The stress-strain state and failure of structural elements with sharp stress concentrators under bending

The paper considers two approaches to assessing the strength of constructions’ elements made of brittle material with sharp stress concentrators under the three-point bending: using a non-local theory of strength (in the top of the sharp notch the stresses are averaged on some basis) and a linear fracture mechanics (the stress intensity factors and the degree of singularity are determined). The finite element method was widely used (ANSYS Workbench, 2D model). These two approaches are connected by the analysis of the stress state at the sharp v-shaped notches with the corresponding approximations of the stress field, which allowed to find the correct values of the stress intensity factors and degrees of singularity on the basis of the optimization procedures. There were conducted the experimental studies of the strength of prismatic samples made of polymethylmethacrylate (PMMA) with a v-shaped notch (the two-edge angles of 25, 90 and 120°) in static three-point bending. In the finite element calculations using a nonlocal strength criterion it is obtained, that a sharp notch with the two-edge angle up to 90° leads to an increase in load of destruction for 15-20 % only compared with the crack-like cut (the angle of 25°) and agrees well with the experimental data. The increase of the two-edge angle of a sharp notch from 25 to 120° leads to increased loads of destruction in 1,5...2 times. There was studied the morphology of fractured surfaces, it is shown that the shallow cuts (up to 1.5 mm) when bending have a grooved fracture surface (a high velocity, periodic picture of cracks’ moving), while the deeper cuts (2.5...5 mm) are characterized by a slow crack propagation and a smooth fracture surface. Information about step of grooves was necessary to establish the size of averaging zone in nonlocal failure criterion.