesh size. Furthermore the finite element models will be compared with the experimental data gathered in the mechanical straightening experiments. A detailed explanation of the LS-DYNA keyword input file is presented in Appendix H for the file SolidBeam02DOF. For the mechanical straightening simulations, each model is build from 8 noded solid elements. The beam is simply supported on virtual pin and roller assembly allowing translation of one end of the beam relative to a fixed edge. The deformation is applied using a rigid indenter located at the peak deformation. A contact algorithm is used to define the interface between the rigid indenter and the workpiece. Unlike the mechanical straightening experiments, the indenter depth is increased monotonically rather than incrementally and the material model assumes a perfectly plastic behaviour with a yield point of 550 MPa.

4.2.2. Results

Before comparing the mechanical straightening results of the experiments with those of the simulations, the number of elements in each mesh is given in table 4.1.

Table 4.1: Four different meshes for the metal bar

Name Total elements

In x-direction (length)

In y-direction (height)

In z-direction (width)

Simulation Time (sec)

SB02DOF 100 2 2 25 17 SB04DOF 800 4 4 50 97 SB08DOF 6400 8 8 100 1359 SB200DOF 12800 8 8 200 4771

In figure 4.5 the mesh of SB08DOF is depicted. [28] The bar is build up in 8 planes containing 50 x 8 elements. The cylindrical tool can also be viewed. Its mesh never changes in any of the finite element models. The mesh is designed such, that the highest density of elements is at the surface that comes in contact with the metal bar. The elements of the cylindrical tool are 6-noded solid elements.

Figure 4.5: SB08DOF in starting position

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To decide which mesh can be used best, a convergence study comparing the

overall calculation times and the computed results of all the meshes was carried out. If the mesh is smaller, the calculation time is of course shorter, however, the corresponding results are less accurate. Figure 4.6 presents the computed x-strain measured along the top, and the bottom surface of the bar at the peak applied load. (The peak applied load position is visible in figure 4.7) It is clearly visible that the red and black lines, corresponding to models SB08DOF and SB200DOF, respectively, are similar to each other. This leads to the conclusion that the mesh in SB08DOF is sufficiently fine to capture the geometry and any further increase in elements only results in longer calculation time. The local influence of the indenter on the upper surface x-strain is also apparent by the sharp inflection. At this location there is still a difference between the SB08DOF and SB200DOF meshes but SB08DOF mesh is adequate as the location of interest lies on the slopes of the parabola, where the strain gages are located, and not at the indenter location.

Figure 4.6: Surface strain measured along the top, and the bottom, of the metal bar

Figure 4.7: SB08DOF at largest bending moment

21

In figure 4.8 the results of the finite element models is compared with the mechanical straightening data. (Scilab programs designed are listed Appendix I)

Starting with the displacement versus force plot (the middle plot in the upper part

of the subplot) there is good agreement between the measured and simulated indenter displacement versus forces plots, especially when the number of elements is increased. As seen in Figure 4.8 mesh SB08DOF and SB200DOF correspond well with the experimentally measured loads and displacements. However, in the elastic region of the finite element models the predicted slope is steeper than for the mechanical straightening experiments. Also when unloaded, the predicted final displacement is a millimeter less than the mechanical straightening experiments. This difference in the displacements arises from assumptions and slight differences between the numerical and experimental set-ups. Parts and components are never entirely rigid or there are still some tiny little spaces left in the testing system. Examination of the experimental unloading versus force data indicates that these lines are not entirely linear, while in theory they should. Machine compliance could account for this non-linear behaviour during loading. However, even with this slight offset, the result of the finite element compare well to the mechanical straightening experiments data, in particular the peak load of 82 kN is in agreement with the calculated value of 75 kN.

The remaining plots in Figure 4.8 compare the surface x-strain values of the finite element models at the approximate strain gage locations. The x-strains were determined

Figure 4.8: Combined results of the mechanical straightening experiments and the finite element models (SB02DOF/cyan; SB04DOF/pink; SB08DOF/red; SB200DOF/black)

22

at the element closest to the gage center, and as noted in Figure 4.6, the magnitude of the x-strain is highly sensitive to the sampling location. On the lower surface, models SB08DOF and SB200DOF correspond almost perfectly to the mechanical straightening data. The use of these finite element models even gives the opportunity to calculate the entire range of the surface strain in the B position where the strain gage failed.

The predicted strain values along the upper surface of the plate (positions U and

V) do not agree as well as on the lower surface. This can be attributed to the sensitivity of the reported strains as a function of position shown in figure 4.6. It is hard to determine the exact position were the strain gages were attached, and even the slightest error in this position results in a large difference in surface strain. (The slope is the steepest for the position the strain gages are placed). An error can thus easily be made resulting in a large offset.

In figure 4.9 the x- and y-position of nodes on the bottom surface (in red) and top surface (in blue) of the bar are plotted for the starting position, at the peak load and after springback. It shows that in the final position the deviation is reduced to within the allowable range of ±3.0 mm. Also, for the blue line a permanent surface deviation is visible in the form a small dent. This is where the force was applied through a cylindrical tool.

Overall the conclusion may be that the finite element model SB08DOF fits well to the measured experimental data of the mechanical straightening experiments.

Figure 4.9: Calculated x- and y-nodal coordinates along the bottom and top of the bar, before straightening, at the peak load and after springback.

23

4.2.3. Influence of constraint and incorporation of weld residual stresses

Based on the successfully calibrated model SB08DOF, two model variations are

examined. The first examines the influence of boundary constraints, while the second attempts to incorporate weld residual stresses into the model. These have been labeled SB08CON and SB08WELD, respectively. The difference between finite element program SB08DOF and SB08CON is that in the “CON” program the translational degrees of freedom along all edge-faces in the x and y directions of the bar are constrained. This situation is meant to approximate the constraints of trying to flatten out a metal plate which has already been welded into a construction.

This constrained set-up would require a complicated test arrangment, but can be readily modeled. In figure 4.10 the displacement versus force plots of the models SB08DOF, SB200DOF and SB08CON are shown. In Appendix J more figures can be seen, containing results from more finite element simulations. Figure 4.10 shows that the applied force, required to deform a similar sized surface deviation, is a factor of two times larger.

Figure 4.10: Displacement vs. force for SB08DOF, SB200DOF and SB08CON showing the increase in required force.

24

In figure 4.11 the displacement versus effective stress plot (von-mises stress), measured in the middle of the metal bar, is presented. From it can be concluded, that the residual stress in the middle of the metal bar approaches the yield limit of NQ1 high tensile steel. In order to examine the influence of pre-existing weld residual stresses, a finite element model SB08WELD was also designed. Weld residual stresses were introduced into the model through the stress initialization option in LS-DYNA. However, this did not have the desired effect. It was possible to specify the initial stresses in the material, but after the first calculation step the material reached equilibrium. Therefore it was concluded that defining residual could not be implemented without first knowing, and later implementing the spatial distribution of the residual stress state.

As a conclusion to the mechanical straightening, it is capable of straightening the plate, albeit with high loads and unacceptable residual stresses. The final conclusion for mechanical straightening is that it is not a suitable procedure.

Figure 4.11: Displacement vs. effective stress in the middle of the bar for SB08DOF, SB200DOF and SB08CON

25

5. Flame straightening

Another procedure to flatten the metal plate is through flame straightening, and is also investigated in this research project. Experiments have been done on metal bar P1 along with a thermo-mechanical simulation of a similar shaped bar.

5.1. Experiments

In figure 5.1 the complete set-up for the flame straightening experiments is depicted. Metal bar P1 is placed on two wooden supports. On the top and bottom surface, close to the peak of the deviation, two thermocouples are spot welded onto the bar. These will measure the surface temperature during the flame straightening experiment. On the bottom surface, exactly below the peak deviation a strain gage is mounted which will record the bottom surface strain during the flame straightening procedure Figure 5.2 shows the torch used to rapidly heat up the upper surface of the plate where the peak deviation is located. During heating the deviation will be exaggerated, but upon quenching the top surface will contract, causing the beam to bend.

Flame straightening works well for thin parts and sheet steel. Its effect on this type material or this geometry is however unknown. Regrettably, the flame straightening experiment failed to generate any appreciate change in geometry. This was confirmed by the strain gage which hardly had any difference in voltage output.

Figure 5.1: Flame straightening experimental set-up

26

During the flame straightening experiments there was a problem with the thermocouples. Temperature for the top surface needed to be increased to 600 degrees Celsius to have any effect. But the spot weld junction could not resist the gas pressure and frequently came loose. Thus, the flame straightening experimental procedure was difficult to quantify. There was hardy any straightening effect. The strain gage voltage output had only a small difference and the temperature measured were sometimes incomplete. Still there are some useful temperature measurements and these will be compared with the finite element simulations.

5.2 Thermo-mechanical simulations

The previously described finite element input file used for mechanical straightening is used as a basis. Adaptations of the model will be explained and the results from the finite element model will be discussed in chapter 5.2.2. In Appendix K a compressed version of the LS-DYNA heat transfer keyword model can be consulted.

5.2.1 LS-DYNA input keyword file (thermal)

LS-DYNA can solve steady state and transient heat transfer problems on 3-dimensional parts. Heat transfer can be coupled with other features in LS-DYNA to provide modeling capabilities for thermo-mechanical simulations. Calculations are done in a perfectly isolated environment, which assumes that there is no convection or radiation from the part. [29]

The two most evident changes in the input file are the mesh and the units. In the flame straightening set-up a different specimen was used. The geometry of P1 was

Figure 5.2: Flame straightening

27

measured and its values were imported in the finite element model, however the mesh size used in SB08DOF was adopted resulting in 6400 elements. Time units are also changed to reflect the transient nature of the flame straightening procedure.

In the control section of SB2DOF it is necessary to enter the *CONTROL_SOLUTION keyword to identify that a coupled structural thermal analysis is performed. *CONTROL_THERMAL_SOLVER and *CONTROL_THERMAL_TIMESTEP also need to be specified. They specify the type of thermal analysis (transient) and the calculation steps for the thermal analysis. Finally contact specification was eliminated.

Because a coupled thermal analysis is performed, both the thermal and mechanical properties need to be defined. [30] This is done in the “Define Parts and Material” section. For the mechanical behavior *MAT_ELASTIC_PLASTIC_THERMAL is chosen and the thermal properties of table 3.2 are filled in. The temperature dependent mechanical properties listed in Table 3.3 specifies values for the material model *MAT_THERMAL_ISOTROPIC_TD. In chapter 3.2 two different temperature dependent thermal conductivity values were defined. The temperature dependent thermal conductivity adopted from Borjenssen (2001) [20] is labeled MAR while the temperature independent value of 44W/moC found in Fuerschbach (2002) [21] is labeled 44C.

For the boundary conditions, the temperature history of the nodes along a transverse line of the upper surface are specified while the beam remains simply supported. The nodal temperatures at the heating location are specified and follow one of the recorded temperature profiles.

5.2.2 Results The temperature profiles predicted by the finite element model are compared with

the experimental flame straightening thermocouple data recorded on the upper and lower faces. (Scilab program designed is listed Appendix L)

28

In figure 5.3 the experimental and predicted temperature profiles at the thermo-

couple locations are plotted. Time is plotted against temperature. The two red lines indicate the behavior measured by the thermocouples during the flame straightening experiments, while the black, green and blue lines are the simulation results. The red line with the highest peak value represents the top surface of the metal bar where the flame was located. Its temperature is increased to 550 oC in 20 sec while the bottom surface only reaches 250 oC. After heating, the upper surface is quenched and the temperature quickly drops in 40 sec to 180 oC, while the lower surface temperature experiences a slower cooling rate. It is during the quenching phase that the actual straightening takes place. The driving force behind the straightening is due to differences in the thermal expansion between the top surface and bottom surfaces, while the temperature dependence of the mechanical properties ensures that the hotter surface is softer facilitating plastic deformation.

The predicted temperature history of the finite element model is also plotted in figure 5.3. The black line represents the prescribed temperature profile of the top surface of the metal bar while the blue and green lines are the predicted temperature profiles along the bottom surface. In chapter 3.2 two different thermal conductivity properties were defined described for the NQ1 high tensile steel. In figure 5.3 the blue line corresponds to temperature dependent thermal conductivity of Martensite found in Borjessen (2001) [20] while the green line corresponds to a constant thermal conductivity of 44 W/moC found in Fuerschbach (2002) [21]. The influence of an increased thermal conductivity is to increase the heating and cooling rates of the bar material. The increased

Figure 5.3: Time versus temperature for the flame straightening case

29

heating rates along the bottom surface correspond better with the experimental results determined during the flame straightening experiments.

However, the finite element model profiles do not seem to fit very well with the experimental data. This could be due in part to the assumption of an ideally insulated environment used by LS-DYNA along with uncertain material parameters. Convection and radiation effects are not being taken into account causing in a much slower cooling rate in the finite element model than in reality. Also in the finite element model only a small patch of nodes from the top surface are heated, rather than both side edges and bottom surface due to convection effects during the flame straightening exercise. These factors undoubtedly contribute to the slower temperature response along the bottom surface.

Although the finite element models predict a discernable temperature difference

between the upper and lower surfaces, it fails to generate appreciable permanent deformation or straightening as shown in figure 5.4. Here the blue line indicates the starting profile of the metal bar while the red line follows the virtual thermal straightening along the upper surface of the bar. After the flame straightening procedure the deviation of the bar was only reduced by a 0.2mm. Based on the experimental and simulation studies, flame straightening was found to be an unsuitable procedure to flatten the metal plate.

Figure 5.4: x- and y-position along the top of the bar, flame straightening

30

Conclusion In this report both mechanical and flame straightening have been examined to straighten a deviation within a plate. While mechanical straightening was able to straighten the plate, it required high loads and resulted in high residual stresses. Flame straightening, on the other hand, was unable to permanently deform the plate. Therefore, neither procedures was found to be acceptable A comparison between the finite element model results and the experimental data for the mechanical straightening case showed a good fit. Using a validated finite element model provided the opportunity to examine the influence of boundary constraints on the applied load. These boundary constraints are more realistic for a metal plate build into a construction rather than having free edges. Although the deviation on the specimen could be flattened within the allowable range, the forces required were great, and therefore it was concluded that mechanical straightening would be an unsuitable method to resolve this deviation. Flame straightening was concluded to be unsuitable as it was unable to significantly flatten the beam. These conclusion were made based on the both the experimental and finite element results which showed there was almost no reduction in the magnitude of the deviation. Further research for straightening the metal plate, should concentrate on different procedures, for example weld cladding whereby weld metal is built up on the surface of the plate.

31

Literature list

1. http://www.hazegray.org/navhist/canada/current/upholder/ (2006) Victoria class (SSK) patrol submarine, HG&UW Sandy McClearn

2. http://en.wikipedia.org/wiki/Victoria_class_submarine (2007) Upholder/Victoria class submarine, US, Wikimedia Foundation Inc.

3. http://www.naval-technology.com/projects/ssk_victoria (2007) SSK Victoria class long range patrol submarines, Canada, SPG Media Group PLC

4. C. Ryan (2004), Victoria class patrol sub information, Volume 6 Issue 4, Seattle US, The Dolphin Bortherhood (USSVI)

5. http://en.wikipedia.org/wiki/Welding (2007) Welding, US, Wikimedia Foundation Inc.

6. http://www.wolffdata.se/scilab/ScilabStarter.pdf (2005), Scilab (4) Starter, Wolffdata

7. http://www.scilab.org/product/dic-mat-sci/M2SCI_doc.htm (2005), M2Sci, Scilab group

8. http://www.scilab.org/doc/demos_html/index.html (2005), Scilab demonstration pages, Scilab group

9. http://www.engineering.usu.edu/cee/faculty/gurro/Software_Calculators/Scilab_Docs/CEE6510_SCILABExamples.htm (2007), SCILAB examples, G.E. Urroz

10. http://www.utexas.edu/its/rc/answers/math/matlab/manual/ReferenceTOC.html (1994), Matlab Online Reference Documentation, The MathWorks Inc.

11. http://en.wikipedia.org/wiki/Martensite (2007) Martensite, US, Wikimedia Foundation Inc.

12. http://www.suppliersonline.com/propertypages/HY80.asp (2000) HY80 alloy steel material property data sheet, Metal Suppliers Online LLC.

13. http://www.matweb.com/search/SpecificMaterial.asp?bassnum=MSHY80 (2006) HY-80 Steel, Automation Creations Inc.

14. S.C. Hodge, J.M. Minicucci & T.F. Trimble (2003), Cyclic Material Properties Test to determine Hardening/Softening Characteristics of HY-80 Steel, Report No. TDA-19195, Groton US, General Dynamics

15. J.A. Mountford, Jr. (2002), Titanium – Properties, Advantages and Applications solving the corrosion problems in marine service, Paper 02170, Houston US, NACE International

16. E. M. Mielink (1991), Metalworking Science and Engineering, TS205.M52, New York US, McGraw-Hill Inc.

17. http://en.wikipedia.org/wiki/Isotropic (2007), Isotropy, US, Wikimedia Foundation Inc.

18. http://en.wikipedia.org/wiki/Vickers_hardness_test (2007), Vickers hardness test, US, Wikimedia Foundation Inc.

19. http://www.tf.uni-kiel.de/matwis/amat/mw1_ge/kap_8/advanced/t8_4_2.html (2004), Hardness, H Föll

20. L. Borjesson & L. Lindgren (2001), Simulation of Multipass Welding With Simultaneous Computation of Material Properties, Vol. 123, Lulea Sweden, ASME

32

21. P.W. Fuerschbach & G.R. Eisler (2002), Determination of Material Properties for Welding Models by Means of Arc Weld Experiments, 6th Intl. Trends in Welding Research, Albuquerque US, Sandia National Laboratories

22. J. Goldak, B. Patel, M. Bibby & J. Moore (1985), Advanced joining of Aerospace Metallic Materials - Computational Weld Mechanics, No. 398, Neuilly Sur Seine France, Agard

23. J.L. Meriam (1952), Mechanics Part I Statics, New York US, John Wiley & Sons Inc.

24. http://en.wikipedia.org/wiki/Bending (2007), Bending, US, Wikimedia Foundation Inc.

25. Measurements Group, Inc. (1994), Instruction Manual Model 2310 Signal Conditioning Amplifier, US, Measurements Group Inc.

26. http://en.wikipedia.org/wiki/LS-DYNA (2007), LS-DYNA, US, Wikimedia 27. http://en.wikipedia.org/wiki/NEdit (2007, NEdit, US, Wikimedia 28. Livermore Software (2002), LS-Pre/Post v1.0, Livermore US, Livermore

Software Technology Corporation 29. A.B. Shapiro (2003), Heat Transfer in LS-DYNA, Livermore US, Livermore

Software Technology Corporation 30. Livermore Software (1999), LS-DYNA Thermal Analysis User Guide, Livermore

US, Livermore Software Technology Corporation 31. Livermore Software (2002), Getting Started with LS-DYNA, Livermore US,

Livermore Software Technology Corporation 32. Livermore Software (2003), LS-DYNA Keyword User’s Manual, Version 970,

Livermore US, Livermore Software Technology Corporation 33. B.N. Maker & X. Zhu (2000), Input Parameters for Metal Forming Simulation

using LS-DYNA, Volume 1, Livermore US, Livermore Software Technology Corporation

34. B.N. Maker & X. Zhu (2001), Input Parameters for Metal Forming Simulation using LS-DYNA, Volume 2, Livermore US, Livermore Software Technology Corporation

35. J.D. Reid (1998), LS-DYNA Examples Manual, Livemore US, Livermore Software Technology Corporation

36. http://www.dynaexamples.com/ (2004), Dyna Examples, LTSC and Dynamore

33

Appendix A: Submarines names and dates

Canadian name HMCS VICTORIA

[876]

HMCS WINDSOR

[877]

HMCS CORNER

BROOK [878]

HMCS CHICOUTIMI

[879] English name HMS

UNSEEN [S41]

HMS UNICORN

[S43]

HMS URSULA

[S42]

HMS UPHOLDER

[S40] Laid down January

1986 February

1989 February

1987 November

1983 Launch date November

1989 April 1992

February 1992

December 1986

UK’s Commission date

June 1991

June 1993

May 1992

June 1990

UK’s Decommission date

July 1994

October 1994

July 1994

April 1993

Canadian Commission data

December 2000

June 2003

March 2003

October 2004

34

Appendix B: Final_bar_geomerty.sce

//DRDC Pacific Calculation T.Romans //last modified: 2 february 2007

//make sure scilab uses the right directory is used!!!//make sure the names of the .txt−files are correct!!!

