Three-dimensional finite element analysis of a crack normal to and terminating at a bi-material interface

Abstract

eigenfunction expansion technique. Zak and Williams [1] showed that the stress field singularity at the tip of a crack perpendicular to an interface or terminating at the interface is of order r −λ , where λ is the real part of the eigenvalue and depends on the elastic properties of the bi-material. Bogy [2] investigated the stress singularity of an infinite crack terminating at the interface with an arbitrary angle of different material components. Cook and Erdogan [3] used the Mellin transform method to derive the governing equation of a finite crack perpendicular to the interface and obtained the stress intensity factors (SIFs). The authors found that the power singularity of stress around the crack tip is not −1/2. Erdogan and Biricikoglu [4] solved the problem of two bounded half planes with a crack going through the interface. Wang and Chen [5] used photoelasticity to determine the stress distribution and the stress intensity factors of a crack perpendicular to the interface [6-8], and also used finite element to analyze cracks perpendicular to bimaterial in a finite elastic body. Chen [9] used the body force method to determine the stress intensity factors for a normal crack terminating at a bi-material interface. Chen et al.[10] used the dislocation simulation approach to investigate the crack tip parameters for a crack perpendicular to an interface in a finite solid. He and Hutchinson [11] also considered cracks approaching the interface at oblique angles. Lin and Mar [6] presented a finite element analysis of the stress intensity factors for cracks perpendicular to the bi-material interface. Chang and Xu [12] presented the singular stress field and the stress intensity factors solution for an inclined crack terminating at a bi-material interface. A theoretical description of the stress singularity at an inclined crack terminating at an anisotropic bi-material interface was proposed by Lin and Sung [13]. Wang and Stahle [14,15] used the dislocation simulation approach to investigate a crack perpendicular to and terminating at the Abstract The objective of the present work is to investigate the interaction between interfaces and cracks normal to and terminating at a metal/alumina interface. The behavior is analyzed by the determination of the J integral and the plastic zone at the crack tip using the three-dimensional finite element methods. The effects of the thickness of the metal/alumina were highlighted. The obtained results allow us to deduce mathematical relations, giving the variation of the J integral and the plastic zone as a function of the crack position and the bi-materials thickness.

A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

“…Adams modeled the crack which was perpendicular to the bimaterial interface and found that the critical value for crack propagation depended upon the maximum stress of the cohesive crack model, as well as the Dundures parameters [34] . Mehidi et al investigated the crack normal to the metal/alumina interface by determining the J integral and the plastic zone at the crack tip using the three-dimensional finite element methods [35] . Muthu et al developed a new variant of the element-free Galerkin (EFG) method, and applied this new method for the inclined bimaterial interface crack problem [36] .…”

Mechanical responses of maxillary canine and surrounding tissues under orthodontic loading: a non-linear three-dimensional finite element analysis

“…There are some studies which have related the stress distribution to the applied force based on the finite element (FE) method [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

A symplectic analytical singular element for the inclined crack terminating at the material interface of composite structures

“…Adams modelled the crack which was perpendicular to the bimaterial interface and found that the critical value for crack propagation depended upon the maximum stress of the cohesive crack model, as well as the Dundures parameters [9] . Mehidi et al investigated the crack normal to the metal/alumina interface by determining the J integral and the plastic zone at the crack tip using the three-dimensional finite element methods [10] . In this study, a new symplectic analytical singular element (SASE) is developed for numerical study of inclined interface crack.…”