Tension equibiaxial

Experiments with rather brittle rubber sheets that contained deliberately introduced initial cracks of the same size and type in both uniaxial and biaxial 

Cavitation near small rigid inclusions is more difficult to induce (Gent and Park, 1984), probably because the volume of rubber subjected to a critical triaxial tension is too small to contain relatively large precursor voids. And larger stresses are necessary to expand small voids less than about 0.5 p,m in diameter. 

If elastomers could be prepared without any microcavities greater than, say, 10 nm in radius, they would be much more resistant to cavitation. This seems an unlikely development, however, so Fq. (10.30) remains an important general fracture criterion for elastomers. It predicts a surprisingly low critical triaxial tension, of the order of only a few atmospheres, for soft, low-modulus elastomers. Conditions of triaxial tension should probably be avoided altogether in these cases. 

Cavitation is an important practical issue when elastomers are used for containing high-pressure gases (Briscoe and Zakaria, 1990). If the gas dissolves in the rubber and migrates to fill the precursor voids, it will be at the (high) external pressure. Then, when the outside pressure is released suddenly, the voids break open in accordance with Fq. (10.30). 

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Several criticisms of these parameters have recently been pointed out. First, they have no specific association with a material plane (i.e., they are scalar parameters), despite the fact that cracks are known to nucleate on specific material planes. With traditional parameters it is difficult to account for the effects of crack closure under compressive loading. Traditional parameters have not been successful at unifying experimental results for simple tension and equibiaxial tension fatigue tests. Finally, a nonproportional loading history can always be constmcted for a given scalar equivalence parameter that holds constant the value of the scalar parameter, but which results in cyclic loading of material planes. For such histories, scalar parameters incorrectly predict infinite fatigue life. 

Data can be obtained from tests in uniaxial tension, uniaxial compression, equibiaxial tension, pure shear and simple shear. Relevant test methods are described in subsequent sections. In principle, the coefficients for a model can be obtained from a single test, for example uniaxial tension. However, the coefficients are not fully independent and more than one set of values can be found to describe the tension stress strain curve. A difficulty will arise if these coefficients are applied to another mode of deformation, for example shear or compression, because the different sets of values may not be equivalent in these cases. To obtain more robust coefficients it is necessary to carry out tests using more than one geometry and to combine the data to optimize the coefficients. 

Fig. 3 Observed in-plane apparent stress vs in-plane macrostrain in the tension face for specimens (a) fractured in equibiaxial tension and (b) extensively deformed.

Fig. 5 Tension-face fracture strains for samples fractured in equibiaxial tension.

Fig. 6 In-plane macrostress vs in-plane macrostrain curves in equibiaxial tension, computed with (broken lines) and without (solid lines) taking account of residual stresses.

He showed that a satisfactory fit to experimental data for tension, pure shear and equibiaxial tension could then be obtained with a three-term expression. Such expressions are very useful for comparing rubbers, but it is not possible to justify them on fundamental grounds. 

For a small circular hole in a large plate under equibiaxial tension, what is the stress concentration factor ... 

They showed that experimental data of Treloar [6] for tension, pure shear and equibiaxial tension could be fitted very well indeed (Figure A2.2) by assuming a... 

Figure A2.2 The three-term Ogden representation compared with the Treloar data for simple tension (o) pure shear (+) and equibiaxial tension (o). (Reproduced with permission from Treloar, Proc. Roy. Soc. A351, 301 (1976) and Ogden, Pwc. Roy. Soc. A326, 565 (1972))...

The behavior of filled elastomers can be primarily described as hyperelastic under static or quasi-static loading dissipative effects are negligible. There have been numerous experimental studies addressing the response of rubber under quasi-static loading conditions, including uniaxial tension/compression, shear, equibiaxial tension [53-56]. 

Figure 3.11 Ogden s four-term model applied to Treloar s results, plotted as nominal stress against extension ratio, o - simple tension H— pure shear equibiaxial tension. (Reproduced from Ogden, R.W. (1972) Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubber-like. Solids Proc. R. Soc. A, 326, 565. Copyright (1972) Royal Society Publishing.)...

FIGURE 32.2 Representative load displacement curve developed by testing of a small punch specimen in equibiaxial tension the curve here reflects typical behavior of GUR 1020. Primary metrics include initial stiffness, peak load, ultimate load, and ultimate displacement. Work-to-failure is shown in gray. Unirradiated (virgin) UHMWPE exhibits a bend and a stretch region as shown. 

An argument to resolve the discrepancy between the failure envelopes obtained for different modes of straining is indicated by the work of Blatz, Sharda, and Tschoegl [42]. These authors have proposed a generalized strain energy function as constitutive equation of multiaxial deformation. They incorporated more of the nonlinear behavior in the constitutive relation between the strain energy density and the strain. They were then able to describe simultaneously by four material constants the stress-strain curves of natural rubber and of styrene-butadiene rubber in simple tension, simple compression or equibiaxial tension, pure shear, and simple shear. 

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