G. B. Sinclair

Path-independent H integrals for three-dimensional fracture mechanics

In fracture mechanics, a number of real applications have intrinsically three-dimensional crack geometries, thereby requiring a means of extracting stress intensity factors under such circumstances. Two approaches to this end are examined here: one, a three-dimensional J-integral; the other, three-dimensional H integrals for each mode. The first integral is well accepted by the fracture mechanics community; the second integrals are newly developed herein. The two are compared on three-dimensional test problems with closed-form solutions that are constructed for this purpose. Analysis is via quarter-point elements on two successively refined grids for each test problem. The results demonstrate that both types of path-independent integral can furnish estimates of stress intensity factors which converge to good levels of accuracy in return for reasonable levels of computational effort.

A comparison of crack-flank displacement fitting for estimating K with a path independent integral

Predicting crack growth under cyclic loading in applications usually requires the efficient extraction of stress intensity factors from finite element analyses of mixed mode situations. Two approaches to this end are examined: one, a competitive fitting procedure using crack-flank displacement data, the other, a path independent integral which can readily distinguish between modes. A protocol is established for comparing the two on a set of about forty test problems which have exact solutions. Analysis is via quarter point elements on a common sequence of three successively refined meshes for each problem. Results show that the path independent integral is more consistently accurate and reliably convergent, yet comparable in implementation effort.

On the fundamental energy argument of elastic fracture mechanics

Energy arguments remain, even today, as probably the most fundamental physically-reasoned justification for the application of linear elastic fracture mechanics to brittle materials. Accordingly, they have attracted and continue to attract quite a number of investigations. Not all of these studies employ the same approach. Unfortunately, nor do they all lead to the same conclusions regarding the implications of elastic fracture mechanics. Here, by examining the energy balance of fracture mechanics from a classical physics viewpoint, equivalent valid approaches are identified. This in turn enables the various contributions over the years to be placed in perspective with respect to whether or not they are correct.

The size dependence of fracture toughness for two embrittled materials

Over the last several years, Hudson and Seward [1-3] have provided extensive compendia of sources of fracture toughnesses for metallic alloys. In these reports, references containing data are identified without any actual toughness values being furnished. This prompted a sequence of notes that sought to indicate what an engineer might find in terms of fracture toughness on consulting the references in [ 1-3]. The findings of this sequence are summarized in its last member (Hoysan and Sinclair [4]), and can be briefly restated as follows. In [4], the plane-strain fracture toughness, K k of twelve different metallic alloys is considered. The alloys are distinguished as to composition and heat treatments and/or processing methods. The criterion for an alloys inclusion is simply that there exists a sufficient number of measurements of K k by independent investigators to gauge variability (>10). For a specific metallic alloy so selected, typically K~, is found to vary by more than a factor of two from its lowest apparently valid value to its highest. Such discrepancies in fracture toughness raise questions as to what are their causes? The intent of the present note is to consider a potentially significant contributor in this regard, namely size effects.