PSI - Issue 66

Antonio R Quiñonero-Moya et al. / Procedia Structural Integrity 66 (2024) 175–180 A. R. Quiñonero-Moya et al. / Structural Integrity Procedia 00 (2025) 000–000

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cement lines were treated as interfaces. An element size of 1 μ m has been set in the interest zone. Due to the vast dispersion of elastic properties found in the literature for the microconstituents of cortical bone Ascenzi et al. (1990); Bensamoun et al. (2008); Lefèvre et al. (2019); Pidaparti and Burr (1992), the elastic properties were calibrated using the load - displacement curves obtained in the experimental tests. These properties are shown in Table 1.

Table 1. Calibrated elastic properties of cortical bone microconstituents. Microconstituent E (GPa)  Osteon 0.86 0.3 Interstitial tissue 0.95 0.3

Fig. 2. Cortical bone specimen 2, finite element model.

The failure of the osteons was not modeled because it was not observed during experimental testing. Instead, crack onset occurs at the cement lines in the artificial notch. The crack then propagates from this first interface to the next through the interstitial tissue. This behavior was captured using two failure models: the cohesive zone model for the cement lines and the variational approach to fracture Phase Field for the interstitial tissue. 3.1. Cohesive zone model The CZM technique relies on the assumption of a cohesive process zone governed by a traction-separation law. Within this cohesive zone ahead of the crack tip, the material suffers a progressive degradation of its mechanical properties. The main advantages of the CZM over other fracture models are that it can capture crack initiation and propagation and reproduce complex scenarios. The main parameters required to characterize the CZM are the interfacial stiffness K n that relates to the traction and separation of the interface, the fracture energy G nc and the damage initiation criterion. Here, the letter n refers to the crack mode opening. A bilinear traction-separation law was used in this work. The quadratic traction initiation criterion (Equation 1) was selected as the damage initiation criterion. This criterion needs the mode I critical strength �� and the mode II critical strength ��� as input data. Then it uses the mode I stress � and the mode II stress �� to assess the failure initiation of the interface. The calibrated cohesive properties of the cement lines are shown in Table 2. � � � � �� � � �� � �� � ��� � � � 1 (1) Table 2. Cohesive properties of the cement lines. K I (MPa/mm) K II (MPa/mm)   c (MPa)   IIc (MPa) G Ic (N/mm) G IIc (N/mm) 10 7 10 7 40.5 79.8 0.086 0.086