Mixed-mode toughness of human cortical bone containing a longitudinal crack in far-field compression

Bone is generally loaded under multiaxial conditions in vivo; as it invariably contains microcracks, this leads to complex mixed-mode stress-states involving combinations of tension, compression and shear. In previous work on the mixed-mode loading of human cortical bone (using an asymmetric bend test geometry), we found that the bone toughness was lower when loaded in far-field shear than in tension (opposite to the trend in most brittle materials), although only for the transverse orientation. This is a consequence of the competition between preferred mechanical vs. microstructural crack-path directions, the former dictated by the direction of the maximum mechanical "driving force" (which changes with the mode-mixity), and the latter by the "weakest" microstructural path (which in human bone is along the osteonal interfaces or cement lines). As most microcracks are oriented longitudinally, we investigate here the corresponding mixed-mode toughness of human cortical bone in the longitudinal (proximal-distal) orientation using a "double cleavage drilled compression" test geometry, which provides a physiologically-relevant loading condition for bone in that it characterizes the toughness of a longitudinal crack loaded in far-field compression. In contrast to the transverse toughness, results show that the longitudinal toughness, measured using the strain-energy release rate, is significantly higher in shear (mode II) than in tension (mode I). This is consistent, however, with the individual criteria of preferred mechanical vs. microstructural crack paths being commensurate in this orientation.