MSC marc training mar103 - baixardoc

10
MA*V2008*Z*Z*Z*SM-MAR103-NT1 1 Experimental Elastomer Analysis MSC.Software Corporation

Transcript of MSC marc training mar103 - baixardoc

MA*V2008*Z*Z*Z*SM-MAR103-NT1 1

Experimental Elastomer Analysis

MSC.Software Corporation

MA*V2008*Z*Z*Z*SM-MAR103-NT1 Experimental Elastomer Analysis

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Part Number: MA*V2008*Z*Z*Z*SM-MAR103-NT1

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Experimental Elastomer Analysis 3

Contents

Experimental Elastomer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Table of Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

CHAPTER 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Course Objective: FEA & Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Course Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11About MSC.Marc Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13About Axel Products, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Data Measurement and Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Typical Properties of Rubber Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Important Application Areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

CHAPTER 2 The Macroscopic Behavior of Elastomers . . . . . . . . . . . . . 21

Microscopic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Temperature Effects, Tg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Time Effects, Viscoelasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Curing Effects (Vulcanization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Damage, Early Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Damage, Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Damage, Chemical Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Deformation States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

CHAPTER 3 Material Models, Historical Perspective . . . . . . . . . . . . . . . 31

Engineering Materials and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Neo-Hookean Material Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Neo-Hookean Material Extension Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . 35Neo-Hookean Material Shear Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Neo-Hookean Material Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A Word About Simple Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402-Constant Mooney Extensional Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Other Mooney-Rivlin Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Ogden Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Foam Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Model Limitations and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Viscoelastic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Determining Model Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Table of Contents

Contents

4 Experimental Elastomer Analysis

CHAPTER 4 Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Lab Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Basic Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58What about Shore Hardness? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Testing the Correct Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Tensile Testing in the Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Compression Testing in the Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Equal Biaxial Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Compression and Equal Biaxial Strain States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Volumetric Compression Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Planar Tension Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Viscoelastic Stress Relaxation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Dynamic Behavior – Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Friction Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Data Reduction in the Lab. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Model Verification Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Testing at Non-ambient Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Loading/Unloading Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Test Specimen Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Fatigue Crack Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Experimental and Analysis Road Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

CHAPTER 5 Material Test Data Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Major Modes of Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Confined Compression Test (UniVolumetric) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Hydrostatic Compression Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Summary of All Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89General Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Mooney, Ogden Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Visual Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Material Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Future Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Adjusting Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Consider All Modes of Deformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98The Three Basic Strain States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Curve Fitting with MSC.Marc Mentat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Experimental Elastomer Analysis 5

Contents

CHAPTER 6 Workshop Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Some MSC.Marc Mentat Hints and Shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . . 108Model 1: Uniaxial Stress Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Model 1: Uniaxial Curve Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Model 1C: Tensile Specimen with Continuous Damage . . . . . . . . . . . . . . . . . . 133Model 1: Realistic Uniaxial Stress Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Model 2: Equi-Biaxial Stress Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Model 2: Equi-Biaxial Curve Fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153Model 2: Realistic Equal-Biaxial Stress Specimen. . . . . . . . . . . . . . . . . . . . . . . 165Model 3: Simple Compression, Button Comp. . . . . . . . . . . . . . . . . . . . . . . . . . . 168Model 4: Planar Shear Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Model 4: Planar Shear Curve Fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Model 4: Realistic Planar Shear Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195Model 5: Viscoelastic Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Model 5: Viscoelastic Curve Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200Model 6: Volumetric Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

CHAPTER 7 Contact Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Definition of Contact Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218Control of Rigid Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220Contact Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221Bias Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222Deformable-to-Deformable Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223Potential Errors due to Piecewise Linear Description: . . . . . . . . . . . . . . . . . . . . 224Analytical Deformable Contact Bodies: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224Contact Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Symmetry Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Rigid with Heat Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Contact Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229Contact Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Exclude Segments During Contact Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . 232Effect Of Exclude Option:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233Contacting Nodes and Contacted Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Friction Model Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235Coulomb ArcTangent Friction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236Coulomb Bilinear Friction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Stick-Slip Friction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238Glued Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239Release Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241Interference Check / Interference Closure Amount . . . . . . . . . . . . . . . . . . . . . . 241

Contents

6 Experimental Elastomer Analysis

Forces on Rigid Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

APPENDIX A The Mechanics of Elastomers. . . . . . . . . . . . . . . . . . . . . . 245

Deformation States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246General Formulation of Elastomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250Finite Element Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Large Strain Viscoelasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254Large Strain Viscoelasticity based on Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 254Illustration of Large Strain Viscoelastic Behavior . . . . . . . . . . . . . . . . . . . . . . . 259

APPENDIX B Elastomeric Damage Models . . . . . . . . . . . . . . . . . . . . . . 261

Discontinuous Damage Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Continuous Damage Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

APPENDIX C Aspects of Rubber Foam Models . . . . . . . . . . . . . . . . . . . 271

Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272Measuring Material Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

APPENDIX D Biaxial & Compression Testing . . . . . . . . . . . . . . . . . . . . 277

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279Overall Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281The Experimental Apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282Analytical Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291Attachment A: Compression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

APPENDIX E Xmgr – a 2D Plotting Tool. . . . . . . . . . . . . . . . . . . . . . . . . 295

Features of ACE/gr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296Using ACE/gr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297ACE/gr Miscellaneous Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

APPENDIX F Notes and Course Critique . . . . . . . . . . . . . . . . . . . . . . . . 303

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306Course Critique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Experimental Elastomer Analysis 7

CHAPTER 1 Introduction

This course is to provide a fundamental

understanding of how material testing and

finite element analysis are combined to

improve your design of rubber and

elastomeric products. Most courses in

elastomeric analysis stop with finite

element modeling, and leave you searching

for material data. This experimental

elastomer analysis course combines

performing the analysis and the material

testing. It shows how the material testing

has a critical effect upon the accuracy of

the analysis.

Chapter 1: Introduction Course Objective: FEA & Laboratory

8 Experimental Elastomer Analysis

Course Objective: FEA & Laboratory

Left Brain

W C1 I1 3–( ) C2 I2 3–( )+=

n

αn

------ λ1

αn λ2

αn λ3

αn

+ +( ) 3–[ ]

n 1=

N

∑=

Computer

Analytical

Objective

Logical

W NkT I1 3–( ) 2⁄=

W G1

2--- I1 3–( )

1

20N---------- I1

23

2–( ) …+ +=

Right BrainLaboratory

Experimental

Subjective

Intuitive

Experimental Elastomer Analysis 9

Course Objective: FEA & Laboratory Chapter 1: Introduction

Course Objective

Discuss the TESTCURVE FIT

ANALYSIS

cycle specific to rubber and elastomers.

Limit scope to material models such as Mooney-Rivlin and Ogden form strain energy models.

Test Material Specimen

Material Model (curve fit)

Test Part

?

Correlation

?Analyze Part

Analyze Specimen

Chapter 1: Introduction Course Objective: FEA & Laboratory

10 Experimental Elastomer Analysis

Course Objective (cont.)

Some important topics covered are:

• What tests are preferred and why?

• Why aren’t ASTM specs always the answer?

• What should I do about pre-conditioning?

• Why are multiple deformation mode tests important?

• How can I judge the accuracy of different material models?

• How do I double check my model against the test data?