//close all figuresxdel(winsid())

//importing data from the experiments//datafloor is the height between laser head and floor//dataP1 and dataP2 are the heights between laser head and bars//dataP1wires and dataP2wires is the same as dataP1 and dataP2 but with wires//wrapped around the to mark the beginning and ending of the weld materialdatafloor=fscanfMat(’081206_floor_measurement.txt’);dataP1=fscanfMat(’081206_P1_outside.txt’);dataP1wires=fscanfMat(’081206_P1_outside_wires.txt’);dataP2=fscanfMat(’081206_P2_outside.txt’);dataP2wires=fscanfMat(’081206_P2_outside_wires.txt’);

//subdividing data in a height column and a distance column//the distance column is the distance between the laserhead and tested surfaceheight_floor=datafloor(:,1);distance_floor=datafloor(:,2);

height_P1=dataP1(:,1);distance_P1=dataP1(:,2);

height_P1wires=dataP1wires(:,1);distance_P1wires=dataP1wires(:,2);

height_P2=dataP2(:,1);distance_P2=dataP2(:,2);

height_P2wires=dataP2wires(:,1);distance_P2wires=dataP2wires(:,2);

//mulitplying by factor and offset//values for calculating (x−)distance and (y−)heightheight_a=0.001526;distance_a=0.076371;height_offset=0.000763;distance_offset=0.038185;

Fh=(height_a.*height_floor)+height_offset;Fd=(distance_a.*distance_floor)+distance_offset;

P1h=(height_a.*height_P1)+height_offset;P1d=(distance_a.*distance_P1)+distance_offset;

P1wh=(height_a.*height_P1wires)+height_offset;P1wd=(distance_a.*distance_P1wires)+distance_offset;

P2h=(height_a.*height_P2)+height_offset;P2d=(distance_a.*distance_P2)+distance_offset;

P2wh=(height_a.*height_P2wires)+height_offset;P2wd=(distance_a.*distance_P2wires)+distance_offset;

//dividing seperate runs after reviewing data//one measurement normally contained three/four //runs of going forward and backward along the surface//of the bar//runs spanned by rows are seperated//this in FhF1(floor height forward run 1)//this in FdB3(floor distance backward run 3)FhF1=Fh(110:400,:);FhB1=Fh(400:640,:);FhF2=Fh(640:910,:);

Feb 02, 07 10:17 Page 1/7Final_bars_geometry.sceFhB2=Fh(910:1120,:);FhF3=Fh(1120:1390,:);FhB3=Fh(1390:1640,:);

FdF1=Fd(110:400,:);FdB1=Fd(400:640,:);FdF2=Fd(640:910,:);FdB2=Fd(910:1120,:);FdF3=Fd(1120:1390,:);FdB3=Fd(1390:1640,:);

P1hF1=P1h(130:276,:);P1hB1=P1h(339:475,:);P1hF2=P1h(547:668,:);P1hB2=P1h(722:827,:);P1hF3=P1h(895:1012,:);P1hB3=P1h(1067:1164,:);P1hF4=P1h(1228:1339,:);P1hB4=P1h(1396:1496,:);P1hF5=P1h(1566:1667,:);P1hB5=P1h(1715:1813,:);

P1dF1=P1d(130:276,:);P1dB1=P1d(339:475,:);P1dF2=P1d(547:668,:);P1dB2=P1d(722:827,:);P1dF3=P1d(895:1012,:);P1dB3=P1d(1067:1164,:);P1dF4=P1d(1228:1339,:);P1dB4=P1d(1396:1496,:);P1dF5=P1d(1566:1667,:);P1dB5=P1d(1715:1813,:);

P1whF1=P1wh(146:291,:);P1whB1=P1wh(374:499,:);P1whF2=P1wh(555:687,:);P1whB2=P1wh(744:860,:);P1whF3=P1wh(915:1045,:);P1whB3=P1wh(1103:1205,:);P1whF4=P1wh(1268:1381,:);P1whB4=P1wh(1430:1545,:);

P1wdF1=P1wd(146:291,:);P1wdB1=P1wd(374:499,:);P1wdF2=P1wd(555:687,:);P1wdB2=P1wd(744:860,:);P1wdF3=P1wd(915:1045,:);P1wdB3=P1wd(1103:1205,:);P1wdF4=P1wd(1268:1381,:);P1wdB4=P1wd(1430:1545,:);

P2hF1=P2h(138:228,:);P2hB1=P2h(290:370,:);P2hF2=P2h(419:499,:);P2hB2=P2h(534:629,:);P2hF3=P2h(664:742,:);P2hB3=P2h(775:853,:);P2hF4=P2h(893:983,:);P2hB4=P2h(1011:1103,:);

P2dF1=P2d(138:228,:);P2dB1=P2d(290:370,:);P2dF2=P2d(419:499,:);P2dB2=P2d(534:629,:);P2dF3=P2d(664:742,:);P2dB3=P2d(775:853,:);P2dF4=P2d(893:983,:);P2dB4=P2d(1011:1103,:);

Feb 02, 07 10:17 Page 2/7Final_bars_geometry.sce

Printed by Thijs Romans − COOP

Tuesday February 06, 2007 1/4Final_bars_geometry.sce

P2whF1=P2wh(108:216,:);P2whB1=P2wh(280:362,:);P2whF2=P2wh(400:476,:);P2whB2=P2wh(516:585,:);P2whF3=P2wh(621:707,:);P2whB3=P2wh(734:810,:);P2whF4=P2wh(841:918,:);P2whB4=P2wh(957:1028,:);

P2wdF1=P2wd(108:216,:);P2wdB1=P2wd(280:362,:);P2wdF2=P2wd(400:476,:);P2wdB2=P2wd(516:585,:);P2wdF3=P2wd(621:707,:);P2wdB3=P2wd(734:810,:);P2wdF4=P2wd(841:918,:);P2wdB4=P2wd(957:1028,:);

//plotting functionsscf(1)subplot(2,3,1);plot(FdF1,FhF1,’r’);plot(FdB1,FhB1,’b’);plot(FdF2,FhF2,’r’);plot(FdB2,FhB2,’b’);plot(FdF3,FhF3,’r’);plot(FdB3,FhB3,’b’);xtitle(’floor measurements’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,3,2);plot(P1dF1,P1hF1,’r’);plot(P1dB1,P1hB1,’b’);plot(P1dF2,P1hF2,’r’);plot(P1dB2,P1hB2,’b’);plot(P1dF3,P1hF3,’r’);plot(P1dB3,P1hB3,’b’);plot(P1dF4,P1hF4,’r’);plot(P1dB4,P1hB4,’b’);plot(P1dF5,P1hF5,’r’);plot(P1dB5,P1hB5,’b’);xtitle(’P1’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,3,3);plot(P1wdF1,P1whF1,’r’);plot(P1wdB1,P1whB1,’b’);plot(P1wdF2,P1whF2,’r’);plot(P1wdB2,P1whB2,’b’);plot(P1wdF3,P1whF3,’r’);plot(P1wdB3,P1whB3,’b’);plot(P1wdF4,P1whF4,’r’);plot(P1wdB4,P1whB4,’b’);xtitle(’P1wires’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,3,4);plot(P2dF1,P2hF1,’r’);plot(P2dB1,P2hB1,’b’);plot(P2dF2,P2hF2,’r’);plot(P2dB2,P2hB2,’b’);plot(P2dF3,P2hF3,’r’);plot(P2dB3,P2hB3,’b’);plot(P2dF4,P2hF4,’r’);plot(P2dB4,P2hB4,’b’);xtitle(’P2’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,3,5);plot(P2wdF1,P2whF1,’r’);plot(P2wdB1,P2whB1,’b’);plot(P2wdF2,P2whF2,’r’);

Feb 02, 07 10:17 Page 3/7Final_bars_geometry.sceplot(P2wdB2,P2whB2,’b’);plot(P2wdF3,P2whF3,’r’);plot(P2wdB3,P2whB3,’b’);plot(P2wdF4,P2whF4,’r’);plot(P2wdB4,P2whB4,’b’);xtitle(’P2wires’,’distance covered (mm)’,’distance from laser head (mm)’);

//sizing gives the size of the column//normal result is SP1dF1 = 147. 1.//normal result is SP1dB1 = 137. 1.//mtlb_fliplr flips the result for the backward runs//this results in SP1dB1 = 1. 137.SP1dF1=size(P1dF1);SP1dB1=size(P1dB1);SP1dB1=mtlb_fliplr(SP1dB1);SP1dF2=size(P1dF2);SP1dB2=size(P1dB2);SP1dB2=mtlb_fliplr(SP1dB2);SP1dF3=size(P1dF3);SP1dB3=size(P1dB3);SP1dB3=mtlb_fliplr(SP1dB3);SP1dF4=size(P1dF4);SP1dB4=size(P1dB4);SP1dB4=mtlb_fliplr(SP1dB4);SP1dF5=size(P1dF5);SP1dB5=size(P1dB5);SP1dB5=mtlb_fliplr(SP1dB5);

SP2dF1=size(P2dF1);SP2dB1=size(P2dB1);SP2dB1=mtlb_fliplr(SP2dB1);SP2dF2=size(P2dF2);SP2dB2=size(P2dB2);SP2dB2=mtlb_fliplr(SP2dB2);SP2dF3=size(P2dF3);SP2dB3=size(P2dB3);SP2dB3=mtlb_fliplr(SP2dB3);SP2dF4=size(P2dF4);SP2dB4=size(P2dB4);SP2dB4=mtlb_fliplr(SP2dB4);

//using sizing results gives values of highest lowest distance points//this is the ending distance and starting distance in a column//P1F1 = 888.38566// 219.98666//P1B1 = 888.38566// 224.87441 P1F1=P1dF1(SP1dF1,:);P1B1=P1dB1(SP1dB1,:);P1F2=P1dF2(SP1dF2,:);P1B2=P1dB2(SP1dB2,:);P1F3=P1dF3(SP1dF3,:);P1B3=P1dB3(SP1dB3,:);P1F4=P1dF4(SP1dF4,:);P1B4=P1dB4(SP1dB4,:);P1F5=P1dF5(SP1dF5,:);P1B5=P1dB5(SP1dB5,:);

P2F1=P2dF1(SP2dF1,:);P2B1=P2dB1(SP2dB1,:);P2F2=P2dF2(SP2dF2,:);P2B2=P2dB2(SP2dB2,:);P2F3=P2dF3(SP2dF3,:);P2B3=P2dB3(SP2dB3,:);P2F4=P2dF4(SP2dF4,:);P2B4=P2dB4(SP2dB4,:);

//putting all the results in one 2x10 for P1 and 2x8 for P2P1d=[P1F1 P1B1 P1F2 P1B2 P1F3 P1B3 P1F4 P1B4 P1F5 P1B5];




P2d=[P2F1 P2B1 P2F2 P2B2 P2F3 P2B3 P2F4 P2B4];

//determining length the of the bars//this is LP1 and LP2L0P1=((P1F1(2,1))+(P1B1(2,1))+(P1F2(2,1))+(P1B2(2,1))+(P1F3(2,1))+(P1B3(2,1))+(P1F4(2,1))+(P1B4(2,1))+(P1F5(2,1))+(P1B5(2,1)))/10;L1P1=((P1F1(1,1))+(P1B1(1,1))+(P1F2(1,1))+(P1B2(1,1))+(P1F3(1,1))+(P1B3(1,1))+(P1F4(1,1))+(P1B4(1,1))+(P1F5(1,1))+(P1B5(1,1)))/10;LP1=L1P1−L0P1;

L0P2=((P2F1(2,1))+(P2B1(2,1))+(P2F2(2,1))+(P2B2(2,1))+(P2F3(2,1))+(P2B3(2,1))+(P2F4(2,1))+(P2B4(2,1)))/8;L1P2=((P2F1(1,1))+(P2B1(1,1))+(P2F2(1,1))+(P2B2(1,1))+(P2F3(1,1))+(P2B3(1,1))+(P2F4(1,1))+(P2B4(1,1)))/8;LP2=L1P2−L0P2;

//one−dimensional interpolation of every run for P1 and P2

//50 steps resulting in 51 datapoints n1=13.06;P1X=[230:n1:883];[P1Yr1]=interp1(P1dF1,P1hF1,P1X,’nearest’);[P1Yr2]=interp1(P1dB1,P1hB1,P1X,’nearest’);[P1Yr3]=interp1(P1dF2,P1hF2,P1X,’nearest’);[P1Yr4]=interp1(P1dB2,P1hB2,P1X,’nearest’);[P1Yr5]=interp1(P1dF3,P1hF3,P1X,’nearest’);[P1Yr6]=interp1(P1dB3,P1hB3,P1X,’nearest’);[P1Yr7]=interp1(P1dF4,P1hF4,P1X,’nearest’);[P1Yr8]=interp1(P1dB4,P1hB4,P1X,’nearest’);[P1Yr9]=interp1(P1dF5,P1hF5,P1X,’nearest’);[P1Yr10]=interp1(P1dB5,P1hB5,P1X,’nearest’);

//50 elementsn2=7.44;P2X=[224:n2:596];[P2Yr1]=interp1(P2dF1,P2hF1,P2X,’nearest’);[P2Yr2]=interp1(P2dB1,P2hB1,P2X,’nearest’);[P2Yr3]=interp1(P2dF2,P2hF2,P2X,’nearest’);[P2Yr4]=interp1(P2dB2,P2hB2,P2X,’nearest’);[P2Yr5]=interp1(P2dF3,P2hF3,P2X,’nearest’);[P2Yr6]=interp1(P2dB3,P2hB3,P2X,’nearest’);[P2Yr7]=interp1(P2dF4,P2hF4,P2X,’nearest’);[P2Yr8]=interp1(P2dB4,P2hB4,P2X,’nearest’);

//calculating one averaged curves for P1 and P2P1Y=(P1Yr1+P1Yr2+P1Yr3+P1Yr4+P1Yr5+P1Yr6+P1Yr7+P1Yr8+P1Yr9+P1Yr10)./10;P2Y=(P2Yr1+P2Yr2+P2Yr3+P2Yr4+P2Yr5+P2Yr6+P2Yr7+P2Yr8)./8;

//plotting one−dimensional interpolation and their real counterparts//plotting averaged curves calculated by interpolated datapointsscf(2);subplot(2,2,1);plot(P1dF1,P1hF1,’r’);plot(P1X,P1Yr1,’b’);plot(P1dB1,P1hB1,’r’);plot(P1X,P1Yr2,’b’);plot(P1dF2,P1hF2,’r’);plot(P1X,P1Yr3,’b’);plot(P1dB2,P1hB2,’r’);plot(P1X,P1Yr4,’b’);plot(P1dF3,P1hF3,’r’);plot(P1X,P1Yr5,’b’);plot(P1dB3,P1hB3,’r’);plot(P1X,P1Yr6,’b’);plot(P1dF4,P1hF4,’r’);plot(P1X,P1Yr7,’b’);plot(P1dB4,P1hB4,’r’);plot(P1X,P1Yr8,’b’);plot(P1dF5,P1hF5,’r’);

Feb 02, 07 10:17 Page 5/7Final_bars_geometry.sceplot(P1X,P1Yr9,’b’);plot(P1dB5,P1hB5,’r’);plot(P1X,P1Yr10,’b’);xtitle(’P1 interpolations’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,2,2);plot(P2dF1,P2hF1,’r’);plot(P2X,P2Yr1,’b’);plot(P2dB1,P2hB1,’r’);plot(P2X,P2Yr2,’b’);plot(P2dF2,P2hF2,’r’);plot(P2X,P2Yr3,’b’);plot(P2dB2,P2hB2,’r’);plot(P2X,P2Yr4,’b’);plot(P2dF3,P2hF3,’r’);plot(P2X,P2Yr5,’b’);plot(P2dB3,P2hB3,’r’);plot(P2X,P2Yr6,’b’);plot(P2dF4,P2hF4,’r’);plot(P2X,P2Yr7,’b’);plot(P2dB4,P2hB4,’r’);plot(P2X,P2Yr8,’b’);xtitle(’P2 interpolations’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,2,3);plot(P1X,P1Y,’b’);xtitle(’P1 interpolation average’,’distance covered (mm)’,’distance from laser head (mm)’);

subplot(2,2,4);plot(P2X,P2Y,’b’);xtitle(’P2 interpolation average’,’distance covered (mm)’,’distance from laser head (mm)’);

//highest lowest column//calculating the starting height and ending height//SP1Y = 1. 51.//HighLowP1Y = 20.334408 18.544715SP1Y=size(P1Y);HighLowP1Y=P1Y(:,SP1Y);SP2Y=size(P2Y);HighLowP2Y=P2Y(:,SP2Y);

//Calculating datapoints for a trendline//f1 and f2 are rows which will be added to PY1 and PY2u=[0:1:50];f1=((HighLowP1Y(1,1)−HighLowP1Y(1,2))/50).*u;f2=((HighLowP2Y(1,1)−HighLowP2Y(1,2))/50).*u;

//Adding trendline (cancelling the offset error of ending point)//Minus offset (to start at zero) //Multiplying by −1 (to let deviation point upward)P1Y=(−1).*((P1Y+f1)−HighLowP1Y(1,1));P2Y=(−1).*((P2Y+f2)−HighLowP2Y(1,1));

//Plotting the rearranged averaged curvesscf(3)subplot(2,1,1)plot(P1X,P1Y,’r’);xtitle(’P1 rearranged interpolation average’,’distance covered (mm)’,’deviation (mm)’);

subplot(2,1,2)plot(P2X,P2Y,’r’);xtitle(’P2 rearranged interpolation average’,’distance covered (mm)’,’deviation (mm)’);




//data preperation for 3D plotsize(P1X);size(P2X);size(P1Y);size(P2Y);P1X=P1X’;P1Y=P1Y’;P1Yadd=[P1Y P1Y];P1Y31=31+P1Y;P1Y31add=[P1Y31 P1Y31];P1Ytot=[P1Yadd P1Y31add];P2X=P2X’;P2Y=P2Y’;P2Yadd=[P2Y P2Y];P2Y31=31+P2Y;P2Y31add=[P2Y31 P2Y31];P2tot=[P2Yadd P2Y31add];PZ=[0;38];PZtot=[0;38;0;38];

//plotting 3D bottom and top surface for P1 and P2//plotting color contour plots below the 3D P1 and P2scf(4)subplot(2,2,1)plot3d(P1X,PZ,P1Yadd,−75,89);plot3d(P1X,PZ,P1Y31add,−75,89);xtitle(’P1’,’distance covered (mm)’,’ ’,’deviation (mm)’);

subplot(2,2,2)plot3d(P2X,PZ,P2Yadd,−75,89);plot3d(P2X,PZ,P2Y31add,−75,89);xtitle(’P2’,’distance covered (mm)’,’ ’,’deviation (mm)’);

subplot(2,2,3)xset("colormap",jetcolormap(64));zm = min(P1Y); zM = max(P1Y);colorbar(zm,zM);Sgrayplot(P1X,PZ,P1Yadd);xtitle(’Surface plot P1’,’covered distance (mm)’,’thickness (0 − 38mm)’);

subplot(2,2,4)xset("colormap",jetcolormap(64));zm = min(P2Y); zM = max(P2Y);colorbar(zm,zM);Sgrayplot(P2X,PZ,P2Yadd);xtitle(’Surface plot P2’,’covered distance (mm)’,’thickness (0 − 38mm)’)

