Material Crack

#167 / Materials Science Easy

In the shown figure, a brittle specimen is loaded with an applied stress of 350 psi (in tension). What is the resulting stress intensity for the crack?

Expand Hint
Fracture toughness:
$$$K_{IC}=Y\cdot \sigma \cdot \sqrt{\pi (a)}$$$
where $$Y$$ is the geometrical factor, $$\sigma$$ is the applied engineering stress, and $$a$$ is the crack length.
Hint 2
Fracture toughness is the stress intensity of when a brittle material will fail due to the combination of an applied stress and crack length.
$$$K_{IC}=Y\cdot \sigma \cdot \sqrt{\pi (a)}$$$
where $$K_{IC}$$ is fracture toughness, $$Y$$ is the geometrical factor, $$\sigma$$ is the applied engineering stress, and $$a$$ is the crack length.

Based on the problem statement:
  • $$\sigma=350\:psi$$
  • $$Y=1.1$$ (since an exterior crack was produced)
  • $$a=3"$$
Therefore,
$$$K_{IC}=1.1\cdot 350psi \cdot \sqrt{\pi (3in)}=1182\:psi\cdot in^{1/2}$$$
$$$1182\:psi\cdot in^{1/2}$$$


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