 Solution

ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2019/paper-1/5/d/solution

The number and spacing of primary slip planes remain fixed, so the length projected on their normal is invariant:

l_{0} cos ϕ_{0} = l_{1} cos ϕ_{1}

. The initial and boundary loading directions are

[514]

and

[211]

, respectively. With normal

[1 \overset{ˉ}{1} 1]

cos ϕ_{0} = \frac{8}{42 3}, cos ϕ_{1} = \frac{2}{6 3} .

Therefore

ϵ_{p} = \frac{cos ϕ _{0}}{cos ϕ _{1}} - 1 = \frac{4}{7} - 1 = 0.5119 ≃ 51.2%.

This is engineering plastic strain in the ideal geometric model; its corresponding logarithmic strain is

ln (4/ 7)

. Elastic extension and changes in slip resistance are neglected, as required by this construction.

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