a pre-study of the tearing behaviour of the flexible

Master's Degree Thesis ISRN: BTH-AMT-EX--2006/D-08--SE

Supervisor: Sharon Kao-Walter, Ph.D. Mech. Eng.

Department of Mechanical Engineering Blekinge Institute of Technology

Karlskrona, Sweden

2006

Mohammed Jalaluddin Hyder Hameeduddin Ahmed

A Pre-Study of the Tearing Behaviour of the Flexible

Materials -Towards Efficiency Packaging

A Pre-Study of the Tearing Behaviour of the Flexible

Materials-towards Efficiency Packaging

Mohammed Jalaluddin Hyder Hameeduddin Ahmed

Department of Mechanical Engineering

Blekinge Institute of Technology

Karlskrona, Sweden

2006

Thesis submitted for completion of Master of Science in Mechanical Engineering with emphasis on Structural Mechanics at the Department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden.

Abstract: In this thesis the tearing behaviour of flexible material is studied. Afinite element model was built in ABAQUS and simulations wereperformed. The experimental tests were carried out to monitor the Loadvs. Extension curve on single-tear specimen of Low DensityPolyethylene (LDPE) and Paperboard. The simulation results werecompared with the experimental results and observed to have goodagreement between them

Keywords: Tearing, Cohesive Zone, ABAQUS, Tensile Test, Finite Element,Essential Work of Fracture (EWF) theory, Mechanical properties,Experimental method, MTS.

2

Acknowledgements

This work was carried out at the department of Mechanical Engineering, Blekinge Institute of Technology, Karlskrona, Sweden, under the supervision of Dr. Sharon Kao-Walter. The thesis was initiated in December 2005.

We want to thank Dr. Sharon Kao-Walter for providing us with this opportunity to work in the field of Fracture Mechanics, guidance encouragement and professional involvement.

We like to thank M.Sc. Etienne Mfoumou for his inspiring guidance and encouragement. His perpetual help and timely suggestions are highly appreciated. And to our Mechanical department for their guidance which enabled us to earn our MSc.

We thank to each and everyone who have directly or indirectly supported our work and helped us with their valuable suggestions.

At last we thank and dedicate this work to our loving family for their unflinching support whenever wherever we needed.

Karlskrona, April 2006

Mohammed Jalaluddin Hyder

Hameeduddin Ahmed

3

Contents

1 Notation 6

2 Introduction, Aim and Overview 9 2.1 Previous Work 10

3 Theory 11 3.1 Flexible Material 11 3.2 Fracture Mechanics 11 3.3 Crack 12

3.3.1 Flat Crack 13 3.3.2 Slant Crack 13

3.4 MODES 14 3.5 Crack Propagation 16 3.6 Essential Work of Fracture (EWF) Theory 17 3.7 Basic Material Properties 19

3.7.1 Isotropic Materials 19 3.7.2 Anisotropic Material 20 3.7.3 Orthotropic Material 21

4 Experimental Work 24 4.1 Specimen Preparation 24 4.2 Tensile Test 25 4.3 Experimentation 26 4.4 Experimental Results 27

4.4.1 Paperboard 27 4.4.2 LDPE 29

5 Simulation 30 5.1 Finite Element Method 30 5.2 Assumptions 31 5.3 Preprocessing 31

5.3.1 Part Geometry 32 5.3.2 Material Modelling 32 5.3.3 Enmeshment and Element type 33 5.3.4 Boundary Conditions 33

5.4 Post processing 34 5.4.1 Paperboard 34 5.4.2 LDPE 36

4

5.5 Comparison of Results 38 5.5.1 Paperboard 38 5.5.2 LDPE 39

6 Conclusion and Further Work 40

7 Reference 41

5

Appendices

A Experimental Work 43 B Simulation Work 50 C Appendix 52 D ABAQUS/CAE Input Files 54

6

1 Notation

A Area

C Stiffness matrix

E Young Modulus

F Force

G Shear Modulus

K Stress Intensity

IK Stress Intensity Factor

IcK Fracture Toughness

l Ligament length

P Tearing Force

r Radius

S Compliance Matrix

t Thickness of Material

FW Total work of Fracture

PW Non-essential work in Plastic zone

EW Work in Process zone

ew Specific Essential Work of Fracture

pw Specific Non-essential work

fw Specific total Fracture work

Tew Out-of-plane Tearing Toughness

X X-Direction

Y Y-Direction

Z Z-Direction

7

v Poison Ratio β Shape Factor Outer Plastic Zone σ Stress ε Strain

8

Abbreviations

ASTM American Society for testing and Material

COD Crack Opening Displacement

DENT Double Edge Notch Tension

EPFM Elastic Plastic Fracture Mechanics

EWF Essential Work of Fracture

FEM Finite Element Method

FM Fracture Mechanics

LDPE Low Density Polyethylene

LEFM Linear Elastic Fracture Mechanics

MTS Mechanical Testing and Simulation

OPZ Outer Plastic Zone

SI Standard International

9

2 Introduction, Aim and Overview

Today in the world of globalization, products are exported from one place to the other giving importance to packaging material. A weaker material leads to breakage during transportation. Therefore the strength of material is of great importance. In packaging flexible materials are used to facilitate tear opening like perforates are provided in case of paper (tissue paper, note book etc.,), stamps, Liquid food packaging (milk, curd, fruit juice etc.,) chocolates, microwaveable food and so on. The package is opened when sufficient force is applied and fracture initiates giving stress concentration around tear opening.

In this thesis we are dealing with tearing behaviour of Flexible materials. When a load is applied and crack propagates from plane mode (Mode I) to out of plane mode (Mode III) trends to Tearing, linear elastic analysis of sharp crack predicts infinite stress around the tip. In real materials stresses at the crack tip will be finite as the radius of the crack tip must be finite. Due to the large plastic area around the crack tip of ductile polymers, linear elastic fracture mechanics (LEFM) fails to provide proper fracture toughness. This problem is considerably solved by using non-linear fracture mechanics method. In this, J-Integral and Essential Work of Fracture (EWF) theory are widely used. Recent studies have indicated that EWF procedure is a very useful method to study the fracture properties of the flexible materials. The concept of EWF was developed initially by Cotterell and Reddel on the bases of ideas proposed by Broberg, who suggested that the total work of fracture ( fW ) dissipated in a pre-crack specimen could be represented as a sum of work consumed into two distinct zones.

