The stress concentration around a semi-infinite cylindrical crack during the shock loading of an elastic medium by a centre of rotation

The problem of the concentration of elastic stresses in an unbounded elasti c medium containing a semi-infinite cylindrical crack is solved using the m ethod of discontinuous solutions. The method enables the problem to be redu ced to a one-dimensional integrodifferential equation in the unknown jump i n displacements in Laplace transform space. The solution of the equation ob tained is based on the combined use of orthogonal functions and time sampli ng of the equation, which leads to an infinite system of linear algebraic e quations. As a result, a wave field disturbed by a crack is constructed, an d a formula is obtained for calculating the stress intensity factor. The wa ve field is analysed numerically, and a graph of the stress intensity facto r as a function of time is plotted. (C) 2001 Elsevier Science Ltd. All righ ts reserved.