//end




39

0 200 400 600 800 1000 1200 140048.8

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Figure B1: Subplot “scf(1)”, raw data of surface deviation of bars P1 and P2

Figure B2: Subplot “scf(2)”, interpolations, real counterparts and averaged interpolations

40

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Figure B3: Subplot “scf(3)”, averaged and rearranged interpolation curves

Figure B4: Subplot “scf(4)”, 3D- and color contour plots from deviation of bars P1 and P2

41

Appendix C: Tensile experiments results

[C1] Stress-strain curves

0

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Strain [-]

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ess

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a)



Figure C1: Stress-strain curves tensile specimen C1

[C4] Stress-strain curves

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Figure C2: Stress-strain curves tensile specimen C4

42

[L1] Stress-strain curves

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Figure C3: Stress-strain curves tensile specimen L1

[L2] Stress-strain curves

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Figure C4: Stress-strain curves tensile specimen L2

43


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Figure C5: Stress-strain curves tensile specimen W2


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Figure C6: Stress-strain curves tensile specimen W3

44

[1] Calculation with displacement driving head

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Figure C7: True stress-strain curves for all specimens, but calculated with displacement driving head

Figure C8: True stress-strain curves for all specimens, but calculated with displacement extensometer

[2] Calculation by extensometer

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45

[W3] Elongation vs. elongation

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ecim

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Figure C9: Elongation measured by driving head vs. elongation measured by extensometer

[W3] Elastic behavior

y = 154817x + 1095.2 y = 23368x - 1.4389

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[2] True stress vs. strain (extensometer) [1] True stress vs. strain

Linear ([2] True stress vs. strain (extensometer)) Linear ([1] True stress vs. strain)

Figure C10: Linear trend line plotted in elastic region of tensile specimen W3

46

Appendix D: Stress and strain formulas Engineering strain:

00

0

L

L

L

LLE

∆=−

=ε

Engineering stress:

0A

PE =σ

True strain:

)1ln(lnln0

0

00

Ef

L

L

T L

LL

L

L

L

dLf

εε +=⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆+=== ∫ :

True stress:

)1(00

EET L

L

A

P

A

P εσσ +=⋅==

L = length [m] A = surface [m2] P = force [N] σ = stress [P] ε = strain [-]

47

Figure E1: Vickers hardness values found for three different drawn lines on the metal bar

Appendix E: Vickers Hardness formulas Vickers Hardness:

MMv RcRH 2.3≈=

Surface formulation of a diamond indenter:

( )2/136sin

2/10

2LA =

Vickers Hardness:

2

854.1

L

F

A

MH v ==

vH = kilogram-force [kg/mm2]

MR = tensile strength [MPa]

c = constant [-] L = length [mm] A = surface [mm2] M = weight [kg]

48

Appendix F: Temperature dependency

Figure F1: Temperature dependency of different crystal structures from Borjesson (2001) [20]

49

Appendix G: Bending formulas Moment of inertia of rectangle area:

12

3bhI x =

Euler Bernoulli beam equation:

xI

Mh

2=σ

Formula of moment:

rFM ⋅=

xI = moment of inertia [m4]

b = thickness [m]

h = height [m] σ = stress [Pa] M = moment [Nm] F = force [N] r = distance [m]

50

Appendix H: SB02DOF keyword file

This appendix breaks down the keyword input file SolidBeam02DOF. *KEYWORD *TITLE Solid Beam in Bending 02 DOF $ $ DRDC Pacific, calculation T.Romans $ $ Last Modified: 2 February, 2007 $ $ Units: mm, ms, kg, kN, GPa, kN-mm $

Figure H1: Part 1 SolidBeam02DOF

Figure H1 is the start of the SolidBeam02DOF input file. LS-DYNA works with input keywords. This provides a flexible and logically organized database, with similar functions grouped together under the same keyword. This combination of functions under a keyword is called a card. Keywords itself can entered in an arbitrary order in the input file. The first line of any input file must begin with *KEYWORD. This identifies the file as containing the keyword format instead of the structured format which can also be used. [31], [32]

Following *KEYWORD, the next card is *TITLE which gives the opportunity to specify a title for the simulation. This title is visible in LS-PrePost and of course serves as a quick recognition point. The dollar signs distinguish lines as comments and are not be read by LS-DYNA. In SolidBeam02DOF several things have been commented, such as the company, the designer and the date.

An important part of any LS-DYNA simulation is working in correct units. Only certain combinations of units are possible. In this simulation, the units are millimeter, millisecond, kilogram, kilo Newton and giga Pascal combination. This because the bar is measured in millimeters and dynamic effects (i.e time) doesn’t influence the mechanical analysis. (For the thermal analysis in chapter 5.2 the meter and second combination is used) $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Control Output $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8 $ *CONTROL_CONTACT $ slsfac rwpna1 islchk shlthk penopt thkchg orient enmass 0.1 1 $ $ usrstr usrfrc nsbcs interm xpene ssthk ecdt tiedprj $ *CONTROL_HOURGLASS $ ihq qh 4 $ *CONTROL_OUTPUT $ npopt neecho nrefup iaccop opifs opnint ikedit iflush

51

1 3 $ *CONTOL_TERMINATION $ endtim endcyc dtmin endneg endmas 172 $ *CONTROL_TIMESTEP $ dtinit tssfac isdo tslimt dt2ms lctm erode ms1st 0.01 $ $


The next section of the SolidBeam02DOF input file is the control output specification. This section can be viewed in figure H2. Keywords are alphabetically arranged. Five different input keywords are being used.

*CONTROL_CONTACT is the first keyword called. In the mechanical straightening a force was applied by using a metal cylinder. A contact between the metal bar and the metal cylinder thus exist. Therefore some contact features have to be described.

Under the *CONTROL_CONTACT keyword two cards can be distinguished. The lower card is entirely empty. This isn’t a problem, because LS-DYNA uses certain default values. [32] There have been however, in the upper card, two values entered. The scale factor for sliding interface for instance is set to 0.1.

*CONTROL_HOURGLASS is used for counteracting the behavior of hourglassing modes of motion. This is a common effect in under integrated finite elements. An hourglass control based on Flanagan-Belytschko is the default used by LS-DYNA.

*CONTROL_OUTPUT sets miscellaneous output parameters. However this keyword does not control any information. It is used for controlling data, which is printed on the screen will the calculation is running. Nodal coordinates, element connectivities, rigid wall definitions and initial velocities are not printed. Print suppression is also in check for element printing.

*CONTROL_TERMINATION tells LS_DYNA when to stop the job. This will be done after 172ms. *CONTROL_TIMESTEP sets the structural time step size. For this input file the initial time step is defined as 0.01ms. Overall LS-DYNA calculates 17s on the SolidBeam02DOF input file. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Database $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ *DATABASE_BINARY_D3PLOT $ dt 1 $ *DATABASE_BINARY_D3THDT $ dt 1 $ *DATABASE_ELOUT $ dt 1 $ *DATABASE_EXTENT_BINARY $ neiph neips maxint strflg sigflg epsflg rltflg engflg 1

52

$ $ cmpflg ieverp beamip dcomp shge stssz n3thdt $ *DATABASE_GLSTAT $ dt 1 $ *DATABASE_HISTORY_NODE $ id1 id2 id3 id4 id5 id6 id7 id8 1011 1012 1014 1063 1066 64 1604 2064 $ *DATABASE_HISTORY_SOLID $ id1 id2 id3 id4 id5 id6 id7 id8 60 61 63 85 86 88 $ *SET_NODE_LIST $ sid 1 $ $ nid1 nid2 nid3 nid4 nid5 nid6 nid7 nid8 1011 1012 1014 1063 1066 64 1064 2064 $ *DEFINE_COORDINATE_VECTOR $ cid 1 $ *DATABASE_NODAL_FORCE_GROUP $ nsid cid 1 1 $ *DATABASE_NODOUT $ dt 1 $ *DATABASE_NODFOR $ dt 1 $ *DATABASE_RBOUT $ dt 1 $ *DATABASE_RCFORC $ dt 1 $ $ Figure H3: Part 3 SolidBeam02DOF

After the output control specification, the database keywords are described. This can be seen in figure H3. In *DATABASE_BINARY_D3PLOT the time interval (1 ms) between complete output states is being defined. In any keyword, with a dt function in it, a time interval is specified. *DATABASE_BINARY_D3THDT for instance determines the interval time, when time history data is recorded. The nodes and solid for which time history data must be recorded are being detailed in *DATABASE_HISTORY_NODE/ SOLID. The type of history data recorded is defined by keywords such as *DATABASE_ELOUT. Here at every millisecond, element data is recorded for for element 63 (id3).

In this research project surface strain is being examined. Strain gages were attached on the metal bar in the mechanical straightening experiments. LS-DYNA however does not include strain tensors for solids. Therefore the default set-up has to be change and this is done by using the *DATABASE_EXTENT_BINARY keyword.

53

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Boundary & Contact Conditions $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ $$$$ Beam is fixed on the Left Side, 1 DOF for the Right Side $ *BOUNDARY_SPC_NODE $ nid cid dofx dofy dofz dofrx dofry dofrz 2 0 1 1 1 1 1 1 22 0 0 1 1 1 1 1 1002 0 1 1 1 1 1 1 1022 0 0 1 1 1 1 1 2002 0 1 1 1 1 1 1 2022 0 0 1 1 1 1 1 $ $ $$$$ Tool has 1 DOF $ *BOUNDARY_SPC_NODE $ nid cid dofx dofy dofz dofrx dofry dofrz 10001 0 1 0 1 1 1 1 10020 0 1 0 1 1 1 1 10009 0 1 0 1 1 1 1 ... ... ... ... ... ... ... ... 14012 0 1 0 1 1 1 1 $ $ $$$$ Prescribed Motion Tool $ *BOUNDARY_PRESCRIBED_MOTION_RIGID $ pid dof vad lcid sf vid death birth 2 2 2 1 -1.0 $ *DEFINE_CURVE $ $ lcid sidr scla sclo offa offo 1 $ $ abscissa ordinate

0 0.000 4 5.000 86 12.000 168 5.000 172 0.000

$ $ $$$$ Contact Properties $ *CONTACT_SURFACE_TO_SURFACE $ ssid msid sstyp mstyp sboxid mboxid spr mpr 1 2 3 3 1 1 $ $ fs fd dc vc vdc penchk bt dt $ $ sfs sfm sst mst sfst sfmt fsf vsf $ $ optional card A $ soft $ $ optional card B $ penmax thkopt shlthk snlog $ $


54

In figure H4 the boundary and contact conditions section is depicted. This section

begins with two *BOUNDARY_SPC_NODE keywords. These keywords specify the object, the beam and the tool, in the virtual space.

The lower edge of the left side of the metal bar consists of three nodes. These are nodes 2, 1002 and 2002. They will be fixed completely and have no available degrees of freedom. The lower edge of right side of the metal bar has one degree of freedom. The nodes on this edge (22, 1022 and 2022), and are allowed to move in the x-direction only. This is the direction of the length of the metal bar.

Three nodes on the diameter of the cylinder, through which the force on the rigid indenter is applied, are defined and they will have only one degree of freedom. This degree of freedom corresponds to the direction of the applied force. To prevent the cylinder from twisting in 3D more nodes on an axial cross-section are fixed this way.

To give the tool a prescribed motion the *BOUNDARY_PRESCRIBED_MOTION _RIGID keyword is used. Part 2 (the tool) will be displaced in the y-direction (2-direction) defined by curve 1. This curve is described in *DEFINE_CURVE. In 4 ms the cylinder will move 5 mm so that it just touches the surface of the metal bar. Then during 82 ms the cylinder will be displaced an additional 7 mm after which it will slowly return to its start position. Through this procedure, the complete loading history, including the springback of the metal bar can be simulated. [33], [34] Finally in this section contact properties are also entered. In the keyword *CONTACT_SURFACE_TO_SURFACE part 1 (the beam) will be the slave segment and part 2 (the tool) the master segment. Slave and master are both parts, build up out of 8-noded solid elements. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Define Parts and Materials $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ *PART $ pid sid mid eosid hgid grav adpopt tmid Beam 1 1 1 $ *PART $ pid sid mid eosid hgid grav adpopt tmid Tool 2 2 2 $ $ $$$$ Materials $ *MAT_PLASTIC_KINEMATIC $ mid ro e pr sigy etan beta 1 7.8e-6 207.0 0.28 0.550 $ $ src srp fs vp $ *MAT_RIGID $ mid ro e pr n couple m alias/re 2 7.8e-6 207.0 0.28 $ $ cmo con1 con2 $

55

$ lco 1 $ $ $$$$ Sections $ *SECTION_SOLID $ secid elform aet 1 $ $ secid elform aet 2 $ $


Before the nodes and elements generation, parts and materials are defined. This section can be viewed in figure H5. In two *PART keywords the beam and the tool are numbered and couples the part and material identification. For the beam a plastic-kinematic material is chosen and for the tool a rigid material. The material properties described in chapter 3 are implemented here. In the keyword *SECTION_SOLID section properties for solid continuum elements are specified. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Define Nodes and Elements $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ $$$$ Node Generation Beam $ *NODE $ nid x y z tc rc 1,224.000,0.000,0.000,0,0 2,238.880,0.485,0.000,0,0 3,253.760,0.948,0.000,0,0 ...,...,...,...,...,... 2078,596.000,31.000,38.000,0,0 $ $ $$$$ Node Generation Tool $ *NODE $ nid x y z tc rc 10001,387.68,41.26,0,0,0 10002,388.90,41.30,0,0,0 10003,390.12,41.50,0,0,0 ...,...,...,...,...,... 14020,387.68,53.76,38.0,0,0 $ $ $$$$ Elements Generation Beam (25x,2y,2z) $ eid pid n1 n2 n3 n4 n5 n6 n7 n8 1,1,1,2,28,27,1001,1002,1028,1027 2,1,2,3,29,28,1002,1003,1029,1028 3,1,3,4,30,29,1003,1004,1030,1029 ...,...,...,...,...,...,...,...,...,... 100,1,1051,1052,1078,1077,2051,2052,2078,2077 $ $ $$$$ Elements Generation Tool $ *ELEMENTS_SOLID $ eid pid n1 n2 n3 n4 n5 n6 n7 n8 10001,2,10001,10002,11002,11001,10020,10020,11020,11020 10002,2,10002,10003,11003,11002,10020,10020,11020,11020

56

10003,2,10003,10004,11004,11003,10020,10020,11020,11020 ...,...,...,...,...,...,...,...,...,... 10064,2,13016,13001,14001,14016,13020,13020,14020,14020 $ *END


In the final section nodes and elements are feed into the input file. This is summarized in figure H6. Node generation between beam and tool is separated. For elements generation this is the case also. In node generation every node is given a point and than its x-coordinate, y-coordinate and z-coordinate follows. The two zeros indicate that the node does not have a rotational or translational constraints. [35], [36]

Every element is given a unique number and associated with a corresponding part identification specified in the next field. The remaining eight field specify the nodal connectivity

*KEYWORD*TITLESolid Beam in Bending 02 DOF$$ DRDC Pacific, calculation T.Romans$$ Last Modified: 2 February, 2007$$ Units: mm, ms, kg, kN, GPa, kN−mm$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Control Ouput$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8$*CONTROL_CONTACT$ slsfac rwpnal islchk shlthk penopt thkchg orien enmass 0.1 1$$ usrstr usrfrc nsbcs interm xpene ssthk ecdt tiedprj

$*CONTROL_HOURGLASS$ ihq qh 4$*CONTROL_OUTPUT$ npopt neecho nrefup iaccop opifs ipnint ikedit iflush 1 3$*CONTROL_TERMINATION $ endtim endcyc dtmin endneg endmas 172$*CONTROL_TIMESTEP$ dtinit tssfac isdo tslimt dt2ms lctm erode ms1st 0.01$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Database$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$*DATABASE_BINARY_D3PLOT$ dt 1$*DATABASE_BINARY_D3THDT$ dt 1$*DATABASE_ELOUT$ dt 1$*DATABASE_EXTENT_BINARY$ neiph neips maxint strflg sigflg epsflg rltflg engflg 1$$ cmpflg ieverp beamip dcomp shge stssz n3thdt 1$*DATABASE_GLSTAT$ dt

Feb 06, 07 11:19 Page 1/12SolidBeam02DOF.k 1$ *DATABASE_HISTORY_NODE$ id1 id2 id3 id4 id5 id6 id7 id8 1011 1012 1014 1063 1066 64 1064 2064$*DATABASE_HISTORY_SOLID$ id1 id2 id3 id4 id5 id6 id7 id8 60 61 63 85 86 88$*SET_NODE_LIST$ sid 1$$ nid1 nid2 nid3 nid4 nid5 nid6 nid7 nid8 1011 1012 1014 1063 1066 64 1064 2064$*DEFINE_COORDINATE_VECTOR$ cid 1$*DATABASE_NODAL_FORCE_GROUP$ nsid cid 1 1$*DATABASE_NODOUT$ dt 1$*DATABASE_NODFOR$ dt 1$*DATABASE_RBDOUT$ dt 1$*DATABASE_RCFORC$ dt 1$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Boundary & Contact Conditions$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Beam is fixed on the Left Side, 1 DOF for the Right Side$*BOUNDARY_SPC_NODE$ nid cid dofx dofy dofz dofrx dofry dofrz 2 0 1 1 1 1 1 1 22 0 0 1 1 1 1 1 1002 0 1 1 1 1 1 1 1022 0 0 1 1 1 1 1 2002 0 1 1 1 1 1 1 2022 0 0 1 1 1 1 1$$$$$$ Tool has 1 DOF$*BOUNDARY_SPC_NODE$ nid cid dofx dofy dofz dofrx dofry dofrz 10001 0 1 0 1 1 1 1 10020 0 1 0 1 1 1 1 10009 0 1 0 1 1 1 1 11001 0 1 0 1 1 1 1

Feb 06, 07 11:19 Page 2/12SolidBeam02DOF.k


Tuesday February 06, 2007 1/6SolidBeam02DOF.k

11020 0 1 0 1 1 1 1 11009 0 1 0 1 1 1 1 12001 0 1 0 1 1 1 1 12020 0 1 0 1 1 1 1 12009 0 1 0 1 1 1 1 13001 0 1 0 1 1 1 1 13020 0 1 0 1 1 1 1 13009 0 1 0 1 1 1 1 14001 0 1 0 1 1 1 1 14020 0 1 0 1 1 1 1 14009 0 1 0 1 1 1 1 10006 0 1 0 1 1 1 1 10012 0 1 0 1 1 1 1 11006 0 1 0 1 1 1 1 11012 0 1 0 1 1 1 1 12006 0 1 0 1 1 1 1 12012 0 1 0 1 1 1 1 13006 0 1 0 1 1 1 1 13012 0 1 0 1 1 1 1 14006 0 1 0 1 1 1 1 14012 0 1 0 1 1 1 1$$$$$$ Prescribed Motion Tool$*BOUNDARY_PRESCRIBED_MOTION_RIGID$ pid dof vad lcid sf vid death birth 2 2 2 1 −1.0$*DEFINE_CURVE$ lcid sidr scla sclo offa offo 1$$ abscissa ordinate 0 0.000 4 5.000 86 12.000 168 5.000 172 0.000 $$$$$$ Contact Properties$*CONTACT_SURFACE_TO_SURFACE$ ssid msid sstyp mstyp sboxid mboxid spr mpr 1 2 3 3 1 1$$ fs fd dc vc vdc penchk bt dt $$ sfs sfm sst mst sfst sfmt fsf vsf

$$ optional card A$ soft

$$ optional card B$ penmax thkopt shlthk snlog 1$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Define Parts and Materials$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ *PART

