Elastic-plastic stress-strain calculation in notched bodies subjected to non-proportional loading

Abstract

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 Modified Method for Calculating Notch-Root Stresses and Strains under Multiaxial Loading

“…Based on the assumption that the strain energy density distribution in the plastic zone ahead of a notch-root is the same as that determined on the basis of the pure elastic stress-strain solution, Mücke and Bernhardi [20], Molski and Glinka [21], and Singh et al [22] developed a similar local elastic-plastic calculation method called the equivalent strain energy density method. In the case of monotonic loading and uniaxial stress condition at the notch-root, ESED method can be expressed in the form …”

Three-dimensional stress fields near notches and cracks

“…Since the theoretical 2D solutions for the stress concentrations regarding holes in infinite bodies have been obtained based on the classical complex variables (Muskhelishvili 1963;Savin 1961), many efforts have been made to achieve planar solutions for holes and notches in infinite plates (Sadowsky and Sternberg 1947;Shin et al 1994;Moftahar et al 1995;Singh et al 1996;Wang et al 1999). However, these planar solutions can not describe the effects of thickness and material properties on the stress fields.…”

Nonlinear energy-based relations and numerical procedure for multiaxial local analysis

“…To make fatigue life prediction methods more conducive to average design environments, great research efforts have been directed to the development of simplified analytical techniques that are more computationally efficient. For multiaxial non-proportional loading, some of the existing models attempt to either incorporate the effect of geometric discontinuity into the constitutive relations, as in Barkey (1993), Barkey et al (1994), 0020 Lee et al (1995), and Gu and Lee (1997), or reformulate uniaxial approximation methods in incremental forms, as in Singh et al (1996). However, it should be noted that the majority of the aforementioned efforts have been directed to monolithic materials.…”