A flow instability criterion for alloys during hot deformation

Flow instability is an intrinsic behavior of materials, especially during hot deformation, and it will be intensified and propagate internal defects, and finally lead to various damages in the significant perturbation. Some phenomenological models in the literature could present the flow instability behavior, but not available for describing the microstructure changes. To overcome this problem, we introduce a dissipation potential as a function of the plastic strain rate, the dislocation density rate, and the heat transfer rate, 퐷(휺̇_푝, 휌̇_푑is, 풒; 휀, 휌_푑is, 휃), coupled with strain, dislocation density, and temperature as the boundary condition to record the microstructure evolution and describe the flow instability. In this function, the stored energy rate marks the dislocation density evolution, i.e., the transient microstructure changes, and one parameter 휂_푀, is introduced to evaluate the efficiency of metallurgy. And the flow instability criterion is derived from the principles of maximum dissipation (or maximum entropy production rate) and orthogonality proposed by HANS ZIEGLER. We obtain the necessary conditions of the flow instability are that the dissipation potential is with entirely positive values due to the large plasticity, and the dissipation potential 퐷(휺̇_푝, 휌̇_푑is, 풒; 휀, 휌_푑is, 휃) is convex, i.e., the associated Hessian matrix is semi-positive. In this work, the function was applied to describe the behavior of Ti6Al4V during hot deformation, and a Kocks-Mecking type model was used to describe the flow stresses as well.