Feb 06, 07 11:19 Page 3/12SolidBeam02DOF.k$ pid sid mid eosid hgid grav adpopt tmidBeam 1 1 1$*PART$ pid sid mid eosid hgid grav adpopt tmidTool 2 2 2$$$$$$ Materials$*MAT_PLASTIC_KINEMATIC$ mid ro e pr sigy etan beta 1 7.8e−6 207.0 0.28 0.550 $$ src srp fs vp $*MAT_RIGID$ mid ro e pr n couple m alias/re 2 7.8e−6 207.0 0.28 $$ cmo con1 con2 $$ lco 1$$$$$$ Sections$*SECTION_SOLID$ secid elform aet 1$*SECTION_SOLID$ secid elform aet 2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Define Nodes and Elements$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Node Generation Beam$*NODE$ nid x y z tc rc1,224.000,0.000,0.000,0,02,238.880,0.485,0.000,0,03,253.760,0.948,0.000,0,04,268.640,1.305,0.000,0,05,283.520,1.833,0.000,0,06,298.400,2.342,0.000,0,07,313.280,2.858,0.000,0,08,328.160,3.400,0.000,0,09,343.040,4.029,0.000,0,010,357.920,4.654,0.000,0,011,372.800,5.078,0.000,0,012,387.680,5.258,0.000,0,013,402.560,4.940,0.000,0,014,417.440,4.476,0.000,0,015,432.320,4.292,0.000,0,016,447.200,4.090,0.000,0,017,462.080,3.852,0.000,0,0




18,476.960,3.455,0.000,0,019,491.840,2.945,0.000,0,020,506.720,2.538,0.000,0,021,521.600,2.071,0.000,0,022,536.480,1.503,0.000,0,023,551.360,1.201,0.000,0,024,566.240,0.834,0.000,0,025,581.120,0.373,0.000,0,026,596.000,0.000,0.000,0,027,224.000,15.500,0.000,0,028,238.880,15.985,0.000,0,029,253.760,16.448,0.000,0,030,268.640,16.805,0.000,0,031,283.520,17.333,0.000,0,032,298.400,17.842,0.000,0,033,313.280,18.358,0.000,0,034,328.160,18.900,0.000,0,035,343.040,19.529,0.000,0,036,357.920,20.154,0.000,0,037,372.800,20.578,0.000,0,038,387.680,20.758,0.000,0,039,402.560,20.440,0.000,0,040,417.440,19.976,0.000,0,041,432.320,19.792,0.000,0,042,447.200,19.590,0.000,0,043,462.080,19.352,0.000,0,044,476.960,18.955,0.000,0,045,491.840,18.445,0.000,0,046,506.720,18.038,0.000,0,047,521.600,17.571,0.000,0,048,536.480,17.003,0.000,0,049,551.360,16.701,0.000,0,050,566.240,16.334,0.000,0,051,581.120,15.873,0.000,0,052,596.000,15.500,0.000,0,053,224.000,31.000,0.000,0,054,238.880,31.485,0.000,0,055,253.760,31.948,0.000,0,056,268.640,32.305,0.000,0,057,283.520,32.833,0.000,0,058,298.400,33.342,0.000,0,059,313.280,33.858,0.000,0,060,328.160,34.400,0.000,0,061,343.040,35.029,0.000,0,062,357.920,35.654,0.000,0,063,372.800,36.078,0.000,0,064,387.680,36.258,0.000,0,065,402.560,35.940,0.000,0,066,417.440,35.476,0.000,0,067,432.320,35.292,0.000,0,068,447.200,35.090,0.000,0,069,462.080,34.852,0.000,0,070,476.960,34.455,0.000,0,071,491.840,33.945,0.000,0,072,506.720,33.538,0.000,0,073,521.600,33.071,0.000,0,074,536.480,32.503,0.000,0,075,551.360,32.201,0.000,0,076,566.240,31.834,0.000,0,077,581.120,31.373,0.000,0,078,596.000,31.000,0.000,0,01001,224.000,0.000,19.000,0,01002,238.880,0.485,19.000,0,01003,253.760,0.948,19.000,0,01004,268.640,1.305,19.000,0,01005,283.520,1.833,19.000,0,01006,298.400,2.342,19.000,0,01007,313.280,2.858,19.000,0,01008,328.160,3.400,19.000,0,0

Feb 06, 07 11:19 Page 5/12SolidBeam02DOF.k1009,343.040,4.029,19.000,0,01010,357.920,4.654,19.000,0,01011,372.800,5.078,19.000,0,01012,387.680,5.258,19.000,0,01013,402.560,4.940,19.000,0,01014,417.440,4.476,19.000,0,01015,432.320,4.292,19.000,0,01016,447.200,4.090,19.000,0,01017,462.080,3.852,19.000,0,01018,476.960,3.455,19.000,0,01019,491.840,2.945,19.000,0,01020,506.720,2.538,19.000,0,01021,521.600,2.071,19.000,0,01022,536.480,1.503,19.000,0,01023,551.360,1.201,19.000,0,01024,566.240,0.834,19.000,0,01025,581.120,0.373,19.000,0,01026,596.000,0.000,19.000,0,01027,224.000,15.500,19.000,0,01028,238.880,15.985,19.000,0,01029,253.760,16.448,19.000,0,01030,268.640,16.805,19.000,0,01031,283.520,17.333,19.000,0,01032,298.400,17.842,19.000,0,01033,313.280,18.358,19.000,0,01034,328.160,18.900,19.000,0,01035,343.040,19.529,19.000,0,01036,357.920,20.154,19.000,0,01037,372.800,20.578,19.000,0,01038,387.680,20.758,19.000,0,01039,402.560,20.440,19.000,0,01040,417.440,19.976,19.000,0,01041,432.320,19.792,19.000,0,01042,447.200,19.590,19.000,0,01043,462.080,19.352,19.000,0,01044,476.960,18.955,19.000,0,01045,491.840,18.445,19.000,0,01046,506.720,18.038,19.000,0,01047,521.600,17.571,19.000,0,01048,536.480,17.003,19.000,0,01049,551.360,16.701,19.000,0,01050,566.240,16.334,19.000,0,01051,581.120,15.873,19.000,0,01052,596.000,15.500,19.000,0,01053,224.000,31.000,19.000,0,01054,238.880,31.485,19.000,0,01055,253.760,31.948,19.000,0,01056,268.640,32.305,19.000,0,01057,283.520,32.833,19.000,0,01058,298.400,33.342,19.000,0,01059,313.280,33.858,19.000,0,01060,328.160,34.400,19.000,0,01061,343.040,35.029,19.000,0,01062,357.920,35.654,19.000,0,01063,372.800,36.078,19.000,0,01064,387.680,36.258,19.000,0,01065,402.560,35.940,19.000,0,01066,417.440,35.476,19.000,0,01067,432.320,35.292,19.000,0,01068,447.200,35.090,19.000,0,01069,462.080,34.852,19.000,0,01070,476.960,34.455,19.000,0,01071,491.840,33.945,19.000,0,01072,506.720,33.538,19.000,0,01073,521.600,33.071,19.000,0,01074,536.480,32.503,19.000,0,01075,551.360,32.201,19.000,0,01076,566.240,31.834,19.000,0,01077,581.120,31.373,19.000,0,0




1078,596.000,31.000,19.000,0,02001,224.000,0.000,38.000,0,02002,238.880,0.485,38.000,0,02003,253.760,0.948,38.000,0,02004,268.640,1.305,38.000,0,02005,283.520,1.833,38.000,0,02006,298.400,2.342,38.000,0,02007,313.280,2.858,38.000,0,02008,328.160,3.400,38.000,0,02009,343.040,4.029,38.000,0,02010,357.920,4.654,38.000,0,02011,372.800,5.078,38.000,0,02012,387.680,5.258,38.000,0,02013,402.560,4.940,38.000,0,02014,417.440,4.476,38.000,0,02015,432.320,4.292,38.000,0,02016,447.200,4.090,38.000,0,02017,462.080,3.852,38.000,0,02018,476.960,3.455,38.000,0,02019,491.840,2.945,38.000,0,02020,506.720,2.538,38.000,0,02021,521.600,2.071,38.000,0,02022,536.480,1.503,38.000,0,02023,551.360,1.201,38.000,0,02024,566.240,0.834,38.000,0,02025,581.120,0.373,38.000,0,02026,596.000,0.000,38.000,0,02027,224.000,15.500,38.000,0,02028,238.880,15.985,38.000,0,02029,253.760,16.448,38.000,0,02030,268.640,16.805,38.000,0,02031,283.520,17.333,38.000,0,02032,298.400,17.842,38.000,0,02033,313.280,18.358,38.000,0,02034,328.160,18.900,38.000,0,02035,343.040,19.529,38.000,0,02036,357.920,20.154,38.000,0,02037,372.800,20.578,38.000,0,02038,387.680,20.758,38.000,0,02039,402.560,20.440,38.000,0,02040,417.440,19.976,38.000,0,02041,432.320,19.792,38.000,0,02042,447.200,19.590,38.000,0,02043,462.080,19.352,38.000,0,02044,476.960,18.955,38.000,0,02045,491.840,18.445,38.000,0,02046,506.720,18.038,38.000,0,02047,521.600,17.571,38.000,0,02048,536.480,17.003,38.000,0,02049,551.360,16.701,38.000,0,02050,566.240,16.334,38.000,0,02051,581.120,15.873,38.000,0,02052,596.000,15.500,38.000,0,02053,224.000,31.000,38.000,0,02054,238.880,31.485,38.000,0,02055,253.760,31.948,38.000,0,02056,268.640,32.305,38.000,0,02057,283.520,32.833,38.000,0,02058,298.400,33.342,38.000,0,02059,313.280,33.858,38.000,0,02060,328.160,34.400,38.000,0,02061,343.040,35.029,38.000,0,02062,357.920,35.654,38.000,0,02063,372.800,36.078,38.000,0,02064,387.680,36.258,38.000,0,02065,402.560,35.940,38.000,0,02066,417.440,35.476,38.000,0,02067,432.320,35.292,38.000,0,02068,447.200,35.090,38.000,0,0

Feb 06, 07 11:19 Page 7/12SolidBeam02DOF.k2069,462.080,34.852,38.000,0,02070,476.960,34.455,38.000,0,02071,491.840,33.945,38.000,0,02072,506.720,33.538,38.000,0,02073,521.600,33.071,38.000,0,02074,536.480,32.503,38.000,0,02075,551.360,32.201,38.000,0,02076,566.240,31.834,38.000,0,02077,581.120,31.373,38.000,0,02078,596.000,31.000,38.000,0,0$$$$$$ Node Generation Tool$*NODE$ nid x y z tc tr10001,387.68,41.26,0,0,010002,388.90,41.30,0,0,010003,390.12,41.50,0,0,010004,392.46,42.21,0,0,010005,396.52,44.92,0,0,010006,399.23,48.98,0,0,010007,400.18,53.76,0,0,010008,396.52,62.60,0,0,010009,387.68,66.26,0,0,010010,378.84,62.60,0,0,010011,375.18,53.76,0,0,010012,376.13,48.98,0,0,010013,378.84,44.92,0,0,010014,382.90,42.21,0,0,010015,385.24,41.50,0,0,010016,386.45,41.30,0,0,010020,387.68,53.76,0,0,011001,387.68,41.26,9.5,0,011002,388.90,41.30,9.5,0,011003,390.12,41.50,9.5,0,011004,392.46,42.21,9.5,0,011005,396.52,44.92,9.5,0,011006,399.23,48.98,9.5,0,011007,400.18,53.76,9.5,0,011008,396.52,62.60,9.5,0,011009,387.68,66.26,9.5,0,011010,378.84,62.60,9.5,0,011011,375.18,53.76,9.5,0,011012,376.13,48.98,9.5,0,011013,378.84,44.92,9.5,0,011014,382.90,42.21,9.5,0,011015,385.24,41.50,9.5,0,011016,386.45,41.30,9.5,0,011020,387.68,53.76,9.5,0,012001,387.68,41.26,19.0,0,012002,388.90,41.30,19.0,0,012003,390.12,41.50,19.0,0,012004,392.46,42.21,19.0,0,012005,396.52,44.92,19.0,0,012006,399.23,48.98,19.0,0,012007,400.18,53.76,19.0,0,012008,396.52,62.60,19.0,0,012009,387.68,66.26,19.0,0,012010,378.84,62.60,19.0,0,012011,375.18,53.76,19.0,0,012012,376.13,48.98,19.0,0,012013,378.84,44.92,19.0,0,012014,382.90,42.21,19.0,0,012015,385.24,41.50,19.0,0,012016,386.45,41.30,19.0,0,012020,387.68,53.76,19.0,0,013001,387.68,41.26,28.5,0,013002,388.90,41.30,28.5,0,0




13003,390.12,41.50,28.5,0,013004,392.46,42.21,28.5,0,013005,396.52,44.92,28.5,0,013006,399.23,48.98,28.5,0,013007,400.18,53.76,28.5,0,013008,396.52,62.60,28.5,0,013009,387.68,66.26,28.5,0,013010,378.84,62.60,28.5,0,013011,375.18,53.76,28.5,0,013012,376.13,48.98,28.5,0,013013,378.84,44.92,28.5,0,013014,382.90,42.21,28.5,0,013015,385.24,41.50,28.5,0,013016,386.45,41.30,28.5,0,013020,387.68,53.76,28.5,0,014001,387.68,41.26,38.0,0,014002,388.90,41.30,38.0,0,014003,390.12,41.50,38.0,0,014004,392.46,42.21,38.0,0,014005,396.52,44.92,38.0,0,014006,399.23,48.98,38.0,0,014007,400.18,53.76,38.0,0,014008,396.52,62.60,38.0,0,014009,387.68,66.26,38.0,0,014010,378.84,62.60,38.0,0,014011,375.18,53.76,38.0,0,014012,376.13,48.98,38.0,0,014013,378.84,44.92,38.0,0,014014,382.90,42.21,38.0,0,014015,385.24,41.50,38.0,0,014016,386.45,41.30,38.0,0,014020,387.68,53.76,38.0,0,0$$$$$$ Elements Generation Beam (25x,2y,2z)$*ELEMENT_SOLID$ eid pid n1 n2 n3 n4 n5 n6 n7 n8 1,1,1,2,28,27,1001,1002,1028,10272,1,2,3,29,28,1002,1003,1029,10283,1,3,4,30,29,1003,1004,1030,10294,1,4,5,31,30,1004,1005,1031,10305,1,5,6,32,31,1005,1006,1032,10316,1,6,7,33,32,1006,1007,1033,10327,1,7,8,34,33,1007,1008,1034,10338,1,8,9,35,34,1008,1009,1035,10349,1,9,10,36,35,1009,1010,1036,103510,1,10,11,37,36,1010,1011,1037,103611,1,11,12,38,37,1011,1012,1038,103712,1,12,13,39,38,1012,1013,1039,103813,1,13,14,40,39,1013,1014,1040,103914,1,14,15,41,40,1014,1015,1041,104015,1,15,16,42,41,1015,1016,1042,104116,1,16,17,43,42,1016,1017,1043,104217,1,17,18,44,43,1017,1018,1044,104318,1,18,19,45,44,1018,1019,1045,104419,1,19,20,46,45,1019,1020,1046,104520,1,20,21,47,46,1020,1021,1047,104621,1,21,22,48,47,1021,1022,1048,104722,1,22,23,49,48,1022,1023,1049,104823,1,23,24,50,49,1023,1024,1050,104924,1,24,25,51,50,1024,1025,1051,105025,1,25,26,52,51,1025,1026,1052,105126,1,27,28,54,53,1027,1028,1054,105327,1,28,29,55,54,1028,1029,1055,105428,1,29,30,56,55,1029,1030,1056,105529,1,30,31,57,56,1030,1031,1057,105630,1,31,32,58,57,1031,1032,1058,1057

Feb 06, 07 11:19 Page 9/12SolidBeam02DOF.k31,1,32,33,59,58,1032,1033,1059,105832,1,33,34,60,59,1033,1034,1060,105933,1,34,35,61,60,1034,1035,1061,106034,1,35,36,62,61,1035,1036,1062,106135,1,36,37,63,62,1036,1037,1063,106236,1,37,38,64,63,1037,1038,1064,106337,1,38,39,65,64,1038,1039,1065,106438,1,39,40,66,65,1039,1040,1066,106539,1,40,41,67,66,1040,1041,1067,106640,1,41,42,68,67,1041,1042,1068,106741,1,42,43,69,68,1042,1043,1069,106842,1,43,44,70,69,1043,1044,1070,106943,1,44,45,71,70,1044,1045,1071,107044,1,45,46,72,71,1045,1046,1072,107145,1,46,47,73,72,1046,1047,1073,107246,1,47,48,74,73,1047,1048,1074,107347,1,48,49,75,74,1048,1049,1075,107448,1,49,50,76,75,1049,1050,1076,107549,1,50,51,77,76,1050,1051,1077,107650,1,51,52,78,77,1051,1052,1078,107751,1,1001,1002,1028,1027,2001,2002,2028,202752,1,1002,1003,1029,1028,2002,2003,2029,202853,1,1003,1004,1030,1029,2003,2004,2030,202954,1,1004,1005,1031,1030,2004,2005,2031,203055,1,1005,1006,1032,1031,2005,2006,2032,203156,1,1006,1007,1033,1032,2006,2007,2033,203257,1,1007,1008,1034,1033,2007,2008,2034,203358,1,1008,1009,1035,1034,2008,2009,2035,203459,1,1009,1010,1036,1035,2009,2010,2036,203560,1,1010,1011,1037,1036,2010,2011,2037,203661,1,1011,1012,1038,1037,2011,2012,2038,203762,1,1012,1013,1039,1038,2012,2013,2039,203863,1,1013,1014,1040,1039,2013,2014,2040,203964,1,1014,1015,1041,1040,2014,2015,2041,204065,1,1015,1016,1042,1041,2015,2016,2042,204166,1,1016,1017,1043,1042,2016,2017,2043,204267,1,1017,1018,1044,1043,2017,2018,2044,204368,1,1018,1019,1045,1044,2018,2019,2045,204469,1,1019,1020,1046,1045,2019,2020,2046,204570,1,1020,1021,1047,1046,2020,2021,2047,204671,1,1021,1022,1048,1047,2021,2022,2048,204772,1,1022,1023,1049,1048,2022,2023,2049,204873,1,1023,1024,1050,1049,2023,2024,2050,204974,1,1024,1025,1051,1050,2024,2025,2051,205075,1,1025,1026,1052,1051,2025,2026,2052,205176,1,1027,1028,1054,1053,2027,2028,2054,205377,1,1028,1029,1055,1054,2028,2029,2055,205478,1,1029,1030,1056,1055,2029,2030,2056,205579,1,1030,1031,1057,1056,2030,2031,2057,205680,1,1031,1032,1058,1057,2031,2032,2058,205781,1,1032,1033,1059,1058,2032,2033,2059,205882,1,1033,1034,1060,1059,2033,2034,2060,205983,1,1034,1035,1061,1060,2034,2035,2061,206084,1,1035,1036,1062,1061,2035,2036,2062,206185,1,1036,1037,1063,1062,2036,2037,2063,206286,1,1037,1038,1064,1063,2037,2038,2064,206387,1,1038,1039,1065,1064,2038,2039,2065,206488,1,1039,1040,1066,1065,2039,2040,2066,206589,1,1040,1041,1067,1066,2040,2041,2067,206690,1,1041,1042,1068,1067,2041,2042,2068,206791,1,1042,1043,1069,1068,2042,2043,2069,206892,1,1043,1044,1070,1069,2043,2044,2070,206993,1,1044,1045,1071,1070,2044,2045,2071,207094,1,1045,1046,1072,1071,2045,2046,2072,207195,1,1046,1047,1073,1072,2046,2047,2073,207296,1,1047,1048,1074,1073,2047,2048,2074,207397,1,1048,1049,1075,1074,2048,2049,2075,207498,1,1049,1050,1076,1075,2049,2050,2076,207599,1,1050,1051,1077,1076,2050,2051,2077,2076




