Strain damage criterion

It simplifies the mathematics however if a strain cumulative damage criterion is assumed since our model expresses stress in terms of the strain history. 

For practical purposes the lower limit of the critical strain can be used as a criterion. This value appears, moreover, to be not much dependent on temperature, so that it can be considered as a material constant. It varies from -03% for PS to 2.2 % for PP. From creep isochrones a stress level can now quite easily be detected at which, within a given time of usage, no damage to the material is to be expected. This stress level is, of course, much lower than the one we found from Figure 7.20. 

The Mohr-Coulomb criterion is used to represent the shear failure of coal. In the modelling studies, after yielding has occurred, the total strain is assumed to consist of three components the elastic, plastic and damage components. 

For URPs, the emphasis is somewhat different. Due to their relatively low stiffness, component deformations under load may be much higher than for metals and the design criteria in step (b) are often defined in terms of maximum acceptable deflections. Thus, for example, a metal panel subjected to a transverse load may be limited by the stresses leading to yield and to a permanent dent. Whereas a URPs panel may be limited by a maximum acceptable transverse deflection even though the panel may recover without permanent damage upon removal of the loads. Even when the design is limited by material failure it is usual to specify the materials criterion in terms of a critical failure strain rather than a failure stress. Thus, it is evident that strain and deformation play a much more important role for URP than they do for metals. As a consequence, step (a) is usually required to provide a full stress/strain/ deformation analysis and, because of the viscoelastic nature of plastics, this can pose a more difficult problem than for metals. 

These data points represent extensive damage and effective failure the loss in stiffness can be used to determine a suitable failure criterion. The normal failure strain provides a useful dimensionless parameter for characterizing fatigue. 

OP loadings at the same equivalent strain amplitudes suggest that the von Mises criterion underestimates the fatigue damage under non-proportional loadings. 

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