Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods

The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors(SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method,whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials,but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency(less time consuming and less spurious boundary effect).

Effects of nano-voids and nano-cracks on the elastic properties of a host medium: xfem modeling with level-set function and free surface energy

This work deals with the influences of nano-heterogeneities in the form of voids/cavities or cracks on the elastic (please confirm which word is correct. effective or elastic? According to the title of paper, I choose elastic.) properties of a host medium. With a relatively large ratio of apparent-surface to volume and particularly strong physical interactions with the surrounding medium at nano-scale, nano-heterogeneities can potentially affect the elastic(effective or elastic?) properties of the parent medium (matrix) containing them in a significant manner. This has been reported by various theoretical and experimental studies, some of them are discussed in the present paper. To describe the positive (reinforcement) or negative (degradation) effect of the nano-heterogeneities from the modeling perspective, it is necessary to take into account the energy of interfaces/surfaces between nano-heterogeneities and the matrix which, by the fact of the relatively large extent of their apparent surface and their strong physical interaction with their neighborhood, can no longer be neglected compared to those of the volume energy. Thus, to account for the effects of interfaces/surfaces in a nanostructured heterogeneous medium, the coherent interface model is considered in the present investigation within a periodic homogenization procedure. In this interface/surface model, the displacement vector is assumed to be continuous across the interface while the stress vector is considered to be discontinuous and satisfying the Laplace-Young equations. To solve these equations coupled to the classical mechanical equilibrium problem, a numerical simulation tool is developed in a two-dimensional (2D) context using the eXtended Finite Element Method (XFEM) and the Level-Set functions. The developed numerical tool is then used to carry out a detailed analysis about the effect of nano-heterogeneities on the overall mechanical properties of a medium. The nano-heterogeneities are present in the medium initially as cylindrical cavities (circular in 2D) before being reduced to plane cracks (line in 2D) by successive flattenings.