Division of Materials Engineering Division of Mechanics

ISRN LUTFD2/TFME – 09/5014 – SE(1-64)

Optimization of exhaust valve with internal water cooling

Master Thesis by Per Karlsson & Rasmus Olson

Supervisors:

Solveig Melin, Div. of Mechanics

Christer Persson, Div. of Materials Engineering

Henrik Andersson, MAN Diesel

ii

iii

Preface This Master Thesis has been conducted at the Division of Mechanics and the Division of Materials Engineering at Lund Institute of Technology in cooperation with MAN Diesel in Copenhagen during spring of 2009. The objective of this study has been to investigate if a new water cooled exhaust valve design could withstand thermal fatigue, and to propose a new, optimized, design. Special focus was placed on describing the material, both in terms of constitutive equations and fatigue properties. We would like to thank Professor Solveig Melin and Docent Christer Persson for great help and guidance. Further, we would like to thank our supervisors at MAN Diesel, Ph.D. Henrik Andersson, Mr. Anders Hansen, Mr. Harro Hoeg and Mr. Henning Joergensen, for their expertise and support. Finally, we would like to thank Mr. Živorad Živković for his helpfulness and patience during the material testing. Lund, June 2009 Per Karlsson & Rasmus Olson

iv

v

Abstract This Thesis has been performed in cooperation with MAN Diesel in Copenhagen and regards the development of an exhaust valve in large two stroke marine engines, with internal cooling channels. The challenge with designing an exhaust valve with cooling is to account for the strains that are created as a consequence of the cooling channels. The presence of cooling channels in the hot valve creates high temperature differences and, therefore, strains inducing thermal fatigue due to start and stop of the engine. It is thus of interest to reduce strains in order to maximize the life time of the valve. This work can be characterized in four different parts, comprising, a material testing, finite element simulations, fatigue testing and, finally, optimization. From material testing, a material model for the valve was chosen. The model was later used in the finite element simulations to find the strains. Along with fatigue testing of the valve material, the strains could be translated into life time and, finally, the valve geometry was optimized to minimize the strains. The aim throughout the Thesis was to find a design that can withstand 10000 thermal cycles, induced by start and stop of the engine. The final design proposal of the exhaust valve reached a life time of 9600 cycles. This result is thus not satisfying, especially when regarding that no safety factor has been taken into consideration.

vi

vii

Sammanfattning Detta examensarbete har utförts i samarbete med MAN Diesel i Köpenhamn och behandlar utvecklingen av en avgasventil för stora marina tvåtaktsmotorer, med interna kylkanaler. Utmaningen med att utforma en avgasventil med internkylning är att dimensionera mot de töjningar som skapas på grund av de stora temperaturskillnaderna i ventilen. Då motorn startas och stoppas utsätts ventilen för en termisk cykel som, genom de inducerade töjningarna, på sikt leder till utmattningshaveri. Därför är det av intresse att undersöka töjningarna och att minimera dessa, så att ventilens livslängd kan maximeras. Arbetet kan delas in i fyra olika delar bestående av en materialkarakteriseringsdel, en finita element simuleringsdel, en utmattningsanalys och, slutligen, en optimeringsdel. Materialdelen gick ut på att bestämma en materialmodell för ventilen, vilken sedermera användes i simuleringsdelen för att beräkna töjningarna. Tillsammans med resultaten från utmattningsanalysen kunde töjningarna översättas till livslängd. Slutligen optimerades utformningen av ventilen för att uppnå minimala töjningar. Målet med studien var att komma fram till en ventilmodell som klarar 10000 termiska cykler. Det slutgiltiga konstruktionsförslaget gav 9600 cykler, vilket inte uppnår målet. Dessutom har, i detta arbete, ingen hänsyn tagits till eventuella säkerhetsfaktorer, vilket ytterligare skulle försämra möjligheterna att nå målet 10000 cykler till brott.

viii

ix

Table of contents Preface ................................................................................................................................... iii Abstract .................................................................................................................................. v Sammanfattning ................................................................................................................... vii Table of contents ................................................................................................................... ix 1. Introduction .................................................................................................................... 1 2. Objectives ....................................................................................................................... 3 3. The situation at present .................................................................................................. 4 4. Design of the study ......................................................................................................... 8 5. Theory ............................................................................................................................ 9

5.1. Theory of plasticity ................................................................................................ 9 5.1.1. Yield criteria ................................................................................................... 9 5.1.2. Plastic hardening ............................................................................................ 9 5.1.3. Chaboche’s constitutive model .................................................................... 11

5.2. Theory of fatigue .................................................................................................. 11 5.2.1. Strain-life approach ...................................................................................... 12 5.2.2. Morrow’s mean stress equation .................................................................... 13 5.2.3. S-N curves .................................................................................................... 13 5.2.4. Load ratio R .................................................................................................. 14

6. Material HIP ........................................................... Fel! Bokmärket är inte definierat. 7. Test procedures ............................................................................................................ 16

7.1. Equipment ............................................................................................................ 16 7.2. Piston steel ............................................................................................................ 18 7.3. Material parameter definitions ............................................................................. 18 7.4. Design of fatigue test ............................................................................................ 21

8. Test results .................................................................................................................... 23 8.1. Constitutive results ............................................................................................... 23 8.2. Fatigue results ...................................................................................................... 28

9. Numerical simulations .................................................................................................. 30 9.1. Finite element analysis ......................................................................................... 30 9.2. Fatigue analysis .................................................................................................... 36

10. Design optimization ................................................................................................. 37 10.1. Optimization study 1 ........................................................................................ 38 10.2. Optimization Study 2 ....................................................................................... 39 10.3. Optimization Study 3 ....................................................................................... 41

11. Analysis of results .................................................................................................... 43 12. Conclusions .............................................................................................................. 45 13. Limitations ............................................................................................................... 46 14. Future recommendations .......................................................................................... 47 References ............................................................................................................................ 48 Appendices ........................................................................................................................... 49

A Piston steel material data .............................................................................................. 49 B Abaqus input file .......................................................................................................... 52

x

1

1. Introduction In achieving reduced emissions in modern engines, an increased combustion temperature is often necessary. An increased level of combustion temperature implies higher thermal stresses in surrounding materials, which have to be regarded during the design process. In order to cope with the higher combustion temperatures, a new exhaust valve design with internal cooling channels, containing e.g. water, has been proposed by MAN Diesel. Active cooling of the valve reduces the temperature, but, also, induces high temperature gradients and strains. The strains created need to be carefully regarded and are therefore the main objective of this Thesis, as well as describing the material both in terms of stress-strain relations and fatigue properties. Marine engines run for a vast amount of time, typically 30 years with 6000 hours per year. In addition, the valve should be able to withstand roughly 10000 start and stop cycles. During start-up and run-down of the engine thermal cycles appears due to temperature gradients, further shortening the life of engine components and valves. One start and stop cycle of the engine is termed one thermal cycle. Exhaust valves are designed to withstand all the thermal cycles during the engine life time. An engine and exhaust valve is illustrated in Figure 1.

