Two Fracture Dynamics Problems of Fiber Reinforced Ceramics

After fiber reinforced ceramics occur a crack, its bridging fibers must engender, moreover the crack usually runs in the format of similarity. In order to analyze easily dynamic problems of fiber reinforced ceramics, bridging fiber segment is substituted for loads. When a crack moves at high speed, its fibers will break continuously. By application of the built dynamic model and the ways of self-similar functions, analytical solutions of the displacements, stresses and dynamic stress intensity factors under the action of a running increasing force Px2/t2 and a motive unit step load, respectively, can be gained, and it is also used to attain the concrete solution by means of superposition theorem.

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 Riemann-Hilbert problem and their closed solutions are obtained rather straightforward by Muskhelishvili’s measure.