A model has been created in ABAQUS/CAE giving adequate properties. Load vs. Displacement graph is plotted in post-processing and compared with the experimental Load vs. Displacement graph.

The purpose of this thesis is to:

Investigating the tearing behaviour of flexible material.

Performing the tearing test on MTS machine.

10

Verifying the tearing behaviour of flexible material by simulating a FE model in ABAQUS.

For solids of complicated geometry, finite elements method (boundary element method) is the appropriate way to calculate stress intensity factor.

Figure 2.1 represents an overview of work during thesis. At first the model with a crack has been made then the numerical simulations are performed in ABAQUS (i.e. an FE Program). The experimental works were performed on the specimens and then the results from numerical Simulation and Experimental measurements are compared.

Figure 2.1. Schematic presentation of thesis work.

2.1 Previous Work

Works have been performed on mechanical and fracture properties of an aluminium foil and polymer laminate that are widely used as packing material. The mechanical and fracture properties of the laminate are studied. A theory of composite material is used to evaluate series of experiments [5]. The plane stress fracture toughness is calculated based on centre crack panel. Different crack sizes have been tested [6].

Modelling

Numerical Simulation in FE

Experimental Measurement

Comparison between Simulated and Experimental

Results

3 Theory

3.1 Flexible Material

Flexible material comprehend of engineering materials according to their tensile strength and stiffness of load bearing fibres in matrix materials with the capabilities of large strain deformation and low bending stiffness. They are mostly characterized by high tearing strength. Nowadays flexible materials are lighter, thinner, stronger, and less expensive than their predecessors with the development of Fracture Mechanics and Lamination Technology. Some of the flexible materials are conveyor belts, tires, coated fabrics, polyesters, etc [8].

3.2 Fracture Mechanics

The application of fracture mechanics was essential in this study. FM is all about figuring out how cracks occur, do they grow further or just hang out and where they are going to popup next. FM will say residual strength as a function of crack size, what is the maximum permissible crack size, how long will it take for a crack to grow from a certain initial size, what is the service life of a structure when a crack-like flaw (e.g. a manufacturing defect) with a certain size is assumed to exist, during the period available for crack detection how often should the structure be inspected for cracks. In simple FM is the study of how crack starts, grow and how to stop, FM approach emphasizes three important variables, namely Applied Stress, Flaw Size, and Fracture Toughness [1, 2, 4].

Figure 3.1. Fracture mechanics approach [4].

FLAW SIZE FRACTURE TOUGHNESS

APPLIED STRESS

12

Stress-strain curve can be obtained from tensile measurement expressing stress is force per unit area.

AF

=σ (3.1)

The deformation of a body due to applied forces is strain’ε ’. It can be expressed as the change in length by the original length.

o

oi

lll −

=ε (3.2)

Figure3.2. Stress-Strain curve [9].

According to Hook’s law the relation between stress and strain.

εσ

=E (3.3)

3.3 Crack

From investigating fallen structures, engineers found that most of the failures began with cracks.

These cracks may be caused by material defects (dislocation, impurities, etc), discontinuities in assembly and/or design (sharp corners, grooves, nicks, voids, etc), harsh environments (thermal stress, corrosion, etc), and damages in service (impact, fatigue, unexpected loads, etc). Most

13

microscopic cracks are arrested inside the material but it takes one run-away crack to destroy the whole structure [4, 8, 9].

Mainly cracks are of two types’ Flat crack and Slant crack.

3.3.1 Flat Crack

Figure 3.3 shows a flat crack with X-axis lies in the crack surface plane and is perpendicular to the crack front, the Y-axis is normal to the crack surface plane, and the Z-axis is along the crack front, forming a right hand system with the X and Y axis. These also serve as the coordinate system for crack front local coordinate system [10].

Figure3.3. Flat crack where X, Y, Z serves both as the global and the

crack-front local coordinate system [10].

3.3.2 Slant Crack

Figure 3.4 shows a slant crack with surface plane at an angle (the slant angleα ) with that of flat crack. Where x coincides with X, y is perpendicular to the slant crack surface, and z is along the straight crack front direction [10].

14

Figure3.4. Slant crack, where X, Y, Z serve as the global coordinate system

and x, y, z as the crack- front local coordinate system [10].

3.4 MODES

The forces which lead to the cracking are simplified into three different modes.

• Mode I: The forces are perpendicular to the crack i.e., if the crack is horizontal then acting force is vertical, pulling the crack open. This is referred to as the opening mode.

Figure3.5. Mode I (Tension, Opening) [9].

15

• Mode II: The forces are parallel to the crack. One force is pushing the top half of the crack back and the other is pulling the bottom half of the crack forward, both along the same line. This creates a shear crack, the crack slides along itself. It is also called in-plane shear because the forces are not causing the material to move out of its original plane.

Figure3.6. Mode II (In-Plane Shear, Sliding) [9].

• Mode III: The forces are perpendicular to the crack i.e., the crack is in front-back direction, the forces are pulling left and right. This causes the material to separate and slide along itself, moving out of its original plane (so it is called out-of-plane shear). The forces could also be pushing left and right and the same effect would occur. But the forces have to be moving in opposite directions in order to grow the crack.

Figure3.7. Mode III (Out-Of-Plane Shear, Tearing) [9].

When a crack occur in mode I (pure opening mode) and propagates to mode III (out of plane shear) it is called tearing. In many cases like tissue paper, stamps, liquid food packing, microwaveable food chocolates, etc.

