Pseudo Stress and Pseudo Strain Based Approaches to Multiaxial Notch Analysis

Abstract

The analysis of notch stresses and strains is one of the key parts of fatigue life prediction of components and structures, In this paper two related approaches are introduced, covering the whole field from uniaxial to multiaxial non-proportional loading. The pseudo stress at the notch root computed by theory of elasticity is introduced as the governing variable for elastic-plastic notch analysis. Although the pseudo stress is just a specially defined nominal stress, it eases notch analysis in comparison to using arbitrarily definable nominal stresses, especially for non-proportional multiaxial loading. Additionally a pseudo strain based approach is introduced and compared to the stress approach. Both proportional and non-proportional loading are discussed, and compared with the approaches of other workers. NOMENCLATURE c = dimensional proportionality constant relating local structural response to loading, e = subscript denoting the elastic part of a quantity E = Young's modulus f("u), 3" = load-notch strain curves f o =criterion for the onset of yielding similar to K , S, ' u = fictitious local strain and local stress computed by theory of elasticity F,, Go, If,, = coefficients of Hill's yield criterion g(u) = stress-strain curve H' =work hardening modulus of an equivalent stress vs. equivalent plastic strain curve K , = (nondimensional) stress concentration factor Lo =load at the start of yielding Lp = fully plastic limit load (elastic-perfectly plastic material) m = counter for different load components Mo, No, Oo = coefficients of Hill's yield criterion n = number of different load components p = subscript denoting the plastic part of a quantity q = subscript denoting an equivalent quantity, e.g. von Mises equivalent stress s = deviatoric part of a stress tensor sij = uij -8 S = nominal stress L = load (force, moment, displacement, etc.) x, y, z = local Cartesian coordinates X, Y, Z =global Cartesian coordinates (for nominal stresses) y = shear strain E =local (notch) strain v = Poisson's ratio u = local (notch) stress a, = yield stress d = hydrostatic pressure d = $ua T = shear stress * Formerly at Technische Hochschule Darmstadt Fachgebiet Werkstoffmechanik. 98 1 982 V. B. KOTTGEN et al.

Optimal design of machine components using notch correction and plasticity models

“…Elastic notch root strains are related to nominal loading through the use of stress concentration factors, and material work-hardening behaviour is accounted for by using the Mró z hardening rule in nominal stress space. Kö ttgen et al [45] proposed two approaches, covering the whole field from uniaxial to multiaxial non-proportional loading. The pseudo-stress at the notch root computed by theory of elasticity is introduced as the governing variable for elasticplastic analysis.…”

“…For details the reader should consult the Refs. [44,45]. Nie and Luan [46] have used the local stress-strain analysis based on Neuber rule and modified Ramberg-Osgood equation for the prediction of fatigue crack initiation life under biaxial stress (plane stress state).…”

Notes on Lipschitz estimates for the stop and play operator in plasticity

“…Here, X is allowed to be either algorithms that correct the elastic stress tensor e σ (t) (from the linear elastic boundary value problem) in order to get an approximationσ (t) to the real elastoplastic stress σ (t) (from the elastoplastic boundary value problem); see e.g. [5]. These algorithms enjoy a high popularity in the engineering community, as they provide a basis for better lifetime prediction for metallic bodies subjected to exterior loads.…”

Current developments and trends on structural durability

“…Two competing physically sound procedures are available, the structural yield surface approach according to Köttgen, Barkey and Socie [9] and the Incremental Neuber's rule according to Buczynski and Glinka [3].…”