Proposal of a New Probabilistic Model for Random Fatigue Crack Growth Using a Noise of Poisson Type
Hiroaki TANAKA-KANEKIYO
Abstract:A probabilistic model describing random fatigue crack growth is newly proposed, in which a stochastic differential equation driven by a temporally inhomogeneous compound Poisson process is applied. The new model has several outstanding features such as (i) we can perfectly remove the probability that a crack length decreases in the process of fatigue failure and (ii) an analytical approach is possible for obtaining probabilistic properties associated with the crack growth process. The former feature gives a quite effective solution over a critical disadvantage point inherent in the so-called diffusive model which has been widely used for describing the random fatigue crack growth. First, the well-known Paris-Erdogan law is extended to a stochastic differential equation by introducing a temporally inhomogeneous compound Poisson process expressing the random behavior of crack propagation resistance. Next, its solution process is analytically derived by the use of the generalized It?o formula and probabilistic properties associated with the random fatigue crack growth process are also clarified. Finally, some numerical examples are given so that we can quantitatively clarify sample behavior of the crack growth and temporal variation of a probability distribution of a crack length. Key Words:Fatigue crack, Random crack growth, Probabilistic model, L'evy process, Compound poisson process, Stochastic differential equation