Skeletal point stresses in circumferentially notched tension bars undergoing tertiary creep modelled with physically based constitutive equations

Constitutive equations are proposed in which the stress level dependence of creep rate is described by a sinh function, and two damage state-parameters are used to model the tertiary softening caused by: (i) grain boundary cavity nucleation and growth, and (ii) the multiplication of mobile dislocations. These constitutive equations are applicable to polycrystalline nickel-base superalloys and are used together with a continuum damage mechanics finite element based solver, DAMAGE XX, to study the behaviour of axisymmetrically notched tension bars and simulate the complex stress states that may be encountered at geometrical stress-raisers in high temperature components. Numerical studies of such bars show that their behaviour can be accurately represented in terms of a ‘skeletal effective stress’ located at a point within the notch throat, and the stress state at this point. It is shown that this conclusion is valid not only for those materials that fail by grain boundary cavitation alone, but also for materials such as superalloys where grain boundary cavitation is accompanied by mobile dislocation multiplication.