PSI - Issue 2_A

Alireza Hassani et al. / Procedia Structural Integrity 2 (2016) 2424–2431 Alireza Hassani , Reza Teymoori Faal / Structural Integrity Procedia 00 (2016) 000–000

2425

2

subjected to a normal loading resulting from a tensile loading acting at the infinity. Special cases including the case of two equal and symmetric cracks and when the ligament between the two cracks is totally occupied by the plastic enclaves, were examined. The problem of an infinite plate weakened by two collinear unequal straight quasi-static cracks which was under far-field uniform constant tension perpendicular to the cracks was studied by Bhargava and Hasan (2011). The problem was analyzed using complex variable technique. The effects of increasing the tension load to a limit value, on the extension of two adjacent interior tips of the two cracks were also investigated. Using the modified Dugdale's model the analytic expressions for the crack opening displacement at each tip of the cracks and the load required to arrest the crack opening when the size of the plastic zone increases were evaluated. Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials was accomplished by Yi et al. (2012). First using the distributed dislocation technique, the problem was reduced to the integral equations of Cauchy-type and solved numerically to find stress intensity factors of crack tips. Next, based on the Dugdale's model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings were investigated. The problem of estimating the plastic zone size (PZS) for an embedded crack within an infinite plane with a circular inclusion was studied by Hoh et al. (2010a). Based on the Dugdale's model of the small scale yielding, the crack problem is reduced to a Cauchy-type singular integral equation by distribution of edge dislocations on the crack borders. The integral equation was solved numerically with an iterative numerical procedure. The PZS and the crack tip opening displacement were finally estimated. They also retreated a similar problem but with coated inclusion (Hoh et al., 2010b). The problem of an infinite elastic-plastic solid with the doubly periodic rectangular-shaped arrays of cracks was the subject of study done by Shi (2015). The solid was under anti-plane loading. The interaction effects of the periodic arrays of cracks on the plastic zone size and the crack tip opening displacement were studied. The problem was solved using the finite cosine and sine Fourier transforms. Ferdjani (2009) formulated the elastostatic antiplane problem of an infinite strip containing a Dugdale's crack parallel to its boundaries. Applying the Fourier transforms, the problem was reduced to a singular integral equation and solved using Chebyshev polynomials. Finally, the length of the plastic zone was computed. The solution was limited to a single crack parallel to boundaries of the layer. The Dugdale's model was originally developed for a stationary Mode I crack and then was extended to a moving crack of fixed length and an expanding crack. The model was extended for an expanding crack to Modes II or III loading by Wu and Huang (2013). The crack was in an infinite plane subjected to a far-field tensile loading. The problem was treated using the dislocation method, that is, by modeling the crack as a distribution of moving dislocations. Explicit relations providing a connection between applied stress, yield stress, crack tip speed, and plastic zone tip speed were obtained for all three loading modes. Finally, the relative crack face displacements and the rates of plastic work were computed. Based on the Dugdale's crack model and Yoffe's model, the problem of a moving interfacial crack located between dissimilar piezoelectric materials was studied by Hu et al. (2015). The materials were under anti-plane shear and in-plane electric and magnetic loadings. It was assumed that the constant length moving crack is magneto electrically permeable. Using the Fourier transform the problem was reduced to dual integral equations. By solving them, the relations for the size of plastic zone, the crack sliding displacement (CSD) were derived. The problem was also retreated for a moving interfacial crack located between dissimilar magnetoelectroelastic materials (Hu et al., 2014). Based on the von Mises yield criterion, Nicholson (1993) extended the Dugdale's model to mixed-mode fracture mechanics including Modes I, II and III. An elastic-plastic plate with an embedded crack and under state of plane stress was considered. The problem was treated by use of the potential functions of complex variable. They also assumed that the stresses on the plastic zones of the crack tips were proportional with the applied stresses. Using this model, the estimates for the values of the crack-opening displacement and the J-integral were given. A model for a transitional phase of mode III cracking associated with changes of the plastic zone shape ahead of a crack tip where the elastic-plastic boundary assumes an elliptical form was presented by Unger (1989). The stress, strain and displacement fields were also presented for both the elastic and the plastic regions. The model compared with others models such as the Dugdale's plastic strip model of Mode I.