An analytical method for calculating notch tip stresses and strains in elastic-plastic isotropic bodies subjected to non-proportional loading sequences is presented. The key elements of the two proposed models are generalized relationships between elastic and elastic-plastic strain energy densities, and the material constitutive relations. These two models form the lower and the upper limits of the actual energy densities at the notch tip. Each method consists of a set of seven linear algebraic relations that can easily be solved for elastic-plastic strain and stress increments, knowing the hypothetical notch tip elastic stress history and the material stress-strain curve. Results of the validation show that the proposed methods compare well with finite element data and each solution set forms the limits of a band within which actual notch tip strains fall.

A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and thermodynamic^ restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.

Linear elastic solution of an axisymmetric boundary value problem is used as a basis to generate its inelastic solution. This method treats the material parameters as field variables. Their distribution is obtained as a part of solution in an iterative manner. Two schemes of updating material parameters are discussed and compared. A procedure for calculation of residual stress field is presented. Application of the method to autofrettage is presented. Residual stress calculation based on actual material curve, isotropic and kinematic hardening models, and variable Bauschinger effect factor (BEF) is carried out. It is concluded that consideration of dependency of BEF on plastic strain makes significant changes to residual hoop stress near the bore for low-level autofrettage. However, this dependency is insignificant for high-level autofrettage. Results obtained here are shown to be in good agreement with experimental and finite element results.

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