Thickness effects may not do what you think they do

A BASIC tenet of linear elastic fracture mechanics (LEFM) is that a critical value of the stress intensity factor controls fracture, at least in brittle instances. For a given material, this critical value is termed the fracture toughness. Accordingly, for LEFM to prove useful in predicting failure for different configurations with a given material, that material’s toughness needs to be largely independent of geometry or, at worst, have any geometry dependence fully understood. Unfortunately fracture toughness values usually are dependent on the thickness of the specimen furnishing them. Fortunately such thickness effects are well recognized, and current LEFM includes an allowance for this phenomena. Typically, physical data on thickness effects exhibit a decrease in toughness with increasing thickness, if not monotonically for small thickness variations then virtually invariably overall for large changes. The usual argument advanced to explain such trends is as follows: increasing thickness increases constraint on any plastic flow present in the interior by virtue of the increased magnitude of the through-thickness normal stress component; with greater constraint, fracture can be expected to be more brittle and occur at lower loads with correspondingly reduced values of toughness; ultimately, though, such through-thickness stresses ought to be asymptotic to a state of generalized plane strain with an attendant limiting lower value for toughness. The usual strategy adopted in view of the physical evidence and companion explanation is to take the apparent limiting lower bound on toughness as the parameter governing fracture. This choice is quite naturally called the plane strain fracture toughness (&), and is hoped to give rise to conservative designs. Exactly how the selection is made and other aspects of determining Kio are detailed in the ASTM E399 standard[l], and the considerable body of testing attempting to apply[l] attests to the wide acceptance of plane strain fracture toughness by the fracture mechanics community. In the light of the foregoing, it is interesting to ask the question as to what, if any, thickness effects are present for a material which essentially displays no plastic flow prior to fracture irrespective of its thickness-the ideally brittle material in an engineering sense. Such a question aims to check the completeness of the usual rationalization of thickness effects. That is, if the explanation offered is the entire story, one would anticipate no effect on toughness due to thickness changes. The question is particularly important in the event that this does not transpire to be the case, since then our current understanding would have been demonstrated to be less than complete, thereby raising the possibility that our technology may not necessarily be conservative. We therefore seek to investigate this issue here. There are numerous experimental studies on thickness effects, in general, reported in the literature: a fairly extensive recent bibliography[2] cites some 101 related references while more recent extensions to [2] by Pieri[3] provide a further 36 articles. In contrast, if one uses accepted estimators of yield region extent r Y, in conjunction with the definition of limited plastic flow implicit in the standards for &[l] (namely ry less than 2% of the crack length), then relatively few of these investigations can be classified as involving brittle response throughout any marked variation in thickness. Some studies which do contribute under these restrictions are: Kinloch and Gledhill[4], Mindess and Nadeau[S], and Smith and Chowdary[6]. The picture emerging from these studies is less than completely clear: while [5] is consistent with no thickness dependence for brittle behavior, [4] typically shows a reduction like that found for ductile