Work hardening

Work hardening is an increase in resistance to further plastic deformation caused by earlier deformation. A useful macroscopic test loads a metal beyond yield, unloads it and reloads in the same direction: further plastic flow then requires a larger stress. In a constitutive equation, this history is represented by evolving internal variables rather than by the current elastic strain alone.^[ref]

In a crystal, multiplication and interaction of dislocations can make later dislocation glide more difficult. Forest hardening and latent hardening describe particular aspects of that obstacle formation. Increased resistance to plastic flow is not the same as a large change in Young's modulus: the elastic unloading slope and the load required to restart permanent deformation measure different properties. Work hardening can delay necking by compensating for the shrinking loaded area.

Latent hardening is increased resistance on one crystal slip system caused by plastic slip on another slip system. The word latent emphasizes that the affected system need not have been active during the earlier loading. It is therefore a statement about interactions between deformation mechanisms, rather than simply about the total amount of deformation.

A simple crystal-plasticity model writes ${\dot{g}}_{\alpha }={\sum }_{\beta }{h}_{\alpha \beta }|{\dot{\gamma }}_{\beta }|$, where $g_{\alpha }$ is the critical resolved shear stress for system $\alpha$ and ${\gamma }_{\beta }$ is slip on system $\beta$. Off-diagonal coefficients represent cross-system hardening, while diagonal coefficients describe self-hardening.^[ref] Changing loading direction after predeformation can activate previously less-favoured slip systems and reveal this history dependence. Predicting the next system to move therefore requires both resolved stress geometry and the evolving resistances.

Forest hardening is resistance to dislocation glide caused by dislocations that cut across a glide plane. An advancing dislocation must negotiate their intersections, form or break junctions, or bow between obstacles. The resulting obstacle network is called a forest because it obstructs motion across the plane, even though it is made of line defects rather than solid inclusions.

The mechanism connects dislocation density with work hardening: a shorter spacing between effective obstacles generally demands greater applied shear stress. It also explains why different slip systems need not evolve independently; slip on one system changes the obstacles encountered by another, contributing to latent hardening. Comparing a specimen before and after controlled plastic deformation tests the increase in flow resistance, while microstructural observation tests whether an assumed obstacle mechanism is plausible. Not every change of yield stress is forest hardening; other microstructural changes can also strengthen a material.