Analytical formulation of a criterion for adiabatic shear failure

Numerical modeling and prediction of adiabatic shear localization require a criterion that is both robust and simple enough so that it can be implemented into numerical codes. This criterion should have a minimum number of adjustable parameters, each of which being measurable, with sufficient generality to avoid adjustments for each new investigated case. This paper presents a detailed analytical study of such a criterion formulated in terms of plastic strain energy density. The criterion contains 3 physical parameters: an exponent b and two energy parameters corresponding to the initiation of the shear band and its final failure. It describes both the initiation and the propagation of the damage (shear band) in the dynamically loaded solid, while b represents the damage tolerance characteristics of the material. We show that the general stress-strain relationship decays exponentially (or close to) with ongoing damage, which allows attainment of very large strains in the shear band. A detailed procedure is reported for the experimental identification of each of the above-mentioned parameters, for any value of the exponent b. The criterion was previously used for dynamic shear localization simulations on empirical grounds [1], that are now firmly established for the first time through a rigorous analysis, including systematic parameters' identification.