16

Strength of packing material is of great importance to avoid any break down during handling. At the same time opening should also keep under consideration, so in some cases perforates are provided to facilitate opening. When a sufficient displacement is applied at the opening concentrates the stress around the tear opening and fracture initiates leads to package opening. [2, 4].

Figure3.8. Tearing [8].

3.5 Crack Propagation

How a crack grows is called “crack propagation” and this take into account when a crack can start to grow and what direction it grows in. There are two ways how it grows, Stress Intensity Factor and Energy.

First from Stress Intensity ( iK ) point of view, the material resists cracking with everything it has or the strength to which a material can stand without

17

cracking is called its fracture toughness ( icK ). I.e. crack can grow when its stress intensity factor reaches the fracture toughness of the material.

icK = iK (3.4)

where i = I,II,III.

From energy point of view, when a crack is formed, new surfaces are also formed, along the edges where the material has split apart. The material has to have enough energy to create these new surfaces or it will not crack. If G is the energy necessary for the crack to grow and R is the material’s resistance to crack growth, the condition for a crack to grow is:

G =R (3.5)

For the crack to be growing continually each time, the change in energy should be equal to change in resistance. If the change in energy is less than the change in resistance, then the crack will not grow any more unless more force is applied. If the change in energy is greater than the change in resistance, there will be unstable crack growth. In this case the crack will grow until the structure fails [2].

3.6 Essential Work of Fracture (EWF) Theory

The concept of EWF theory is the total work of fracture FW dissipated in a pre-cracked specimen could be represented as the sum of two distinct zones. As shown in figure 3.9. The double edge notched tension (DENT) specimen that is pre-cracked along the horizontal to leave a ligament region ‘l’ that undergoes the actual deformation in tension under a load ‘F’ along the vertical. The zones are outer plastic zone and process zone. The work dissipated in the process zone, EW and the work required yielding the material in plastic zone, PW it depends on the geometry of the specimen tested. The total work of fracture FW is sum of these two zones [7, 15, 16].

PEF WWW += (3.6)

18

Figure3.9. Process zone, Ligament, Plastic zone and Pre-crack [7].

In mode I fracture the height of the outer plastic zone is proportional to the torn ligament length l therefore.

tlwtlwW peF ∗∗∗+∗∗= 2β (3.7)

lwwtl

Wpe

F ∗∗+=∗

β (3.8)

tlWw F

f ∗= (3.9)

19

Figure3.10. Linear relationship between the specific total fracture work

( fw ) and torn length (l) [7].

Here fw is the specific total fracture work, ew is the specific essential work of fracture (per unit area) and pw is the specific non-essential work of fracture (per unit volume). β is the shape factor for outer plastic zone (OPZ), and t is specimen thickness [7].

3.7 Basic Material Properties

3.7.1 Isotropic Materials According to [13,14,17,19], a material which has the same mechanical properties in all directions is termed as isotropic material. Numerous materials used in daily life are isotropic in nature, where by definition the material properties are independent of directions. Such materials have only two independent variables (i.e. elastic constants), in their stiffness and compliance matrices, as opposed to the 21 elastic constants in the general anisotropic materials.

The two elastic constants are usually expressed as the Young’s modulus E and the Poisson’s Ratio v . However, the alternative elastic constants K (bulk modulus) and/or G (shear modulus) can also be used. For isotropic materials, G and K can be found from E and v by a set of equations, and vice-versa.

20

Figure3.11. Isotropic Material [14].

Hooke’s law for isotropic materials in compliance matrix form is given by,

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

++

+−−

−−−−

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

xy

zx

yz

zz

yy

xx

xy

zx

yz

zz

yy

xx

vv

vvv

vvvv

E

σσ

σσ

σσ

εε

εε

εε

100000010000001000000100010001

1

The stiffness matrix is equal to the inverse of the compliance matrix, and is given by:

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−

−−

−−

−+=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

xy

zx

yz

zz

yy

xx

xy

zx

yz

zz

yy

xx

vv

vvvv

vvvvvv

vvE

εε

εε

εε

σσ

σσ

σσ

210000002100000021000000100010001

)21)(1(

3.7.2 Anisotropic Material A material which has different physical properties in different directions is termed as anisotropic material. There are no planes of material symmetry.

21

Figure3.12. Anisotropic Material [14].

σε ×= S (3.10)

or,

εσ ×= C (3.11)

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

xy

zx

yz

zz

yy

xx

xy

zx

yz

zz

yy

xx

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

εε

εε

εε

σσ

σσ

σσ

666564636261

565554535251

464544434241

363534333231

262524232221

161514131211

where C is the stiffness matrix, S is the Compliance matrix and S = 1−C .

3.7.3 Orthotropic Material A material having mechanical properties that are different in three mutually perpendicular directions at a point in a body of it and that have three mutually perpendicular planes of material symmetry is termed as Orthotropic Material.

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

xy

zx

yz

zz

yy

xx

xy

zx

yz

zz

yy

xx

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

σσ

σσ

σσ

εε

εε

εε

666564636261

565554535251

464544434241

363534333231

262524232221

161514131211

22

By convention, the 9 elastic constants in orthotropic constitutive equations are comprised of 3 Young’s modulii ,,, zyx EEE the 3 Poisson’s ratios

xyzxyz vvv ,, and the 3 shear modulii xyzxyz GGG ,, .

