ENSC1004 - Lecture 14

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ENSC1004 - Lecture 13
Mechanical Failure 2 cont. - Slides

Elliptical Shaped Crack

• For a plate with an elliptical shaped crack, max stress at the crack tip is:
  ${\sigma }_{max}={\sigma }_o[1+2(\frac{a}{\rho }{)}^{1/2}]$

Stress Intensity Factor

• Pre-existing cracks in a material act as stress risers
  • Stress along isn’t valid to predict fracture of brittle materials
• Stress intensity factor ($K$) measures the severity of an nominal stress on a brittle material with pre-existing cracks for fracture:
  $K=Y\sigma \sqrt{\pi a}$
  $K$ $-$ measured in $MPa\sqrt{m}$
  $a$ $-$ crack length
  $Y$ $-$ parameter based on size and shape of flaw and specimen
  $Y$ is dimensionless
  $\sigma$ $-$ nominal stress
• When we increase the applied load, $K$ increases
  • When critical value is reached ($K_c$), fracture occurs
  • $K_c$ is an intrinsic property of the material

In designing a structural component, the possibility of brittle fracture needs to be considered, in addition to yielding

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Mechanical Failure 3 - Slides

Failure by Fatigue

• Failure by fatigue is the largest cause of failure in metals
• Fatigue refers to failure of structures/components that are subjected to fluctuating and cyclic loads

General Characteristics of Fatigue:

• Occurs at stresses considerably lower than ${\sigma }_y$
• Occurs after length period of repeated stress-strain cycles
• Occurs in a brittle manner, even in ductile materials
• Fatigue is catastrophic

S-N Curves

• Some materials have a fatigue limit
  • Below a set mean stress, they will never fail by fatigue
• The higher the stress amplitude, the lower the # of cycles to failure
• Fatigue strength is the level of stress that a material will survive $10^7$ fatigue cycles

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ENSC1004 - Lecture 15