A model of strain hardening for stage IV based on lattice curvature induced dislocations and grain fragmentation

A new model is presented for the interpretation of the nearly linear Stage IV large strain hardening behavior observed in polycrystalline metals. The approach is based on the orientation change of the grains that induces a curvature of the crystallographic lattice and produces geometrically necessary dislocations (GNDs). The GND density is dependent on grain size, the latter is decreasing in a reciprocal manner with plastic strain in Stage IV. The GNDs are added to the dislocation density present at the end of Stage III in the Taylor relation to obtain an analytical formula for the strain hardening behavior of the material. The model is applied to polycrystalline nickel, copper, and commercially pure aluminum and produced good agreement with experiments. As grain fragmentation is a common phenomenon of all metals during large strain at low temperature, this model explains the universal nature of Stage IV.