Work Hardening


The tensile test of material strength is probably one of the most common means of characterising a material’s strength, although similar tests in compression are also ubiquitous. The stress strain curve of a typical tensile stress strain test for a ductile metal is well known, initially exhibiting a conventional linear elastic section, then as strain is increased, there is increased non linearity and a rising curve, leading ultimately to a maximum, consistent with necking in the material’ and then a fairly rapid drop off in stress followed by rupture or fracture. It is useful, especially for engineering design purposes, to record the limit of non-linearity as the ‘yield point’ (or if there is no distinct transition) the ‘proof stress’ (at a specific strain, typically 0.2%). Beyond this yield point, as the strain increases the stress also increases, but generally more slowly, and this behaviour is known as work hardening.

Work hardening, the phenomenon of increasing strength with increased strain beyond the yield point is typically associated with dislocation build up in the material and the consequent loss of ductility.  This can both be a problem i) if one is trying to roll such metals into thin sheet and work hardening makes this progressively more difficult (in which case a stress relieving anneal may be necessary), or ii) a benefit, if one is trying to achieve a higher strength material merely by work hardening, rather than changing the alloy composition.  Such work hardening works very well, but there is also a consequent loss in ductility, as the metal has effectively been taken ‘further along’ its typical stress-straincurve (although this is seldom a problem, especially if one is aware of the strain limit change).  It should be noted that the increase in yield strength due to work hardening is lost when the material is annealed (either intentionally or when the material is heated during hot forming/processing operations and welding).  

The shape of the stress-strain trace exhibits, above yield, a concave downwards curve. This curve displays an increasingly rising shape with increased work hardening of the material.  The behaviorand extent of this portion of the curve is characterised by the Ramberg-Osgood relationship (first published in 1943) which specifically takes into account this work hardening effect, in the form of a power law equation: 

            Where:     ε is the strain,
                            σ is the stress,
                            σₒ is the yield stress
                            E is Young’s modulus
                            α and n are constants relating to work hardening, with α typically
                            being close to 1.0, and n the work hardening exponent, typically
                            between 3 and 20 (often ~ 5)

This formulation works well, and from a full stress–strain plot for the material, one can obtain all the relevant parameters, and particularly the work hardening exponent, n.

It is also of interest that this latter Ramberg-Osgood relationship has special relevance in characterising fracture toughness in terms of Crack Tip Opening Displacement (CTOD) or J integral terms, enabling one to switch from one to the other using the work hardening exponent, in a formulation due to Fong Shih.

The message is simple - work hardening can be used to increase the strength of materials but beware of changes in ductility and the effect of heating during manufacture/processing.

Published in Technical Tips by Origen Engineering Solutions on 1 February 2019