Stress triaxiality and Lode angle along surfaces of elastoplastic structures

Abstract

a b s t r a c tExpressions for the stress triaxiality and the Lode angle along surfaces of elastoplastic structures are established in case of monotonic loading. The stress triaxiality is shown to be governed by the accumulated plastic strain when traction free boundary condition is considered. The exact expressions obtained are generalized to any loading thanks to the proposal of a multiaxiality rule or heuristics whose two parameters are determined from elastic computations of the structure considered: a first one with the elastic properties of the material, a second one quasi-incompressible. The multiaxiality rule proposed can then deal with both plane strain and plane stress conditions. The stress triaxiality at the surface is shown related to the Lode angle. The corresponding expressions are validated on different structures and loadings. Finally, two applications are presented: the enhancement of energetic methods for plasticity post-processing and the enhancement of homogenization localization laws.

Rapid method for low cycle fatigue properties: thickness effect on the fatigue crack initiation life of welded joints

“…Knowing stress and strain histories is necessary to determine the fatigue crack initiation life of welded joints (especially at the critical points of the structure). To avoid time‐consuming nonlinear FEA, simplified estimation methods of the elastic–plastic strain and stress are generally used . Nevertheless, these methods lack accuracy.…”

“…To avoid time-consuming nonlinear FEA, simplified estimation methods of the elastic-plastic strain and stress are generally used. [19][20][21][22] Nevertheless, these methods lack accuracy. Recently, a new approach inspired by constraint operatorbased approaches was developed by Herbland.…”

“…Fatigue analysis requires the calculation of elastic–plastic stresses and strains at the critical points of the structure (points of initiation for the fatigue crack). To avoid time‐consuming nonlinear finite element computations, simplified estimation methods of the elastic–plastic strain and stress (such as the Neuber rule, Molski‐Glinka, Chaboche, Darlet or Ye) are used.…”

A modified Neuber’s rule for welded cruciform joints under low-cycle actions

“…Similar to other energy-based indicators, [32][33][34][35][36][37][38] the new energy-based indicator in equation (6) provides an alternative definition of fatigue driving force for welded plate connections. The energy-based fatigue driving force in equation (6) becomes tractable if Neuber's rule predicts closely the evolution of notch stresses and strains at the weld toe with increasing loads.…”

“…Over the past few decades, different methods [2][3][4][5][6] have evolved to estimate the inelastic stress and strain at the weld toe, in lieu of the time-consuming finite element (FE) analysis. Neuber's rule 4 (NR) represents one of the most widely used approaches, which articulates that the geometrical mean of the effective stress and strain concentration factors is equal to the elastic theoretical stress concentration factor.…”