3D thickness effects around notch and crack tip stress/strain fields

R.C.O Góes,M.A Meggiolaro,J.T.P Castro

doi:10.3221/igf-esis.33.12

Abstract

Notches and cracks are usually approximately modeled as two-dimensional problems using solutions from plane elasticity to quantify localized stress/strain concentration effects around their tips. However, they may be associated with high gradients that can severely restrict local Poisson-induced transversal strains and cause important 3D stress fields around those tips. Fatigue crack initiation and growth, plastic zone sizes and shapes, and localized constraint effects that affect toughness are typical problems associated with such 3D effects, which may lead to non-conservative damage and life predictions if neglected. To quantify how important they can be, first finite element techniques are used to simulate thickness and notch-tip radius effects in the fields around such tips, and to evaluate their importance from the structural design point of view. Then, versatile sub-modeling techniques are used to study similar effects along the fronts of short and long cracks, and a stepwise re-meshing routine is used to show how an initially straight crack must slightly curve its front during its propagation by fatigue, due to the unavoidable 3D effects that always surround real crack tips.

Highlights

For design purposes, the maximum stresses max that act at notch tips are usually calculated using a linear elastic (LE) stress concentration factor (SCF) Kt to multiply the nominal stress n that would act there if the notch had no effect on the stress and strain fields that surround it: max Kt n (1)Since Kirsch and Inglis studied circular and elliptical notches in infinite plates, a few analytical and many numerical and experimental SCF have been obtained for many other notch geometries from their 2D approximations, assuming idealized plane stress, plane strain, or axisymmetric conditions [1,2]
Fatigue crack initiation and growth, plastic zone sizes and shapes, and localized constraint effects that affect toughness are typical problems associated with such 3D effects, which may lead to non-conservative damage and life predictions if neglected
The maximum stresses max that act at notch tips are usually calculated using a linear elastic (LE) stress concentration factor (SCF) Kt to multiply the nominal stress n that would act there if the notch had no effect on the stress and strain fields that surround it:

Summary

INTRODUCTION

The maximum stresses max that act at notch tips are usually calculated using a linear elastic (LE) stress concentration factor (SCF) Kt to multiply the nominal stress n that would act there if the notch had no effect on the stress and strain fields that surround it: max Kt n (1). 2D models of notched components have limitations, even in simple cases like a notched plate loaded by a uniform nominal stress. In such cases the material works under pl- far from the notch tips, but the stress/strain fields that surround the tips are 3D, due to the Poisson restriction induced by the stress/strain gradients that act there. Instead of the single SCF value traditionally used in 2D analyses Kt max/ n max/ n, independent stress and strain concentration factors K max/ n and K max/ n must be used to analyze 3D notch problems, even in LE cases.

FE MODELS FOR CRACKS AT THE BORDER OF LARGE PLATES

GROWTH OF EDGE CRACKS WITH INITIALLY STRAIGHT FRONTS IN LARGE PLATES

Plate Height

Findings

CONCLUSIONS