Abstract
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.
Highlights
The critical distance approach is well established as a method for the prediction of fatigue and fracture, and is being used extensively both in research and in engineering design
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
The second type of TCD method involves a modification of fracture mechanics, whereby the critical distance appears as the length of an imaginary crack located at the notch, or, alternatively, as the magnitude of finite crack growth increments [6]
Summary
The critical distance approach is well established as a method for the prediction of fatigue and fracture, and is being used extensively both in research and in engineering design. 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 second type of TCD method involves a modification of fracture mechanics, whereby the critical distance appears as the length of an imaginary crack located at the notch, or, alternatively, as the magnitude of finite crack growth increments [6] Once such a modification is accepted, normal linear-elastic fracture mechanics approaches can be used. It is interesting to note that, when we conducted a different analysis of bone, to predict indentation fracture, for which a non-linear material model was needed, we found that T=1 [13]
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