ИСТИНА

The influence of the specific features of the behavior of heterogeneous materials on asymptotic solutions near macro-cracks in a hardening material is studied. The corresponding constitutive relations are used that describe different types of physical nonlinearities and the observed in experiments phenomena. The case of plane stress state is considered. The calculations are performed with the use of experimental data obtained for cast-iron and structural graphite. An approximation for material functions is suggested. This approximation allows one to describe the experimental strain diagrams with a reasonable degree of accuracy. For specific material functions, the distributions of stresses, strains, and displacements near the crack tip are obtained. These distributions are compared with those following from the solution of a similar problem for a plastically incompressible medium. The conditions of the crack growth initiation are determined with the use of the invariant integral. It is shown that the amplitude of singularity for the material with stress-state dependent properties is substantially lower than the corresponding value obtained for the incompressible material.