Calculation of Thermal Trapping in Shear Bands

The microstructure associated with heterogeneous shear deformation observed in shock-loaded materials implies the possibility of transient local temperatures which far exceed those expected under homogeneous deformation. The possible consequences of high local temperatures and resulting thermal softening are explored by using thermodynamic considerations to derive equations for the evolution of shear band temperatures. Inclusion of the equations in a finite-difference wavecode along with a previously developed model which accurately describes shockwave risetime behavior allows calculation of temperature states in the shock front. At low stresses, risetimes are long compared to thermal diffusion times and shear bands stay in thermal equilibrium with surrounding material, but at high stresses where risetimes are very short, shear band temperatures greatly exceed bulk temperatures before thermal equilibriumoccurs. Decreasing yield strength with increasing shear band temperature followed by yield strength recovery as the shear bands cool produces an elastic precursor on reshock which cannot be obtained with standard elastic-plastic models. Good agreement is obtained with experimental data on aluminum. The calculations thus lend some credence to physical ideas of thermal trapping in shear bands.