Instability analysis and shear band spacing in gradient-dependent thermoviscoplastic materials with finite speeds of thermal waves

摘要: We analyze the stability of a homogeneous solution coupled nonlinear equations governing simple shearing deformations strain-rate gradient-dependent thermoviscoplastic body in which thermal disturbances propagate at finite speed. The is perturbed by an infinitesimal amount and linear perturbation variables axe derived. Conditions for these perturbations to grow are deduced. shear band spacing, L s , defined as = inf t 0 ≥0 (2 π / ξ m ( )) where wave number introduced time that has maximum growth rate . It found relaxation (i.e. ratio coefficient second time-derivative temperature heat equation first time-derivative) significantly affects spacing value ) maximum.