Description
The strain energy density stored in the material and calculated by the area under the - curve represents the total amount of energy stored in the material only in the case of pure shear. In all other cases, there is a divergence between the actual and calculated stored energy in the material, which is maximum in the case of pure hydrostatic loading, where, according to the von Mises criterion, no energy is stored. This paradox is resolved if a second constitutive equation is introduced, that relates hydrostatic pressure p with the volume change . These two curves, namely and (p-) are essential for a complete description of material behaviour up to failure. Thus, two criteria must be accounted for when considering failure and two constitutive equations that describe material response. According to this criterion, an upper limit to allowable strains is set either by a critical value ΤV,0 of the elastic energy density due to volume change (dilatational energy) or by a critical value ΤD,0 of the elastic energy density due to change in shape (distortional energy). The volume of material is considered to have failed by extensive plastic flow when the distortional energy Τd reaches the critical value ΤD,0 or by extensive dilatation when the dilatational energy Τv reaches a critical value ΤV,0. The two critical values ΤD,0 and ΤV,0 are considered material constants independent of the shape of the volume of material considered and the induced loading, but dependent on the strain rate and temperature.
Read more about this topic: T-criterion
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