2

Figure 1. Left shows entire engine with the exhaust valve marked in red. Right shows an enlarged drawing of the exhaust valve. The diameter of the valve head is 289 mm.

3

2. Objectives The objective of this Master Thesis is to design a new exhaust valve with internal cooling channels that can withstand 10000 engine start and stop cycles. With internal cooling, large temperature differences arise between the cooling channels and the valve head surface, creating strains. The strains cause fatigue and, therefore, have a large impact on the life time of the exhaust valve. This Master Thesis aims to find a feasible exhaust valve design by minimizing the strains. The preliminaries are that the maximum temperature of the cooled exhaust valve may not exceed 475ºC, and that the valve has to withstand, roughly, 2 billion valve opening- and closing cycles.

4

3. The situation at present At the time-being, the exhaust valves at MAN Diesel are completely solid structures. With an increase in combustion temperature, the temperatures in the valve might exceed tolerable levels. This is illustrated in Figure 2, showing the temperature distribution at running conditions.

Figure 2. Axisymmetric model showing the temperature distribution in the valve at running conditions. N.B. the temperature scales differ between Figure 2 and Figure 3.

In order to reduce the temperature in the valve, internal water cooling has been proposed. By introducing internal cooling channels in the valve, the temperatures can be reduced. MAN Diesel has proposed a first possible design solution, which also has been the starting point for this Thesis, as shown in Figure 3.

5

Figure 3. Axisymmetric model showing the temperature distribution in the water cooled valve assuming a channel of water cooling. N.B. the temperature scales differ between Figure 2 and Figure 3.

The temperature of the cooling water has been set to 75°C. When comparing Figure 2 with Figure 3 one can notice a significant difference in maximum temperature. Thus, the design of the cooled exhaust valve emerges as a challenge.

6

Figure 4. Each box is dedicated a mean process temperature and heat transfer coefficient. Thermo-elements are marked by numbers.

The valve experiences different temperatures along the boundary depending on location. The boundary had been divided, by MAN Diesel, into different boxes, each holding a specific process mean temperature and heat transfer coefficient as illustrated in Figure 4. This information constituted the base for calculating the temperature distribution, employing the Finite Element Method (FEM). From Figure 4 one can also notice how accurately calculated values correspond to measured values. In order to manufacture a valve with internal cooling channels, a metal powder material has been considered. The current design uses a different material, explaining why the properties of the metal powder thoroughly have to be examined to adequately investigate the feasibility of a new water cooled valve. A 3-D model of the valve with internal cooling was provided by MAN Diesel as shown in Figure 5.

7

Figure 5. 3-D model of the valve with internal water cooling.

8

4. Design of study A literature study was first undertaken in the areas of plasticity and low cycle fatigue for stainless steels. Additionally, a study of MAN Diesel's previous investigations in the field was performed. In order to correctly define the required material parameters, especially considering the valve material, a certain number of experiments needed to be conducted. The extent of experiments was restricted by the limited number of test specimens of HIP steel at hand. To decrease the errors induced by handling during testing, the experiments were initially performed on another, cheaper and more available, steel material in order to fully learn the correct handling of the machinery. As the material parameters were retrieved and analyzed, the data was used to set up a constitutive model in the commercial finite element code Abaqus [1]. A simulation of the exhaust valve was run in Abaqus, and the results obtained were used to determine the procedure of the following fatigue experiments. Once the fatigue limits for different strain ranges were known, this information was used to optimize the lifetime with the aid of the commercial software Hyperworks [2].

Material testing

Abaqus simulation

Fatigue testing

Optimization

9

5. Theory In the following Section the use of a few different theories is introduced to the reader in order to fully be acquainted with the design challenges that need to be overcome. An exhaust valve is subjected to high temperatures during operation. The use of valve cooling channels further induces large temperature differences within the valve. These temperature differences cause high temperature gradients in the material, inducing strain and stress gradients. Large strains, inducing plasticity in the material, are vital to account for. Further, the exhaust valves are exposed to temperature cycling during starting and stopping of the engine, implying the necessity of fatigue life designing. In this context, a valve must be designed to withstand all temperature cycles during an engine life.

5.1. Theory of plasticity

5.1.1. Yield criteria For an uniaxial stress state it is rather easy to determine when a material goes from elastic to plastic behavior. This is when, what is defined as, the yield stress is exceeded. For a multiaxial stress state the situation is more complicated, and a criterion of yield has to be established. The most commonly used criterion when dealing with metals is the von Mises criterion [3], cf. (Eq. 1). The criterion is independent of the hydrostatic stress and from whether the stress state is compressive or tensile. Due to this, the von Mises yield criterion represents a cylindrical surface in the principal stress space, as shown in Figure 6.

( ) ( ) ( )[ ] 021

02

322

312

21 =−−+−+− yσσσσσσσ (Eq. 1)

where σ1, σ2 and σ3 denotes the principal stresses, σ1> σ2> σ3, and σy0 the initial yield stress.

Figure 6. Cylindrical von Mises yield surface in principal stress space.

5.1.2. Plastic hardening When a material is loaded beyond its initial yield stress, plastic strains develop. If the stresses in the material increase as the plastic strains increase, the material is said to harden plastically. The opposite is called soften plastically. The cases are illustrated in Figure 7. The material always unloads elastically, even if it has been plastically deformed, and the plastic strains do

σ1

σ2

σ1 = σ2 = σ3

σ3

10

not recover. If the material is loaded again it will behave elastic, until it reaches the current yield stress, σy, which, in general, differs from the initial yield stress because the material has either hardened or softened due to previous loading.

Figure 7. Plastic hardening and softening.

Since the yield surface is a generalization of the yield stress, the yield surface has to change during multiaxial plastic deformation, just as the yield stress does during uniaxial plastic deformation. The von Mises yield surface can change in two ways; it can keep the size and shape fixed and move in the principal stress space, Figure 8a, called kinematic hardening as introduced by Melan [4], or keep its center and shape fixed but changing its size, Figure 8b, called isotropic hardening as attributed to Hill [5]. A combination of the two is also possible and is called mixed hardening, introduced by Hodge [6]. When the yield surface changes its position in the principal stress space due to plastic loading, the movement of the center of the yield surface can be described by a tensor. This is called the back-stress tensor, αij, and is illustrated in Figure 8a.

Figure 8. Kinematic hardening (a) and isotropic hardening (b).