The compliance matrix takes the form,

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−

−−

−−

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

xy

zx

yz

zz

yy

xx

xy

zx

yz

zy

yz

x

xz

z

zy

yx

xy

z

zx

y

yx

x

xy

zx

yz

zz

yy

xx

G

G

G

EEv

Ev

Ev

EEv

Ev

Ev

E

σσ

σσ

σσ

εε

εε

εε

2100000

02

10000

002

1000

0001

0001

0001

where,

y

yx

x

xy

x

xz

z

zx

z

zy

y

yz

Ev

Ev

Ev

Ev

Ev

Ev

=== ,,

The stiffness matrix for the orthotropic materials, found from the inverse of the compliance matrix and it is given by,

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

Δ

−

Δ

+

Δ

+Δ

+

Δ−

Δ

+Δ

+

Δ

+

Δ

−

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

xy

zx

yz

zz

yy

xx

xy

zx

yz

yx

yxxy

yx

yxxzyz

yx

yzxyxz

xz

xyzxzy

xz

xzzx

xz

zyxzxy

zy

zyyxzx

zy

yzzxyx

zy

zyyz

xy

zx

yz

zz

yy

xx

GG

GEE

vvEE

vvvEE

vvvEE

vvvEE

vvEE

vvvEE

vvvEE

vvvEE

vv

εε

εε

εε

σσ

σσ

σσ

200000020000002000

0001

0001

0001

23

where,

zyx

zxyzxyxzzxzyyzyxxy

EEEvvvvvvvvv 21 −−−−

=Δ

The fact that the stiffness matrix is symmetric requires that the following statements hold,

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪

⎬

⎫

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

Δ

+=

Δ

+Δ

+=

Δ

+Δ

+=

Δ

+

yx

yzxyxz

zy

zyyxzx

yx

yzxzzy

xz

xyzxzy

xz

zxxzxy

zy

yzzxyx

EEvvv

EEvvv

EEvvv

EEvvv

EEvvv

EEvvv

24

4 Experimental Work

4.1 Specimen Preparation

In this experiment we are dealing with LDPE and Paperboard materials of geometry 50*25 mm. The materials were first placed in lab for 24 hours before the test (i.e. at co24 temperature and of relative humidity of 20%) to avoid any effect of change temperature and humidity during experiment. Then the materials were measured and marked. The specimens were made with exact width but more in height with approximately 50 mm more than specified height for better grip as the height of gripper/clamp is approximately 20 mm each. Then, crack has been developed at the centre of the specimen i.e. at 12.5 mm in width, of length 25 mm from one end. Before the crack development, the specimen was little piled to facilitate pilling after crack developed. During the crack development, the specimen is placed on smooth surface. In this case fibre plate has been used so as to have smooth surface. While producing a crack, the blade was inclined, not perpendicular to the specimen to get a smooth and flat crack as shown in figure (3.3). The blade should be inclined properly in crack direction or we may get slant crack as shown in figure (3.4). And if the blade is perpendicular then the crack edges may not be sharp. As decided to test 5 specimens, 10 specimens were made as there may be some damage during pilling of LDPE and mounting of specimen in gripper/clamp at crack initiation point.

Figure4.1. Part geometry of the specimen.

25

Precautions:

1. There should be no moment of specimen during crack development.

2. Pilling should be slow to avoid deformation.

3. During pilling, less force should be applied to avoid elongation.

4. When producing a crack, the cut should be straight and proper to get a good crack edge.

4.2 Tensile Test

At BTH, the tensile test was performed on MTS QTest100. The experimental results were recorded using the software MTSWorks4. The testing machine has a traversing cross-head. It is mounted with the load cell and the grippers as shown in the figure 4.2 below. In this experiment, a load cell of 100 N has been used. Various types of grippers like rectangle, Pneumatic etc. can be used according to requirement. In this case, Pneumatic grippers were used through out the experiment. The grippers were equipped with centre marking to facilitate the correct position when the specimen is mounted vertically. The lower grip was fixed while the upper grip was free to move in the horizontal plane. The specimen is mounted in such a way that, first the upper grip and then the lower grip were closed simultaneously to facilitate mounting. By doing so, the specimen is mounted perfectly and deformation at crack initiation point can be avoided and better results are achieved. The set-up was operated using ‘Play button’ in the software interface. Load vs. Displacement curves were plotted for analysis.

26

Figure4.2. MTS Tensile test machine.

4.3 Experimentation

The experimentation was performed on Paperboard and LDPE with a load capacity of 100 N. A total of ten satisfactory specimens five each of paperboard and LDPE were tested.

The experiment was started with the following steps: 1. MTS machine was initiated and the software activated on the

computer.

2. A test method was chosen, constant rate of Grip Separation Method (ASTM 882).

3. SI units were used.

4. The inputs were set in Method> Edit> Method> Configuration- items> Inputs. The given Inputs were the specimen’s thickness, width and test speed according to the material used in the experiment.

5. The cross-head was traversed to obtain the required grip separation of 40 mm.

27

6. The distance between gripers/clamps has been set to 40mm instead of 50mm. If same distance is considered, the specimen gets over stretched and the crack initiation point gets affected resulting in an improper result.

7. The test speed was set to 1mm/min.

8. Care should be taken while mounting the specimen such that neither preload developed nor would it slack too much, as both of these can affect the result.

9. The test can be started using the ‘Play’ button either from handset or interface of the computer.

10. After the tensile test was completed, there appears a prompt in the software informing the cross- head’s return to its original position, demounting the specimen was followed by acceptance of the prompt.

11. The tests were performed under the room temperature co24 and a relative humidity of 20 %.

12. Results were obtained from the review window were exported in the form of text files for further analysis.

4.4 Experimental Results

4.4.1 Paperboard

Stress vs. Displacement graph is plotted (figure 4.3) for a Paperboard 2-leg trousers of length 25 mm.

28

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 5 10 15 20Displacement [mm]

Stre

ss [M

Pa]

Figure4.3. Stress vs. Displacement for paperboard.

Load Vs Displacement graph for Paperboard is plotted (figure 4.4) for 2-leg trousers of length 25 mm.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16

Displacement [mm]

Lo

ad

[N]

Figure4.4. Load vs. Displacement for paperboard.

29

4.4.2 LDPE

Stress vs. Displacement graph for LDPE is plotted (figure 4.5) for 2-leg trousers of length 25 mm.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 5 10 15 20 25Displacement [mm]

Stre

ss [M

Pa]

Figure 4.5. Stress vs. Displacement for LDPE.

Load vs. Displacement curves for LDPE is plotted (figure 4.6) for 2-leg trousers of length 25 mm in figure given below.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Load

[N]

Figure4.6. Load vs. Displacement for LDPE.

