Issue 11

D. Taylor, Frattura ed Integrità Strutturale, 11 (2009) 3-9; DOI: 10.3221/IGF-ESIS.11.01 4 approache s [4, 5] and they have been found to be necessary in certain other materials, such as concrete, where the critical distance can be so large as to be similar to the size of the test specimen. In this paper, I consider the evidence for and against the use of a constant L value in continuous-fibre composite laminate materials, both from a fundamental scientific perspective and from the viewpoint of the practical engineering application of the TCD. T HE TCD: A BRIEF INTRODUCTION or those not familiar with critical distance methods, here follows a brief introduction. A recent paper provides further information [6] and those interested in a more comprehensive review are directed to a recent book on the subject [7]. In the great majority of cases, the TCD is implemented using a linear elastic stress analysis. The point of maximum stress is located (e.g. at the root of a notch) and a line is drawn from this point which is known as the focus path. Stress is plotted as a function of distance, r, along this line. There are two different variants of the approach, which I refer to as the Point Method and the Line Method. In the Point Method, the stress is considered at a single point, located at a distance of r=L/2. In the Line Method, the stress to be considered is the average stress along the line from r=0 to 2L. Failure is predicted to occur if this stress is greater than some critical value,  o . Fig. 1 illustrates these approaches schematically. 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. The point and line methods have the great advantage of simplicity: they can be very easily used in conjunction with finite element analysis and applied to any type of stress concentration feature, including those on engineering components. Extensive research has shown that they can give very accurate predictions in a wide variety of materials, for those mechanisms of failure which involve cracking, such as brittle fracture and fatigu e [7]. An important relationship exists between the two constants in the TCD and the material’s fracture toughness, K c . This relationship can be derived by assuming that the TCD is applicable to cracks as well as notches: 2 1        o c K L   (1) Figure 1 : Schematic illustration of the Point Method and Line Method A PPLICATION OF THE TCD TO COMPOSITE MATERIALS he use of this approach in the field of composites stems from the seminal paper by Whitney and Nuismer in 1974 [3] which was followed a short time later by a slightly more detailed treatment in a book by Whitney et al [8]. The original paper has been extremely influential in this field: at the time of writing there have been over 300 citations to this paper, in publications ranging from fundamental studies to engineering applications. The paper is very comprehensive, describing both the PM and the LM, which Whitney and Nuismer referred to as the Point Stress Criterion and the Average Stress Criterion. The validity of the method was tested against experimental data: Figs 2 a nd 3 a re examples reproduced from the original paper. The theoretical link to K c (as in Eq. 2 a bove) was also derived. Importantly, F T