When using the von Mises criterion and isotropic hardening, the yield surface will increase in size if the material hardens plastically. A consequence of this will be that the predicted yield stress is increased for both tension and compression. For the uniaxial case this is illustrated in Figure 9a. Experimental results for metals and steels do not agree well with this prediction [7]. Instead, experimental results show that the material reaches plasticity much earlier than

σ

ε

Plastic hardening

Plastic softening

αij

σ1

σ2 σ3

σ1

σ2 σ3

a) b)

11

predicted, when the loading is reversed. This phenomenon is called the Bauschinger effect [8]. The kinematic hardening model predicts this more accurately because the size of the yield surface is kept fixed during plastic deformation, see Figure 9b for the uniaxial loading case.

Figure 9. Uniaxial stress strain curves for isotropic hardening (a) and kinematic hardening (b). σy0 is the initial yield stress and σy is the current yield stress.

5.1.3. Chaboche’s constitutive model Chaboche’s constitutive model [9] aims at describing mixed hardening, i.e. it is a combination of isotropic and kinematic hardening. In this Thesis it was decided to only use the kinematic part of the model and, therefore, the isotropic part is not described. The kinematic part the back-stress can be composed by several back-stress components, kα , each component defined from (Eq. 2)

1 1( )pl plk k k k k k

y k

C CC

α ε σ α γ α ε ασ

= − − + (Eq. 2)

where kα is the rate of change for the back-stress components, Ck and γk are material parameters, kC the rate of change of Ck with respect to temperature, and plε describes the equivalent plastic strain rate. The overall back-stress is then calculated according to (Eq. 3):

∑=

=N

kk

1αα (Eq. 3)

where N is the number of back-stress components.

5.2. Theory of fatigue Designing for fatigue involves the usage of the term total fatigue life to failure, meaning the amount of stress- or strain cycles until failure of the material is recorded. The number of cycles the component can withstand until failure is termed the fatigue life. When testing for fatigue life, laboratory specimens, which are smooth surfaced and uncracked prior to testing, are run with controlled ranges of stress or strain. The life of the specimen is stated as the total amount of cycles achieved before rupture of the specimen.

2(σy0 + hardening)

σy0

σ

ε

σy

-σy

2σy0

σy0

σ a) b)

σy

σy - 2σy0

12

When discussing fatigue, two main approaches are at hand; a stress-life or a strain-life approach. Considering a stress-life approach, the stress is controlled, whereas for strain-life the strain amplitude during cycling is controlled. The strain-life approach is described in the following Section.

5.2.1. Strain-life approach During cycling with locally large plastic strains the fatigue life is shortened, and the use of Low Cycle Fatigue (LCF) dimensioning applies under these circumstances. A suitable model for predicting the number of cycles to failure, fN , denoting the number of fully reversed cycles to failure at a strain-life approach is a model proposed by Coffin [10] and Manson [11].

' (2 )2

p cf fN

εε

∆= (Eq. 4)

Here 2

pε∆ is the plastic strain amplitude, 'fε the ductility coefficient and c the fatigue

ductility exponent. Coffin [10] and Manson [11] noticed a linear relationship between the logarithm of plastic strain amplitude and the logarithm of cycles to failure, a relationship valid for metallic materials. Another, similar, relationship was proposed by Basquin [12]

' (2 )2

ba f fNσ σ σ∆

= = (Eq. 5)

where σ∆ is the stress range, aσ is the cyclic stress amplitude, 'fσ is the fatigue strength

coefficient and b the fatigue strength exponent. From (Eq. 5) and the relation

2 2e a

E Eε σσ∆ ∆

= = (Eq. 6)

where E is Young’s modulus, it is found that Basquins equation (Eq. 5) can be written as

'

(2 )2

f befN

Eσε∆

= (Eq. 7)

Combining equation (Eq. 4) and (Eq. 7), and splitting the total strain into one elastic ( eε∆ ) and one plastic part ( pε∆ ) according to:

2 2 2pe εεε ∆∆∆

= + (Eq. 8)

one obtains

''(2 ) (2 )

2f b c

f f fN NEσε ε∆

= + (Eq. 9)

13

The first term on the right hand side of (Eq. 9) describes the elastic component of the total strain amplitude, and the second term the corresponding plastic component. The material parameters must be determined by experiments.

5.2.2. Morrow’s mean stress equation Fatigue life of materials can be influenced by different mean stress levels. In order to account for these mean stress effects, Morrow [13] has proposed a manner to incorporate the effect by the following relationship:

''(2 ) (2 )

2f m b c

f f fN NE

σ σε ε−∆

= + (Eq. 10)

where mσ is the mean stress level defined according to

max min

2mσ σσ +

= (Eq. 11)

Notice that (Eq. 10) only modifies the elastic part of (Eq. 9).

Figure 10. Definition of maximum and minimum stresses σmax and σmin, stress amplitude σa, mean stress σm and stress range Δσ with t denoting time.

5.2.3. S-N curves The S-N curve is often used to describe the fatigue life for materials at different strain or stress levels. In Figure 11 S depicts a stress or strain level and N the number of cycles to failure at corresponding stress or strain level.

Figure 11. Schematic S-N curve

S

N

14

5.2.4. Load ratio R Fully reversed stress cycles with zero mean stress are not always representative for general applications, explaining why other load cases need to be defined. The load ratio, R, is an useful parameter describing the characteristics of a load cycle. The load ratio R is defined as follows:

min min

max max

,R Rσ εσ εσ ε

= =

(Eq. 12)

Here Rσ denotes the ratio between maximum and minimum stress and Rε the ratio between maximum and minimum strain. Thus R = -1 for fully reversed cycles, R = 0 for zero-tension or strain cycles fatigue, and R = 1 for a static load case.

15

6. Valve material The material to be used in the exhaust valve is delivered by Metso Minerals and is called SNCrW by internal MAN Diesel standards. It is an austenitic steel and is manufactured using hot isostatic pressing (HIP). During the HIP-process a powder mixture is placed in a container, subjected to a high temperature at vacuum. This removes moisture and air from the powder. The container is, thereafter, exposed to a high pressure by an inert gas at elevated temperatures. The result of the HIP-process is a material with strong metallurgical bonds and few internal voids [14]. The chemical composition of the steel from Metso Minerals can be seen in Table 1, together with the material properties in Table 2, for clarity. Table 1. Chemical composition of the HIP-material. Nominal for chemical composition means “average”. Normally a deviation of +/- 10 % is fully accepted, but this is not an imperative demand as long as the mechanical property demands are fulfilled [15].

C Si Mn S P Cr Ni W Fe Nominal 0.25 1 1 20 10 2 balanced Max 0.30 0.030 0.040 balanced Table 2. Material properties at different temperatures for the HIP-material [16]. Poisson’s ratio, v, equals 0,3 for all temperatures.

