Evaluating the crack-tip bridging stress in a bovine cortical bone

Recent experimental studies on human and bovine cortical bone shows that fracture strength of a cortical bone cannot be characterized by a single value of fracture toughness, but rather by variable crack growth resistance values. The mechanism of resistance of a crack extension in a bone is generally defined by R-curve behavior, which can be expressed as the relation between crack growth resistance values and crack extension. Crack bridging stress in front of a crack has been shown to be the main source of this resistance of the bone crack extension. The calculation of this bridging stress is important for predicting fracture stress in cortical bone material. In this study, a theoretical model based on weight function was developed to evaluate the bridging stress in front of a cortical bone crack tip. The main goal of this research was to investigate the role of specimen orientation on bridging stress. The hypothesis used was that specimen orientation has significant influence on the bridging stress. Two specific aims are developed to support this hypothesis: determination of the bridging stress along a crack length and investigation of the orientation effect on bridging stress. A weight function formulation was used to calculate crack opening displacements. The bridging stress along a crack can be found by minimizing the experimental and calculated crack opening displacements using a least square formulation. Finally, the bridging stress variation along a crack extension was examined in the specimen along two different orientations. The developed analytical model produces a gradually increasing trend of bridging stress with crack extension which depends on the orientation of the specimen extraction.