A critical distance study of stress concentrations in bone

Abstract

The Theory of Critical Distances (TCD) is a method used to study the failure of material in situations where stress concentrations, such as holes and notches, are present. This method uses two material constants: a critical length and a critical stress. The elastic stress field close to the stress concentration is examined, applying a fracture criterion. The TCD has been applied to predict brittle fracture in various different materials and various types of notches but it has not previously been applied to bone. Since bone fails by brittle fracture with limited plasticity, it is expected that the TCD will be applicable. Experimental data were obtained from the literature on the effects of sharp notches and holes loaded in various ways (tension, torsion and bending). These tests were modelled using finite element analysis. It was found that the TCD could be successfully applied to predict the load required for brittle fracture as a function of the type and size of the stress concentration feature. The critical distance was found to be almost constant, about 0.3–0.4 mm, for all types of bone studied: the critical stress was found to be related to the material's ultimate tensile strength by a constant factor of T=1.33. The results of this study will be of practical value in the assessment of stress concentration features introduced during surgery and of naturally occurring bone defects.