Dislocation thermal obstacle

Fig. 7.20. The stress-temperature history for a thin film of elastic-plastic material on a relatively thick substrate during a temperature excursion is shown. The dependence of plastic strain rate on stress is prescribed by the plastic rate equation (7.81) and is based on the assumption that resistance to plastic determination is due to thermally activated motion of dislocations past obstacles. After one temperature cycle, the response adopts a repeated cyclic behavior for fixed temperature limits.

Dislocations move when they are exposed to a stress field. At stresses lower than the critical shear stress, the conservative motion is quasi-viscous and is based on thermal activation that overcomes the obstacles which tend to pin the individual dislocations. At very high stresses, > t7crit, the dislocation velocity is limited by the (transverse) sound velocity. Damping processes are collisions with lattice phonons. 

Aided by thermal energy, dislocations may overcome obstacles even when the external stress is not sufficient to exert a force that exceeds the strength of the obstacle. This is called a thermally activated process (appendix C.l provides a general introduction to this concept). 

Thus, there is a vacancy concentration gradient between dislocation 1 and 2. It is determined by the difference of the two densities and by the distance I between the dislocations. In a material containing several obstacles, I is proportional to the mean distance of the obstacles. This gradient causes diffusion of vacancies from dislocation 2 to dislocation 1. In this argument, we assumed that the vacancy concentration at both dislocations can still be described by using the Boltzmann equation which is valid only in thermal equilibrium. This is a valid assumption provided that the energy tV is small compared to the enthalpy of vacancy formation Qy. 

Thermally activated dislocation glide past obstacles... 

In the present discussion, it will be assumed that the plastic response is dominated by the thermally activated glide of crystal dislocations past discrete obstacles in the lattice. With reference to (7.78), the plastic rate equation proposed by Frost and Ashby (1982) has the form... 

At higher stresses, thermally activated dislocation motion such as dislocation climb out of its slip plane limits the rate of steady state creep. When a lattice vacancy exchanges position with an atom in a dislocation core, a jog is formed and in the process an element of the dislocation moves to a parallel slip plane one atom distance away. Dislocations can get around obstacles by repeated climb events. The direction of climb is controlled by the applied stress state, but, of course, the rate increases with stress as the material acts to reduce its free-energy state. The rate of climb under constant stress is controlled by the rate of diffusion. The theory of dislocation creep mechanisms begins with the well-known Johnston-Gilman equation... 

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