Degr. [C]

Density [kg/m3]

E-modul [Gpa]

Therm. Exp. [10e-6/C]

Therm. Conduct. [W/mK]

20 7900 200 12,5 100 7870 196 15,5 13,8 200 187 16,5 15 300 7780 177 17,5 16,7 400 169 17,9 18,3 500 7700 162 18,2 19,6

16

7. Test procedures

7.1. Equipment During the work with determining material parameters, extensive testing of specimens in a MTS tension-compression machine at Lund University, Sweden, was undertaken. The MTS machine is shown in Figure 12. In addition to the servo hydraulic MTS machine, a High Temperature Extensometer, see Figure 13, and an oven were used to perform elevated temperature tests. The High Temperature Extensometer measures the strain amplitude of the test specimen by two ceramic extension rods, that are in contact with the specimen during the tension-compression tests. The High Temperature Extensometer was mounted onto the oven, which enclosed the specimen to ensure a stable temperature. The oven, opened with a specimen mounted, is seen in Figure 12.

Figure 12. MTS machine.

17

Figure 13. High Temperature Extensometer.

The oven was calibrated by using a test specimen with thermo elements mounted into it, see Figure 14, to find the relation between oven set temperature and test specimen temperature. Due to small leakage gaps between the oven and the MTS machine, a slight flow of hot air leaves the top and cold air enters the bottom of the oven. This creates a so called chimney effect, with small temperature differences along the vertical direction of the specimen. To reduce this effect, the leakage gaps were filled with heat resistant cotton. The chimney effect depends on the temperature, and at 150°C it equaled a difference of 10°C between the lower and the upper thermo elements, and at 300°C the difference was measured to be 16°C.

Figure 14. Test specimen with three thermocouples at the center part of the specimen, marked by arrows. Measures are in mm.

A control system by Instron was used to monitor the MTS machine during tests. The control system gives the user the possibility to choose between performing strain controlled, force controlled or position controlled testing. One can also choose the frequency for the tension-compression cycles, especially helpful during fatigue testing. The control system could also be governed through a PC. The test specimens were machined by MAN Diesel into a shape seen in Figure 15 with the following dimensions:

18

Length (L): 127 mm (5 inches). Width at the ends (W1): 19.05 mm (3/4 inches) Second width (W2): 12.7 mm (1/2 inches) Width at center (W3): 6.35 mm (1/4 inches)

Figure 15. Test specimen.

7.2. Piston steel Prior to performing tests with the HIP-steel, a cheaper and more available steel, cut out from a piston by MAN Diesel, was used to perform testing in the MTS machine. The main purpose of these tests was to gain experience in the handling of the machinery. As a secondary objective, the Chaboche material model parameters were found, cf. Appendix A.

7.3. Material parameter definitions When using the Chaboche model, explained in the Theory section, Abaqus requires certain data to fully determine the material parameters needed in the model. A choice was made to only regard kinematic hardening, and, in this, case the Chaboche model requires four material parameters as input; E, ν, C and γ where ν denotes Poisson’s ratio. Abaqus requires data pairs, ( iσ , pl

iε ), for a stabilized tension-compression cycle, visualized in Figure 16. Here iσ and pl

iε denotes the stress and the plastic strain. The plastic strain for each data pair is determined by

0pl ii i pE

σε ε ε= − − (Eq. 13)

where 0pε denotes the plastic strain at zero stress, cf. Figure 16. The finite element

implementation in Abaqus is given in Appendix B.

Figure 16. Stabilized stress-tension loop with strain on horizontally and stress on vertical axis.

To provide Abaqus with acquired data pairs, tension-compression tests were pursued. Test specimens were mounted into the MTS machine and the High Temperature Extensometer was

L

W3 W2 W1

19

fitted onto the specimen. The control system was programmed with a PC, and for each test strain range load limits, position limits, number of cycles and frequencies were defined. These limits are necessary so that the machine stops once the test specimen breaks. When designing the tests it was important to regard the choice of temperatures and strain amplitudes for the test specimens. Additionally, Abaqus requires a stabilized loop. For this purpose the number of cycles to reach a stabilized loop was to be found.

From earlier investigations by MAN Diesel, the temperature interval the valve experiences were known to be in the range from room temperature (25°C) to a maximum of 479°C. It was decided to perform testing at room temperature, 300°C and 450°C, to cover the full temperature range. When analyzing the results, the stress-strain curves for 300°C and 450°C were surprisingly similar. Therefore an additional test, at 200°C, was performed.

Since the exact strain amplitudes in the valve were not known in advance it was decided to perform strain tests starting at 0,1 % strain amplitude until fracture, with increments of 0,1 % in strain amplitude.

When planning the tests it was desired to keep the amount of specimens needed for the material parameter definition to a minimum. For this reason, tests were carried out to see if the results from a specimen tested at a certain strain amplitude could corresponded to a specimen tested at the same strain amplitude, but with preceding cycles at a lower strain amplitude. Figure 17 shows two tests where Test 1 started at the strain amplitude 0,6 % directly, Test 2 started at a strain amplitude of 0,1 %, increasing its strain amplitude by steps of 0,1 % until reaching 0,6 %. At this strain amplitude, 0,6 %, Test 1 and Test 2 were compared to investigate the correlation between results. As can be noted from Figure 17, the two test loops correspond very well. For this reason, it was decided that it was sufficient to use one specimen for recording data from several strain amplitudes.

Figure 17. Two tests at different start strain amplitudes.

20

In order to find the number of cycles required to reach a stabilized loop, strain tests were performed at a few different strain amplitudes. A stabilized loop was defined to be stable when it had reached a point where the shape of the loop did not change from one cycle to another within an accuracy of a change in relative stress range less than 0,5 % over ten cycles. Figure 18 shows 500 loops for a certain specimen, and as seen the specimen softens and reaches a stabilized loop after, approximately, 200 cycles at the strain amplitude 0,6 %.

Figure 18. Cyclic test with 500 cycles at strain amplitude 0,6 %.

Figure 19 shows another 200 cycles at a strain amplitude of 0,7 % for the same specimen as in Figure 18. As can be seen, the stabilized loop is reached almost directly. A stabilized loop is reached quicker if the specimen has already been cycled at a lower strain amplitude. As a conclusion from these results, it was decided to run 200 cycles at the smaller strain amplitudes, and 100 cycles for the larger strain amplitudes in order to prepare the test specimens used in this study.

21

Figure 19. Cyclic test with 200 cycles at strain amplitude 0,7 %.

