Strength calculations of perforated cylinders with combined use of the boundary element method and non-local fracture criteria

Abstract

When using local fracture criteria, it is usually assumed that fracture begins when the maximum equivalent stress reaches the limit value at least at one point in the body. But under conditions of an inhomogeneous stressed state, it is advisable to use nonlocal failure criteria, which take into account the uneven distribution of stresses and give estimates of ultimate loads that are closer to the experimental data. A numerical algorithm for the strength of plane construction elements is constructed using the gradient fracture criterion and the boundary element method (the fictitious stress method). Numerical calculation was carried out with the help of a program written in Fortran. Calculation results obtained using the criterion of maximum stress, gradient fracture criterion; point stress criteria are compared both among themselves and with the experimental data. Results of brittle fracture experiments on hard rubber cylinders with a hole are presented. It is shown that the values of limit loads provided by nonlocal criteria are closer to the experimental values than given by local criterion. The estimates obtained with the help of the local criterion for maximum stresses are substantially lower than the experimental ones. The Nuismer criterion gives higher estimates of ultimate loads compared to the local criterion, but these estimates are still less than the experimental values, while the values of the ultimate load by the gradient criterion are the closest to the experimental results. The use of nonlocal failure criteria in the design of structures with stress concentrators will increase the estimates of ultimate loads.