Hardness and work hardening

Hardness is a measure of a material’s resistance to localised plastic deformation, e.g. a small indent or scratch. A high hardness comes from a combination of high \( \sigma_{\rm{y}} \) and high \( \sigma_{\rm{u}} \).

Hardness is important when considering a material’s resistance to wear. For example, we want to make chain saw teeth from a hard material so that frequent replacement is not required.

Mohs scale for hardness is based on the ability of one natural sample of material to scratch another material visibly. The harder the material is, the easier it is to leave a mark when scratching other softer materials, and the higher the Mohs hardness it has.

Ten standard minerals with their Mohs hardness are given below for reference.

A Vickers hardness test is a more quantitative measurement of hardness. An indentation is made with a known applied force and the contact area is measured using micrometre under a microscope. See here for the geometry of Vickers hardness test.

The Vickers hardness number \( H_{\rm{v}} \), in HV (kgf mm⁻²) is the ratio of the applied force \( F \), in kgf, to the contact area \( A \), in mm²,

\[ {H_{\rm{v}}} = 1.854\frac{F}{{{D^2}}} \]

where \( D \) is the average length of the diagonal left by the indenter, measured in millimetres.

Hardness and yield stress are very closely related. Generally, higher yield stress means higher hardness. But hardness defined in a more localised way. From plastic flow analysis (using finite element method), we have the following relationship between the yield stress \( \sigma _{\rm{y}} \) and Vickers hardness \( H_{\rm{v}} \),

\[ {\sigma _{\rm{y}}} \approx \frac{{{H_{\rm{v}}}}}{3} \]

However, the yield stress obtained using this relationship may be underestimated as we did not consider the effect of work hardening.

It is observed that the hardness and strength of materials are increased in the area of plastic deformation. This process is called work hardening, strain hardening or forest hardening. When plastic deformation takes place, dislocations glide in the active slip systems. After these dislocations meet other dislocations that are not in these slip system, they either intersect to produce jogs or combine together to form Lomer locks. In both cases, the dislocations are stuck (sessile) and it is therefore harder for plastic deformation to take place.

To explore work hardening further, see the mechanism of plasticity TLP.

Work hardening is an important mechanical process in manufacturing materials. Many manufacturing processes involve permanently deforming the material into the desired shape. It is advantageous that their hardness has increased so they will not be easily worn out, but this also makes the material more brittle and therefore more susceptible to fracture. Later in this TLP, we will explore fracture further.