A variable material property approach for elastic-plastic analysis of proportional and nonproportional loading

A linear elastic solution of a boundary value problem is used as the basis to generate the corresponding inelastic solution. This method treats the material parameters as field variables, and their distribution is obtained as part of the solution in an iterative manner. Five different schemes to update these material parameters are discussed and compared. A procedure for the calculation of the residual stress field is presented.;In this context, a general axisymmetric method of elastic-plastic analysis is proposed. Application of this method to the residual stress prediction for an autofrettaged cylinder and a cold worked fastener hole is presented. Lame's linear-elastic solution is used in these applications. Residual stress calculations based on the actual material curve, isotropic or kinematic hardening models, and a variable Bauschinger effect factor (BEF) is carried out. It is concluded that the consideration of the dependency of the BEF on plastic strain makes significant changes to the 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 experiment, and finite element results.;A total deformation theory capable of analyzing a sequence of linear nonproportional loading is proposed. Each linear loading path is defined with reference to its previous loading path, analogous to proportional loading. The application of the proposed formulation to tension-torsion loading of thin tubes and pressure-torsion loading of thick-walled cylinders is carried out. It is shown that for stress controlled processes, the proposed method gives the same plastic strain field as does incremental plasticity. For load controlled processes, where stresses are not known a priori, a method to estimate the plastic strain for linear hardening materials is proposed. This method calculates the necessary stress fields using conventional deformation plasticity. These stresses are then used in the proposed total deformation formulation to predict plastic strains. The plastic strain field resulting from this method is compared with finite element results using incremental plasticity. The results are in very good agreement. The proposed method significantly reduces computation time.