Abstract: An clastic-vise oplastic constitutive model is proposed instead of the usual elastoplastic model. It is assumed tha when crack-lip is approached the viscosity coefficient tends to zero (η=η₀r). Asymptoic analysis of the dynamic field near a propagating crack-tip is given, and the uniparameler solution is obtained. The numerical result is given for various Mach number and viscosity coefficient, Based on the asymptotic solution, a fracture criterion is proposed and the stability of crack propagation is discussed.

Key words: fractional differential equation, Caputo fractional derivative, Green function, Laplace transform, Fourier transform, sine (cosine) transform