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

Table of contents
- a 6
  - Solution a
- b 6
  - Solution b
- c 6
  - i c
    - Solution i
  - ii c
    - Solution ii
  - iii c
    - Solution iii
- d 6
  - i d
    - Solution i
  - ii d
    - Solution ii
  - iii d
    - Solution iii

a

Solution

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} .

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.

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.

c

i

Solution

TODO: user-deferred biology. This printed subpart is intentionally deferred under the current nonbiology-only scope.

ii

Solution

TODO: user-deferred biology. This printed subpart is intentionally deferred under the current nonbiology-only scope.

iii

Solution

TODO: user-deferred biology. This printed subpart is intentionally deferred under the current nonbiology-only scope.

d

i

Solution

TODO: user-deferred biology. This printed subpart is intentionally deferred under the current nonbiology-only scope.

ii

Solution

TODO: user-deferred biology. This printed subpart is intentionally deferred under the current nonbiology-only scope.

iii

Solution

TODO: user-deferred biology. This printed subpart is intentionally deferred under the current nonbiology-only scope.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version