30

5 Simulation

The simulation work has been done in ABAQUS which is a simulation program, based on the finite element method. ABAQUS allows models to be created quickly and easily by producing or importing the geometry of the structure to be analyzed. The results obtained by simulations were compared with the experimental results.

5.1 Finite Element Method

Finite element analysis (FEA) is a numerical technique for calculating the strength and behaviour of engineering structures. In the finite element method, the actual continuum of body of matter is represented as an assemblage of sub-divisions called finite elements. More the number of elements result will be more precise, the process is know as meshing and meshing will be denser at the complicated parts or at the point of interest. These elements are consider to be inter connected at specified points know as nodes or nodal points. The nodes usually lay on the element boundaries where an adjacent element is considered to be connected [17, 18].

The solutions of a general continuum by the finite element method follow the following steps.

• Discretization of structure.

• Selection of proper interpolation model.

• Derivation of element stiffness matrices (characteristic matrices) and load vectors.

• Assemblage of elements equations to obtain the equilibrium equations.

• Solution of system equation to find nodal values of displacement.

• Computation of element strains and stresses.

31

5.2 Assumptions

The following assumptions were made while creating a model.

1) Poisson ratio was assumed to be 0.3.

2) Materials were assumed to be isotropic and linear elastic.

3) Materials were assumed to be homogenous.

5.3 Preprocessing

In this stage the model of the physical problem was defined and an ABAQUS input file was created.

Following tasks were performed to create a model in ABAQUS/CAE.

• Part A three-dimensional, deformable body and a shell extrusion element base feature part were selected. An Approximate size of 200 mm for the sketcher sheet was given. We should choose this value to be on the order of the largest dimensions of our finished part. Then we give the required dimensions to create our part. We divided our model into two parts.

• Property In this module, we define a material and its properties. In our model, we have given Young modulus, Poisson ratio and thickness as input data. A shell homogenous section has been created.

• Assembly A part created exist its own coordinate system, independent of other parts in the model. In Assembly module, we create instances of our parts and to position the instances relatives to each other in a global coordinate system, thus creating as assembly.

As there were two parts to assemble, first we join the two parts using “parallel edge by edge” function then we use Tie function so that the model is joined properly by selecting one surface as master surface and the other as slave surface in the Interaction module.

32

• Step In this module, we create, configure analysis procedure and output requests. Depending upon the required output procedure is defined in this case we are dealing with load, displacement, and stress so we define as Static. And we have selected an increment of 500 with a time period of 1 sec.

• Load In this module we give the required loads and boundary conditions in this case one end is Fixed and at other end we applied Displacement.

• Mesh In this module, we generate a finite element mesh. In our case four node S4R quadrilateral elements were used.

• Job In this module we analyze our model. After completing all the tasks in defining a model, here we submit a job for analysis and monitor its progress.

• Visualization The Visualization module provides graphical display of finite element models and results. The reaction forces and the corresponding Displacement was our interest.

5.3.1 Part Geometry

A 2-leg trousers model featuring of length 50mm, width 25mm and thickness 12.5 mm. The trousers are filleted by a radius of 4 mm as shown in the figure 4.1.

5.3.2 Material Modelling

Table5.1. Mechanical Properties for Simulation.

Material Young Modulus

[MPa]

Poisson Ratio Thickness

[mm]

Paperboard 2755 0.3 0.10438

LDPE 135 0.3 0.02730

33

In the property module, the model has the parameters tabulated is table 5.1 with the material mentioned. The parameters were taken from [13]. The chosen units were consistent and in SI (mm) form.

5.3.3 Enmeshment and Element Type

Element type S4R is assigned to the model in the mesh module. The first letter of this element’s name indicates to shell element and the first number indicates to four-node element. The number of elements for this model is 780.

5.3.4 Boundary Conditions

To define the boundary condition one end was fixed (i.e. left) and it was assigned with zero degrees of freedom by means of encastre option in the boundary command for all steps. And a Displacement/Rotation of 40 mm is applied on the other end (i.e. right) in U1 direction as shown in the figure 5.1.

Figure5.1. Boundary conditions.

34

5.4 Post processing

The result of numerical simulations can be seen in the Visualization Module.

5.4.1 Paperboard

Stress vs. Displacement graph for paperboard is plotted (Figure 5.2) for 2-leg trousers of length 25 mm. In this graph we have notice a smooth line with a constant slope. This is because the Young Modulus is constant and the material is assumed to be elastic.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14


Stre

ss [M

Pa]

Figure5.2. Stress vs. Displacement curve for paperboard.

Load vs. Displacement graph for paperboard is plotted (Figure 5.3) for 2-leg trousers of length 25 mm. In this graph we have notice a smooth line with a constant slope. This is because the Young Modulus is constant and the material is assumed to be elastic.

35

0

0.2

0.4

0.6

0.8

1

1.2


Load

[N]

Figure5.3. Load vs. Displacement curve for paperboard.

Figure 5.4 showing the Stress concentration at the crack initiation point for a 2 leg trouser of length 25mm. It is clear from the stress distribution figure that stresses are max at the crack initiation point. Concentration of the stress depends upon the nature of material. If the material is brittle in nature then the stress concentration will be more

Figure 5.4. Stress concentration at the crack initiation point for

paperboard.

36

5.4.2 LDPE

Stress vs. Displacement graph for LDPE is plotted (figure 5.5) for a 2 leg trouser of length 25 mm. In this graph we have notice a smooth line with a constant slope. This is because the Young Modulus is constant and the material is assumed to be elastic.

0

0.005

0.01

0.015

0.02

0.025


Stre

ss [M

Pa]

Figure5.5.Stress vs. Displacement for LDPE.

Load vs. Displacement graph for LDPE is plotted (figure 5.6) for a 2 leg trouser of length 25 mm. In this graph we have notice a smooth line with a constant slope. This is because we have assumed a constant Young Modulus and the material is elastic.

37

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Load

[N]

Figure5.6. Load vs. Displacement for LDPE.

