Continuum damage mechanics modelling of circumferentially notched tension bars undergoing tertiary creep with physically-based constitutive equations

Abstract

The paper reports the result of finite element computations, based on Continuum Damage Mechanics (CDM), carried out on circumferentially notched tension bars undergoing tertiary creep and failure. The material constitutive equations are physically based and generalised from thos applicable to polycrystalline nickel-based superalloys. The equations describe the stress level dependence of creep rate using a sinh function and two damage state parameters to model tertiary softening caused by: (i) grain boundary cavity nucleation and growth, and (ii) the multiplication of mobile dislocations. The paper presents values of the computed lifetimes, normalised with respect to plain bar lifetimes at the same average applied stress across the notch throat, and determines their sensitivity to a wide range of material parameters. The parameters include those which determine: the relative strength of the two damage rate mechanisms; the power v, to which the stress-state sensitivity parameter ( Σ 1/ Σ e ) is raised for damage evolution due to grain boundary cavitation; and, their dependence upon the applied stress levels. The effects of the material parameters on the predicted transition from notch strengthening to notch weakening are rationalised analytically using a stress state modified Skeletal Point stress methodology. The predictive capability of this methodology was found to be extremely good in most circumstances but broke down seriously when the uniaxial ductility was reduced to approximately 1%.