Stress Analysis for Perforated Cylinders with Combined Use of the Boundary Element Method and Nonlocal Fracture Criteria

Abstract

When using local fracture criteria, it is usually assumed that a fracture begins when the maximum equivalent stress reaches the limit value at least at one point of the body. However, under conditions of an inhomogeneous stress state, it is suitable to use nonlocal failure criteria which take into account the nonuniformity of the stress distribution and yield limit load estimates that are closer to the experimental data. An algorithm of the joint use of the boundary element method (in the version of the fictitious stress method) and gradient fracture criterion for calculations of the strength of plane construction elements is composed. The computations are carried out using a program written in FORTRAN. Results on the limit loading obtained numerically and analytically based on the local criterion of maximum stress and nonlocal fracture criteria (gradient criterion and Nuismer criterion) are compared both among themselves and with the experimental data on the failure of ebonite specimens. A brittle fracture of ebonite cylinders with a hole under diametric compression is studied experimentally. It is shown that nonlocal criteria lead to limit loading values which are closer to the experimental ones than the local criterion. The estimates obtained by the local maximum stress criterion are significantly less than the experimental ones. The estimates found for limit loads by the Nuismer criterion are greater than similar ones determined by the local criterion; nevertheless, they are less than the experimental ones, while the limit load values according to the gradient criterion are closest to the experimental values. Using the nonlocal fracture criteria in designing constructions with stress concentrators will allow us to increase the design values of the limit loads.