Elastic strain energy density decomposition in failure of ductile materials under combined torsion-tension

Abstract

The constitutive behavior and failure of ductile materials are described in the present work for a general case of loading in terms of the secant moduli, which depend on the first (dilatational) and second (deviatoric) strain invariants. This approach exposes the distinct behavior of materials to the equivalent normal and shear stresses. The secant moduli enable the establishment of two (instead of one) constitutive equations necessary for the complete description of these materials. Emphasis is given in the accuracy of the resulting constitutive equations in terms of their predictions relative to actual experimental data for two materials systems. Failure predictions, according to T-criterion, are derived for two materials under combined torsion and tension, which are in good agreement with experimental data. Finally, the associated failure surfaces in a stress space are presented as well.

Numerical Simulation of Unstable Rock Failure Mechanisms Through Analysis of Energy Transformations

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“…For rock failure, the available energy resource is elastic strain energy through elastic deformation, which also could explain why failure also can be defined as the loss of the ability of the material to store elastic strain energy (Andrianopoulos and Manolopoulos 2014;Chen et al 2017). Rock is anisotropic and behaves both elastically and inelastically during its failure process.…”

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“…Where σi and εi are the main stresses and strains, respectively, and ν is the Poisson ratio. Consequently material properties under stresses produce shear strain may have essential equation to the relationship thus; σeq = f(εeq) [26].…”

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