Analysis of micro fracture in human Haversian cortical bone under compression

A procedure to investigate local stress intensity factors in human Haversian cortical bone under compression is presented. The method combines a customised experimental setting for micro-compression tests of millimetric bone specimens and a finite element contact model conforming to the bone morphology that tracks advancing microcracks. The non-interpenetration conditions along the crack edges are ensured by penalty constraints of which the parameters are optimised for minimum contact pressure error with respect to the crack orientations. A cohesive crack opening law is implemented in the wake of the crack tips to remain consistent with the progressive tearing of collagen fibrils. The displacement solution is searched by a Newton-Raphson scheme containing a double loop first on the displacements and second on the frictional contact and cohesive condition updates at the crack interfaces. The experimental Dirichlet boundary conditions are acquired by digital image cross-correlation of bone light microscopy observations and then imported into the model. The local mechanical elastic moduli are measured by nanoindentation and microextensometry. The comparison of the macroscopic stress-strain numerical response with the experiment reveals the existence of narrow diffuse damaged zones near the major cracks where the local stress intensity factors can be calculated.