Probabilistic Analysis of Fatigue Life
by Estimation of Distribution of Crack Length
using Second-Order Third-Moment Method
Ki Seok Kim
This paper presents a new secant approach to estimate the path of growth of mixed-mode fatigue crack and proposes the second-order third-moment method to predict the probabilistic distribution of fatigue life.
Lower limit of macro-crack length, which is applicable to linear elastic fracture mechanics, is defined. Fatigue life of micro-crack is approximated with a constant growth rate corresponding to the lower limit of macro-crack length. The dual boundary element method is employed for the analysis of macro-crack. The mixed-mode stress intensity factors are evaluated by displacement extrapolation method. Paris-Erdogan law and maximum circumferential stress criterion are adopted to determine the crack growth rate and tangent direction, respectively. Integral equation of Paris-Erdogan law is discretized for a given increment of loading cycle. In each loading step, crack increment is assumed as a parabola, but discretized as a straight line with secant direction. The parabola is updated iteratively until the tangent of the assumed parabola converges to the growth direction at the new crack tip.
The probabilistic distribution of crack length is approximated as three-parameter lognormal by the second-order third-moment method incorporated with the proposed incremental formulation. Initial crack length and the coefficient of Paris-Erdogan equation are considered as random variables. For each loading step, the mean, standard deviation and skewness of crack length are approximated by those of previous step. The distribution of fatigue life is estimated from material properties and the S-N curve is derived numerically by the proposed method. The fatigue life for a given probability of failure is evaluated from the distribution of crack length. Proposed method produces a good approximation of the distribution of crack length compared with the results of the Monte Carlo simulation. In the evaluation of probability of failure, proposed method needs much less computational cost than the first-order reliability method.
Fatigue Crack, Fatigue Life, S-N Curve, Stress Intensity Factor, Dual Boundary Element Method, Second-Order Third-Moment Method, Probability of Failure