Probabilistic prediction of multiple fracture under service conditions

Abstract The probability of fracture initiation, propagation, and arrest is one of the important problems facing designers, analysts, and operators of modern structures including nuclear reactors. The question of fracture requires special considerations which include the random nature of the loading and the statistical nature of the material's response to fracture under the imposed service loads. In most structural applications it is essential to know not only if and when fracture will occur under normal and off-normal operating conditions, but also to have some knowledge of the fracture propagation configurations and their resulting influence on the integrity of the structure. In this paper we address the problem of multiple fracture propagation configurations in structures under service conditions. This is accomplished by introducing a generalized energy criterion for multiple brittle fracture in nonhomogeneous and anisotropic materials. The fracture criterion is expressed in terms of the so-called Hartz function H which measures the difference between the total instantaneous strain energy release rate G T and the rate at which energy is required for the formation of new fracture surfaces R T . Strain energy release rates are computed for a variety of symmetric as well as asymmetric fracture propagation configurations from finite element solutions of incrementally related boundary value problems. These solutions yield a deterministic influence parameter α which is used to relate the applied loading to the probabilistic expression for the strain energy release rate. A similar treatment is given to the function R T for which the influence parameter β must be determined experimentally. The parameters, α and β, depend upon the relative locations, sizes and orientations of the primary and secondary cracks as well as flaws, and secondary imperfections present in the material. In addition the parameter β depends upon the relative values of the specific surface energy associated with the possible primary and secondary fracture paths. This is important for anisotropic materials such as ceramics mixed-oxide fuels and concrete, and for materials experiencing stress-corrosion fracture, where the energies associated with intergranular and transgranular fracture, for example, may differ significantly. From the probabilistic expressions for G T and R T , the Hartz function is determined as a random variable h which describes the multiple fracture process. The formulations developed in this presentation are applied to a single edge notched panel experiencing multiple fracture under assumed random loadings. Some interesting symmetric as well as asymmetric fracture configurations are studied and the results are related to reported experimental observations. The approach presented here may have applications in the areas of fatigue crack propagation, stress corrosion cracking, and fail-safe design optimization. Current studies are aimed at simulating the influence of grain structure anisotropy, intergranular corrosive attack, and creep deformation on multiple fracture in polycrystalline materials.