PSI - Issue 2_A

Alireza Hassani et al. / Procedia Structural Integrity 2 (2016) 2424–2431 Author name / Structural Integrity Procedia 00 (2016) 000–000

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In the present study, under the assumption of the small-scale yielding, plastic zone sizes are determined in an isotropic elastic layer containing multiple cracks subjected to anti-plane deformation. The analysis takes into account the interaction between arbitrary located cracks which significantly changes the plastic region. For arbitrary oriented cracks, their interactions were not considered in previous investigations. In fact, this work is an extension of the work (Ferdjani, 2009) for multiple cracks which is done by means of a different method namely the distributed dislocation technique. 2. Formulation We consider a layer with thickness � weakened by a Volterra-type screw dislocation with Burgers vector � � situated at a point with coordinates ��, � � �, Fig. 1.

Fig. 1. Schematic view of the strip with a screw dislocation. The solution of the aforementioned dislocation, can be derived using the method of images (Hassani et al., 2015). The relevant displacement field is given by ���, �� � � � 2� ���� �� � ����� � � � � 2 � ������ � 2 � � � ��� �� � ����� � � � � 2 � ������ � 2 � �� (1) where � � ���. The traction-free boundary conditions for the layer edges are � �� ��, �� � � and � �� ��, �� � �. We may easily observe that Eq. (1) is multiple-valued on the dislocation cut, � � �, � � � � . The constitutive equations under anti-plane deformation are � �� � � � � � � � �� � � � � � � (2) where, � is the shear modulus of elasticity of material. From Eqs (2) and (3), stress components become � �� � � � ��������� �� � 1 �������� � ���� ��� � � � �� � 1 �������� � ������� � � � �� � � �� � � � �� � � ������� � � � �� �������� � ������� � � � �� � ������� � � � �� �������� � ������� � � � �� � (3)