Numerical study of the deformations of two coplanar circular cracks during their coalescence L. Legranda, V. Lazarusb aUPMC Univ Paris 6, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, France, legrand@lmm.jussieu.fr bUniv Paris-Sud, UPMC Univ Paris 6, CNRS, UMR 7608, FAST, France Abstract Consider two planar circular cracks embedded in an infinite linear elastic media and submitted to mode I tensile loading. Bueckner-Rice weight functions theory allows us to update the stress intensity factor when the crack fronts are slightly deformed in their plane. Using an incremental numerical method based on this theory, we study the propagation of these two cracks when they interact each other taking into account the non-linearities induced by their deformations. The advantage of this method in comparison to more standard finite element methods is that only the crack fronts have to be meshed. Using a Griffith threshold law, we notice important deformations of the crack fronts are observed and a drastically decreasing threshold loading when the fronts approach each other. Keywords: Brittle fracture, Toughening, Finite element method, Elastic line model The present study focuses on the coalescence phenomenon of two circular cracks. What is the critical loading to reach the coalescence? Is the crack advance facilitated due to the presence of the secondary crack? What is the shape of the cracks during their propagation? Those questions are considered in the present article. To do it accurately, the main difficulty is to calculate the three-dimensional stress intensity factors along all the fronts by taking into account the crack shape changes induced by the interaction between the cracks. In the literature, we can find papers treating of interacting cracks but they never take into account the cracks fronts deformation during propagation (see [2−5] and [8]). Here, the effects of the crack front shape changes are analized independently of the edge effects. For this purpose, two small cracks are considered, so we can make the assumption that the medium is infinite and subjected to remote loading. For this reason, methods based on integral equations are adapted here: the sole cracked area is needed. Moreover, in the present case of in-plane propagation, it is just necessary to mesh the 1D outline of the cracks. Using Bueckner-Rice formalism [7], the work of Bower and Ortiz [1] provides some examples of this approach in mode I. More recently, Lazarus [6] developped a simplified variant of their method without significant loss of accuracy. All these works only deal with a sole crack. In the present paper, we extend to two cracks in order to study their final coalescence. 1
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