Issue 11

D. Taylor, Frattura ed Integrità Strutturale, 11 (2009) 3-9; DOI: 10.3221/IGF-ESIS.11.01 3 On the application of the Theory of Critical Distances for prediction of fracture in fibre composites David Taylor Engineering School, Trinity College Dublin, Ireland; dtaylor@tcd.ie A BSTRACT . This paper is concerned with the fracture of composite materials containing stress concentration features such as notches and holes. In particular, it addresses the question of the use of the Theory of Critical Distances (TCD) – a method which is widely used for predicting notch effects in fatigue and fracture. The TCD makes use of a length constant, L, known as the critical distance, which is normally assumed to be a material property. However, many workers in the field of composite materials have suggested that the critical distance is not a constant, but rather is a function of notch size. I examined the evidence for this assertion, and concluded that it arises for four different reasons, two of which (process zone size and constraint) are real material effects whilst the other two (choice of test specimen and estimation of the stress field) arise due to errors in making the assessments. 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. K EYWORDS . Fibre composites; fracture; notch; hole; critical distance I NTRODUCTION hen engineering components fail, they almost always do so from stress concentration features: geometrical discontinuities such as holes, notches and corners. Fibre composite materials are no exception, and much work has been done over the years to understand and predict the effects of these features on the load-bearing capacity of these materials. 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). Here I will consider the application of this theory to the broad range of long-fibre laminate-type composite materials, and from the outset I should point out that I do not consider myself an expert on this class of materials. In that respect the paper is being written from the outside looking in, and I apologise in advance for any errors or misunderstandings that may arise as a result. My investigations into the TCD began in the field of metal fatigue, where the approach has been used for over half a century [1, 2]. Examination of the published literature revealed that the same methodology was also being applied to predict monotonic fracture in composites, since first being proposed by Whiney and Nuismer in 1974 [3]. Further reading showed that work in the two areas (metal fatigue and composite fracture) 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. As a result, the approach has developed some particular characteristics: for example in the field of metal fatigue it is generally assumed that the critical distance, L, which is the fundamental parameter in the theory, is a material constant, unaffected by the geometry of the notch. In composites research, however, it has become common to assume that L is not a material constant, but rather that it varies with the size of the notch. This question is of fundamental importance because the theory is much easier to use if we can assume a constant value for L. If a constant value of L cannot be accepted then more fundamental studies are needed to develop a general approach which would allow L to be calculated for any problem. Some workers, including ourselves, have indeed proposed such W