Crack growth at nonuniform speed beneath the boundary of a half-plane

Abstract eng:
A semi-infinite crack propagates at sub-Rayleigh piece-wise constant speed in a homogeneous isotropic half-plane in the direction parallel to the half-plane boundary. Freund’s approximate algorithm for the problem on a semi-infinite crack propagating in the whole plane is generalized for the half-plane case. The implementation of the method requires successive solution of two coupled Volterra convolution equations admitting a closed-form solution. The kernels of the system are the four weight functions of the transient problem on a semiinfinite crack propagating at constant speed parallel to the boundary and subjected to certain loading. By the Fourier and Laplace transforms the model problem reduces to an order-2 vector Riemann-Hilbert problem. A method of partial factorization and convolution integral equations for its numerical solution is proposed. The dynamic Griffith criterion for the determination of the piece-wise speed is applied.

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