Why is hardening and brittle nature so related?What is work hardening or strain hardening as far as true stress strain diagram is concerned?


Brittleness describes the inability of a material to absorb a considerable amount of plastic deformation. Thus, the material fails without a lot of deformation. Hardening, on the other hand is the process of increasing a material's yield strength $\sigma_y$

The principle used for work/strain hardening has to do with residual strain.

If you stretch e.g. steel beyond its elastic limit, i.e. beyond $\epsilon_{el}$, or $\sigma_y$, it starts to yield, any further work done on the material will result in plastic deformation and is therefore irreversible. Only the work done up to the elastic limit is reversible. For example, if you stretch the material in the $\sigma$-$\epsilon$-diagram (~steel) to the point $\epsilon_{pl}$ and then remove the load, a residual strain $\epsilon_r$ will remain.

If you reset your testing apparatus and measure the material's stress-strain diagram again, it will now follow the green line, as the material has undergone strain-hardening. It has now an elastic limit $\epsilon_{el,2}\approx\epsilon_{pl}-\epsilon_r$

The elastic modulus $E$ remains more or less the same. ($E$ is rather affected by the alloy components). Ultimately, its yield strength $\sigma_y$ has increased.

The "green" material will now undergo less deformation $\epsilon$ up to its failure than the initial material (blue), thus it can be considered more brittle.

In general, if you consider one material, you can make it harder, but that will also leave it more brittle.

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