Research On The Application Of The Mento-Carlo Simulation Based On Importance Sampling Method In The Analysis Of Probabilistic Fracture Mechanics

Reactor pressure vessels and other large equipments which usually limited by manufacturing processes, are inevitably contains defects, the safety of those structures are related to uncertainties such as initial crack location and size, the material properties and fracture toughness, etc. Probabilistic fracture mechanics (PFM) methodology by considering these uncertainties as random variables, quantitatively evaluates the structure safety in the form of failure probability. As a common numerical simulation, Monte-Carlo (MC) simulation has been increasingly applied in the field of PFM analysis, however, it was mainly limited to simple-sampling-based MC simulation for the existing research, which, in order to ensure the precision, always low in efficiency as it requires a large number of iterations. A PFM analysis program based on the MC simulation of importance sampling is developed. Using the program, the PFM analysis of the plate under combined tension and bending, combined primary stress and secondary stress are discussed.(1) Combined with probability theory, random number generator program is developed, and the random numbers generated from the program are tested. The importance sampling method, including the structure of the importance density function and the solutions for design points are studied. C languages are used for developing PFM analysis programs based on importance sampling MC simulation. Through an example analysis, it’s indicated that the optimal coefficient of variation (COV) of the importance density function equal to the COV of the probability density function can get the most accurate results.(2) The stress intensity factor and J-integral of the crack tip are estimated for the plates under combined tension and bending with different crack shapes and different crack depths, the results are compared with the finite elements results. Furthermore, the failure probability based on both linear and non-linear crack initiation criteria are calculated. Comparisons of the failure probability between different failure criteria under various load ratios are discussed. The results show that the stress intensity factor and the J-integral are reliable; under a giving failure criterion, the load level and the failure criteria have significant effect on the failure probability. However, the load ratio makes a little contribution to the failure probability for a given failure criterion. As the load ratio, λ increases, the maximum failure probability corresponding to the model appears crack depth a/t becomes smaller, but the maximum failure probability occurred in the plates with crack depth a/t=0.2～0.4.(3) The double criterions of R6are applied for calculating the failure probability of the plates under various load ratios and temperature field with different crack shapes, different crack depths under different number of iterations. Comparisons of the failure probability between the simple sampling method and the importance sampling method under different crack depths, a/t and load ratios, A are studied. The results show that the importance sampling method can effectively improve the calculating efficiency. When0<λ<1, the maximum failure probability appeared in the plates with crack depth a/t=0.3～0.4. Sensitivity analysis shows that the effective measures with improving the fracture toughness, reducing the loads and improving the level of crack detection, can enhance the reliability of structure with defects.