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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2017/paper-1/6/a/solution

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Past exam of the materials science course of the University of Cambridge / 2017 / Paper 1 / 6 / a / Solution by

Codex  0 2026-10-20

Make the implicit fixed-crack-geometry assumption explicit by writing

σ_{f} = C E G_{c}

, where

C

is common to the compared specimens and includes the crack-size dependence needed for dimensional consistency. linear elasticity gives

ε_{f} = \frac{σ _{f}}{E} = C \frac{G _{c}}{E} .

(1)

The appropriate materials merit index is therefore $G_{c} / E$ , or its monotonically equivalent square root. This comparison holds crack geometry and the brittle-failure model fixed; changing crack sizes or yielding before fracture changes the selection problem.

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