7.4. Design of fatigue tests When doing fatigue tests one needs to choose between performing strain controlled or force controlled testing. In strain controlled tests the strain amplitude is defined, whereas the force amplitude is defined in force controlled testing. During strain controlled testing, the strain is measured with a high temperature extensometer which only works accurately below frequencies of, approximately, 0,5 Hz, implying a full cycle time of 2 seconds. Above testing frequencies of 0,5 Hz, the rods on the extensometer commence to slide along the test specimen, resulting in an incorrect strain range. During force controlled testing, maximum frequencies of about 25 Hz are allowed, giving significantly shorter fatigue test time as compared to strain controlled tests. The valve which is the object of this Thesis is subjected to elevated temperatures creating strains which, further, induces stresses in the material. For this purpose it is more appropriate to use strain controlled fatigue testing in order to more precisely match the real life conditions the valve is exposed to. However, fatigue testing time is a major limiting factor when performing strain controlled tests, explaining why force controlled fatigue tests are to prefer. Therefore it was decided to first find a stabilized strain controlled loop and, later on, try to fit this loop with a similar force controlled loop. Typically, 2000 - 4000 strain controlled cycles were required to reach a satisfyingly stabilized loop. When switching from strain controlled to force controlled testing, the force range from the final loops in the strain controlled tests defined the new, force controlled, test. By this procedure the testing time was largely reduced.

22

A limiting factor when switching from strain controlled to force controlled testing is the influence of softening or hardening of the material. During strain controlled tests the stress range varies as a consequence of softening or hardening of the material, whereas the strain range is affected during force controlled testing. This is shown in Figure 20, where the difference in strain- and force controlled testing is visualized.

Figure 20. Force controlled and strain controlled loops for a softening material.

The largest strains observed in the calculations using the finite element model of the valve were along the water cooling channels. The strain range, Rε-ratio, and temperature in this region were all parameters constituting a starting point for the fatigue tests. From the finite element model, a maximum strain range of 0,92 % at a Rε -ratio of, approximately, 0,25 at temperature 90°C were obtained for the most critical node in the model. For nodes adjacent to the most critical one temperatures reached 140°C, explaining why the test temperature was conservatively defined to 150°C for all tests. Further, tests with different strain ranges were performed in order to obtain an S-N curve. To obtain a general S-N curve similar strain ranges were tested for Rε = -1 and Rε = 0,5. In the case of no specimen failure, the tests were ended at 2 million cycles.

23

8. Test results

8.1. Constitutive results In the following Section the obtained constitutive material data for the tests are presented. The test strain ranges considered were 0,4 % to 1,4 %. The strains in the model were slightly higher than this, but with the subsequent optimization in mind, a lower test strain range was chosen to achieve more accurate data supporting calculations during the optimization procedure.

Figure 21. Stress-strain curves at 25°C.

24

Figure 22. Stress-strain curves at 200°C.

Figure 23. Stress-strain curves at 300°C.

25

Figure 24. Stress-strain curves at 450°C.

To illustrate the differences in constitutive behavior depending on temperature Figure 25 displays the stress-strain curve for 1, 2%ε∆ = at four different temperatures. One can notice a distinct difference between room temperature and the three elevated temperatures. The elevated temperatures provides curves that are, almost, identical.

26

Figure 25. Stress-strain curves for Δε=1,2 % at four different temperatures.

During testing, an interesting observation regarding the hardening and softening mechanisms of the material was made. The material hardens or softens depending on temperature and strain range. During tests at room temperature, the test specimen softens throughout the entire strain range. At 200°C the specimen softens initially, until the strain range reaches 1,0 % where it starts to harden. At temperatures 300°C and 450°C the test specimen hardens throughout the entire strain range. This is observed in Figure 26 and Figure 27 where cyclic hardening and softening is illustrated for strain ranges 0,6 % and 1,2 % at different temperatures.

27

Figure 26. Cyclic hardening and softening for different temperatures at strain range 0,6 %.

Figure 27. Cyclic hardening and softening for different temperatures at strain range 1,2 %.

28

8.2. Fatigue test results The following tests were conducted at 150°C: Table 3. Fatigue test results.

Strain Range Rε

Max strain

Min strain

Cycles to failure

0,28% 0,5 0,56% 0,28% >2000000 0,56% 0,5 0,56% 0,28% >2000000 0,34% 0,5 0,69% 0,35% 57000 0,44% 0,5 0,88% 0,44% 46000 0,52% 0,5 1,03% 0,52% 7913 0,60% 0,5 1,19% 0,60% 7269 0,68% 0,5 1,35% 0,68% 5541 0,24% -1 0,12% -0,12% >2000000 0,36% -1,01 0,17% -0,18% >2000000 0,34% -0,99 0,18% -0,17% >2000000 0,48% -1,05 0,23% -0,24% 9591 0,60% -1,03 0,29% -0,30% 6289 0,80% -1 0,40% -0,40% 4379 0,98% -1,06 0,47% -0,50% 3127

The data from Table 3 are visualized in Figure 28. For rationality, the tests with strain ranges in the interval between -0,99 and -1,06 are denoted by R = -1 in Figure 28.

Figure 28. S-N curve at 150°C for SNCrW with approximated lines for LCF and HCF.

As noticed from Figure 28, the R-ratio has little impact on the life time in the low cycle fatigue region. This agrees well with the Morrow equation, Eq. 10. Furthermore, one data point in Figure 28 for R = 0,5 has been excluded for future fatigue analysis since this specimen had been used before. This particular specimen had already been run at a strain

29

range of 0,24 % for 2 million cycles, and was, therefore, not regarded as giving reliable results.

30

9. Numerical simulations

9.1. Finite element analysis During the finite element analysis and simulations of the valve, an axisymmetrical model has been used. This model satisfies the geometry of the valve, except from that the two cooling channels, connecting the center with the cooling hole, are not included. The connecting cooling channels might give further complications in terms of high strains, but was, however, not included as an objective for this Thesis and left to MAN Diesel for future examination. The exhaust valve is subjected to different loading conditions during its life time, which has been the basis for the finite element analysis. In order to match these conditions, three different loading situations have been simulated, depicted in Figure 29. In Step 1 the valve is heated according to temperatures during full running conditions, as discussed in Section 3 of this Thesis. In Step 2, the hot valve is subjected to a pressure of 20 MPa along the valve head surface. Simultaneously, a boundary condition locks the movements of the valve seat in the vertical direction. Finally, in Step 3, the entire valve is cooled down to 25°C and the pressure is released. Prior to analysis of all the steps, the valve temperature was set to 25°C. By analyzing these three steps, the strains induced in each step can be retrieved and analyzed.

Figure 29. The three steps of the analysis.

For the finite element analysis Abaqus [1] requires plastic strain data, as input, described in (Eq. 13), and visualized in Figure 30 for a strain range of 1,0 %.

Valve seat

31

Figure 30. Plastic strain data obtained from constitutive testing.

When running the finite element analysis with the provided material data, Abaqus [1] returns the material parameters for the Chaboche model as seen from Table 4. Table 4. Chaboche model material parameters.

25°C 200°C 300°C 450°C Yield stress (MPa) 233 187 180 175 C (MPa) 185535 116496 118257 118384 Gamma ( - ) 878 631 673 679

For the finite element analysis the linear continuum axisymmetrical elements CAX3 and CAX4, defined by Abaqus [1], were used. CAX3 refers to triangular elements whereas CAX4 to four-sided elements. The size of the element sides were 2,5 mm, apart from the refined areas where the side length was set to 0,8 mm, cf. Figure 31.

