Dislocation distribution function of two fracture dynamics problems concerning aluminum alloys

By the approaches of the theory of complex functions, dynamic propagation problems on the surfaces of mode I crack subjected to unit-step loads and instantaneous impulse loads located at the origin of the coordinates were studied for Aluminum alloys, respectively. Analytical solutions to stresses, displacements, dynamic stress intensity factors and dislocation distribution functions are gained by the methods of self-similar functions. The problems considered can be very facilely transformed into Riernann-Hilbert problem and their closed solutions are obtained rather straightforward by Muskhelishvili's measure.