PSI - Issue 28

Behzad V. Farahani et al. / Procedia Structural Integrity 28 (2020) 218–225 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2019) 000–000

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suggested stress-dead zone concept, and all results compared to a reference solution reported by Paris and Sih (Paris and Sih 1965). 2. Mathematical formulations Theoretically (Anderson 2005), the compliance calibration method is based on the Irwin-Kies relation. In 1956, Irwin (Irwin 1956) proposed an energy approach for fracture that is essentially equivalent to the Griffith model, except that Irwin’s approach is in a form that is more convenient for solving engineering problems. Irwin defined an Energy Release Rate- ℊ , which is a measure of the energy available for an increment of crack extension. That is the rate of change in potential energy with the crack area. Since ℊ is obtained from the derivative of a potential, it is also called the crack extension force or the crack driving force. However, this work follows the compliance function formula extended to the LEFM analysis of the finite plates consisting of slant cracks subjected to a mode I loading condition, as extensively presented in the previously published work by the authors (Farahani, de Melo, da Silva Tavares, et al. 2020). In addition, the SIF associated to the stress dead-zone concept � � ��� � could be calculated through the following relationship (Farahani, de Melo, da Silva Tavares, et al. 2020): � ��� � √ � � � � � �� � �� � ���� �, (1) where and stand as the material Young’s modulus and fracture energy, respectively. Moreover, is the remote stress, denotes the plate width and therefore � � ⁄ , is the angle of the crack in respect to the loading direction and � is the stress-dead zone parameter calculated by: � � �� � � ��� � ����� � � . (2) It must be noted that is the proportional factor of the stress dead-zone associated to the finite plate with horizontal central notch � � ���� which has been characterised as � �.2 (Farahani et al. 2019). Considering as the slant crack length, it must be noted that the stress dead-zone is predicted by a parallelogram shape with diagonals of 2 and 2 . The minor diagonal is the slant crack length and the major one presents the stress dead zone dimension, which can take the following form. Fig. 3 clarifies the physical meaning of the dead zone. � � . (3) Experimentally, to compute the SIF from DIC data captured during the test, a computational iterative routine was implemented. Generally, this function links the overdeterministic SIF calculation algorithm and the stress in the defined problem domain, as described in (Farahani, Tavares, Moreira, et al. 2017). Considering plane problem of a homogeneous isotropic solid, Williams’ series expansion for plane stress state was applicable as stated in the following equations where the importance of � ��� is indicated. �� � ∑ � �� � � � � � �� ��2 � ���� � � � � � � � � � �� � � � � � � �� � � � � �� �� , ���� (4) �� � ∑ � �� � � � � � �� ��2 � ���� � � � � � � � � � �� � � � � � � �� � � � � �� �� , ���� (5) �� � ∑ � �� � � � � � �� �� ����� � � � � � � � � � �� � � � � � � �� � � � � �� �� ���� , (6) � ��� � �� √2 . (7)