Issue 10

D. Taylor et alii, Frattura ed Integrità Strutturale, 10 (2009) 12-20; DOI: 10.3221/IGF-ESIS.10.02 12 The theory of critical distances applied to problems in fracture and fatigue of bone David Taylor, Saeid Kasiri, Emma Brazel Engineering School, Trinity College, Dublin 2, Ireland dtaylor@tcd.ie A BSTRACT . The theory of critical distances (TCD) has been applied to predict notch-based fracture and fatigue in a wide range of materials and components. The present paper describes a series of projects in which we applied this approach to human bone. Using experimental data from the literature, combined with finite element analysis, we showed that the TCD was able to predict the effect of notches and holes on the strength of bone failing in brittle fracture due to monotonic loading, in different loading regimes. Bone also displays short crack effects, leading to R-curve data for both fracture toughness and fatigue crack propagation thresholds; we showed that the TCD could predict this data. This analysis raised a number of questions for discussion, such as the significance of the L value itself in this and other materials. Finally, we applied the TCD to a practical problem in orthopaedic surgery: the management of bone defects, showing that predictions could be made which would enable surgeons to decide on whether a bone graft material would be needed to repair a defect, and to specify what mechanical properties this material should have. K EYWORDS . Bone; Fracture; Fatigue; Critical Distance. I NTRODUCTION he critical distance approach is now well established as a method for the prediction of fatigue and fracture, and is being used extensively both in research and in engineering design. A recent book [1] d escribes the approach in detail. It is applicable for predicting failure in bodies containing notches or other stress concentrations, in situations where the mechanism of failure is one involving cracking. It has been employed by many workers for the solution of problems which can be described as essentially linear-elastic, i.e. problems in which any non-linear material behaviour (due to plasticity or damage) is localised in a small process zone: in this respect it has been used to predict brittle fracture and fatigue in all types of materials: metals, polymers, ceramics and composites. The history of this type of use goes back more than fifty years: more recent work has shown that the approach can also be applied to problems involving more extensive plasticity, such as low and medium-cycle fatigue and the static fracture of tough metallic materials. The present paper is concerned with the application of these methods, hereafter referred to as the Theory of Critical Distances (TCD), to the prediction of a number of fracture problems in a particular material which is of interest to us all: human bone. What follows is essentially a summary of work conducted in our research group over the last four years, published previously in a number of journal articles. We hypothesised that the TCD could be applied to human bone, because bone is a quasi-brittle, fibrous composite material whose mechanical behaviour has many similarities with that of two well-known classes of engineering materials, namely fibre reinforced polymers and concrete. The TCD has previously been applied successfully to both of these types of materials [2, 3] . The mechanism of failure in bone always involves cracking, and the failure process is accompanied by both plasticity (of a limited but significant extent) and damage (in the form of microcracks, delaminations etc). We attempted to use the TCD to predict experimental data, taken from the literature, on the monotonic fracture of bone samples containing cracks, notches and holes, and on the fatigue behaviour T