Three-point bending of eccentric edge crack specimens under mixed mode loading

The occurrence of cracks in structural elements during their operation is due to the degradation of the material or the presence of hidden defects. Because of this, the structure can fail at lower external loads and before reaching its service life limit. As a rule, the failure of the structure caused by the growth of nucleated cracks develops under mixed loading. In this paper, to study such failure mechanism, a specimen of an eccentric beam of rectangular cross-section with a notch (crack) is investigated and its behavior is considered under asymmetric bend loading. Mixed strain modes I/II are obtained by shifting either the crack or the point of external load application. The finite element method was used to calculate stress intensity factors for I and II fracture modes, as well as -stresses for various geometrical parameters of the beam and loading conditions. The ratios of the crack length to the width of the beam and the length of the span to the width were varied. An analysis of known methods for calculating -stresses was carried out. The analysis showed that, in the finite element closest to the crack tip, there are strong oscillations of displacements, which are not described in the literature. Therefore, in order to find -stresses with the highest possible accuracy, it is suggested to determine them from displacements by cutting off 3-4 nodes closest to the crack tip. Experimental studies on the fracture toughness of spheroplast and polymethyl methacrylate in a mixed mode were performed. For each type of loading and beam geometry, 3-5 identical specimens were tested. The tests were carried out under static load until the complete fracture of the specimens. In all experiments, the crack initiation angle and the critical load were recorded. The direction of fracture and the critical load magnitude were predicted by applying a generalized maximum tensile stress criterion that takes into account the second (nonsingular) stress term in the Williams expansion. The results obtained demonstrate that the experimental and numerical values of critical loads are in good agreement. The error in determining the crack initiation angle does not exceed 5%.