LAUSR

Abstract In this article, for the first time, probabilistic fracture of cracked nano-graphene sheets is investigated using stochastic fracture analysis and scaled boundary finite element method. Probabilities of fracture as well as the first four moments of stresses including average and variances are calculated for all bonds at different crack angles, assuming normalized crack length, failure stress and applied traction as uncertain variables. The results show that the third moment of stresses is zero which proves that input stochastic parameters are normal ones. Maximum probable bonds in fracture are the crack tip ones. The fracture probabilities in a nano-graphene sheet having a central crack decrease as the directions of applied traction and crack change from normal state to parallel one. In addition, the sensitivity of probabilistic fracture to the normalized crack length was perused at different crack angles which show that the maximum sensitivity of fracture probability is in central crack θ= 0° at the crack normalized length 0.3 to 0.4. The sensitivity analysis of fracture probability to the applied traction for each crack angle is done, as well. Comparing the results of stochastic fracture analysis with Monte Carlo simulation showed good agreement between two methods which is the validity evidence of the presented method.