Issue 11

D. Taylor, Frattura ed Integrità Strutturale, 11 (2009) 3-9; DOI: 10.3221/IGF-ESIS.11.01 8 Sharper notches are better in this respect because they give steeper gradients, and the best strategy is to use at least two different notch types, as shown here. Process Zone Size The above two effects arise essentially due to errors or inaccuracies, however there are also some reasons why the value of L would tend to increase in reality. The first of these relates to the size of the process zone. To illustrate this I have chosen some data from Kennedy et al [13] , who tested centre-notched plates of an orthotropic graphite/epoxy composite, using very sharp, crack-like notches. I have chosen this data because it shows the largest change in L which I have been able to find. According to these workers, L changed by a factor of 3, from 8.4mm to 24.4mm, when the length of the notch was increased from 6.35mm to 305mm. The value of a /W was kept constant at 0.25, which is convenient because it means we can rule this out as a complicating factor. The value of L gives an approximate estimate of the size of the process zone, or damage zone that occurs ahead of the notch prior to failure. From this we can conclude that the larger specimens were failing under LEFM conditions because the size of the damage zone at failure was much smaller than the remaining ligament (W- a ). However this is not the case for the smaller specimens, for which L was a significant proportion of (W- a ), and for the very smallest specimen it is likely that the process zone had spread completely across the specimen width before failure. We have encountered similar situations before, most obviously in the case of building materials such as concrete, which have equally large L values of the order of 5-10mm. If the specimen size is particularly small then this can lead to the absurd situation in which the critical point (or part of the critical line) lies outside the specimen. In such cases if the TCD can be used at all it must be with a smaller value of L. Approaches developed by myself and colleagues [5] and also by Leguillon [4], allow L to vary in such cases by using two failure criteria – one stress based and one stress-intensity based, which are assumed to apply simultaneously. The details of the approach are beyond the scope of the present paper: suffice it to say that the result is an L value which is constant when the remaining ligament (W-a) is much larger than L, but changes in size in such a way that it remains always smaller than (W-a). These modified approaches can be applied to problems of the type shown above, and should be able to give improved predictions. However, it may not be worth the trouble. Regarding the data from Kennedy et al , which as I said showed the largest variation in L of any which I could find for composite materials, if we use a constant L value it is possible to predict all the data with errors no greater than 13% on stress. This seems strange at first but the anomaly is resolved by noting that the stress distance curves are quite shallow, even for relatively sharp notches, so a large change in distance r gives only a relatively small change in stress. Consequently it is permissible to make a relatively large error in the value of L because this will lead to only a small error in the predicted strength. Constraint Effects When reading articles on composite materials I was struck by the fact that little attention seems to be given to possible changes in constraint that arise when changing specimen thickness. In metallic materials the measured fracture toughness can change considerably if thickness is reduced in such a way as to reduce the out-of-plane constraint, changing from plane strain to plane stress conditions. Some workers have reported this effect in composite materials, but in most papers it is not mentioned, and Awerbuch and Madhukar actually reported a case of the opposite effect, whereby the measured toughness increased with increasing specimen thickness [9]. Given that most composite-laminate specimens tested are quite thin, one would expect that they are experiencing either plane stress or conditions which are intermediate between plane stress and plain strain. The change in K c is due largely to changes in the degree of triaxiality in the plastic zone, and though the polymer and metal matrices of these composites will yield, it is possible that these effects are modified by the existence of microdamage in these zones. Considering the relationship between fracture toughness and L (Eq. 1 a bove) one would expect L to increase on moving from plane strain to plane stress, and we showed previously that this is indeed the case for brittle fracture in metal s [14] . A feature of small cracks in all materials is that they have lower fracture toughness values than large cracks. This effect occurs if the crack length is similar to, or less than, L. Such cracks will require less stress intensity to cause failure, so for a given specimen thickness they will experience more constraint, and hence can be expected to show a smaller value of L. C ONCLUSIONS 1) Some apparent changes in the critical distance L with notch size reported in the literature arise due to inaccuracies caused by the choice of test specimen and the use of imprecise methods of stress analysis.