32

Figure 31. The mesh with refinements in areas with high strains.

As a consequence of the valve’s elevated temperature, high thermal strains are induced in the material. The thermal strains do not imply fatigue in the material, explaining why these strains have not been a subject for analysis in this Thesis. The strain components that causes fatigue of the valve is the mechanical strain, which consists of one elastic and one plastic part. In Abaqus [1] one can not view the mechanical strain. Instead, the elastic and plastic strains are presented separately. Furthermore, the strain ranges obtained from the finite element analysis are the maximum in-plane principal strains. Since the strain range discrepancy between different steps is the major parameter influencing the fatigue life, it was decided to analyze this difference. The largest strain range observed in the analysis was the strain difference between Step 1 and 3, namely the heated valve without pressure and the cooled valve. These elastic and plastic strain ranges are visualized in Figure 32 and Figure 33.

33

Figure 32. Elastic strain range difference between Steps 1 and 3.

Figure 33. Plastic strain range difference between Steps 1 and 3.

As can be seen in Figure 32 and Figure 33, the maximum principal strain ranges are present tangentially along the center hole and the cooling channel. To better illustrate the mechanical strain ranges along these highly exposed edges, plots can be seen in Figure 35 and Figure 36. The paths along which these strain ranges are depicted in Figure 35 and Figure 36 are shown in Figure 34.

34

Figure 34. Center hole marked red and cooling channel marked green.

Figure 35. Mechanical strain range along the center hole path seen in Figure 34.

Starting node Starting node

CW-direction

35

Figure 36. Mechanical strain range along the cooling channel path seen in Figure 34.

Since nodes can be shared between surrounding elements, there are several different strain values at each node. The maximum strain range values have been calculated by choosing the largest strain value in each node. These reach magnitudes of 0,92 % in the center hole, and 0,57 % in the cooling channel. For these contour plots and the strain range graphs presented above, a strain range average has been calculated at each node and, therefore, slightly lower values are obtained, cf. Figure 35 and Figure 36.

36

9.2. Fatigue analysis With the obtained strain ranges from the finite element analysis, the fatigue life was calculated with aid of the S-N curve. The maximum strain range in the center hole (0,92 %) and cooling channel (0,57 %) are marked in the S-N curve in Figure 37. These strains give a fatigue life of, approximately, 3500 cycles for the center hole and 7200 cycles for the cooling channel.

Figure 37. The S-N curve at 150°C for SNCrW with the maximum strain ranges marked.

37

10. Design optimization After having performed the finite element analysis and received the strains and corresponding life time for the valve, an optimization of the valve geometry was carried out with the aim to reduce the strains and increase the life time of the valve. The optimization studies were performed using the commercial software Hyperworks [2]. In order to run an optimization study a main objective function needs to be defined, as well as variables and constraints. The variables in the optimization study were typically coordinates and radiuses, whereas the constraints were the maximum temperatures along with maximum strain levels induced by the combustion pressure. The main objective throughout all the studies was always to minimize the maximum strain and, thereby, maximizing the life time. After having defined the input data, Hyperworks [2] starts the optimization study by changing the variables iteratively, until an optimum with the respect to the target is achieved. When changing the variables the geometry is affected and, thereby, the mesh is also changed. This is referred to as morphing of elements. By morphing it is simply meant that the mesh is stretched to fit the new variables in the corresponding iterative step. An example of a morphed mesh is shown in Figure 38.

Figure 38. Morphed mesh. The elliptical hole is moved from its original, yellow, position in positive x- and y-directions.

The outer boundary of the valve could not be changed since this would affect the functionality of the valve. Very small geometrical changes of the outer boundary could, theoretically, be tolerable, but in order to limit the amount of variables for the optimization study the outer boundary was regarded as fixed throughout this Thesis. It was decided to limit the design cases to three different optimization studies of the internal geometry, as discussed in detail below.

38

10.1. Optimization Study 1 In optimization Study 1, the focus was set on optimizing the position of the elliptical cooling channel in order to minimize temperature induced strains. The variables for the elliptical cooling channel were the x- and y-coordinates, meaning that a change in position for the elliptical cooling channel was allowed. The shape of the cooling channel was held fix throughout the study. Along with the elliptical cooling channel position study, the position of the lower part of the center hole and its size was optimized in this study as seen in Figure 39. The point marked with the black arrow could move freely in the y-direction. The two points marked with green arrows were coupled, and could move freely in the y-direction. The same conditions were valid for the red arrows in the x-direction. Additionally, the size of the radius could be increased or decreased, marked by yellow arrows in Figure 39.

Figure 39. Variables for the center hole geometry.

The maximum strain obtained from the finite element analysis could be either the strain difference between Steps 2 and 3, i.e. the heated valve with applied pressure and the cooled valve, or between Steps 1 and 3, i.e. the heated valve without pressure and the cooled valve. The objective function was set so that it minimized the largest one of these two strain differences. In addition to the objective function, a few constraints were defined. The strain difference between Steps 2 and 3, which corresponds to the strain induced by the pressure, was set to be below 0,2 %. This limit was chosen so that the strain range was kept below the fatigue limit, in order to withstand an infinite amount of pressure cycles. Since the valve seat has been fixed in the y-direction as a boundary condition, instead of introducing a surface contact in this region, unrealistically high strains were observed. Therefore, the nodes in the vicinity of the valve seat has been excluded in relation to the pressure constraint. Further, a maximum temperature of 475°C along the valve perimeter was set as a second constraint.

39

The result from optimization Study 1, satisfying the constraints, is shown in Figure 40 with the new strains for the optimized geometry displayed in Table 5.

Figure 40. Optimized shape and boundary lines marking the original shape.

Table 5. Strain ranges for optimized and original structure.

Strain range Life time (cycles) optimized original optimized original Elliptical cooling channel 0,43% 0,57% 11000 7200 Center hole - study 1 0,66% 0,92% 5800 3500

One clearly notices the improvement in strain range and cycle life time for the optimized elliptical cooling channel and the new center hole position as compared to the original design.

10.2. Optimization Study 2 In optimization Study 2, the center hole has been heavily modified in an attempt to further reduce the maximum strains in this area. To reduce the high strain concentrations around the tip of the center hole, a geometry with a larger radius was designed and, later, optimized. The already optimized position of the elliptical cooling channel was kept fixed. The variables selected in this study are visualized in Figure 41. The points marked with green arrows were coupled and allowed to move in the y-direction. The red arrow marked point could also move, independently of the green arrows, in the y-direction. Finally, the radius could be increased and decreased which is illustrated by the, yellow arrows in Figure 41.

