On the problem of fracture mechanics of physically nonlinear materials

Abstract

For the construction of fracture mechanics of physically nonlinear materials, we join two different approaches. One of the approaches is the method of successive approximations in a small parameter characterizing a negligible deviation from the Hooke law. A solution of the proper problem of the linear theory of elasticity is considered as the zero approximation. By using the second method, the singularity of stresses in the vicinity of a cracklike defect is established in the process of solution of the elastic problem. According to the second method, the material is regarded as incompressible, deviations from a linear rheological law are considerable, and the material in the vicinity of a defect and in the whole plate obeys various power dependences of small elastic strains on the corresponding stresses. The interrelations between stress intensity factors are introduced for the first time, which are also valid for their critical values. By specific examples, we demonstrate the effects of the parameters of physical nonlinearity of materials, value of the applied load, and type of strain. In conclusion, we give a short survey of the scientific literature on the solution of problems concerning elastoplastic hardening of cracked bodies in the case of antiplane strain and their use for rupture cracks.