Graph showing the stress concentration at the crack initiation point for a 2 legs trouser of length 25 mm. It is clear from the stress distribution figure that stresses are max at the crack initiation point. Concentration of the stress depends upon the nature of material. If the material is brittle in nature then the stress concentration will be more where as less for ductile.

Figure5.7. Stress concentration at crack initiation point for LDPE.

38

5.5 Comparison of Results

5.5.1 Paperboard

Figure 5.8 represents the comparison of Load vs Displacement between Experimental and Simulated results. As decided, the experimental test was performed on five satisfactory specimens and the result nearer to the simulated result has been selected. The experimental Load vs. Displacement results of remaining specimens can be seen in Appendix A.

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20Displacement [mm]

Load

[N]

Exp Paper

Sim PAPER

Crack initiation point

Figure 5.8. Load vs. Displacement curve for paperboard.

The crack initiation point was at 6.05 mm as shown in figure 5.8. The slope of curves for the experimental and simulated curve is calculated from initial point to crack initiation point and found to be 0.0848 and 0.0469 respectively. The Young modulus chosen for simulation of paperboard is in Cross Direction. This could be the reason that the slope value of simulation is less than the experimental value. In real, orthotropic material (paperboard) is stiffer in Machine direction than in Cross Direction as the Young modulus is higher in Machine Direction. Therefore for further work, Young modulus can be chosen in Machine Direction for orthotropic material to get good agreement.

It has been noticed that the slope in simulation curve is constant through out. This could be due to the reason that the Young modulus is constant.

39

5.5.2 LDPE

Figure 5.9 represents the comparison of Load vs Displacement between Experimental and Simulated results. As decided, the experimental test was performed on five satisfactory specimens and the result nearer to the simulated result has been selected. The experimental Load vs. Displacement results of remaining specimens can be seen in Appendix A.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Load

[N]

Exp LDPESim LDPE

Crack Initiation point

Figure 5.9 Load vs. Displacement for LDPE.

The crack initiation point was at 9.03 mm as shown in figure 5.9. The slope of curves for the experimental and simulated curve is calculated from initial point to the crack initiation point and found to be 0.0319 and 0.0301 respectively.

A good agreement between experimental and simulated has been notice with some variation between them, this could be the reason that young modulus is not constant thought out the experiment where as in simulation we have taken Young modulus values to be constant. It seems that the plastic region does not affect much on the tearing.

40

6 Conclusion and Further Work

The main objectives of this thesis were to investigate the tearing behaviour and verifying it by simulating a FE model in ABAQUS. The experimental tests were performed on single-tear specimen of LDPE and Paperboard, to monitor load vs. extension curve. The results obtained were compared with simulated results and found good agreement between them.

A non-monotonic load variation was observed in experimental results. This is due to the vibration of the machine. It is observed that there is some difference in the experimental and simulated results of paper. This could be due to paper is orthotropic in nature and in the simulation it is assumed to be isotropic.

Incase of LDPE, it seems that the plastic region does not affect much on the tearing and it needs more studies in the future.

Some suggestions of work within this field that can be done in the future:

• Perform the experiment on laminated material.

• The results can be more improved by increasing the number of elements around the crack initiation point and using fracture mechanics theory.

• Create FE model considering crack propagation.

• Process zone can be investigated deeply and microscopically.

• Using other kind of materials in the simulations instead of elastic material to describe the properties of specimen closer to the reality.

• Paper could be defined as an orthotropic material for having a more precise result.

41

7 Reference

1. M. Janssen, J. Zuidema, R.J.H. Wanhill (1991), Fracture Mechanics, New York, ISBN: 0-415-34622-3.

2. Introduction about Cracking. Dec. (2005), http://simscience.org/cracks/advanced/cracks1.html

3. Tore Dahlberg, Anders Ekberg, (2002), Failure Fracture Fatigue An Introduction, Sweden, ISBN: 91-44-02096-1.

4. T.L. Anderson, (2005), Fracture Mechanics Fundamental and Applications, Third Edition, U.S.A., ISBN: 0-8493-1656-1.

5. Sharon Kao-Walter, Per Stahle, (2004), Fracture Toughness of a Laminated Composite, Fracture of polymers, Composites and Adhesives II Elsevier Science, Elsevier Publications, BTH, Sweden, ISBN: 91-7295-048-X.

6. Etienne Mfoumou, Sharon Kao-Walter, (2003), Fracture Toughness Testing of Non-standard specimen. Research Report NO 2004:05, BTH, Sweden.

7. Janet S.S. Wong, Didac Ferrer-Balas, Robert K.Y.Li, Yiu-Wing Mai, Maria Lluisa Maspoch, Hung-Jue Sue (2003), On tearing of ductile polymer films using the essential work of fracture method, Acta Materialia 51(2003)4129-4938, Australia.

8. Torbjörn Dartman (2002), Flexible Composites – strength, Deformation and Fracture Processes in Woven and D.O.S. Reinforcement Materials.

9. Fracture Mechanics, Dec. (2005), http://efunda.com/formulae/solid_mechanics/fracture_mechanics/fm_intro.cfm.

10. Elmoiz Mahgoub, Xiaomin Deng, Michael A. (2003), Sutton. Three dimensional stress and deformation fields around flat and slant crack under remote mode I loading conditions. Engineering Fracture Mechanics 70(2003)2527-2542, University of South Carolina, U.S.A.

11. Jefferson K. Kim. Virginia Tech Materials Science and Engineering. Dec. (2005),

42

http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/anal/kim/intensity.html

12. Eliahu Zahavi, Vladimir Torbilo (1996) Fatigue Design Life Expectancy of Machine Parts. U.S.A. ISBN: 0-8493-8970-4.

13. Jacob Dahlstrom, Tobias Karlsson, (2002), Mechanical Analysis of Laminated Packaging Materials, Master’s Thesis, BTH, Sweden.

