Temperature rise due to fast-moving dislocations
In this paper, the method of discrete dislocation plasticity (DDP) is extended to include explicitly the thermal effects of moving dislocations. In this manner, localization of heat during fast deformation can be calculated exactly. The thermal effects included are the thermal dissipation due to dislocation drag, the temperature dependence of the drag coefficients themselves and a temperature dependent obstacle strength through a simple Arrhenius-type dependence. An analytical solution is presented and the temperature distribution is calculated using a time-dependent Galerkin finite-element solution. The two solutions are compared to provide a mutual validation. Then, the stress-strain curves are calculated for Al under simple shear for constant temperatures of 100, 298 and 900K. The stress-strain curves reflect the temperature dependence of the drag coefficients, since the deformation takes place at a strain rate of 106s-1, which is well within the drag-controlled regime. Finally, the temperature distributions for Al and Ti are calculated. At 7.5% shear strain, the maximum temperature rise is of the order of 20K in Ti. This is orders of magnitude lower than the melting temperature,thetemperaturewhichhas experimentally observedtobereached.It isanticipatedthatthisis caused by crack propagation which will be modelled by a DDP approach in future work.