Fracture of brittle beams under antisymmetrical four-point bending - Kurguzov, Vladimir Dmitriyevich; Kuznetsov, Denis Aleksandrovich (Computational Continuum Mechanics, 2025)
The nucleation of cracks in structural elements during their service life is due to the degradation of the material or the presence of hidden defects. The structure therefore loses its original load-bearing capacity and fails under significantly lower external loads. As a rule, the fracture of structures due to crack growth occurs under mixed loading. In this paper, an eccentric beam of rectangular cross-section with an edge crack subjected to antisymmetric four-point loading is considered. By changing the position of the crack relative to the center of the beam, it is possible to obtain the entire range of mixed fracture modes: I+II, pure I and pure II modes. Using the finite element method, stress intensity coefficients for modes I and II of failure, as well as T-stresses, were obtained for different geometric parameters of the beam and different loading conditions. The length of the crack, its position relative to the beam center, and the length of the short span were varied. The methods commonly used for calculating T-stresses were analyzed. In the element closest to the crack tip, strong displacement oscillations, not mentioned in the literature, are observed, therefore to determine T-stresses with the highest possible accuracy it is suggested to calculate them from displacements, cutting off the 3-4 nodes closest to the crack tip. Experimental studies of the fracture toughness of ebonite in a mixed mode were carried out. For each type of loading and geometry, 3-5 identical specimens were tested. The tests were carried out under static load until the specimens were completely destroyed. In all experiments, the crack initiation angle and critical load were recorded. Six failure criteria were used to predict both failure direction and critical load: the generalized maximum tangential stress criterion, the extended maximum tangential strain criterion, the generalized strain energy density criterion, the generalized maximum averaged stress criterion, the maximum elastic energy release rate criterion and the generalized maximum elastic energy release rate criterion. The results obtained demonstrate good agreement between the experimental values of critical loads and the numerical calculations. The error in determining the crack initiation angle does not exceed 5%. Considering that the experimental results agree with the predictions of failure criteria for the beam subjected to antisymmetric four-point bend loading, this type of a beam specimen can be used to study mixed-type fracture in the elements manufactured from engineering materials, such as, for example, plexiglass, ebonite, and getinax.
Keywords: fracture mechanics; beam specimen; mixed mode loading; four-point bend; T-stress; finite element analysis