Simulation and modelling of forest hardening in body centre cubic crystals at low temperature

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Abstract
In body centred cubic (bcc) crystals at low temperatures, the thermally activated motion of screw dislocations by the kink-pair mechanism governs the yield properties and also affects the strain hardening properties. In this work, the average strength of dislocation junctions is derived and numerically estimated in the case of Nb and Ta crystals. This allows us to extend an existing simulation of dislocation dynamics in bcc crystals to the case of the motion of a screw dislocation line through a random distribution of forest obstacles. Numerical results are presented in the case of Ta crystals and at two temperatures, 160 K and 215 K. They are complemented by a simple model that applies quite generally to bcc metals at low temperatures. It is shown that forest hardening is made up of two contributions, a free-length effect that depends on the length of the mobile screw segments and whose dependence on forest obstacle density is logarithmic and a line tension effect linearly proportional to the obstacle density. As a result of the thermally activated character of screw dislocation mobility, the relative weight of the two contributions to forest hardening depends on the temperature and strain rate.