Maximum strain range locations

40

Figure 41. The variables for the new center hole geometry in Study 2.

The objective function and the constraints are the same as in optimization Study 1. The new optimized shape, satisfying the constraints in Study 2, is shown in Figure 42. The corresponding data are presented inTable 6. Strain ranges and corresponding cycle life time for optimized center hole in Study 2, compared with the original shape. Table 6 together with data referring to the original design.

41

Figure 42. The optimized new center hole geometry, with the boundary lines marking the original shape.

Table 6. Strain ranges and corresponding cycle life time for optimized center hole in Study 2, compared with the original shape.

Strain range Life time (cycles) optimized original optimized original Elliptical cooling channel 0,43% 0,57% 11000 7200 Center hole - study 2 0,47% 0,92% 9600 3500

By looking at the strains and life times in Table 6, the newly designed center hole geometry clearly gives better results than the original center hole design.

10.3. Optimization Study 3 In optimization Study 3 a new, circular shaped, cooling channel replaced the elliptically shaped cooling channel in an attempt to reduce the maximum strains around the cooling channel. The variables for the circular hole were merely the position of its center, x- and y-coordinates, and the radius of the circular cooling channel. The objective function and the constraints were the same as in the two previous studies. The optimized design satisfying the constraints is shown in Figure 43, along with the strain ranges and corresponding cycle life time in Table 7.

Maximum strain range locations

42

Figure 43. The optimized shape in Study 3, with the circular hole instead of the elliptical shaped.

Table 7. Strain ranges and corresponding cycle life time for an optimized circular cooling channel, compared with the elliptical cooling channel.

Strain range Life time (cycles) optimized original optimized original Elliptical cooling channel 0,43% 0,57% 11000 7200 Circular cooling channel 0,62% 6300

From the results presented in Table 7 one can notice the higher strain range and shorter life time for the circular cooling channel as compared with the elliptical one. This explains why the elliptical cooling channel is to favor.

Maximum strain range location

43

11. Analysis of results The valve design presented in optimization Study 2 is the finally proposed design solution emerging from this Thesis. This design solution has the lowest strain ranges and, therefore, also the longest fatigue life, 9600 cycles. Compared to the original design, which had a fatigue life of 3500 cycles, this is a significant improvement. However, the goal with the Thesis was to achieve a valve design that could withstand 10000 cycles. The proposed design, with 9600 cycles, may seem close to this goal, but it should be observed that no safety factor has been taken into account. Including a safety factor, the 9600 cycles will lead to a fatigue life further from the goal. When discussing the use of a safety factor, one must consider if the safety factor shall be applied on the strain range or on the fatigue life, since the choice gives different results. This difference is explained by the logarithmic relationship between the strain range and the fatigue life. The final design proposal, as a result of this Thesis, with the elastic strains, plastic strains and temperature distribution, is shown in Figure 44, Figure 45 and Figure 46.

Figure 44. Elastic strain range between Steps 1 and 3 for the proposed design.

44

Figure 45. Plastic strain range between Steps 1 and 3 for the proposed design. The location of the maximum strain is in the area of the valve seat and is, therefore, ignored.

Figure 46. Temperature distribution in the proposed design.

45

12. Conclusions The proposed valve design solution in this Thesis will, unfortunately, not fulfill the requirements of 10000 cycles. The valve reaches strain levels which leads to a fatigue life of 9600 cycles, excluding the necessary safety factor and is, therefore, not sufficient for the intended application proposed by MAN Diesel. This new, optimized, valve design is, however, a significant improvement when comparing it to the original design, which only could withstand 3500 cycles. The locations of maximum strain ranges discussed in this Thesis are at the perimeters of the elliptical cooling channel, and the centre hole. The strain ranges located on the centre hole account for the highest strain range in the valve. The strain ranges along the elliptical cooling channel could, possibly, be decreased if a new geometry of the cooling channel would be regarded; only the position of the elliptical cooling channel has been optimized in this Thesis. The fatigue life of the valve would, however, not be improved since the limiting factor is the strain range at the center hole. As mentioned, the highest strain ranges are located in the center hole area of the valve. A possible explanation to this is that, since most of the valve material is close to the center hole and this mass has high temperature differences in relation to the mass surrounding the centre hole, the result will be large forces, and, therefore, high strains in this exposed area. The combination of high temperature differences and a large lump mass are influential factors as regards causing high strains.

46

13. Limitations After having completed this Thesis, a few limitations of this study have been noticed and are, therefore, discussed in this Section. A factor that has not been regarded so far is the influence from using water as the cooling fluid. With the presence of water in the channels there is a high risk that water causes corrosion which can reduce the fatigue life. This effect is difficult to predict, and, therefore, it is of interest to perform tests in this area to fully understand what influence water has on the fatigue life. The cooling channel and center hole are connected by a channel which has not been a subject of study in this Master Thesis. As can be seen in Figure 5 there are two connecting cooling channels, required to regulate the in flow and out flow of the cooling fluid. There are a few possible ways of designing these connecting channels, but the risk of high strain concentrations remains, and the choice must therefore be carefully analyzed. The fatigue tests performed in this Thesis have mostly been force controlled but designed to resemble the initial, strain controlled tests. This approach can be questioned, but due to the great difference in testing time, it was not possible to perform completely strain controlled testing. In order to obtain a more reliable S-N curve, more strain ranges should have been tested. For statistical purposes, several tests at the same strain range should have been preferred. More fatigue tests could not be performed, simply due to the fact that the amount of test specimens was limited. Fortunately, the critical strain ranges present in the valve were all in the LCF region, where more fatigue tests were undertaken. The valve was designed in such a manner that the strain range induced by the combustion pressure did not exceed the strain range limit 0,20 %. This limit was an assumption of infinite life, which could have been verified by fatigue tests. The amount of pressure cycles the valve is exposed to during its life time is in the order of 2 billions, and, therefore, fatigue tests in this strain region is advisable.

47

14. Future recommendations As the proposed design solution in this Thesis does not fulfill the requirements of the fatigue life set by MAN Diesel, the focus of future studies should be to reduce the maximum strain range levels. A way to reduce these levels could be to replace the cooling water with air cooling. Air cooling will lead to considerably lower thermal gradients in the structure, which will help to reduce the high strain concentrations. However, the placement of the cooling channel may need to be redesigned to satisfy the condition of maximum 475°C together with several other design complications.

48

References

[1] Abaqus, Version 6.8. [2] Altair Hyperworks, Version 9.0. [3] von Mises, R. (1913). Mechanik der festen körper im plastisch deformablen

zustand. Nachrichten der Gesellschaft der Wissenschaften in Göttingen. Mathematisch-Physiskalische Klasse, Göttingen, pages 582-592.

