Dislocation Distribution Functions of the Edges of Mode I Crack under Several Boundary Conditions

Abstract

Dislocation distribution functions of mode I dynamic crack subjected to two loads were studied by the methods of the theory of complex variable functions. By this way, the problems researched can be translated into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation. The analytical solutions attained relate to the crack propagation velocity and time, but the solutions have nothing to the other parameters. In terms of the relationship between dislocation distribution functions and displacements, analytical solutions of dislocation distribution functions were gained, and variation rules of dislocation distribution functions were depicted.