Mathematical model of brittle fracture of a cracked part
The problem of prediction of subzero operability of steel structures and protection against brittle fracture is solved by purely empirical methods based on impact bending test results or criteria of fracture mechanics. Force, energy and deformation methods of fracture mechanics are employed for a comparative assessment of crack resistance in materials of critical structures operating under severe conditions. However, the method is difficult to use in designing welded machines and constructions which have a variety of shapes and affected by welding factors and loading conditions. This gave rise to a number of projects on physical methods of brittle fracture prediction. In this work, we address a method in which the known criterion of brittle fracture is applied to a small material volume ahead of the crack tip (fracture process zone). For this to do, a mathematical model of loading of the fracture process zone in an elastoplastic part is developed. The method allows for the assessment of the influence of mechanical characteristics of the material and operating temperature on the resistance of the part to brittle fracture. To determine design coefficients and to verify functional dependencies, we use the literature experimental values of the critical stress intensity factor derived at subzero temperatures. The comparative analysis of the experimental and calculated data shows that the dependences calculated by the proposed method are consistent with the test results. This work confirms the applicability of physical models of brittle fracture, and the used mechanical characteristics of steel are more acceptable for engineers.