On the application of the Theory of Critical Distances for prediction of fracture in fibre composites

David Taylor

doi:10.3221/igf-esis.11.01

Abstract

This paper is concerned with the fracture of composite materials containing stress concentrationfeatures such as notches and holes. In particular, it addresses the question of the use of the Theory of CriticalDistances (TCD) – a method which is widely used for predicting notch effects in fatigue and fracture. The TCDmakes use of a length constant, L, known as the critical distance, which is normally assumed to be a materialproperty. However, many workers in the field of composite materials have suggested that the critical distance isnot a constant, but rather is a function of notch size. I examined the evidence for this assertion, and concludedthat it arises for four different reasons, two of which (process zone size and constraint) are real material effectswhilst the other two (choice of test specimen and estimation of the stress field) arise due to errors in making theassessments. From a practical point of view, the assumption of a constant value for L leads to only small errors,so it is recommended for engineering design purposes.

Highlights

When engineering components fail, they almost always do so from stress concentration features: geometrical discontinuities such as holes, notches and corners
This paper is concerned with one particular method of prediction, which goes by various names but which I will call the Theory of Critical Distances (TCD)
Further reading showed that work in the two areas has proceeded on parallel lines for the last thirty years, both in fundamental research and in industrial applications, with workers in one field being apparently unaware of the activities of those in the other

Summary

INTRODUCTION

They almost always do so from stress concentration features: geometrical discontinuities such as holes, notches and corners. There are other variants of the TCD; for example some workers use L in a modified form of linear elastic fracture mechanics LEFM) in which L is considered to be the length of an imaginary crack at the notch root, or alternatively the crack is considered to advance in finite growth steps of magnitude 2L. These methods do not concern us here, except in so far as they can be combined with the stress-based methods to give approaches in which L is no longer a constant. This relationship can be derived by assuming that the TCD is applicable to cracks as well as notches: L

APPLICATION OF THE TCD TO COMPOSITE MATERIALS

DOES L VARY WITH NOTCH SIZE?

Findings

CONCLUSIONS