Analytical investigation of crack tip fields in viscoplastic materials

Abstract

A macroscopic stationary crack in viscoplastic materials is considered under mode I creep loading conditions. Typical representations of constitutive laws with internal variables. (back stress) which can be derived from a scalar potential function are used to model the inelastic material behaviour. It is shown that, in the limit of high stresses, the constitutive equation adopt the form of Norton's law thus leading to a singular field of the HRR-type at the crack tip, if the material functions for the constitutive equations are represented by power laws. The amplitude of the crack tip field can be evaluated using a crack tip integral. It reduces to the well-known C ^* expression at the crack tip and includes additonal domain integrals which ensure the independence of the choice of the integration contour and the area enclosed around the crack tip in regions where primary creep and linear eleastic effects cannot be neglected. The paper concentrates on results characterising the crack tip fields which can be derived analytically. Numerical aspects focused upon the right modelling of the crack tip zone, the range of validity of the crack tip field and the calculation of the crack tip parameter and the creep zones will be discussed in a subsequent paper.