Dynamic $T$-Stress for a Mode-I Crack in an Infinite Elastic Plane

An integral equation method is presented to determine dynamic elastic $T$-stress. Special attention is paid to a single crack in an infinite elastic plane subjected to impact loading. By using the Laplace and Fourier transforms, the associated initial-boundary value problem is transformed to a Fredholm integral equation. The dynamic $T$-stress in the Laplace transform domain can be expressed in terms of its solution. Moreover, an explicit expression for initial $T$-stress is derived in closed form. Numerically solving the resulting equation and performing the inverse Laplace transform, the transient response of $T$-stress is determined in the time space, and the response history of the $T$-stress is shown graphically. Results indicate that $T$-stress exhibits apparent transient characteristic.