Transient stress intensity factors for a cracked plane strip under anti-plane point forces

Abstract

The transient elastodynamic stress intensity factors of a semi-infinite crack in an elastic infinite strip of finite width are analyzed. The crack is subjected to a pair of suddenly applied anti-plane concentrated point loadings on its faces at a distance l away from the crack-tip. The crucial steps in the analysis are the direct application of integral transforms together with the Wiener-Hopf technique. The functions of exponential type, which are introduced by the fixed characteristic lengths in geometry and in loading, must be split explicitly into the form of product and sum, respectively, of regular functions in the Wiener-Hopf equation. Instead of performing the quotient splitting directly, however, the corresponding term is expanded first in a series. The solution is then constructed as a series accordingly. Each term in the solution series can be interpreted as the contribution of waves that have reflected at the strip surfaces different times. Exact expressions are obtained for the resulting mode-III stress intensity factors as functions of time. For illustration, the first three terms in the series for the stress intensity factor history are then computed. The results are exact for the time interval from initial loading until the first wave scattered at the crack tip is reflected three times at the strip surface and returns to the crack tip. Numerical results show that the maximum of the transient stress intensity factors of symmetric strips are larger than the ones for asymmetric strips. Moreover the smaller strip height is, the larger is the dynamic overshot on the stress intensity factors for the cases of the symmetric strips.