100,1,1051,1052,1078,1077,2051,2052,2078,2077$$$$$$ Elements Generation Tool$*ELEMENT_SOLID$ eid pid n1 n2 n3 n4 n5 n6 n7 n810001,2,10001,10002,11002,11001,10020,10020,11020,1102010002,2,10002,10003,11003,11002,10020,10020,11020,1102010003,2,10003,10004,11004,11003,10020,10020,11020,1102010004,2,10004,10005,11005,11004,10020,10020,11020,1102010005,2,10005,10006,11006,11005,10020,10020,11020,1102010006,2,10006,10007,11007,11006,10020,10020,11020,1102010007,2,10007,10008,11008,11007,10020,10020,11020,1102010008,2,10008,10009,11009,11008,10020,10020,11020,1102010009,2,10009,10010,11010,11009,10020,10020,11020,1102010010,2,10010,10011,11011,11010,10020,10020,11020,1102010011,2,10011,10012,11012,11011,10020,10020,11020,1102010012,2,10012,10013,11013,11012,10020,10020,11020,1102010013,2,10013,10014,11014,11013,10020,10020,11020,1102010014,2,10014,10015,11015,11014,10020,10020,11020,1102010015,2,10015,10016,11016,11015,10020,10020,11020,1102010016,2,10016,10001,11001,11016,10020,10020,11020,1102010017,2,11001,11002,12002,12001,11020,11020,12020,1202010018,2,11002,11003,12003,12002,11020,11020,12020,1202010019,2,11003,11004,12004,12003,11020,11020,12020,1202010020,2,11004,11005,12005,12004,11020,11020,12020,1202010021,2,11005,11006,12006,12005,11020,11020,12020,1202010022,2,11006,11007,12007,12006,11020,11020,12020,1202010023,2,11007,11008,12008,12007,11020,11020,12020,1202010024,2,11008,11009,12009,12008,11020,11020,12020,1202010025,2,11009,11010,12010,12009,11020,11020,12020,1202010026,2,11010,11011,12011,12010,11020,11020,12020,1202010027,2,11011,11012,12012,12011,11020,11020,12020,1202010028,2,11012,11013,12013,12012,11020,11020,12020,1202010029,2,11013,11014,12014,12013,11020,11020,12020,1202010030,2,11014,11015,12015,12014,11020,11020,12020,1202010031,2,11015,11016,12016,12015,11020,11020,12020,1202010032,2,11016,11001,12001,12016,11020,11020,12020,1202010033,2,12001,12002,13002,13001,12020,12020,13020,1302010034,2,12002,12003,13003,13002,12020,12020,13020,1302010035,2,12003,12004,13004,13003,12020,12020,13020,1302010036,2,12004,12005,13005,13004,12020,12020,13020,1302010037,2,12005,12006,13006,13005,12020,12020,13020,1302010038,2,12006,12007,13007,13006,12020,12020,13020,1302010039,2,12007,12008,13008,13007,12020,12020,13020,1302010040,2,12008,12009,13009,13008,12020,12020,13020,1302010041,2,12009,12010,13010,13009,12020,12020,13020,1302010042,2,12010,12011,13011,13010,12020,12020,13020,1302010043,2,12011,12012,13012,13011,12020,12020,13020,1302010044,2,12012,12013,13013,13012,12020,12020,13020,1302010045,2,12013,12014,13014,13013,12020,12020,13020,1302010046,2,12014,12015,13015,13014,12020,12020,13020,1302010047,2,12015,12016,13016,13015,12020,12020,13020,1302010048,2,12016,12001,13001,13016,12020,12020,13020,1302010049,2,13001,13002,14002,14001,13020,13020,14020,1402010050,2,13002,13003,14003,14002,13020,13020,14020,1402010051,2,13003,13004,14004,14003,13020,13020,14020,1402010052,2,13004,13005,14005,14004,13020,13020,14020,1402010053,2,13005,13006,14006,14005,13020,13020,14020,1402010054,2,13006,13007,14007,14006,13020,13020,14020,1402010055,2,13007,13008,14008,14007,13020,13020,14020,1402010056,2,13008,13009,14009,14008,13020,13020,14020,1402010057,2,13009,13010,14010,14009,13020,13020,14020,1402010058,2,13010,13011,14011,14010,13020,13020,14020,1402010059,2,13011,13012,14012,14011,13020,13020,14020,1402010060,2,13012,13013,14013,14012,13020,13020,14020,1402010061,2,13013,13014,14014,14013,13020,13020,14020,1402010062,2,13014,13015,14015,14014,13020,13020,14020,14020

Feb 06, 07 11:19 Page 11/12SolidBeam02DOF.k10063,2,13015,13016,14016,14015,13020,13020,14020,1402010064,2,13016,13001,14001,14016,13020,13020,14020,14020$*END




63

Appendix I: Scilab mechanical straightening m-files Mechanical_straightening_combined.sce Figure I1 Xstrain_mechanical_straightening_LS-DYNA.sce Figure I2 XY_displacement_bar.sce Figure I3


//make sure scilab uses the right directory is used!!!!!!!!//make sure the names of the .txt−files are correct!!!!!!!!


///////////////////////////////////////////////////////////////////// "experimental" data loading and handling///////////////////////////////////////////////////////////////

//loading "experimental" data files into scilab//the consecutive numbers are from an increasing apllied //force//mm60_1, mm60_2, mm65, mm70 and mm75 are measured not by //force, but by y−displacement of the barkN5=fscanfMat(’5kN.unt’);kN10=fscanfMat(’10kN.unt’);kN15=fscanfMat(’15kN.unt’);kN20=fscanfMat(’20kN.unt’);kN25=fscanfMat(’25kN.unt’);kN30=fscanfMat(’30kN.unt’);kN35=fscanfMat(’35kN.unt’);kN375=fscanfMat(’37.5kN.unt’);kN40=fscanfMat(’40kN.unt’);kN45=fscanfMat(’45kN.unt’);kN50=fscanfMat(’50kN.unt’);kN55=fscanfMat(’55kN.unt’);kN60=fscanfMat(’60kN.unt’);kN65=fscanfMat(’65kN.unt’);kN70=fscanfMat(’70kN.unt’);kN75=fscanfMat(’75kN.unt’);kN80=fscanfMat(’80kN.unt’);mm60_1=fscanfMat(’60mm−1.unt’);mm60_2=fscanfMat(’60mm−2.unt’);mm65=fscanfMat(’65mm.unt’);mm70=fscanfMat(’70mm.unt’);mm75=fscanfMat(’75mm.unt’);

//subdiving "experimental" data into sperate columns//_1, _2, _3, _4 and _5 are columns containing strain gage //data//_Lo means load and this column contains the force values//_Di means distance and this column contains the //y−displacement valueskN5_1=kN5(:,1);kN5_2=kN5(:,2);kN5_3=kN5(:,3);kN5_4=kN5(:,4);kN5_5=kN5(:,5);kN5_Lo=kN5(:,6);kN5_Di=kN5(:,7);

kN10_1=kN10(:,1);kN10_2=kN10(:,2);kN10_3=kN10(:,3);kN10_4=kN10(:,4);kN10_5=kN10(:,5);kN10_Lo=kN10(:,6);kN10_Di=kN10(:,7);

kN15_1=kN15(:,1);kN15_2=kN15(:,2);

Feb 06, 07 10:55 Page 1/19Mechanical_straightening_combined.scekN15_3=kN15(:,3);kN15_4=kN15(:,4);kN15_5=kN15(:,5);kN15_Lo=kN15(:,6);kN15_Di=kN15(:,7);









Feb 06, 07 10:55 Page 2/19Mechanical_straightening_combined.sce


Tuesday February 06, 2007 1/10Mechanical_straightening_combined.sce







mm60_1_1=mm60_1(:,1);mm60_1_2=mm60_1(:,2);mm60_1_3=mm60_1(:,3);mm60_1_4=mm60_1(:,4);mm60_1_5=mm60_1(:,5);mm60_1_Lo=mm60_1(:,6);mm60_1_Di=mm60_1(:,7);

mm60_2_1=mm60_2(:,1);mm60_2_2=mm60_2(:,2);mm60_2_3=mm60_2(:,3);mm60_2_4=mm60_2(:,4);mm60_2_5=mm60_2(:,5);mm60_2_Lo=mm60_2(:,6);mm60_2_Di=mm60_2(:,7);

mm65_1=mm65(:,1);mm65_2=mm65(:,2);mm65_3=mm65(:,3);mm65_4=mm65(:,4);

Feb 06, 07 10:55 Page 3/19Mechanical_straightening_combined.scemm65_5=mm65(:,5);mm65_Lo=mm65(:,6);mm65_Di=mm65(:,7);

mm70_1=mm70(:,1);mm70_2=mm70(:,2);mm70_3=mm70(:,3);mm70_4=mm70(:,4);mm70_5=mm70(:,5);mm70_Lo=mm70(:,6);mm70_Di=mm70(:,7);

mm75_1=mm75(:,1);mm75_2=mm75(:,2);mm75_3=mm75(:,3);mm75_4=mm75(:,4);mm75_5=mm75(:,5);mm75_Lo=mm75(:,6);mm75_Di=mm75(:,7);

//calculations "experimental" data//multiplying by factor and offset//values are for calculating voltage into microstrain,//force and y−displacementkN5_Lo=−6.*kN5_Lo;kN10_Lo=−6.*kN10_Lo;kN15_Lo=−6.*kN15_Lo;kN20_Lo=−6.*kN20_Lo;kN25_Lo=−6.*kN25_Lo;kN30_Lo=−6.*kN30_Lo;kN35_Lo=−6.*kN35_Lo;kN375_Lo=−6.*kN375_Lo;kN40_Lo=−6.*kN40_Lo;kN45_Lo=−6.*kN45_Lo;kN50_Lo=−6.*kN50_Lo;kN55_Lo=−6.*kN55_Lo;kN60_Lo=−8.*kN60_Lo;kN65_Lo=−8.*kN65_Lo;kN70_Lo=−8.*kN70_Lo;kN75_Lo=−8.*kN75_Lo;kN80_Lo=−10.*kN80_Lo;mm60_1_Lo=−10.*mm60_1_Lo;mm60_2_Lo=−10.*mm60_2_Lo;mm65_Lo=−10.*mm65_Lo;mm70_Lo=−10.*mm70_Lo;mm75_Lo=−10.*mm75_Lo;

kN5_Di=−2.*kN5_Di;kN10_Di=−2.*kN10_Di;kN15_Di=−2.*kN15_Di;kN20_Di=−2.*kN20_Di;kN25_Di=−2.*kN25_Di;kN30_Di=−2.*kN30_Di;kN35_Di=−2.*kN35_Di;kN375_Di=−2.*kN375_Di;kN40_Di=−2.*kN40_Di;kN45_Di=−2.*kN45_Di;kN50_Di=−2.*kN50_Di;kN55_Di=−2.*kN55_Di;kN60_Di=−2.*kN60_Di;kN65_Di=−2.*kN65_Di;kN70_Di=−2.*kN70_Di;kN75_Di=−2.*kN75_Di;kN80_Di=−2.*kN80_Di;mm60_1_Di=−2.*mm60_1_Di;mm60_2_Di=−2.*mm60_2_Di;mm65_Di=−2.*mm65_Di;mm70_Di=−2.*mm70_Di;mm75_Di=−2.*mm75_Di;




kN5_1=500.2526.*kN5_1;kN10_1=500.2526.*kN10_1;kN15_1=500.2526.*kN15_1;kN20_1=500.2526.*kN20_1;kN25_1=500.2526.*kN25_1;kN30_1=500.2526.*kN30_1;kN35_1=500.2526.*kN35_1;kN375_1=500.2526.*kN375_1;kN40_1=500.2526.*kN40_1;kN45_1=500.2526.*kN45_1;kN50_1=500.2526.*kN50_1;kN55_1=500.2526.*kN55_1;kN60_1=1000.505.*kN60_1;kN65_1=1000.505.*kN65_1;kN70_1=1000.505.*kN70_1;kN75_1=1000.505.*kN75_1;kN80_1=1000.505.*kN80_1;mm60_1_1=2001.011.*mm60_1_1;mm60_2_1=2001.011.*mm60_2_1;mm65_1=2001.011.*mm65_1;mm70_1=2001.011.*mm70_1;mm75_1=2001.011.*mm75_1;

kN5_2=500.2526.*kN5_2;kN10_2=500.2526.*kN10_2;kN15_2=500.2526.*kN15_2;kN20_2=500.2526.*kN20_2;kN25_2=500.2526.*kN25_2;kN30_2=500.2526.*kN30_2;kN35_2=500.2526.*kN35_2;kN375_2=500.2526.*kN375_2;kN40_2=500.2526.*kN40_2;kN45_2=500.2526.*kN45_2;kN50_2=500.2526.*kN50_2;kN55_2=500.2526.*kN55_2;kN60_2=1000.505.*kN60_2;kN65_2=1000.505.*kN65_2;kN70_2=1000.505.*kN70_2;kN75_2=2001.011.*kN75_2;kN80_2=2001.011.*kN80_2;mm60_1_2=((2001.011*7.28054)+(2001.011.*mm60_1_2));mm60_2_2=((2001.011*7.28054)+(2001.011.*mm60_2_2));mm65_2=((2001.011*7.28054)+(2001.011.*mm65_2));mm70_2=((2001.011*7.28054)+(2001.011.*mm70_2));mm75_2=((2001.011*7.28054)+(2001.011.*mm75_2));




kN5_5=−500.2526.*kN5_5;kN10_5=−500.2526.*kN10_5;kN15_5=−500.2526.*kN15_5;kN20_5=−500.2526.*kN20_5;kN25_5=−500.2526.*kN25_5;kN30_5=−500.2526.*kN30_5;kN35_5=−500.2526.*kN35_5;kN375_5=−500.2526.*kN375_5;kN40_5=−500.2526.*kN40_5;kN45_5=−500.2526.*kN45_5;kN50_5=−500.2526.*kN50_5;kN55_5=−500.2526.*kN55_5;kN60_5=−1000.505.*kN60_5;kN65_5=−1000.505.*kN65_5;kN70_5=−1000.505.*kN70_5;kN75_5=−1000.505.*kN75_5;kN80_5=−1000.505.*kN80_5;mm60_1_5=−2001.011.*mm60_1_5;mm60_2_5=−2001.011.*mm60_2_5;mm65_5=−2001.011.*mm65_5;mm70_5=−2001.011.*mm70_5;mm75_5=−2001.011.*mm75_5;

/////////////////////////////////////////////////////////////////// "finite element" data loading and handling/////////////////////////////////////////////////////////////

//loading "finite element" data files into scilab//SB02CON−E60_xstrain_C.txt means;//1) program SB02CON//2) element 60 (N stands for node)//3) containing xstrain data//4) de "C"leaned fileSB02CON_E60_xstr=fscanfMat(’SB02CON−E60−xstrain_C.txt’);SB02CON_E61_xstr=fscanfMat(’SB02CON−E61−xstrain_C.txt’);SB02CON_E63_xstr=fscanfMat(’SB02CON−E63−xstrain_C.txt’);SB02CON_E85_xstr=fscanfMat(’SB02CON−E85−xstrain_C.txt’);SB02CON_E88_xstr=fscanfMat(’SB02CON−E88−xstrain_C.txt’);SB02CON_effstress=fscanfMat(’SB02CON−effstress_C.txt’);SB02CON_xstress_down=fscanfMat(’SB02CON−xstress−down_C.txt’);SB02CON_xstress_up=fscanfMat(’SB02CON−xstress−up_C.txt’);SB02CON_N1011_ydisp=fscanfMat(’SB02CON−N1011−ydisp_C.txt’);SB02CON_N1012_ydisp=fscanfMat(’SB02CON−N1012−ydisp_C.txt’);




SB02CON_N1014_ydisp=fscanfMat(’SB02CON−N1014−ydisp_C.txt’);SB02CON_N1063_ydisp=fscanfMat(’SB02CON−N1063−ydisp_C.txt’);SB02CON_N1064_ydisp=fscanfMat(’SB02CON−N1064−ydisp_C.txt’);SB02CON_N1066_ydisp=fscanfMat(’SB02CON−N1066−ydisp_C.txt’);SB02CON_yforce=fscanfMat(’SB02CON−yforce_C.txt’);

SB02DOF_E60_xstr=fscanfMat(’SB02DOF−E60−xstrain_C.txt’);SB02DOF_E61_xstr=fscanfMat(’SB02DOF−E61−xstrain_C.txt’);SB02DOF_E63_xstr=fscanfMat(’SB02DOF−E63−xstrain_C.txt’);SB02DOF_E85_xstr=fscanfMat(’SB02DOF−E85−xstrain_C.txt’);SB02DOF_E88_xstr=fscanfMat(’SB02DOF−E88−xstrain_C.txt’);SB02DOF_effstress=fscanfMat(’SB02DOF−effstress_C.txt’);SB02DOF_xstress_down=fscanfMat(’SB02DOF−xstress−down_C.txt’);SB02DOF_xstress_up=fscanfMat(’SB02DOF−xstress−up_C.txt’);SB02DOF_N1011_ydisp=fscanfMat(’SB02DOF−N1011−ydisp_C.txt’);SB02DOF_N1012_ydisp=fscanfMat(’SB02DOF−N1012−ydisp_C.txt’);SB02DOF_N1014_ydisp=fscanfMat(’SB02DOF−N1014−ydisp_C.txt’);SB02DOF_N1063_ydisp=fscanfMat(’SB02DOF−N1063−ydisp_C.txt’);SB02DOF_N1064_ydisp=fscanfMat(’SB02DOF−N1064−ydisp_C.txt’);SB02DOF_N1066_ydisp=fscanfMat(’SB02DOF−N1066−ydisp_C.txt’);SB02DOF_yforce=fscanfMat(’SB02DOF−yforce_C.txt’);

SB04CON_E420_xstr=fscanfMat(’SB04CON−E420−xstrain_C.txt’);SB04CON_E422_xstr=fscanfMat(’SB04CON−E422−xstrain_C.txt’);SB04CON_E426_xstr=fscanfMat(’SB04CON−E426−xstrain_C.txt’);SB04CON_E570_xstr=fscanfMat(’SB04CON−E570−xstrain_C.txt’);SB04CON_E576_xstr=fscanfMat(’SB04CON−E576−xstrain_C.txt’);SB04CON_effstress=fscanfMat(’SB04CON−effstress_C.txt’);SB04CON_xstress_down=fscanfMat(’SB04CON−xstress−down_C.txt’);SB04CON_xstress_up=fscanfMat(’SB04CON−xstress−up_C.txt’);SB04CON_N2021_ydisp=fscanfMat(’SB04CON−N2021−ydisp_C.txt’);SB04CON_N2023_ydisp=fscanfMat(’SB04CON−N2023−ydisp_C.txt’);SB04CON_N2026_ydisp=fscanfMat(’SB04CON−N2026−ydisp_C.txt’);SB04CON_N2224_ydisp=fscanfMat(’SB04CON−N2224−ydisp_C.txt’);SB04CON_N2227_ydisp=fscanfMat(’SB04CON−N2227−ydisp_C.txt’);SB04CON_N2230_ydisp=fscanfMat(’SB04CON−N2230−ydisp_C.txt’);SB04CON_yforce=fscanfMat(’SB04CON−yforce_C.txt’);


