ПРО ВЗАЄМОДІЮ ДВОХ ТРІЩИН НА МЕЖІ ПОДІЛУ МАТЕРІАЛІВ

Abstract

Plane deformation problem of the interaction of two collinear cracks between isotropic heterogeneous half-spaces loaded at infinity by normal and tangential stresses is considered. To find the solution, the representation of stresses and displacements through a function that is analytical in the entire complex plane except of the crack regions is used. With the help of these representations, the problem is reduced to the Riemann-Hilbert problem, for the specified piecewise analytical function with jumps along the segments of cracks. An analytical representation of the solution with unknown coefficients, which is determined from the conditions at infinity and the conditions of unambiguous displacements when traversing the contours of cracks, is written. The implementation of the latter leads to the need of calculatson the integrals from the functions with oscillating root singularities. Based on the obtained solution, analytical expressions are written for stresses at different segments outside the crack and jumps of displacements on the cracks. The behavior of stresses and derivatives of the displacements jumps at different parts of the material interface are established. Complex coefficients of stress intensity and energy release rate near the vertices of the right crack are found. The dependences of these factors on the mechanical characteristics of materials, size and mutual location of cracks, as well as on the intensities of the remote normal and tangential stresses are analyzed. The results are presented in the form of tables and graphs. In particular, an increase of the energy release rate for the crack tip when another crack approaches is shown. Graphs of changes in the jump of displacements for different ratios of modulus of elasticity of the upper and lower materials and different ratios of intensities of external normal and tangential stresses are also shown. It was found, in particular, that with a significant difference in the modulus of elasticity and with a significant shear stress field, the interpenetration of materials occurring because of the oscillating singularity near the crack vertices becomes noticeable.