Past exam of the materials science course of the University of Cambridge / 2017 / Paper 1 / 6 / b

Table of contents
- Solution b

Solution

The maximum recoverable elastic energy per initial volume is the area under the linear stress–strain curve up to failure:

u_{f} = \int_{0}^{ε_{f}} Eε d ε = \frac{1}{2} E ε_{f}^{2} = \frac{σ _{f}^{2}}{2 E} .

Using

σ_{f} = C E G_{c}

gives

u_{f} = C^{2} G_{c} /2

, so maximize $G_{c}$ for the fixed geometry.

G_{c}

has units of energy per crack area, while

u_{f}

has energy per specimen volume; the geometric factor supplies the necessary inverse length. The cancellation of

E

is why the strain-maximizing index from (a) is not appropriate here.

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