[4] Melan, E. (1938). Zur plastizitätdes räumlichen kontinuums. Ingenieur-Archiv, IX,

116-126. [5] Hill, R. (1950). The Mathematical Theory of Plasticity. Oxford University Press. [6] Hodge, P. G. J. (1957). Piecewise linear hardening. In 9th International Congress

of Applied Mechanics, volume 8, pages 65-72. University of Brussels, Belgium. [7] Ottosen, N. S. and Ristinmaa, M. (2005). The Mechanics of Constitutive Modeling,

Elsevier. [8] Bauschinger, J. (1886). Über die Veränderung der Elastizitätsgrenze und der

Festigkeit des Eisens und Stahls durch Strecken und Quetschen, durch Erwärmenund Abkühlen und durch oftmal wiederholte Beanspruchung. Mitteilungen 15 aus dem mechanisch – technischen Laboratorium der K. polytechnichen Schule München.

[9] Lemaitre, J., and J.-L. Chaboche (1990), Mechanics of Solid Materials,

Cambridge University Press.

[10] Coffin Jr, L. F and Schenectady, N. Y. (1954). A study of the effects of cyclic thermal stresses on a ductile metal. Transactions of American Society of American Engineers, 76 p. 931-950.

[11] Manson, S.S. (1954). Behavior of materials under conditions of thermal stresses.

National advisory commission on aeronautics: Report 1170. Cleveland: Lewis Flight propulsion laboratory.

[12] Basquin, OH. (1910). The exponential law of endurance tests. Proceedings of the

American Society for Testing and Materials 10, 625-30.

[13] Morrow, J.D. (1968). Fatigue Design Handbook-Advances in Engineering, vol. 4, Sec. 3.2, pp. 21-29. Warrendale, PA: Society of Automotive Engineers.

[14] MMS handbook 6, Pulverteknik utgåva 3 (1995).

[15] MAN Diesel SNCrW material sheet.

[16] Material properties provided by Harro Hoeg at MAN Diesel.

49

Appendices

A Piston steel material data Table 8. Chemical composition of the piston steel [16].

C Si Mn S P Cr Ni Mo Fe min 0,13 0,22 0,58 0,9 0,3 balanced max 0,2 0,27 0,71 0,035 0,035 1,2 0,4 0,5 balanced

Figure 47. Stress strain curves at 25°C for the piston steel.

50

Figure 48. Stress-strain curves at 300°C for the piston steel.

Figure 49. Stress-strain curves at 450°C for the piston steel.

51

Table 9. Chaboche model material parameters.

25°C 300°C 450°C Yield stress (MPa) 356 313 277 C (MPa) 435882 372098 272585 Gamma ( - ) 1320 1346 1103

Table 10. Number of cycles to failure for the piston steel at different strain ranges with Rε=-1.

Strain range Number of cycles 0,60% 10762 0,80% 5100 0,80% 6052 1,20% 613

52

B Abaqus input file ** material SNCrW ** Material Version Date: 2009/04/21 ** ** MATERIALS ** *Material, name=SNCRW ** thermal conductivity->temperature dependent ** [lambda]=W/(m*K), [T]=°C *Conductivity 12.5, 20. 13.8,100. 15.,200. 16.7,300. 18.3,400. 19.6,500. 20.4,600. 22.1,700. 23.3,800. ** density->temperature dependent ** [rho]=kg/m^3, [T]=°C *Density 7900., 20. 7870.,100. 7780.,300. 7700.,500. 7610.,700. ** youngs modulus->temperature dependent ** poissons ratio->constant value ** [E]=Pa, [ny]=[], [T]=°C *Elastic 2.00e+11, 0.3, 20. 1.96e+11, 0.3, 100. 1.87e+11, 0.3, 200. 1.77e+11, 0.3, 300. 1.69e+11, 0.3, 400. 1.62e+11, 0.3, 500. ** thermal expansion coefficient->temperature dependent ** [alpha]=1/K, [T]=°C *Expansion 1.55e-05,100. 1.65e-05,200. 1.75e-05,300. 1.79e-05,400. 1.82e-05,500. 1.86e-05,700. ** yield stress->combined isotropic and kinematic hardening, temperature depende ** [sigma_y]=Pa, [kin_C]=Pa, [kin_g]=[], [T]=°C *PLASTIC, HARDENING=COMBINED, DATA TYPE =PARAMETERS 233000000.,1.85535E+11,878.0 ,25.0 187000000.,1.16496E+11,631.0 ,200.0 180000000.,1.18257E+11,673.0 ,300.0 175000000.,1.18384E+11,679.0 ,450.0 ** ** ** PREDEFINED FIELDS ** ** Name: Field-1 Type: Temperature *Initial Conditions, type=TEMPERATURE

53

ALLNODES, 25. ** ---------------------------------------------------------------- ** ** STEP: Step-1 ** *Step, name=Step-1 *Static 1., 1., 1e-05, 1. ** ** PREDEFINED FIELDS ** ** Name: Field-1 Type: Temperature *Temperature, op=NEW ** Name: Field-2 Type: Temperature *Temperature, op=NEW, file=../../thermal/output/wcvalve_hra4.fil, bstep=1 ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** *Output, field *Element Output, VARIABLE = PRESELECT, POSITION=NODES E, EE, PE, THE, PEEQ ** ** FIELD OUTPUT: F-Output-2 ** *Node Output NT, *Output, history, frequency=0 *End Step ** ---------------------------------------------------------------- ** ** STEP: Step-2 ** *Step, name=Step-2 25 deg all over *Static 1., 1., 1e-05, 1. ** ** BOUNDARY CONDITIONS ** ** Name: BC-1 Type: Displacement/Rotation *Boundary AB_BC_N, 2, 2 ** ** LOADS ** ** Name: Load-1 Type: Pressure *Dsload AB_PRESSURE_S, P, 2e+07 ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1, F-Output-2 ** *Output, field *Node Output

54

NT, *Element Output, VARIABLE = PRESELECT, POSITION=NODES E, EE, PE, THE, PEEQ *Output, history, frequency=0 *End Step ** ---------------------------------------------------------------- ** ** STEP: Step-3 ** *Step, name=Step-3 cold no pressure *Static 1., 1., 1e-05, 1. ** ** BOUNDARY CONDITIONS ** ** Name: BC-1 Type: Displacement/Rotation *Boundary, op=NEW ** ** LOADS ** ** Name: Load-1 Type: Pressure *Dsload, op=NEW ** ** PREDEFINED FIELDS ** ** Name: Field-2 Type: Temperature *Temperature, op=NEW ** Name: Predefined Field-3 Type: Temperature *Temperature, op=NEW ALLNODES, 25. ** ** OUTPUT REQUESTS ** *Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1, F-Output-2 ** *Output, field *Node Output NT, *Element Output, VARIABLE = PRESELECT, POSITION=NODES E, EE, PE, THE, PEEQ *Output, history, frequency=0 *End Step