Fundamental solution and the weight functions of the transient problem on a semi-infinite crack propagating in a half-plane

摘要

The two-dimensional transient problem that is studied concerns asemi-infinite crack in an isotropic solid comprising an infinite strip and ahalf-plane joined together and having the same elastic constants. The crackpropagates along the interface at constant speed subject to time-independentloading. By means of the Laplace and Fourier transforms the problem isformulated as a vector Riemann-Hilbert problem. When the distance from thecrack to the boundary grows to infinity the problem admits a closed-formsolution. In the general case, a method of partial matrix factorization isproposed. In addition to factorizing some scalar functions it requires solvinga certain system of integral equations whose numerical solution is computed bythe collocation method. The stress intensity factors and the associated weightfunctions are derived. Numerical results for the weight functions are reportedand the boundary effects are discussed. The weight functions are employed todescribe propagation of a semi-infinite crack beneath the half-plane boundaryat piecewise constant speed.