1、Physical TestingLecture 3Copyright 2006 ABAQUS, Inc.L3.2OverviewModes of DeformationUniaxial Tension Planar Tension Uniaxial Compression Equibiaxial TensionVolumetric CompressionLoading HistoryTest the Right MaterialSummaryModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.Mod

2、es of DeformationCopyright 2006 ABAQUS, Inc.L3.4Modes of DeformationWhat do we mean by modes of deformationAnd why will we talk so much about them?Initially (1930s 1950s) all focus was on uniaxial tests and fitting coefficients to uniaxial data.Researchers observed that these uniaxial fits (for phen

3、omenological models) did not correlate with data taken from other types of tests.Need to perform other tests and use this data for fitting too.These other tests are from different strain states than uniaxial thus the phrase “modes of deformation.”Modeling Rubber and Viscoelasticity with ABAQUSCopyri

4、ght 2006 ABAQUS, Inc.L3.5Modes of DeformationStrain states, testing and curve fittingNeeds:Simple test to perform, simple specimen to prepare.Single state of strain/stress in the specimen, homogeneous, no gradient of strain/stress (away from grips). This is related to both analytical solution and me

5、asurement issues. “Pure” state of strain.Simple deformation modeneed analytical solution for curve fitting.In general, one wants to perform several types of tests (modes of deformations) and curve fit a material model using multiple test data sets.Modeling Rubber and Viscoelasticity with ABAQUSCopyr

6、ight 2006 ABAQUS, Inc.L3.6Modes of DeformationThe common tests for rubberUniaxial tension (simple tension) Uniaxial CompressionPlanar Tension Equibiaxial TensionVolumetric CompressionModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.7Modes of Deformation: Uniaxial Tension,

7、 Simple TensionWhat is simple tension?Uniaxial loadingFree of lateral constraintModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.8Modes of Deformation: Uniaxial Tension, Simple TensionMeasure strain only in the region where a uniform state of strain existsDo not use cross

8、head travel to measure strain!Use non-contact measurements:Laser ExtensometerVideo ExtensometerModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.9Modes of Deformation: Planar Tension, aka Plane Strain TensionWhat is planar tension?Uniaxial loadingPerfectlateral constraintA

9、ll thinning occurs in one directionModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.10Modes of Deformation: Planar Tension, aka Plane Strain TensionStrain measurement is particularly criticalSome material flows from the gripsThe effective height is smaller than starting h

10、eight so 10:1 width:height is neededModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.11Modes of Deformation: Simple CompressionRequirements:Uniaxial loadingNo lateral constraintModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.12Modes of Deforma

11、tion: Simple CompressionIt is experimentally difficult to minimize lateral constraint due to friction at the specimen loading platen interfaceFriction effects alter the stress-strain curvesThe friction is not known and cannot be accurately corrected Even very small friction levels have an effect at

12、very small strainsEasy to prepare specimen, but difficult to achieve friction free test, thusdifficult to achieve state of pure compressionWould prefer to perform equibiaxial tension test instead!Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.13Modes of Deformation: Equ

13、ibiaxial TensionWhy?Same strain state as compressionCannot do pure compressionCan do pure biaxialModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.14Modes of Deformation: Equibiaxial TensionAnalysis of the specimen justifies geometryModeling Rubber and Viscoelasticity with

14、 ABAQUSCopyright 2006 ABAQUS, Inc.L3.15Modes of Deformation: Equibiaxial TensionModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.16Modes of Deformation: Equibiaxial TensionAlternate equibiaxial jigsHere is another testing jig used to achieve equibiaxial stress state.Ballo

15、on inflation can also be used to achieve equibiaxial tension.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.17Modes of Deformation: Typical Test DataGet acquainted with typical test data from 3 shear modesModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABA

16、QUS, Inc.L3.18Modes of Deformation: Volumetric CompressionDirect measure of the stress required to change the volume of an elastomerRequires resolute displacement measurement at the fixtureValid for (nearly) incompressible material onlyModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 AB

17、AQUS, Inc.L3.19Modes of Deformation: Volumetric CompressionConfined compressionTechnically, this test is called a confined compression test. We make use of the fact that for solid rubber the bulk modulus is much higher than the shear modulus. At very low stress the material shears to fill the rigid

18、container, and the response is dominated by the bulk (volumetric) properties of the material.This test should not be used for voided (foam) materials.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.20Modes of Deformation: Volumetric CompressionTrue volumetric compression

19、, valid for foams (and solids).True volume compression can be achieved using a fluid filled rigid pressure chamber. The specimen is sealed against fluid penetration. This test fixture is expensive and relatively rare.Another alternative to gather volumetric information is to perform a uniaxial tensi

20、on experiment and measure the lateral strains.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.21Modes of Deformation: Volumetric CompressionInitial slope = bulk modulusTypically, only highly constrained applications require an accurate measure of the entire pressurevolum

21、e relationship.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.Loading HistoryCopyright 2006 ABAQUS, Inc.L3.23Loading HistoryInitial loading, typical of data from existing standards1.21.00.80.60.40.20.00.00.20.40.60.81.0StrainModeling Rubber and Viscoelasticity with ABAQUSC

22、opyright 2006 ABAQUS, Inc.Stress (MPa)L3.24Loading History1.21.00.8Initial Loading0.60.40.20.00.00.20.40.60.81.0StrainModeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.Stress (MPa)L3.25Loading HistoryConsistencyBe careful that the real component and the test specimen share th

23、e same load history and pre-conditioning.Is the analysis for a 1st load condition (installation for instance)? Then test the virgin material.Is the analysis for a repeated use condition? Then test the specimen after pre-conditioning.Be careful to test at consistent strain rates for each deformation

24、mode. Test at strain rates consistent with the real component use situation.Modeling Rubber and Viscoelasticity with ABAQUSCopyright 2006 ABAQUS, Inc.L3.26Loading HistorySome common elastomers exhibit dramatic strain amplitude and cycling effects at moderate strain levelsConclusions:Test to realistic strain levelsUse application specific load