Abstract
An expression is derived for the probability of crack growth in a material with penny cracks of random size and orientation. It is assumed that crack growth occurs when the maximum local Mode I stress intensity factor, Kll, exceeds Klc, the criterion is generalized for the three‐dimensional problem. The location along the crack front and the magnitude of Kll are determined conditional on a penny crack of prescribed size and orientation. The probability distribution function of Kll is then computed using a derived probability density function for the crack size. The probability of crack growth is expressed as a function of four dimensionless parameters: The expected number of cracks in a volume; the expected value of the Mode I stress intensity factor for a crack normal to the direction of stress, divided by Klc, the probability density function of a normalized crack size; and the Poisson ratio. A study that quantifies the effects of the four dimensionless parameters is presented.
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