A Fracture Dynamics Model for Fiber Reinforced Ceramics
After fiber reinforced ceramics occur a crack, their fibrous position form bridging fibers, moreover a crack usually extends in the modality of similarity. In order to analyze facilely problems of fiber reinforced ceramics, bridging fiber segment is substituted for loads. A dynamic model of crack propagation is built and its fracture dynamics problems are researched by the approaches of self-similar functions. When a crack propagates at high speed its fiber continues to break. By application of the theory of complex functions, the problems dealt with can be easily translated into Remann-Hilbert problem. Using the built dynamic model and the ways of self-similar functions, analytical study of the displacements, stresses, dynamic stress intensity factor and bridging fibrous fracture velocity α under the action of a running constant force P and an running increasing load Pt, respectively, can be attained, and it is also utilized to obtain the concrete solution of the model by means of superposition theorem.
Wei Pan and Jianghong Gong
N. C. Lü et al., "A Fracture Dynamics Model for Fiber Reinforced Ceramics", Advanced Materials Research, Vols. 105-106, pp. 34-37, 2010