14. Staab G.H, (1999), Laminar Composites, Butterworth-Heinemann, Boston, U.S.A., ISBN: 0-7506-7124-6.

15. Tamas Barany, Tibor Czigany and Jozsef Karger-Kocsis (2003), Essential Work of Fracture Concept in Polymers. Periodica Polytechnica SER, MECH. ENG.Vol.47, NO.2,pp.91-102(2003). Germany.

16. P. Gupta, G.L. Wilkes, A. M. Sukhadia, R.K. Krishnaswamy, M. J. Lamborn, S.M. Wharry, C. C. Tso, P. J. DesLauriers, T. Mansfield, and F. L. Beyer. “Processing-Structure-Property Studies of Films of Linear Low Density Polyethylene As Influenced By the Short Chain Branch Length in Copolymers of Ethylene/1-Butene, Ethylene/1-Hexene and Ethylene/1-Octene Synthesized By a Single Site Metallocene Catalyst”.

17. Kaluvala Santhosh (2005), Thin Layered Laminates Testing and Analysis. Master’s Thesis BTH, Sweden.

18. Niels Ottosen and Hans Petersson (1992), Introduction to Finite Element Method.

19. K.Bertram, Broberg,(1999), Crack and Fracture, Academic Press U.S.A. ISBN: 0-12-134130-5.

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A. Experimental Work

A.1 Mounting the specimen in the testing machine

Figure A.1 represents the specimen during experimentation, between pneumatic grippers.

Figure A.1. Specimen mounted.

A.2 Paperboard

Figure A.2 representing the Load vs. Displacement Graph for paperboard specimen 1.

44

Paper-1

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16Displacement [mm]

Load

[N]

Figure A.2. Load vs. Displacement for Paperboard.


Paper-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2 4 6 8 10 12 14 16 18 20Displacement [mm]

Load

[N]


45


Paper-4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16 18Displacement [mm]

Load

[N]



Paper-5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 2 4 6 8 10 12 14 16 18 20Displacement [mm]

Load

[N]


46

A.3 LDPE

Figure A.6 representing the Load vs. Displacement Graph for LDPE specimen 1.

LDPE-1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 2 4 6 8 10 12Displacement [mm]

Load

[N]

Figure A.6. Load vs. Displacement for LDPE.


47

LDPE-2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4 5 6 7 8 9 10Displacement [mm]

Load

[N]



LDPE-3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4 5 6 7 8 9 10Displacement [mm]

Load

[N]


48


LDPE-5

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4 5 6 7 8 9Displacement [mm]

Load

[N]


A.4 Tensile Test

Figure A.4 represents Tensile test for 2-leg trousers LDPE of length 25 mm.

49

Tensile

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6Displacement [mm]

Load

[N]

Figure A.4.Tensile test for LDPE .

50

B. Simulation Work

Figure B.1 shows a mesh model created in ABAQUS/CAE

Figure B.1.Mesh model in ABAQUS/CAE.

B.1 Paperboard

Figure B.2 shows a stress-concentration at the crack initiation point created in ABAQUS/CAE.

Figure B.2. Stress distribution at crack initiation point for paperboard.

51

B.2 LDPE

Figure B.3 shows a stress-concentration at the crack initiation point created in ABAQUS/CAE.

FigureB.3. Stress distribution at crack initiation point for LDPE.

B.3 Load Comparison

Figure B.4 represents the comparison of loads between simulated and experimental results.

0

0.2

0.4

0.6

0.8

1

1.2

1 2

Load

[N]

ExpSim

FigureB.3. Bar Graph Comparison.

52

C. Appendix

C.1 Linear elastic fracture mechanics (LEFM)

The material in linear elastic fracture mechanics is assumed to be isotropic and linear elastic. Therefore on this assumption, the stress field near the crack tip is calculated using the theory of elasticity. The crack will grow as the stress near the crack initiation point exceeds the material fracture toughness. Linear elastic fracture mechanics is applied only when the inelastic deformation is small compared to the size of the crack which is known as small-scale yielding. If large zones of plastic deformation develop before the crack grows Elastic Plastic Fracture Mechanics is used.

C.2 Fracture Toughness

The resistance to fracture of a material is known as its fracture toughness. Fracture toughness generally depends on temperature, environment, loading rate, the composition of the material and its microstructure, together with geometric effects (constraint). The fracture toughness can be considered the limiting value of stress intensity just as the yield stress might be considered the limiting value of applied stress.

The fracture toughness varies with specimen thickness until limiting conditions (maximum constraint) are reached. Maximum constraint conditions occur in the plane strain state [11].

C.3 Essential Work of Fracture (EWF)

A general idea of the essential work fracture is the separation of the total fracture energy of a pre-cracked specimen into the geometry independent (essential work) and geometry dependent (non-essential work). Using the trousers-tear specimen also called as single-tear, for elastic fracture, the out-of-plane tearing toughness Tew can be expressed by

53

tPwTe

2= (c.1)

where P is the tearing force and t is the thickness of specimen. [7]

54

D. ABAQUS/CAE Input Files

D.1 Paperboard

*Heading Displacement on Paperboard ** Job name: Thesis_Paperboard Model name: Model-1 *Preprint, echo=NO, model=NO, history=NO, contact=NO ** ** PARTS ** *Part, name=Part-1 *End Part ** *Part, name=Part-2 *End Part ** ** ** ASSEMBLY ** *Assembly, name=Assembly ** *Instance, name=Part-1-1, Part=Part-1 *Node 1, -25., 25., 12.5 2, -4., 25., 12.5 3, -4., 25., 0. . . . 438, 0., 3.70588303, 1.25 439, 0., 2.47058868, 1.25 440, 0., 1.23529434, 1.25 *Element, type=S4R 1, 1, 9, 117, 58 2, 9, 10, 118, 117 3, 10, 11, 119, 118 . . . 388, 438, 439, 102, 103 389, 439, 440, 101, 102 390, 440, 100, 8, 101 *Nset, nset=_PickedSet2, internal, generate 1, 440, 1 *Elset, elset=_PickedSet2, internal, generate

