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Transcript of MSC marc training mar103 - baixardoc
MA*V2008*Z*Z*Z*SM-MAR103-NT1 Experimental Elastomer Analysis
Copyright © 2008 MSC.Software Corporation
All rights reserved. Printed in U.S.A.
Corporate Europe
MSC.Software Corporation MSC.Software GmbH
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Santa Ana, CA 92707 81829 München, GERMANY
Telephone: (714) 540-8900 Telephone: (49) (89) 431 987 0
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Telephone: (81) (3) 3505 0266
Fax: (81) (3) 3505 0914
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–( )+=
Wµ
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?