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TcriterionThe Tfailure criterion^{[1]}^{[2]} is rather a set of failure criteria, that correlate the reversible elastic energy density storage process with both brittle and ductile failure. The development of this criterion is based on the unacceptable fact that pure hydrostatic loading of metals following the von Mises yield law, results in no failure, since the von Mises criterion is a function of deviatoric stresses. 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 Θ. These two curves, namely and (pΘ) 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 Τ_{V,0} of the elastic energy density due to volume change (dilatational energy) or by a critical value Τ_{D,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 Τ_{d} reaches the critical value Τ_{D,0} or by extensive dilatation when the dilatational energy Τ_{v} reaches a critical value Τ_{V,0}. The two critical values Τ_{D,0} and Τ_{V,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. Additional recommended knowledgeDeployment for Isotropic MetalsFor the development of the criterion, a continuum mechanics approach is adopted. The material volume is considered to be a continuous medium with no particular form or manufacturing defect. It is also considered to behave as a linear elastic isotropically hardening material, where stresses and strains are related by the generalised Hook’s law and by the incremental theory of plasticity with the von Mises flow rule. For such materials, the following assumptions are considered to hold:
(d) The increment in plastic work per unit volume using (4.16) is:
LimitationsThe criterion will not predict any failure due to distortion for elasticperfectly plastic, rigidplastic, or strain softening materials. For the case of nonlinear elasticity, appropriate calculations for the integrals in and (12) and (13) accounting for the nonlinear elastic material properties must be performed. The two threshold values for the elastic strain energy T_{V,0} and T_{D,0} are derived from experimental data. A drawback of the criterion is that elastic strain energy densities are small and comparatively hard to derive. Nevertheless, example values are presented in the literature as well as applications where the Tcriterion appears to perform quite well. References

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Tcriterion". A list of authors is available in Wikipedia. 