MCEN90029 - Advanced Solid Mechanics - Engineering Assignment Help

Assignment Task

PART A

Case 1

A material exhibits a stress intensity factor range vs. crack propagation relation during fatigue loading, as shown in the figure below. The central zone region (II) represents the classic ‘Paris’ power law. The region (I) shows a case of smaller cracks, and the region (III) indicates an acceleration of crack propagation until final rupture.

Where C 0 and exponent m are material parameters, is the threshold level range, is the applied stress intensity factor range and is the fracture toughness in plane strain or plane stress. Considering the cyclic crack propagation in a centre-cracked infinite steel plate under the constant amplitude cyclic stress, derive expressions for

1) The number of cycles N starting from an initial crack a i to a final crack a f
2) With an initial crack a i = 5 mm propagating to a final crack a f = 15 mm, how does a change of the constant amplitude cyclic stress affect the number of cycles? Please explain this relation.

Case 2

Illustrate how the size and shape of the plastic zone ahead of a crack tip changes with strain hardening of a cracked material undergoing Mode I-loading. Show your working and state any assumptions made.

PART B

Research a well-documented failure case that occurred as a result of fracture. There is no restriction on the structure/material that you choose, but the case must should be previously reported and published through credible media, e.g. newspapers, journal articles, scientific reports etc.

1) Provide a background summary of the events leading to the fracture event (600 words max). Include in your summary a description of the material involved, the physical load environment that the material was subject to, and evidence for the fracture. Provide an explanation for what caused the fracture, giving reference to the material behaviour.

2) Was the failure type I or type II? Provide 3 logical ways that the fracture may have been prevented.

3) Draw a free-body diagram of a region of the material at the time of failure and estimate the forces on the material at the initiation of fracture.

4) Using your answer to 3) above, estimate the stress intensity factor ahead of the crack.

5) Plot the stresses in the material in the vicinity of the crack tip in one chosen direction. You may wish to find a creative way to display your results.

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