SB08CON_E3240_xstr=fscanfMat(’SB08CON−E3240−xstrain_C.txt’);SB08CON_E3244_xstr=fscanfMat(’SB08CON−E3244−xstrain_C.txt’);SB08CON_E3251_xstr=fscanfMat(’SB08CON−E3251−xstrain_C.txt’);SB08CON_E3940_xstr=fscanfMat(’SB08CON−E3940−xstrain_C.txt’);SB08CON_E3952_xstr=fscanfMat(’SB08CON−E3952−xstrain_C.txt’);SB08CON_effstress=fscanfMat(’SB08CON−effstress_C.txt’);SB08CON_xstress_down=fscanfMat(’SB08CON−xstress−down_C.txt’);SB08CON_xstress_up=fscanfMat(’SB08CON−xstress−up_C.txt’);SB08CON_N4040_ydisp=fscanfMat(’SB08CON−N4040−ydisp_C.txt’);SB08CON_N4045_ydisp=fscanfMat(’SB08CON−N4045−ydisp_C.txt’);SB08CON_N4051_ydisp=fscanfMat(’SB08CON−N4051−ydisp_C.txt’);SB08CON_N4848_ydisp=fscanfMat(’SB08CON−N4848−ydisp_C.txt’);SB08CON_N4853_ydisp=fscanfMat(’SB08CON−N4853−ydisp_C.txt’);SB08CON_N4860_ydisp=fscanfMat(’SB08CON−N4860−ydisp_C.txt’);SB08CON_yforce=fscanfMat(’SB08CON−yforce_C.txt’);




//subdividing "finite element" data into seperate columns//all imported files contain two column martrixes//the first is time data, the second; the data of interestSB02CON_E60_xstr=SB02CON_E60_xstr(:,2);SB02CON_E61_xstr=SB02CON_E61_xstr(:,2);SB02CON_E63_xstr=SB02CON_E63_xstr(:,2);SB02CON_E85_xstr=SB02CON_E85_xstr(:,2);SB02CON_E88_xstr=SB02CON_E88_xstr(:,2);SB02CON_effstress=SB02CON_effstress(:,2);SB02CON_xstress_down=SB02CON_xstress_down(:,2);SB02CON_xstress_up=SB02CON_xstress_up(:,2);SB02CON_N1011_ydisp=SB02CON_N1011_ydisp(:,2);SB02CON_N1012_ydisp=SB02CON_N1012_ydisp(:,2);SB02CON_N1014_ydisp=SB02CON_N1014_ydisp(:,2);SB02CON_N1063_ydisp=SB02CON_N1063_ydisp(:,2);SB02CON_N1064_ydisp=SB02CON_N1064_ydisp(:,2);SB02CON_N1066_ydisp=SB02CON_N1066_ydisp(:,2);SB02CON_yforce=SB02CON_yforce(:,2);

SB02DOF_E60_xstr=SB02DOF_E60_xstr(:,2);SB02DOF_E61_xstr=SB02DOF_E61_xstr(:,2);SB02DOF_E63_xstr=SB02DOF_E63_xstr(:,2);SB02DOF_E85_xstr=SB02DOF_E85_xstr(:,2);SB02DOF_E88_xstr=SB02DOF_E88_xstr(:,2);SB02DOF_effstress=SB02DOF_effstress(:,2);SB02DOF_xstress_down=SB02DOF_xstress_down(:,2);SB02DOF_xstress_up=SB02DOF_xstress_up(:,2);SB02DOF_N1011_ydisp=SB02DOF_N1011_ydisp(:,2);SB02DOF_N1012_ydisp=SB02DOF_N1012_ydisp(:,2);SB02DOF_N1014_ydisp=SB02DOF_N1014_ydisp(:,2);SB02DOF_N1063_ydisp=SB02DOF_N1063_ydisp(:,2);SB02DOF_N1064_ydisp=SB02DOF_N1064_ydisp(:,2);SB02DOF_N1066_ydisp=SB02DOF_N1066_ydisp(:,2);SB02DOF_yforce=SB02DOF_yforce(:,2);

SB04CON_E420_xstr=SB04CON_E420_xstr(:,2);




SB04CON_E422_xstr=SB04CON_E422_xstr(:,2);SB04CON_E426_xstr=SB04CON_E426_xstr(:,2);SB04CON_E570_xstr=SB04CON_E570_xstr(:,2);SB04CON_E576_xstr=SB04CON_E576_xstr(:,2);SB04CON_effstress=SB04CON_effstress(:,2);SB04CON_xstress_down=SB04CON_xstress_down(:,2);SB04CON_xstress_up=SB04CON_xstress_up(:,2);SB04CON_N2021_ydisp=SB04CON_N2021_ydisp(:,2);SB04CON_N2023_ydisp=SB04CON_N2023_ydisp(:,2);SB04CON_N2026_ydisp=SB04CON_N2026_ydisp(:,2);SB04CON_N2224_ydisp=SB04CON_N2224_ydisp(:,2);SB04CON_N2227_ydisp=SB04CON_N2227_ydisp(:,2);SB04CON_N2230_ydisp=SB04CON_N2230_ydisp(:,2);SB04CON_yforce=SB04CON_yforce(:,2);


SB08CON_E3240_xstr=SB08CON_E3240_xstr(:,2);SB08CON_E3244_xstr=SB08CON_E3244_xstr(:,2);SB08CON_E3251_xstr=SB08CON_E3251_xstr(:,2);SB08CON_E3940_xstr=SB08CON_E3940_xstr(:,2);SB08CON_E3952_xstr=SB08CON_E3952_xstr(:,2);SB08CON_effstress=SB08CON_effstress(:,2);SB08CON_xstress_down=SB08CON_xstress_down(:,2);SB08CON_xstress_up=SB08CON_xstress_up(:,2);SB08CON_N4040_ydisp=SB08CON_N4040_ydisp(:,2);SB08CON_N4045_ydisp=SB08CON_N4045_ydisp(:,2);SB08CON_N4051_ydisp=SB08CON_N4051_ydisp(:,2);SB08CON_N4848_ydisp=SB08CON_N4848_ydisp(:,2);SB08CON_N4853_ydisp=SB08CON_N4853_ydisp(:,2);SB08CON_N4860_ydisp=SB08CON_N4860_ydisp(:,2);SB08CON_yforce=SB08CON_yforce(:,2);


SB200DOF_E6479_xstr=SB200DOF_E6479_xstr(:,2);SB200DOF_E6488_xstr=SB200DOF_E6488_xstr(:,2);SB200DOF_E6501_xstr=SB200DOF_E6501_xstr(:,2);SB200DOF_E7878_xstr=SB200DOF_E7878_xstr(:,2);SB200DOF_E7902_xstr=SB200DOF_E7902_xstr(:,2);SB200DOF_effstress=SB200DOF_effstress(:,2);

Feb 06, 07 10:55 Page 9/19Mechanical_straightening_combined.sceSB200DOF_xstress_down=SB200DOF_xstress_down(:,2);SB200DOF_xstress_up=SB200DOF_xstress_up(:,2);SB200DOF_N8079_ydisp=SB200DOF_N8079_ydisp(:,2);SB200DOF_N8088_ydisp=SB200DOF_N8088_ydisp(:,2);SB200DOF_N8012_ydisp=SB200DOF_N8102_ydisp(:,2);SB200DOF_N9686_ydisp=SB200DOF_N9686_ydisp(:,2);SB200DOF_N9696_ydisp=SB200DOF_N9696_ydisp(:,2);SB200DOF_N9710_ydisp=SB200DOF_N9710_ydisp(:,2);SB200DOF_yforce=SB200DOF_yforce(:,2);

//calculations "finite element" data//multiplying by factorSB02CON_effstress=(1000.*SB02CON_effstress);SB02DOF_effstress=(1000.*SB02DOF_effstress);SB04CON_effstress=(1000.*SB04CON_effstress);SB04DOF_effstress=(1000.*SB04DOF_effstress);SB08CON_effstress=(1000.*SB08CON_effstress);SB08DOF_effstress=(1000.*SB08DOF_effstress);SB200DOF_effstress=(1000.*SB200DOF_effstress);

SB02CON_xstress_down=(1000.*SB02CON_xstress_down);SB02DOF_xstress_down=(1000.*SB02DOF_xstress_down);SB04CON_xstress_down=(1000.*SB04CON_xstress_down);SB04DOF_xstress_down=(1000.*SB04DOF_xstress_down);SB08CON_xstress_down=(1000.*SB08CON_xstress_down);SB08DOF_xstress_down=(1000.*SB08DOF_xstress_down);SB200DOF_xstress_down=(1000.*SB200DOF_xstress_down);

SB02CON_xstress_up=(1000.*SB02CON_xstress_up);SB02DOF_xstress_up=(1000.*SB02DOF_xstress_up);SB04CON_xstress_up=(1000.*SB04CON_xstress_up);SB04DOF_xstress_up=(1000.*SB04DOF_xstress_up);SB08CON_xstress_up=(1000.*SB08CON_xstress_up);SB08DOF_xstress_up=(1000.*SB08DOF_xstress_up);SB200DOF_xstress_up=(1000.*SB200DOF_xstress_up);

SB02CON_E60_xstr=(1000000.*SB02CON_E60_xstr);SB02CON_E61_xstr=(1000000.*SB02CON_E61_xstr);SB02CON_E63_xstr=(1000000.*SB02CON_E63_xstr);SB02CON_E85_xstr=(1000000.*SB02CON_E85_xstr);SB02CON_E88_xstr=(1000000.*SB02CON_E88_xstr);SB02DOF_E60_xstr=(1000000.*SB02DOF_E60_xstr);SB02DOF_E61_xstr=(1000000.*SB02DOF_E61_xstr);SB02DOF_E63_xstr=(1000000.*SB02DOF_E63_xstr);SB02DOF_E85_xstr=(1000000.*SB02DOF_E85_xstr);SB02DOF_E88_xstr=(1000000.*SB02DOF_E88_xstr);SB04CON_E420_xstr=(1000000.*SB04CON_E420_xstr);SB04CON_E422_xstr=(1000000.*SB04CON_E422_xstr);SB04CON_E426_xstr=(1000000.*SB04CON_E426_xstr);SB04CON_E570_xstr=(1000000.*SB04CON_E570_xstr);SB04CON_E576_xstr=(1000000.*SB04CON_E576_xstr);SB04DOF_E420_xstr=(1000000.*SB04DOF_E420_xstr);SB04DOF_E422_xstr=(1000000.*SB04DOF_E422_xstr);SB04DOF_E426_xstr=(1000000.*SB04DOF_E426_xstr);SB04DOF_E570_xstr=(1000000.*SB04DOF_E570_xstr);SB04DOF_E576_xstr=(1000000.*SB04DOF_E576_xstr);SB08CON_E3240_xstr=(1000000.*SB08CON_E3240_xstr);SB08CON_E3244_xstr=(1000000.*SB08CON_E3244_xstr);SB08CON_E3251_xstr=(1000000.*SB08CON_E3251_xstr);SB08CON_E3940_xstr=(1000000.*SB08CON_E3940_xstr);SB08CON_E3952_xstr=(1000000.*SB08CON_E3952_xstr);SB08DOF_E3240_xstr=(1000000.*SB08DOF_E3240_xstr);SB08DOF_E3244_xstr=(1000000.*SB08DOF_E3244_xstr);SB08DOF_E3251_xstr=(1000000.*SB08DOF_E3251_xstr);SB08DOF_E3940_xstr=(1000000.*SB08DOF_E3940_xstr);SB08DOF_E3952_xstr=(1000000.*SB08DOF_E3952_xstr);SB200DOF_E6479_xstr=(1000000.*SB200DOF_E6479_xstr);SB200DOF_E6488_xstr=(1000000.*SB200DOF_E6488_xstr);SB200DOF_E6501_xstr=(1000000.*SB200DOF_E6501_xstr);




SB200DOF_E7878_xstr=(1000000.*SB200DOF_E7878_xstr);SB200DOF_E7902_xstr=(1000000.*SB200DOF_E7902_xstr);

SB02CON_N1011_ydisp=(−1.*SB02CON_N1011_ydisp);SB02CON_N1012_ydisp=(−1.*SB02CON_N1012_ydisp);SB02CON_N1014_ydisp=(−1.*SB02CON_N1014_ydisp);SB02CON_N1063_ydisp=(−1.*SB02CON_N1063_ydisp);SB02CON_N1064_ydisp=(−1.*SB02CON_N1064_ydisp);SB02CON_N1066_ydisp=(−1.*SB02CON_N1066_ydisp);SB02DOF_N1011_ydisp=(−1.*SB02DOF_N1011_ydisp);SB02DOF_N1012_ydisp=(−1.*SB02DOF_N1012_ydisp);SB02DOF_N1014_ydisp=(−1.*SB02DOF_N1014_ydisp);SB02DOF_N1063_ydisp=(−1.*SB02DOF_N1063_ydisp);SB02DOF_N1064_ydisp=(−1.*SB02DOF_N1064_ydisp);SB02DOF_N1066_ydisp=(−1.*SB02DOF_N1066_ydisp);SB04CON_N2021_ydisp=(−1.*SB04CON_N2021_ydisp);SB04CON_N2023_ydisp=(−1.*SB04CON_N2023_ydisp);SB04CON_N2026_ydisp=(−1.*SB04CON_N2026_ydisp);SB04CON_N2224_ydisp=(−1.*SB04CON_N2224_ydisp);SB04CON_N2227_ydisp=(−1.*SB04CON_N2227_ydisp);SB04CON_N2230_ydisp=(−1.*SB04CON_N2230_ydisp);SB04DOF_N2021_ydisp=(−1.*SB04DOF_N2021_ydisp);SB04DOF_N2023_ydisp=(−1.*SB04DOF_N2023_ydisp);SB04DOF_N2026_ydisp=(−1.*SB04DOF_N2026_ydisp);SB04DOF_N2224_ydisp=(−1.*SB04DOF_N2224_ydisp);SB04DOF_N2227_ydisp=(−1.*SB04DOF_N2227_ydisp);SB04DOF_N2230_ydisp=(−1.*SB04DOF_N2230_ydisp);SB08CON_N4040_ydisp=(−1.*SB08CON_N4040_ydisp);SB08CON_N4045_ydisp=(−1.*SB08CON_N4045_ydisp);SB08CON_N4051_ydisp=(−1.*SB08CON_N4051_ydisp);SB08CON_N4848_ydisp=(−1.*SB08CON_N4848_ydisp);SB08CON_N4853_ydisp=(−1.*SB08CON_N4853_ydisp);SB08CON_N4860_ydisp=(−1.*SB08CON_N4860_ydisp);SB08DOF_N4040_ydisp=(−1.*SB08DOF_N4040_ydisp);SB08DOF_N4045_ydisp=(−1.*SB08DOF_N4045_ydisp);SB08DOF_N4051_ydisp=(−1.*SB08DOF_N4051_ydisp);SB08DOF_N4848_ydisp=(−1.*SB08DOF_N4848_ydisp);SB08DOF_N4853_ydisp=(−1.*SB08DOF_N4853_ydisp);SB08DOF_N4860_ydisp=(−1.*SB08DOF_N4860_ydisp);SB200DOF_N8079_ydisp=(−1.*SB200DOF_N8079_ydisp);SB200DOF_N8088_ydisp=(−1.*SB200DOF_N8088_ydisp);SB200DOF_N8102_ydisp=(−1.*SB200DOF_N8102_ydisp);SB200DOF_N9686_ydisp=(−1.*SB200DOF_N9686_ydisp);SB200DOF_N9696_ydisp=(−1.*SB200DOF_N9696_ydisp);SB200DOF_N9710_ydisp=(−1.*SB200DOF_N9710_ydisp);

//plotting functions for both "experimental" and //"finite element" data//mm75_Di didn’t contain any data (experimental error)//therefore it is commentedscf(1)plot(SB02DOF_N1064_ydisp,SB02DOF_yforce,’m’);plot(SB04DOF_N2227_ydisp,SB04DOF_yforce,’c’);plot(SB08DOF_N4853_ydisp,SB08DOF_yforce,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_yforce,’k’);plot(SB02CON_N1064_ydisp,SB02CON_yforce,’y’);plot(SB04CON_N2227_ydisp,SB04CON_yforce,’b’);plot(SB08CON_N4853_ydisp,SB08CON_yforce,’g’);xtitle(’displacement vs. force’,’displacement [mm]’,’force [kN]’);legend(’SB02DOF’,’SB04DOF’,’SB08DOF’,’SB200DOF’,’SBO2CON’,’SB04CON’,’SB08CON’);

scf(2)plot(SB02DOF_N1064_ydisp,SB02DOF_effstress,’m’);plot(SB04DOF_N2227_ydisp,SB04DOF_effstress,’c’);plot(SB08DOF_N4853_ydisp,SB08DOF_effstress,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_effstress,’k’);plot(SB02CON_N1064_ydisp,SB02CON_effstress,’y’);plot(SB04CON_N2227_ydisp,SB04CON_effstress,’b’);plot(SB08CON_N4853_ydisp,SB08CON_effstress,’g’);

