A dynamic piecewise-exponential model for transient crack problems of functionally graded materials with arbitrary mechanical properties

A dynamic piecewise-exponential model (DPE model) is developed to investigate the transient fracture problems of functionally graded materials (FGMs) with arbitrary mechanical properties. In this model, a new approximate method for the graded modulus and mass density is presented; therefore, the problem can be solved analytically. The influences of graded ratios and variation forms of the modulus and mass density on the dynamic stress intensity factors (DSIFs) are investigated, respectively. It is found that the ratio and variation form of the modulus have pronounced influences on the peak value, steady value and overshoot characteristics of the DSIFs, while those of the mass density have relatively slight influences.