An Initial Value Problem of Crack Propagation in Anti-Plane Strain.
WATERVLIET ARSENAL N Y
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A problem of Mode III crack propagation is considered in which the crack tip speed is an arbitrary function of time. For purposes of comparison and elucidation, the solution is obtained by two independent methods. By one method the problem is reduced to a standard Abel integral equation through the use of integral transforms by the alternative method the problem is formulated as a Riemann-Hilbert problem through the use of complex variables. It is found that the transient component of the problem can be constructed from an equivalent static problem by properly adjusting the crack tip position. Author