55

1, 390, 1 ** Region: (Section-1:Picked) *Elset, elset=_PickedSet2, internal, generate 1, 390, 1 ** Section: Section-1 *Shell Section, elset=_PickedSet2, material=Paper-1 0.104, 5 *End Instance ** *Instance, name=Part-2-1, part=Part-2 -12.5, 0., -12.5 *Node 1, 37.5, 25., 12.5 2, 16.5, 25., 12.5 3, 16.5, 25., 0. . . . 438, 12.5, 3.70588303, 1.25 439, 12.5, 2.47058868, 1.25 440, 12.5, 1.23529434, 1.25 *Element, type=S4R 1, 1, 9, 117, 58 2, 9, 10, 118, 117 3, 10, 11, 119, 118 . . . 388, 438, 439, 102, 103 389, 439, 440, 101, 102 390, 440, 100, 8, 101 *Nset, nset=_PickedSet2, internal, generate 1, 440, 1 *Elset, elset=_PickedSet2, internal, generate 1, 390, 1 *Surface, type=ELEMENT, name=_PickedSurf16, internal __PickedSurf16_SNEG, SNEG ** Constraint: Constraint-1 *Tie, name=Constraint-1, adjust=yes _PickedSurf16, _PickedSurf15 *End Assembly ** ** MATERIALS ** *Material, name=Paper-1 *Elastic 2755., 0.3 ** BOUNDARY CONDITIONS **

56

** Name: BC-2 Type: Displacement/Rotation *Boundary _PickedSet10, encastre ** Name: BC-3 Type: Displacement/Rotation **Boundary _PickedSet11, 1, 1, 0. ** ** *Step, amplitude=ramp,inc=500 Tearing *Static 0.01,1.,,0.01 *Boundary _PickedSet11, 1, 1, 40. ** ** OUTPUT REQUESTS ** *Output,field,variable=preselected *Element output S, E, **Output,history,var=var=preselected **Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** **Output, field **Node Output **CF, RF, RM, RT, U **Element Output, directions=YES **ALPHA, LE, PE, PEEQ, PEMAG, PS, S, TSHR, VS ** ** HISTORY OUTPUT: H-Output-1 ** ** ** **Output, history, variable=PRESELECT *elprint 1 S11, *nodeprint,nset=_PickedSet11 U1, RF1 *End Step

57

D.2 LDPE

*Heading Displacement on LDPE ** Job name: Thesis_LDPE Model name: Model-1 *Preprint, echo=NO, model=NO, history=NO, contact=NO ** ** PARTS ** *Part, name=Part-1 *End Part ** *Part, name=Part-2 *End Part ** ** ** ASSEMBLY ** *Assembly, name=Assembly ** *Instance, name=Part-1-1, Part=Part-1 *Node 1, -25., 25., 12.5 2, -4., 25., 12.5 3, -4., 25., 0. . . . 438, 0., 3.70588303, 1.25 439, 0., 2.47058868, 1.25 440, 0., 1.23529434, 1.25 *Element, type=S4R 1, 1, 9, 117, 58 2, 9, 10, 118, 117 3, 10, 11, 119, 118 . . . 388, 438, 439, 102, 103 389, 439, 440, 101, 102 390, 440, 100, 8, 101 *Nset, nset=_PickedSet2, internal, generate 1, 440, 1 *Elset, elset=_PickedSet2, internal, generate

58

1, 390, 1 ** Region: (Section-1:Picked) *Elset, elset=_PickedSet2, internal, generate 1, 390, 1 ** Section: Section-1 *Shell Section, elset=_PickedSet2, material=LDPE-1 0.027, 5 *End Instance ** *Instance, name=Part-2-1, part=Part-2 -12.5, 0., -12.5 *Node 1, 37.5, 25., 12.5 2, 16.5, 25., 12.5 3, 16.5, 25., 0. . . . 438, 12.5, 3.70588303, 1.25 439, 12.5, 2.47058868, 1.25 440, 12.5, 1.23529434, 1.25 *Element, type=S4R 1, 1, 9, 117, 58 2, 9, 10, 118, 117 3, 10, 11, 119, 118 . . . 388, 438, 439, 102, 103 389, 439, 440, 101, 102 390, 440, 100, 8, 101 *Nset, nset=_PickedSet2, internal, generate 1, 440, 1 *Elset, elset=_PickedSet2, internal, generate 1, 390, 1 ** Region: (Section-1:Picked) *Tie, name=Constraint-1, adjust=yes _PickedSurf16, _PickedSurf15 *End Assembly ** ** MATERIALS ** *Material, name=LDPE-1 *Elastic 135.0, 0.3 ** ** BOUNDARY CONDITIONS ** ** Name: BC-2 Type: Displacement/Rotation

59

*Boundary _PickedSet10, encastre ** Name: BC-3 Type: Displacement/Rotation **Boundary _PickedSet11, 1, 1, 0. ** ** *Step, amplitude=ramp,inc=500 Tearing *Static 0.01,1.,,0.01 *Boundary _PickedSet11, 1, 1, 40. ** ** OUTPUT REQUESTS ** *Output,field,variable=preselected *Element output S, E, **Output,history,var=var=preselected **Restart, write, frequency=0 ** ** FIELD OUTPUT: F-Output-1 ** **Output, field **Node Output **CF, RF, RM, RT, U **Element Output, directions=YES **ALPHA, LE, PE, PEEQ, PEMAG, PS, S, TSHR, VS ** ** HISTORY OUTPUT: H-Output-1 ** **Output, history, variable=PRESELECT *elprint 1 S11, *nodeprint,nset=_PickedSet11 U1, RF1 *End Step

Department of Mechanical Engineering, Master’s Degree Programme Blekinge Institute of Technology, Campus Gräsvik SE-371 79 Karlskrona, SWEDEN

Telephone: Fax: E-mail:

+46 455-38 55 10 +46 455-38 55 07 [email protected]

a pre-study of the tearing behaviour of the flexible

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