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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3.2. Phase field model The PF model is an extension of Griffith's classical fracture mechanics principle. It is based on minimizing the proposed potential energy shown in Equation 2. This formulation is known as the AT2 model. The model simulates sharp cracks as diffuse cracks using a continuous damage variable . Another important parameter of this model is the characteristic length � . The characteristic length controls the width of the band in which the crack is diffused. � � � � , � � �� � � �� � � � � �� | | � � � (2) The determination of � and � for the interstitial tissue needs to be made. The value of 0.52 N/mm for � proposed by Brown et al. (2000) has been used in this work. A parametric study was conducted to determine the appropriate Results are shown here for the model of test specimen 2. The calibration of � was made as follows. Three different values were tested (2.5  m, 5  m and 10  m), the 2.5  m value was discarded because the crack did not reach propagation. Both the 5  m and 10  m models had the same crack path, but the predicted load displacement curve was different, as shown in Fig. 3. The first failed constituent is the cement line surrounding the osteon located right at the artificial notch. The failure of that interface produced a sudden load drop, as can be seen in Fig. 3. After that, several cracks started appearing on the interfaces due to the CZM failure. The PF model predicts a crack propagating through the interstitial tissue from one failed interface to another. The value of � governs failure onset for the interstitial tissue. The lower the value of � , the tougher the material will be. In the case of � = 10  m, the crack propagated through the interstitial tissue as soon as the first cement line failed, so a huge load drop is observed in Fig. 3. On the other hand, the model with � = 5  m was able to bear the load further, so the first load drop corresponds to the cement line failure and the second load drop corresponds to the combined failure of the rest of the cement lines and interstitial tissue. value of � . 4. Results

Fig. 3. Load - displacement curves for specimen 2.