Estimation of the Strength of Plates with Cracks Based on the Maximum Stress Criterion in a Scale-Dependent Generalized Theory of Elasticity

Abstract

The problem of the strength of a plate made of a brittle material with through mode I cracks is discussed. In contrast to the approach based on the singular solution of the classical theory of elasticity for a plane with a crack and on linear fracture mechanics, we propose to use nonsingular solutions obtained within the generalized elasticity theory and, as a result, to implement a method, conventional for the strength estimation of solids with stress concentration, based on the maximum stress criterion. The maximum stress is determined from a nonsingular solution of the generalized elasticity equations for a plane with a crack. The reported experimental results for plates with cracks under tension and bending confirm the solution obtained by the proposed method and allow it to be compared with a solution based on linear fracture mechanics. In fact, a new concept of fracture mechanics is put forward, which is free of singular solutions and allows the problems of fracture mechanics to be treated as problems of stress concentration. Comparison of the obtained analytical solutions with the experimental data has shown that the scale factor of generalized elasticity determines the critical state in fracture mechanics with no less accuracy than the critical stress intensity factor and therefore can be used as a fracture criterion. The resulting explicit nonsingular solutions allow the prediction of the stress concentration caused by a crack.