Issue 37

S. Vantadori et alii, Frattura ed Integrità Strutturale, 37 (2016) 215-220; DOI: 10.3221/IGF-ESIS.37.28 216 are oriented parallel to the bone axis, which consists of a vascular canal (or Haversian canal) surrounded by concentric lamellae. The interface between osteons and interstitial lamellae is called cement line (Fig. 1). When the osteons alignment is perpendicular to the loading direction (transversal specimens), the stress state under three- point bending loading is biaxial due to normal stresses produced by bending and shear stresses at the cement line interface between osteons and interstitial lamellae [9]. In such a case, the crack starting from the notch is subjected to Mixed Mode loading (Mode I and Mode II). On the other hand, when the osteons alignment is parallel to the loading direction (longitudinal specimens), the stress state is uniaxial. In such a case, the crack starting from the notch is subjected to Mode I loading. The Two-Parameter Model can be directly applied for the latter case, whereas a modified formulation is hereafter proposed for the former case in order to take into account that the crack is also subjected to Mode II loading. More precisely, the unloading compliance expression related to a single kinked crack is determined by employing the Castigliano theorem in the manner suggested by Paris [10], and the effective crack length is computed. Then, the critical stress- intensity factor at the crack tip is evaluated as a function of that related to a straight crack having length equal to the projected length of the effective kinked crack [11,12]. vascular canal interstitial lamellae cement line osteon Figure 1 : Cortical bone microstructure level. Finally, the fracture toughness results here obtained are compared with those related to a femur of an 18-month-old bovine [13], experimentally determined according to the standard ASTM E399-1 [14]. T WO - PARAMETER MODEL ccording to the Two-Parameter Model, the specimens present a notch in the lower part of the middle cross section (Fig. 2). The three-point bending tests are performed under crack mouth opening displacement control (average speed equal to 0.1 mm h -1 ). W L S B aa 0 (a) W L S B a 0 (b) a 1 a 2  Figure 2 : Crack propagates under: (a) pure Mode I; (b) Mixed Mode. Each specimen is monotonically loaded: after the peak load is achieved, the post-peak stage follows and, when the force is equal to about 95% of the peak load, the specimen is fully unloaded. Then, the specimen is reloaded up to failure. A