A method for calculating elasto-plastic notch tip strains and stresses in bodies subjected to multiaxial loading has been presented. The method has been formulated in terms of strain energy density relationships. Two approximate formulae are derived based on the analysis of strain energy density in the notch tip region. The two formulae represent the lower and upper limits of the band within which the actual elasto-plastic notch tip strains can be found. All necessary relationships are derived for a general multiaxial stress state. The calculated notch tip strain and stress components are compared with experimental and finite element data obtained for a variety of loading conditions and materials. This method may be particularly useful for stress/strain analysis of notched components subjected to lengthy multiaxial cyclic loading histories. Nomenclature E ESED F H Kt IG K~ Mb nl~ n2 P R Ri Ro t T W W ~ -modulus of elasticity -equivalent strain energy density -axial load -elasto-plastic modulus -theoretical elastic stress concentration factor -strain concentration factor -stress concentration factor -bending moment -exponents of power law stress-strain curve -pressure -radius of a cylindrical specimen -internal radius of a pipe -outside radius of a pipe -deviatoric stresses -equivalent nominal stress -wall thickness -torque -strain energy density -strain energy density at the notch tip obtained from linear elastic solution * On leave from Warsaw University of Technology.358
A method for predicting time-dependent stresses and strains in the case of localized creep has been developed. This method is based on strain energy density considerations and is an extension of the method previously developed by the authors for localized time-independent plasticity problems. The solution method has been derived in a general form so that it may be applied to multiaxial notch tip stress states. This technique has been used to predict creep effects and the associated stress redistribution at the root of a notched zirconium alloy pipe and in a thin notched plate made of aluminum, both subjected to thermal creep. The predictions have been compared with the finite element data and good agreement obtained. The computational time for calculating the notch tip stresses and strains was much shorter than that required for the finite element analysis. The method can be particularly useful for the analysis of creep effects in the case of cyclic loading with hold times where the FEM calculations are very time consuming.
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