The Equivalent Strain Energy Density approach re‐formulated and applied to sharp V‐shaped notches under localized and generalized plasticity

Abstract

In the case of a rounded notch, the stress and strain at the notch tip can be determined by the traditional Neuber rule or by the Equivalent Strain Energy Density (ESED) approach, as formulated by Glinka and Molski. In the latter case the elastoplastic strain energy density at the notch tip is thought of as coincident with that determined under purely elastic conditions. For sharply V-shaped notches this approach is not directly applicable, since the strain energy density at the notch tip tends toward infinity both for a material obeying an elastic law and a material obeying a power hardening law. By using the notch stress intensity factors, the present paper suggests a re-formulation of the ESED approach which is applied no longer at the notch tip but to a finite size circular sector surrounding the notch tip. In particular we have adopted the hypothesis that, under plane strain conditions, the value of the energy concentration due to the notch is constant and independent of the two constitutive laws. When small scale yielding conditions are present, such a hypothesis immediately results in the constancy of the strain energy averaged over the process volume. As a consequence, plastic notch stress intensity factors valid for sharp V-shaped notches can be predicted on the basis of the linear elastic stress distributions alone

On the use of linear-elastic local stresses to design load-carrying fillet-welded steel joints against static loading

“…In other words, although, within the process zone, the local mechanical behaviour of metallic materials is highly non-linear, metallic materials can directly be designed against static loading by simply using a linear-elastic constitutive law to determine the required stress fields [21]. This fact can be justified by using an energy argument as reported by Lazzarin and Zambardi [27] who have proven that the linearelastic energy equals the elasto-plastic one, when these quantities are averaged within the entire fatigue process zone. From a practical point of view, the fact that a simple linear-elastic constitutive law can be used to determine the relevant stress fields results in a great simplification of the static assessment process, this leading to a reduction of the time and costs associated with the design process.…”

Fatigue damage criteria classification, modelling developments and trends for welded joints in marine structures

“…Williams' solution σ(r λ−1 , θ) will not change for transient thermal loading (Ferro et al 2005) and can be used to take welding induced residual stress into account. Although for MCF and HCF the far field response is linear elastic, notch elastoplasticity can be taken into account by introducing the Ramberg-Osgood equation (Lazzarin and Zambardi 2002). An extended (N)SIF formulation for blunt notches is available as well (Lazzarin and Filippi 2006).…”

A Review of the Fatigue Strength of Load Carrying Shear Welded Joints

“…An average density of the stem of energy (SED), the criterion has been proposed and formalized by Lazzarin and Zambardi (2002;2001) at the beginning for sharp, within a radius of zero, V nicks, in view of the problems two-dimensional stress ( plan or simple stem hypothesis) and has been studied and applied for the failures static and the assessment of the service life of the fatigue of the components of the jagged and welded subject to different conditions of loading (Berto and Lazzarin, 2014;. The approach has subsequently been formalized for loading axis spider diagrams (Lazzarin et al, 2008b), as well as for the u-and blunt nicks V- (Lazzarin and Berto, 2005;, by means of the expressions obtained by Filippi et al (2002) for the fields of stress before the blunt notches and has been successfully applied on a wide range of materials and the conditions of loading (Berto and Lazzarin, 2014;.…”