Monte Carlo Method For Solving The Discussion Of The Stress Intensity Factor

Since last century, there is a rule in many accidents. When plastic materials fracture, stress is very low. Based on the analyses of crack extension mechanism for brittle fracture process, we will find that the cause is that the materials exist crack. Fracture mechanics which study crack appear.In the project application of fracture mechanics, stress intensity factor is a important mechanics parameter. It can assess safe, analyze failure reason, measure fracture toughness. So stress intensity factor is a importance parameter in the fracture mechanicsIn the paper, the postulate of Monte-Carlo is introduced. The stress function is solved. The stress function is used of calculating stress intensity factor in the paper. The method is proved efficacious by examples.First, the basic knowledge of Monte-Carlo method is introduced, such as, calculating process, the constringency and error, producing random number, sampling random variable. According to this knowledge, the excellence and disadvantage of Monte-Carlo method are discussed. In the paper, the examples of Monte-Carlo method are introduced; we will find that the problems which have three dimensional models and complex geometry limit can be solved easily by Monte-Carlo method. The program is easy. It costs less time.Second, based on the analyses of Monte-Carlo method, the solution of positive definite symmetrical matrix and differential equation are introduced. It is very difficulty to confirm the probability model. So confirming the probability is important. Some numerical experiments are introduced to indicate the process of the Monte-Carlo methodThird, according to the inherent relation between the crack shape and the stress intensity factor distribution along the crack front, the stress intensity factor is solved by Monte-Carlo method. Some numerical experiments are introduced to indicate Monte Carlo method. Comparing to other numerical method, Monte-Carlo method is convenient. And if the Monte Carlo method is combined with other numerical method, it will be more efficacious.Last, Monte Carlo method may apply to 3-D problem. The method of solving 3-D problem is the same as the method of solving 2-D problem.