Elastic-viscoplastic analysis of the tip field of a mode I quasi-static propagating crack under plane stress condition

The analysis of crack tip field is more complex in creeping materials because of the influence of rate-sensitivity. An elastic-viscoplastic constitutive model is adopted and a rate-sensitive constitutive relationship is derived for elastic-perfectly-plastic materials, under the assumption that the viscosity coefficient is a power function of the rate of effective plastic strain. It is obtained through dimension match that the crack tip field possesses power singularity, and the singularity exponent is uniquely determined by the power exponent in the supposed viscosity coefficient. The governing equation of quasi-static propagating crack tip field under plane stress condition is derived, and the boundary conditions are given for mode I crack. Numerical solution of governing equation is conducted by using two-parameter shooting method in combination with possible value range for each material parameter, and variations of crack tip field characters according to each material parameter are discussed. The results indicate that the stress field at crack tip is continuous when the material complies with the perfect-plastic rule, without the irrational discontinuity line that exists in some non-viscosity solutions. The stress intensity is dominated by the material viscosity and the Poisson's ratio has no influence on tip field. Moreover, there exists no elastic unloading zone within the tip field.