Mathematical Model of Brittle Fracture of a Cracked Part

The service life and brittle fracture of steel structures at subzero temperatures is predicted with purely empirical methods based on impact bending test results or fracture mechanics criteria. Force, energy and deformation methods of fracture mechanics are used for a comparative assessment of fracture toughness in safety-related structures operating under harsh environment conditions. However, such methods are not efficient enough for the design of welded engineering components and structures due to their complex shapes, welding factors, and loading conditions. This has led to the development of specific physical methods for brittle fracture prediction. This paper proposes a method based on the application of the known brittle fracture criterion to a small material volume ahead of the crack tip (pre-fracture zone). A mathematical model was developed to describe the loading of the pre-fracture zone in a part made of an elastic-plastic material. The effect of mechanical characteristics of the material and service temperature on the brittle fracture resistance of the part was evaluated using the proposed method. The design coefficients were calculated and the functional dependencies were verified using the literature experimental data on the critical stress intensity factors obtained at subzero temperatures. A comparative analysis of the experimental and numerical results showed that the curves calculated by the proposed method are consistent with the test results. This work confirms the applicability of physical models of brittle fracture which use the mechanical characteristics of steel more suitable for engineering applications.