Strip Yield Model for a Crack in a Plate of Arbitrary Thickness

Andrei G Kotousov

doi:10.4028/www.scientific.net/kem.293-294.253

Abstract

This paper presents new analytical results on the crack tip opening displacement (CTOD) for a through-the-thickness crack in an infinite plate of arbitrary thickness. These results are based on a new fundamental solution for an edge dislocation obtained earlier and published elsewhere. The analytical predictions of CTOD for various ratios of the crack length to the plate thickness are compared with an independent three-dimensional elasto-plastic finite element (FE) study. It is shown that both analytical and numerical results are in a good agreement when the numerical calculations are not affected by the size of the FE mesh and finite boundaries of the FE model.

Highlights

For plate-like structures, the cross-sectional thickness has a strongly influence on both the fatigue crack growth rates [1,2] and the fracture toughness, especially when the size of the process zone is comparable to the plate thickness
In the case of fatigue crack growth, this difference often manifests itself in a transition from flat to slant crack growth in thin structures [3]. This difference in the in-plane and out-of-plane constraints may significantly affect the accuracy of predictions [2] when the base-line fatigue crack growth curves generated using standard specimens are applied to predict the fatigue life of engineering structures of thin cross section
Under the small scale yielding (SSY) condition, the effect of inplane constraint on fatigue crack growth is relatively weak, as confirmed by experimental observations [6] indicating that biaxial loading only moderately alter the crack growth rates

Summary

INTRODUCTION

For plate-like structures, the cross-sectional thickness has a strongly influence on both the fatigue crack growth rates [1,2] and the fracture toughness, especially when the size of the process zone is comparable to the plate thickness This is primarily due to significant difference between the stressstate at the tip of a through-thickness crack in a plate of arbitrary thickness and that corresponding to either the idealized plane-stress or plane-strain conditions. Accurate assessment of the thickness effect on fatigue crack growth rates and fracture toughness has relied on computational methods, such as the finite element method, where the results are to some extent dependent on the mesh density of the finite element model Newman and his colleagues [3,12] conducted detailed full three-dimensional finite element analyses for through-thickness cracks in an elastic-perfectly plastic material. The analysis is based on the generalized plane-strain theory of Kane and Mindlin [13], which is summarized

GENERALIZED PLANE STRAIN THEORY

FUNDAMENTAL SOLUTION FOR EDGE DISLOCATION

Bessel function of nth order and κ