Feb 06, 07 10:55 Page 11/19Mechanical_straightening_combined.scextitle(’displacement vs. effective stress middle’,’displacement [mm]’,’stress [MPa]’);legend(’SB02DOF’,’SB04DOF’,’SB08DOF’,’SB200DOF’,’SBO2CON’,’SB04CON’,’SB08CON’);

scf(3)plot(SB02DOF_N1064_ydisp,SB02DOF_xstress_down,’m’);plot(SB04DOF_N2227_ydisp,SB04DOF_xstress_down,’c’);plot(SB08DOF_N4853_ydisp,SB08DOF_xstress_down,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_xstress_down,’k’);plot(SB02CON_N1064_ydisp,SB02CON_xstress_down,’y’);plot(SB04CON_N2227_ydisp,SB04CON_xstress_down,’b’);plot(SB08CON_N4853_ydisp,SB08CON_xstress_down,’g’);xtitle(’displacement vs. x−stress bottom’,’displacement [mm]’,’stress [MPa]’);legend(’SB02DOF’,’SB04DOF’,’SB08DOF’,’SB200DOF’,’SBO2CON’,’SB04CON’,’SB08CON’);

scf(4)plot(SB02DOF_N1064_ydisp,SB02DOF_xstress_up,’m’);plot(SB04DOF_N2227_ydisp,SB04DOF_xstress_up,’c’);plot(SB08DOF_N4853_ydisp,SB08DOF_xstress_up,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_xstress_up,’k’);plot(SB02CON_N1064_ydisp,SB02CON_xstress_up,’y’);plot(SB04CON_N2227_ydisp,SB04CON_xstress_up,’b’);plot(SB08CON_N4853_ydisp,SB08CON_xstress_up,’g’);xtitle(’displacement vs. x−stress top’,’displacement [mm]’,’stress [MPa]’);legend(’SB02DOF’,’SB04DOF’,’SB08DOF’,’SB200DOF’,’SBO2CON’,’SB04CON’,’SB08CON’);

scf(5)plot(kN5_Di,kN5_Lo,’b’);plot(kN10_Di,kN10_Lo,’b’);plot(kN15_Di,kN15_Lo,’b’);plot(kN20_Di,kN20_Lo,’b’);plot(kN25_Di,kN25_Lo,’b’);plot(kN30_Di,kN30_Lo,’b’);plot(kN35_Di,kN35_Lo,’b’);plot(kN375_Di,kN375_Lo,’b’);plot(kN40_Di,kN40_Lo,’b’);plot(kN45_Di,kN45_Lo,’b’);plot(kN50_Di,kN50_Lo,’b’);plot(kN55_Di,kN55_Lo,’b’);plot(kN60_Di,kN60_Lo,’b’);plot(kN65_Di,kN65_Lo,’b’);plot(kN70_Di,kN70_Lo,’b’);plot(kN75_Di,kN75_Lo,’b’);plot(kN80_Di,kN80_Lo,’b’);plot(mm60_1_Di,mm60_1_Lo,’b’);plot(mm60_2_Di,mm60_2_Lo,’b’);plot(mm65_Di,mm65_Lo,’b’);plot(mm70_Di,mm70_Lo,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_yforce,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_yforce,’m’);plot(SB08DOF_N4853_ydisp,SB08DOF_yforce,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_yforce,’k’);//plot(mm75_Di,mm75_Lo,’b’);xtitle(’displacement vs. force’,’displacement [mm]’,’force [kN]’);

scf(6)plot(kN5_1,kN5_Lo,’b’);plot(kN10_1,kN10_Lo,’b’);plot(kN15_1,kN15_Lo,’b’);plot(kN20_1,kN20_Lo,’b’);plot(kN25_1,kN25_Lo,’b’);plot(kN30_1,kN30_Lo,’b’);plot(kN35_1,kN35_Lo,’b’);plot(kN375_1,kN375_Lo,’b’);plot(kN40_1,kN40_Lo,’b’);plot(kN45_1,kN45_Lo,’b’);plot(kN50_1,kN50_Lo,’b’);plot(kN55_1,kN55_Lo,’b’);plot(kN60_1,kN60_Lo,’b’);




plot(kN65_1,kN65_Lo,’b’);plot(kN70_1,kN70_Lo,’b’);plot(kN75_1,kN75_Lo,’b’);plot(kN80_1,kN80_Lo,’b’);plot(mm60_1_1,mm60_1_Lo,’b’);plot(mm60_2_1,mm60_2_Lo,’b’);plot(mm65_1,mm65_Lo,’b’);plot(mm70_1,mm70_Lo,’b’);plot(mm75_1,mm75_Lo,’b’);plot(SB02DOF_E63_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E426_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3251_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E6501_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage A/[1]>> strain vs. force’,’microstrain [−]’,’force [kN]’);

scf(7)plot(kN5_2,kN5_Lo,’b’);plot(kN10_2,kN10_Lo,’b’);plot(kN15_2,kN15_Lo,’b’);plot(kN20_2,kN20_Lo,’b’);plot(kN25_2,kN25_Lo,’b’);plot(kN30_2,kN30_Lo,’b’);plot(kN35_2,kN35_Lo,’b’);plot(kN375_2,kN375_Lo,’b’);plot(kN40_2,kN40_Lo,’b’);plot(kN45_2,kN45_Lo,’b’);plot(kN50_2,kN50_Lo,’b’);plot(kN55_2,kN55_Lo,’b’);plot(kN60_2,kN60_Lo,’b’);plot(kN65_2,kN65_Lo,’b’);plot(kN70_2,kN70_Lo,’b’);plot(kN75_2,kN75_Lo,’b’);plot(kN80_2,kN80_Lo,’b’);plot(mm60_1_2,mm60_1_Lo,’b’);plot(mm60_2_2,mm60_2_Lo,’b’);plot(mm65_2,mm65_Lo,’b’);plot(mm70_2,mm70_Lo,’b’);plot(mm75_2,mm75_Lo,’b’);plot(SB02DOF_E61_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E422_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3244_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E6488_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage B/[2]>> strain vs. force’,’microstrain [−]’,’force [kN]’);

scf(8)plot(kN5_3,kN5_Lo,’b’);plot(kN10_3,kN10_Lo,’b’);plot(kN15_3,kN15_Lo,’b’);plot(kN20_3,kN20_Lo,’b’);plot(kN25_3,kN25_Lo,’b’);plot(kN30_3,kN30_Lo,’b’);plot(kN35_3,kN35_Lo,’b’);plot(kN375_3,kN375_Lo,’b’);plot(kN40_3,kN40_Lo,’b’);plot(kN45_3,kN45_Lo,’b’);plot(kN50_3,kN50_Lo,’b’);plot(kN55_3,kN55_Lo,’b’);plot(kN60_3,kN60_Lo,’b’);plot(kN65_3,kN65_Lo,’b’);plot(kN70_3,kN70_Lo,’b’);plot(kN75_3,kN75_Lo,’b’);plot(kN80_3,kN80_Lo,’b’);plot(mm60_1_3,mm60_1_Lo,’b’);plot(mm60_2_3,mm60_2_Lo,’b’);plot(mm65_3,mm65_Lo,’b’);plot(mm70_3,mm70_Lo,’b’);plot(mm75_3,mm75_Lo,’b’);plot(SB02DOF_E60_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E420_xstr,SB04DOF_yforce,’m’);

Feb 06, 07 10:55 Page 13/19Mechanical_straightening_combined.sceplot(SB08DOF_E3240_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E6479_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage C/[3]>> strain vs. force’,’microstrain [−]’,’force [kN]’);

scf(9)plot(kN5_4,kN5_Lo,’b’);plot(kN10_4,kN10_Lo,’b’);plot(kN15_4,kN15_Lo,’b’);plot(kN20_4,kN20_Lo,’b’);plot(kN25_4,kN25_Lo,’b’);plot(kN30_4,kN30_Lo,’b’);plot(kN35_4,kN35_Lo,’b’);plot(kN375_4,kN375_Lo,’b’);plot(kN40_4,kN40_Lo,’b’);plot(kN45_4,kN45_Lo,’b’);plot(kN50_4,kN50_Lo,’b’);plot(kN55_4,kN55_Lo,’b’);plot(kN60_4,kN60_Lo,’b’);plot(kN65_4,kN65_Lo,’b’);plot(kN70_4,kN70_Lo,’b’);plot(kN75_4,kN75_Lo,’b’);plot(kN80_4,kN80_Lo,’b’);plot(mm60_1_4,mm60_1_Lo,’b’);plot(mm60_2_4,mm60_2_Lo,’b’);plot(mm65_4,mm65_Lo,’b’);plot(mm70_4,mm70_Lo,’b’);plot(mm75_4,mm75_Lo,’b’);plot(SB02DOF_E88_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E576_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3952_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E7902_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage U/[4]>> strain vs. force’,’microstrain [−]’,’force [kN]’);

scf(10)plot(kN5_5,kN5_Lo,’b’);plot(kN10_5,kN10_Lo,’b’);plot(kN15_5,kN15_Lo,’b’);plot(kN20_5,kN20_Lo,’b’);plot(kN25_5,kN25_Lo,’b’);plot(kN30_5,kN30_Lo,’b’);plot(kN35_5,kN35_Lo,’b’);plot(kN375_5,kN375_Lo,’b’);plot(kN40_5,kN40_Lo,’b’);plot(kN45_5,kN45_Lo,’b’);plot(kN50_5,kN50_Lo,’b’);plot(kN55_5,kN55_Lo,’b’);plot(kN60_5,kN60_Lo,’b’);plot(kN65_5,kN65_Lo,’b’);plot(kN70_5,kN70_Lo,’b’);plot(kN75_5,kN75_Lo,’b’);plot(kN80_5,kN80_Lo,’b’);plot(mm60_1_5,mm60_1_Lo,’b’);plot(mm60_2_5,mm60_2_Lo,’b’);plot(mm65_5,mm65_Lo,’b’);plot(mm70_5,mm70_Lo,’b’);plot(mm75_5,mm75_Lo,’b’);plot(SB02DOF_E85_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E570_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3940_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E7878_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage V/[5]>> strain vs. force’,’microstrain [−]’,’force [kN]’);

scf(11)plot(kN5_Di,kN5_1,’b’);plot(kN10_Di,kN10_1,’b’);plot(kN15_Di,kN15_1,’b’);plot(kN20_Di,kN20_1,’b’);plot(kN25_Di,kN25_1,’b’);plot(kN30_Di,kN30_1,’b’);




plot(kN35_Di,kN35_1,’b’);plot(kN375_Di,kN375_1,’b’);plot(kN40_Di,kN40_1,’b’);plot(kN45_Di,kN45_1,’b’);plot(kN50_Di,kN50_1,’b’);plot(kN55_Di,kN55_1,’b’);plot(kN60_Di,kN60_1,’b’);plot(kN65_Di,kN65_1,’b’);plot(kN70_Di,kN70_1,’b’);plot(kN75_Di,kN75_1,’b’);plot(kN80_Di,kN80_1,’b’);plot(mm60_1_Di,mm60_1_1,’b’);plot(mm60_2_Di,mm60_2_1,’b’);plot(mm65_Di,mm65_1,’b’);plot(mm70_Di,mm70_1,’b’);//plot(mm75_Di,mm75_1,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_E63_xstr,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_E426_xstr,’m’);plot(SB08DOF_N4853_ydisp,SB08DOF_E3251_xstr,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_E6501_xstr,’k’);xtitle(’<<strain gage A/[1]>> displacement vs. strain’,’displacement [mm]’,’microstrain [−]’);

scf(12)plot(kN5_Di,kN5_2,’b’);plot(kN10_Di,kN10_2,’b’);plot(kN15_Di,kN15_2,’b’);plot(kN20_Di,kN20_2,’b’);plot(kN25_Di,kN25_2,’b’);plot(kN30_Di,kN30_2,’b’);plot(kN35_Di,kN35_2,’b’);plot(kN375_Di,kN375_2,’b’);plot(kN40_Di,kN40_2,’b’);plot(kN45_Di,kN45_2,’b’);plot(kN50_Di,kN50_2,’b’);plot(kN55_Di,kN55_2,’b’);plot(kN60_Di,kN60_2,’b’);plot(kN65_Di,kN65_2,’b’);plot(kN70_Di,kN70_2,’b’);plot(kN75_Di,kN75_2,’b’);plot(kN80_Di,kN80_2,’b’);plot(mm60_1_Di,mm60_1_2,’b’);plot(mm60_2_Di,mm60_2_2,’b’);plot(mm65_Di,mm65_2,’b’);plot(mm70_Di,mm70_2,’b’);//plot(mm75_Di,mm75_2,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_E61_xstr,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_E422_xstr,’m’);plot(SB08DOF_N4853_ydisp,SB08DOF_E3244_xstr,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_E6488_xstr,’k’);xtitle(’<<strain gage B/[2]>> displacement vs. strain’,’displacement [mm]’,’microstrain [−]’);

scf(13)plot(kN5_Di,kN5_3,’b’);plot(kN10_Di,kN10_3,’b’);plot(kN15_Di,kN15_3,’b’);plot(kN20_Di,kN20_3,’b’);plot(kN25_Di,kN25_3,’b’);plot(kN30_Di,kN30_3,’b’);plot(kN35_Di,kN35_3,’b’);plot(kN375_Di,kN375_3,’b’);plot(kN40_Di,kN40_3,’b’);plot(kN45_Di,kN45_3,’b’);plot(kN50_Di,kN50_3,’b’);plot(kN55_Di,kN55_3,’b’);plot(kN60_Di,kN60_3,’b’);plot(kN65_Di,kN65_3,’b’);plot(kN70_Di,kN70_3,’b’);

Feb 06, 07 10:55 Page 15/19Mechanical_straightening_combined.sceplot(kN75_Di,kN75_3,’b’);plot(kN80_Di,kN80_3,’b’);plot(mm60_1_Di,mm60_1_3,’b’);plot(mm60_2_Di,mm60_2_3,’b’);plot(mm65_Di,mm65_3,’b’);plot(mm70_Di,mm70_3,’b’);//plot(mm75_Di,mm75_3,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_E60_xstr,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_E420_xstr,’m’);plot(SB08DOF_N4853_ydisp,SB08DOF_E3240_xstr,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_E6479_xstr,’k’);xtitle(’<<strain gage C/[3]>> displacement vs. strain’,’displacement [mm]’,’microstrain [−]’);

scf(14)plot(kN5_Di,kN5_4,’b’);plot(kN10_Di,kN10_4,’b’);plot(kN15_Di,kN15_4,’b’);plot(kN20_Di,kN20_4,’b’);plot(kN25_Di,kN25_4,’b’);plot(kN30_Di,kN30_4,’b’);plot(kN35_Di,kN35_4,’b’);plot(kN375_Di,kN375_4,’b’);plot(kN40_Di,kN40_4,’b’);plot(kN45_Di,kN45_4,’b’);plot(kN50_Di,kN50_4,’b’);plot(kN55_Di,kN55_4,’b’);plot(kN60_Di,kN60_4,’b’);plot(kN65_Di,kN65_4,’b’);plot(kN70_Di,kN70_4,’b’);plot(kN75_Di,kN75_4,’b’);plot(kN80_Di,kN80_4,’b’);plot(mm60_1_Di,mm60_1_4,’b’);plot(mm60_2_Di,mm60_2_4,’b’);plot(mm65_Di,mm65_4,’b’);plot(mm70_Di,mm70_4,’b’);//plot(mm75_Di,mm75_4,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_E88_xstr,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_E576_xstr,’m’);plot(SB08DOF_N4853_ydisp,SB08DOF_E3952_xstr,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_E7902_xstr,’k’);xtitle(’<<strain gage U/[4]>> displacement vs. strain’,’displacement [mm]’,’microstrain [−]’);

scf(15)plot(kN5_Di,kN5_5,’b’);plot(kN10_Di,kN10_5,’b’);plot(kN15_Di,kN15_5,’b’);plot(kN20_Di,kN20_5,’b’);plot(kN25_Di,kN25_5,’b’);plot(kN30_Di,kN30_5,’b’);plot(kN35_Di,kN35_5,’b’);plot(kN375_Di,kN375_5,’b’);plot(kN40_Di,kN40_5,’b’);plot(kN45_Di,kN45_5,’b’);plot(kN50_Di,kN50_5,’b’);plot(kN55_Di,kN55_5,’b’);plot(kN60_Di,kN60_5,’b’);plot(kN65_Di,kN65_5,’b’);plot(kN70_Di,kN70_5,’b’);plot(kN75_Di,kN75_5,’b’);plot(kN80_Di,kN80_5,’b’);plot(mm60_1_Di,mm60_1_5,’b’);plot(mm60_2_Di,mm60_2_5,’b’);plot(mm65_Di,mm65_5,’b’);plot(mm70_Di,mm70_5,’b’);//plot(mm75_Di,mm75_5,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_E85_xstr,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_E570_xstr,’m’);




plot(SB08DOF_N4853_ydisp,SB08DOF_E3940_xstr,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_E7878_xstr,’k’);xtitle(’<<strain gage V/[5]>> displacement vs. strain’,’displacement [mm]’,’microstrain [−]’);

scf(16)subplot(2,3,1);plot(kN5_4,kN5_Lo,’b’);plot(kN10_4,kN10_Lo,’b’);plot(kN15_4,kN15_Lo,’b’);plot(kN20_4,kN20_Lo,’b’);plot(kN25_4,kN25_Lo,’b’);plot(kN30_4,kN30_Lo,’b’);plot(kN35_4,kN35_Lo,’b’);plot(kN375_4,kN375_Lo,’b’);plot(kN40_4,kN40_Lo,’b’);plot(kN45_4,kN45_Lo,’b’);plot(kN50_4,kN50_Lo,’b’);plot(kN55_4,kN55_Lo,’b’);plot(kN60_4,kN60_Lo,’b’);plot(kN65_4,kN65_Lo,’b’);plot(kN70_4,kN70_Lo,’b’);plot(kN75_4,kN75_Lo,’b’);plot(kN80_4,kN80_Lo,’b’);plot(mm60_1_4,mm60_1_Lo,’b’);plot(mm60_2_4,mm60_2_Lo,’b’);plot(mm65_4,mm65_Lo,’b’);plot(mm70_4,mm70_Lo,’b’);plot(mm75_4,mm75_Lo,’b’);plot(SB02DOF_E88_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E576_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3952_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E7902_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage U/[4]>> strain vs. force’,’microstrain [−]’,’force [kN]’);subplot(2,3,2);plot(kN5_Di,kN5_Lo,’b’);plot(kN10_Di,kN10_Lo,’b’);plot(kN15_Di,kN15_Lo,’b’);plot(kN20_Di,kN20_Lo,’b’);plot(kN25_Di,kN25_Lo,’b’);plot(kN30_Di,kN30_Lo,’b’);plot(kN35_Di,kN35_Lo,’b’);plot(kN375_Di,kN375_Lo,’b’);plot(kN40_Di,kN40_Lo,’b’);plot(kN45_Di,kN45_Lo,’b’);plot(kN50_Di,kN50_Lo,’b’);plot(kN55_Di,kN55_Lo,’b’);plot(kN60_Di,kN60_Lo,’b’);plot(kN65_Di,kN65_Lo,’b’);plot(kN70_Di,kN70_Lo,’b’);plot(kN75_Di,kN75_Lo,’b’);plot(kN80_Di,kN80_Lo,’b’);plot(mm60_1_Di,mm60_1_Lo,’b’);plot(mm60_2_Di,mm60_2_Lo,’b’);plot(mm65_Di,mm65_Lo,’b’);plot(mm70_Di,mm70_Lo,’b’);//plot(mm75_Di,mm75_Lo,’b’);plot(SB02DOF_N1064_ydisp,SB02DOF_yforce,’c’);plot(SB04DOF_N2227_ydisp,SB04DOF_yforce,’m’);plot(SB08DOF_N4853_ydisp,SB08DOF_yforce,’r’);plot(SB200DOF_N9696_ydisp,SB200DOF_yforce,’k’);xtitle(’displacement vs. force’,’displacement [mm]’,’force [kN]’);subplot(2,3,3);plot(kN5_5,kN5_Lo,’b’);plot(kN10_5,kN10_Lo,’b’);plot(kN15_5,kN15_Lo,’b’);plot(kN20_5,kN20_Lo,’b’);plot(kN25_5,kN25_Lo,’b’);plot(kN30_5,kN30_Lo,’b’);

Feb 06, 07 10:55 Page 17/19Mechanical_straightening_combined.sceplot(kN35_5,kN35_Lo,’b’);plot(kN375_5,kN375_Lo,’b’);plot(kN40_5,kN40_Lo,’b’);plot(kN45_5,kN45_Lo,’b’);plot(kN50_5,kN50_Lo,’b’);plot(kN55_5,kN55_Lo,’b’);plot(kN60_5,kN60_Lo,’b’);plot(kN65_5,kN65_Lo,’b’);plot(kN70_5,kN70_Lo,’b’);plot(kN75_5,kN75_Lo,’b’);plot(kN80_5,kN80_Lo,’b’);plot(mm60_1_5,mm60_1_Lo,’b’);plot(mm60_2_5,mm60_2_Lo,’b’);plot(mm65_5,mm65_Lo,’b’);plot(mm70_5,mm70_Lo,’b’);plot(mm75_5,mm75_Lo,’b’);plot(SB02DOF_E85_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E570_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3940_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E7878_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage V/[5]>> strain vs. force’,’microstrain [−]’,’force [kN]’);subplot(2,3,4);plot(kN5_1,kN5_Lo,’b’);plot(kN10_1,kN10_Lo,’b’);plot(kN15_1,kN15_Lo,’b’);plot(kN20_1,kN20_Lo,’b’);plot(kN25_1,kN25_Lo,’b’);plot(kN30_1,kN30_Lo,’b’);plot(kN35_1,kN35_Lo,’b’);plot(kN375_1,kN375_Lo,’b’);plot(kN40_1,kN40_Lo,’b’);plot(kN45_1,kN45_Lo,’b’);plot(kN50_1,kN50_Lo,’b’);plot(kN55_1,kN55_Lo,’b’);plot(kN60_1,kN60_Lo,’b’);plot(kN65_1,kN65_Lo,’b’);plot(kN70_1,kN70_Lo,’b’);plot(kN75_1,kN75_Lo,’b’);plot(kN80_1,kN80_Lo,’b’);plot(mm60_1_1,mm60_1_Lo,’b’);plot(mm60_2_1,mm60_2_Lo,’b’);plot(mm65_1,mm65_Lo,’b’);plot(mm70_1,mm70_Lo,’b’);plot(mm75_1,mm75_Lo,’b’);plot(SB02DOF_E63_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E426_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3251_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E6501_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage A/[1]>> strain vs. force’,’microstrain [−]’,’force [kN]’);subplot(2,3,5);plot(kN5_2,kN5_Lo,’b’);plot(kN10_2,kN10_Lo,’b’);plot(kN15_2,kN15_Lo,’b’);plot(kN20_2,kN20_Lo,’b’);plot(kN25_2,kN25_Lo,’b’);plot(kN30_2,kN30_Lo,’b’);plot(kN35_2,kN35_Lo,’b’);plot(kN375_2,kN375_Lo,’b’);plot(kN40_2,kN40_Lo,’b’);plot(kN45_2,kN45_Lo,’b’);plot(kN50_2,kN50_Lo,’b’);plot(kN55_2,kN55_Lo,’b’);plot(kN60_2,kN60_Lo,’b’);plot(kN65_2,kN65_Lo,’b’);plot(kN70_2,kN70_Lo,’b’);plot(kN75_2,kN75_Lo,’b’);plot(kN80_2,kN80_Lo,’b’);plot(mm60_1_2,mm60_1_Lo,’b’);plot(mm60_2_2,mm60_2_Lo,’b’);




plot(mm65_2,mm65_Lo,’b’);plot(mm70_2,mm70_Lo,’b’);plot(mm75_2,mm75_Lo,’b’);plot(SB02DOF_E61_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E422_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3244_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E6488_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage B/[2]>> strain vs. force’,’microstrain [−]’,’force [kN]’);subplot(2,3,6);plot(kN5_3,kN5_Lo,’b’);plot(kN10_3,kN10_Lo,’b’);plot(kN15_3,kN15_Lo,’b’);plot(kN20_3,kN20_Lo,’b’);plot(kN25_3,kN25_Lo,’b’);plot(kN30_3,kN30_Lo,’b’);plot(kN35_3,kN35_Lo,’b’);plot(kN375_3,kN375_Lo,’b’);plot(kN40_3,kN40_Lo,’b’);plot(kN45_3,kN45_Lo,’b’);plot(kN50_3,kN50_Lo,’b’);plot(kN55_3,kN55_Lo,’b’);plot(kN60_3,kN60_Lo,’b’);plot(kN65_3,kN65_Lo,’b’);plot(kN70_3,kN70_Lo,’b’);plot(kN75_3,kN75_Lo,’b’);plot(kN80_3,kN80_Lo,’b’);plot(mm60_1_3,mm60_1_Lo,’b’);plot(mm60_2_3,mm60_2_Lo,’b’);plot(mm65_3,mm65_Lo,’b’);plot(mm70_3,mm70_Lo,’b’);plot(mm75_3,mm75_Lo,’b’);plot(SB02DOF_E60_xstr,SB02DOF_yforce,’c’);plot(SB04DOF_E420_xstr,SB04DOF_yforce,’m’);plot(SB08DOF_E3240_xstr,SB08DOF_yforce,’r’);plot(SB200DOF_E6479_xstr,SB200DOF_yforce,’k’);xtitle(’<<strain gage C/[3]>> strain vs. force’,’microstrain [−]’,’force [kN]’);//end




74

Figure I1: Combined results of the mechanical straightening experiments and the finite element models




//loading xstrain data into scilabSolidBeam02DOF_xstrain=fscanfMat(’SolidBeam02DOF−xstrain_C.txt’);SolidBeam02DOF_xstrain_down=fscanfMat(’SolidBeam02DOF−xstrain−down_C.txt’);SolidBeam04DOF_xstrain=fscanfMat(’SolidBeam04DOF−xstrain_C.txt’);SolidBeam04DOF_xstrain_down=fscanfMat(’SolidBeam04DOF−xstrain−down_C.txt’);SolidBeam08DOF_xstrain=fscanfMat(’SolidBeam08DOF−xstrain_C.txt’);SolidBeam08DOF_xstrain_down=fscanfMat(’SolidBeam08DOF−xstrain−down_C.txt’);SolidBeam200DOF_xstrain=fscanfMat(’SolidBeam200DOF−xstrain_C.txt’);SolidBeam200DOF_xstrain_down=fscanfMat(’SolidBeam200DOF−xstrain−down_C.txt’);

//creating X−postions columns for the xstrainmm02=[231.44:14.88:588.56]’;mm04=[227.72:7.44:592.28]’;mm08=[225.860:3.72:594.14]’;mm200=[224.93:1.86:595.07]’;

//columns containing which elements are usedelementnumbering02=SolidBeam02DOF_xstrain(:,1);elementnumbering04=SolidBeam04DOF_xstrain(:,1);elementnumbering08=SolidBeam08DOF_xstrain(:,1);elementnumbering200=SolidBeam200DOF_xstrain(:,1);

//subdiving the xstrain data and multiplying it with the //desired factorxstrain02=(1000000.*(SolidBeam02DOF_xstrain(:,2)));xstrain02_down=(1000000.*(SolidBeam02DOF_xstrain_down(:,2)));xstrain04=(1000000.*(SolidBeam04DOF_xstrain(:,2)));xstrain04_down=(1000000.*(SolidBeam04DOF_xstrain_down(:,2)));xstrain08=(1000000.*(SolidBeam08DOF_xstrain(:,2)));xstrain08_down=(1000000.*(SolidBeam08DOF_xstrain_down(:,2)));xstrain200=(1000000.*(SolidBeam200DOF_xstrain(:,2)));xstrain200_down=(1000000.*(SolidBeam200DOF_xstrain_down(:,2)));

//plotting functionsscf(1)plot(mm02,xstrain02,’c’);plot(mm04,xstrain04,’m’);plot(mm08,xstrain08,’r’);plot(mm200,xstrain200,’k’);xtitle(’X−strain along the top of the bar at largest beding moment <14.88/7.44/3.72/1.86 − 6.99 length strain gage>’,’distance [mm]’,’microstrain [−]’);

scf(2)plot(mm02,xstrain02_down,’c’);plot(mm04,xstrain04_down,’m’);plot(mm08,xstrain08_down,’r’);plot(mm200,xstrain200_down,’k’);xtitle(’X−strain along the bottom of the bar at largest bending moment <14.88/7.44/3.72/1.86 − 6.99 length strain gage>’,’distance [mm]’,’microstrain [−]’);

scf(3)subplot(2,1,1)plot(mm02,xstrain02,’c’);plot(mm04,xstrain04,’m’);plot(mm08,xstrain08,’r’);plot(mm200,xstrain200,’k’);xtitle(’X−strain along the top of the bar at largest bending moment’,’distance [mm]’,’microstrain [−]’);subplot(2,1,2)plot(mm02,xstrain02_down,’c’);

Feb 06, 07 11:05 Page 1/2Xstrain_mechanical_straightening_LS−DYNA.sceplot(mm04,xstrain04_down,’m’);plot(mm08,xstrain08_down,’r’);plot(mm200,xstrain200_down,’k’);xtitle(’X−strain along the bottom of the bar at largest bending moment’,’distance [mm]’,’microstrain [−]’);//end

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76

Figure I2: Surface strain measured along the top, and the bottom, of the metal bar




//loading X and Y postions data into scilabXdispdatadown=fscanfMat(’X−disp−data−down_C.txt’);Xdispdataup=fscanfMat(’X−disp−data−up_C.txt’);Ydispdatadown=fscanfMat(’Y−disp−data−down_C.txt’);Ydispdataup=fscanfMat(’Y−disp−data−up_C.txt’);

//subdividing data into seperate columnsX1d=Xdispdatadown(:,2);X2d=Xdispdatadown(:,3);X3d=Xdispdatadown(:,4);X1u=Xdispdataup(:,2);X2u=Xdispdataup(:,3);X3u=Xdispdataup(:,4);Y1d=Ydispdatadown(:,2);Y2d=Ydispdatadown(:,3);Y3d=Ydispdatadown(:,4);Y1u=Ydispdataup(:,2);Y2u=Ydispdataup(:,3);Y3u=Ydispdataup(:,4);

//defining a trendling for rotation//adding a minus offset to this trendline//offset is different for distance and heightoff=[0.050271604:−0.012567901:−1.206518519];off1=(−0.485+off)’;

offu=[0.0509:−0.012725:−1.222];offu=(−0.485+offu)’;offd=[−1.222:0.012725:0.0509];offd=(−0.485+offd)’;

//adding the offset to the y−position to get//the desired y−position, which compare to the//mechanical straightening experimentsY1d=Y1d+offd;Y2d=Y2d+offd;Y3d=Y3d+offd;Y1u=Y1u+offu;Y2u=Y2u+offu;Y3u=Y3u+offu;

//plotting functionsscf(1)subplot(2,1,1)plot(X1u,Y1u,’b’);plot(X2u,Y2u,’r’);plot(X3u,Y3u,’g’);xtitle(’XY positions of nodes along the top of the bar’,’distance [mm]’,’height [mm]’)subplot(2,1,2)plot(X1d,Y1d,’b’);plot(X2d,Y2d,’r’);plot(X3d,Y3d,’g’);xtitle(’XY positions of nodes along the bottom of the bar’,’distance [mm]’,’height [mm]’)

Y1uu=−31.0+Y1u;Y2uu=−31.0+Y2u;Y3uu=−31.0+Y3u;

Feb 06, 07 11:05 Page 1/2XY_displacement_bar.scescf(2)plot(X1u,Y1uu,’b’);plot(X2u,Y2uu,’b’);plot(X3u,Y3uu,’b’);plot(X1d,Y1d,’r’);plot(X2d,Y2d,’r’);plot(X3d,Y3d,’r’);xtitle(’XY positions of nodes along the bottom [red] and the top [blue] the bar’,’distance [mm]’,’height [mm]’)

scf(3)plot(X1dd,Y1d,’b’);plot(X2dd,Y2d,’r’);plot(X3dd,Y3d,’g’);xtitle(’XY positions’,’distance [mm]’,’height [mm]’)//end

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78

Figure I3: x- and y-position of nodes along the bottom and top of the bar, mechanical straightening

79

Appendix J: Plots of finite element variations

Figure J1: Displacement vs. force for different finite element programs

Figure J2: Displacement vs. effective stress in the middle of the bar for different finite element programs

80

Figure J3: Displacement vs. surface stress (in x-direction top) for different finite element programs

Figure J4: Displacement vs. surface stress (in x-direction bottom) for different finite element programs

81

Appendix K: Compressed heat transfer keyword file

*KEYWORD*TITLESolid Beam in Bending 08 DOF, Heat Transfer 44Conductivity$$ DRDC Pacific, calculation T.Romans$$ Last Modified: 7 February, 2007$$ Units: m, s, kg, N, Pa, J, K$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Control Ouput$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8$*CONTROL_SOLUTION$ soln 2$*CONTROL_TERMINATION $ endtim endcyc dtmin endneg endmas 288 $*CONTROL_THERMAL_SOLVER$ atype ptype solver cgtol gpt eqheat fwork sbc 1$*CONTROL_TIMESTEP$ dtnit tssfac isdo tslimt dt2ms lctm erode ms1st 0.0001$*CONTROL_THERMAL_TIMESTEP$ ts tip its tmin tmax dtemp tscp 1 1 0.1 5$*CONTROL_OUTPUT$ npopt neecho nrefup iaccop opifs ipnint ikedit 1 3$*CONTROL_HOURGLASS$ igh qh 4$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Database$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$*DATABASE_BINARY_D3PLOT$ dt lcdt 1$*DATABASE_BINARY_D3THDT$ dt 1$*DATABASE_EXTENT_BINARY$ neiph neips maxint strflg sigflg epsflg rltflg engflg 1$$ cmpflg ieverp beamip 1$*DATABASE_ELOUT

Feb 15, 07 12:17 Page 1/4SB08DOFHT_44C_Compressed.k$ dt 1$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Define Parts and Materials$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$*PART$ pid sid mid eosid hgid grav adpopt tmidBeam 1 1 1 1$$$$$$ Sections$*SECTION_SOLID$ secid elform aet 1 1$$$$$$ Mechanical Material Properties$*MAT_ELASTIC_PLASTIC_THERMAL$ mid ro 1 7.8e3$$ t1 t2 t3 t4 t5 t6 293 398 523 648 773 873$$ e1 e2 e3 e4 e5 e6 210e+9 204e+9 196e+9 185e+9 170e+9 158e+9$$ pr1 pr2 pr3 pr4 pr5 pr6 0.31 0.31 0.31 0.31 0.31 0.31$$ alpha1 alpha2 alpha3 alpha4 alpha5 alpha6 1.1e−5 1.3e−5 1.5e−5 1.7e−5 1.9e−5 2.1e−5$$ sigy1 sigy2 sigy3 sigy4 sigy5 sigy6 550e+6 482e+6 415e+6 348e+6 280e+6 221e+6$$ etan1 etan2 etan3 etan4 etan5 etan6 30e+9 30e+9 30e+9 30e+9 30e+9 30e+9$$$$$$ Thermal Material Properties$*MAT_THERMAL_ISOTROPIC_TD$ tmid tro tgrlc tgmult 1 0$$ t1 t2 t3 t4 t5 t6 293 398 523 648 773 873$$ c1 c2 c3 c4 c5 c6 456 500 556 600 652 733$$ k1 k2 k3 k4 k5 k6 44 44 44 44 44 44$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Boundary Conditions$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

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$*BOUNDARY_SPC_NODE$ nid cid dofx dofy dofz dofrx dofry dofrz 1 0 1 1 1 1 1 1 101 0 0 1 0 1 1 1 1001 0 1 1 1 1 1 1 1101 0 0 1 0 1 1 1 2001 0 1 1 1 1 1 1 2101 0 0 1 0 1 1 1 3001 0 1 1 1 1 1 1 3101 0 0 1 0 1 1 1 4001 0 1 1 1 1 1 1 4101 0 0 1 0 1 1 1 5001 0 1 1 1 1 1 1 5101 0 0 1 0 1 1 1 6001 0 1 1 1 1 1 1 6101 0 0 1 0 1 1 1 7001 0 1 1 1 1 1 1 7101 0 0 1 0 1 1 1 8001 0 1 1 1 1 1 1 8101 0 0 1 0 1 1 1$*SET_NODE_LIST$ sid 2$$ nid1 nid2 nid3 nid4 nid5 nid6 nid7 nid8 841 842 843 844 845 1841 1842 1843 1844 1845 2841 2842 2843 2844 2845 3841 3842 3843 3844 3845 4841 4842 4843 4844 4845 5841 5842 5843 5844 5845 6841 6842 6843 6844 6845 7841 7842 7843 7844 7845 8841 8842 8843 8844 8845$*BOUNDARY_TEMPERATURE_SET$ nid/sid lcid cmult loc 2 1 1$*DEFINE_CURVE$ lcid sidr scla sclo offa offo 1$$ abscissa ordinate 0 328 20 826 34.5 726 58.5 467 169.5 357 288 325$$$$$$ Thermal Boundary Conditions$*INITIAL_TEMPERATURE_SET$ nsid/nid temp 0 328$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Define Nodes and Elements$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Node Generation Beam$*NODE1,0.230000,0.000000,0.000000,0,0

Feb 15, 07 12:17 Page 3/4SB08DOFHT_44C_Compressed.k2,0.236530,0.000160,0.000000,0,03,0.243060,0.000318,0.000000,0,0.........8907,0.869940,0.031138,0.038000,0,08908,0.876470,0.031057,0.038000,0,08909,0.883000,0.031000,0.038000,0,0$$$$$$ Elements Generation Beam (100x,8y,8z)$*ELEMENT_SOLID$ eid pid n1 n2 n3 n4 n5 n6 n7 n81,1,1,2,103,102,1001,1002,1103,11022,1,2,3,104,103,1002,1003,1104,11033,1,3,4,105,104,1003,1004,1105,1104.........6398,1,7805,7806,7907,7906,8805,8806,8907,89066399,1,7806,7807,7908,7907,8806,8807,8908,89076400,1,7807,7808,7909,7908,8807,8808,8909,8908$*END

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84

Appendix L: Flame_straightening.sce


//make sure scilab uses the right directory is used!!!//make sure the names of the .txt−files are correct!!!


///////////////////////////////////////////////////////////////// plotting temperature versus time calculations/////////////////////////////////////////////////////////////

//importing datadata01=fscanfMat(’FlameStraighteningExcel.txt’);data02=fscanfMat(’Temp_44C_down.txt’);data03=fscanfMat(’Temp_44C_top.txt’);data04=fscanfMat(’Temp_MAR_down.txt’);data05=fscanfMat(’Temp_MAR_top.txt’);

//subdividing and selecting experimental dataX=data01(:,1);Y1=data01(:,2);Y2=data01(:,3);

X=[0:2:1168]’;Y1=Y1(1215:1799,:);Y2=Y2(1215:1799,:);

//plotting experimental datascf(1)plot(X,Y1,’r’)plot(X,Y2,’g’)

//interpolation of experimental dataXr=[0:3.2:1168];[Yr1]=interp1(X,Y1,Xr,’nearest’);[Yr2]=interp1(X,Y2,Xr,’nearest’);

//plotting interpolations into experimental data plotplot(Xr,Yr1,’b’)plot(Xr,Yr2,’b’)

//further selection of experimental dataXrF=[−0.4:3.2:290.8];Yr1=Yr1’;Yr1F=Yr1(129:220,:);Yr2=Yr2’;Yr2F=Yr2(129:220,:);

//subdividing finite element dataXDT44C=(data02(:,1));YDT44C=−273+(data02(:,2));XTT44C=(data03(:,1));YTT44C=−273+(data03(:,2));XDTMAR=(data04(:,1));YDTMAR=−273+(data04(:,2));XTTMAR=(data05(:,1));YTTMAR=−273+(data05(:,2));

//combined plotting functionsscf(2)plot(XrF,Yr1F,’r’);plot(XrF,Yr2F,’r’);plot(XDT44C,YDT44C,’g’);plot(XTT44C,YTT44C,’g’);plot(XDTMAR,YDTMAR,’b’);

Feb 07, 07 15:13 Page 1/2Flame_straightening.sceplot(XTTMAR,YTTMAR,’b’);xtitle(’Time vs. temperature (constant 44 conductivity [green] / martensite conductivity [blue])’,’time [sec]’,’temprature [celsius]’);

///////////////////////////////////////////////////////////////// plotting x− and y−positions of nodes on top surface/////////////////////////////////////////////////////////////

//importing datadatax10=fscanfMat(’x_pos_top_44C_C.txt’);datay11=fscanfMat(’y_pos_top_44C_C.txt’);datax12=fscanfMat(’x_pos_top_MAR_C.txt’);datay13=fscanfMat(’y_pos_top_MAR_C.txt’);

//subdividing datapt44CX_0=datax10(:,2);pt44CX_288=datax10(:,3);pt44CY_0=datay11(:,2);pt44CY_288=datay11(:,3);ptMARX_0=datax12(:,2);ptMARX_288=datax12(:,3);ptMARY_0=datay13(:,2);ptMARY_288=datay13(:,3);

//plotting datascf(3)plot(pt44CX_0,pt44CY_0,’b’);plot(pt44CX_288,pt44CY_288,’r’);xtitle(’<44 Conductivity> x− and y−position of nodes along the top surface (time 0 [blue] / time 288 [red])’,’distance [m]’,’height [m]’);

scf(4)plot(ptMARX_0,ptMARY_0,’b’);plot(ptMARX_288,ptMARY_288,’r’);xtitle(’<Martensite> x− and y−position of nodes along the top surface (time 0 [blue] / time 288 [red])’,’distance [m]’,’height [m]’);//end

Feb 07, 07 15:13 Page 2/2Flame_straightening.sce


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Figure L1: Time versus temperature for the flame straightening case

analysis of plate straightening approaches

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