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Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.

The parameters of a narrow small-scale plastic zone in an elastoplastic piece-wise homogeneous body undergoing a shear near the tip of an interfacial crack are calculated under plane strain conditions using the Wiener-Hopf method. Crack faces are in contact with friction. The plastic zone issuing out of the crack tip at an angle to a plane interface between media is modeled as the straight line of a displacement discontinuity involving two sections. Both tangential and normal displacements undergo the discontinuity at the section adjacent to the crack tip that models material destruction area. At the other section, only the tangential displacement experiences the discontinuity. The angle between the plastic zone and interface between the media is defined from the condition that the rate of energy dissipation in the zone is maximal. The sizes of the entire plastic zone, destruction zone and shear opening displacement of the crack in its tip are determined. It is studied how the friction of the crack faces, load, and the mechanical characteristics of the material influence on the parameters of the plastic zone and stress-strain state in the vicinity of the crack tip.

We developed a generalized multiphase-field modeling framework for addressing the problem of brittle fracture propagation in quartz sandstones at microscopic length scale. Within this numerical approach, the grain boundaries and crack surfaces are modeled as diffuse interfaces. The two novel aspects of the model are the formulations of (I) anisotropic crack resistance in order to account for preferential cleavage planes within each randomly oriented quartz grain and (II) reduced interfacial crack resistance for incorporating lower fracture toughness along the grain boundaries that might result in intergranular crack propagation. The presented model is capable of simulating the competition between inter- and transgranular modes of fracturing based on the nature of grain boundaries, while exhibiting preferred fracturing directions within each grain. In the full parameter space, the model can serve as a powerful tool to investigate the complicated fracturing processes in heterogeneous polycrystalline rocks comprising of grains of distinct elastic properties, cleavage planes, and grain boundary attributes. We demonstrate the performance of the model through the representative numerical examples.

This paper investigates the dynamic fracture problems of interfacial cracks in piezoelectric–piezomagnetic (PE–PM) bi-layered composite structures under in-plane coupled electro-magneto-mechanical impact loadings by means of the extended finite element method (X-FEM). Considering the magnetoelectrically impermeable crack-face conditions and multi-filed coupled properties in the PE–PM composites, novel and more suitable crack-tip enrichment functions for interfacial cracks in PE–PM bi-layered composite structures are newly derived and implemented in the X-FEM, where the Newmark method is applied and proved to be effective. As the fracture parameter, the J -integral is evaluated using the domain-form of the path-independent contour integral. For dynamic analysis of interfacial cracks in infinite PE–PM bi-layered composite structures, absorbing layers based on the Sarma absorbing boundary conditions are adopted and applied to avoid the unphysical wave reflections at the artificially introduced boundaries in the X-FEM meshes. In the numerical examples, the validity of the proposed scheme is verified by comparing the numerical solutions provided by the X-FEM with either analytical results obtained by solving the corresponding singular integral equations or possible stationary values obtained by introducing the corresponding absorbing layers. Finally, by the numerical examples, the effects of the applied dynamic loadings, time variable and structural geometries on the dynamic J -integral are analyzed and discussed in detail. Some important conclusions are drawn, which should be helpful for the design and applications of the PE–PM layered composite structures.

The fracture of interfacial crack is the main failure type of jointed rock mass. Therefore, it is very important to study the interfacial fracture of jointed rock mass. For the similarity of jointed rock mass and composites (all are composed by two parts, intact materials and their contact interfaces), the interface fracture mechanics widely used for analysis the interface crack of the composites (bimaterials) can be applied to study the interfacial fracture of jointed rock mass. Therefore, based on the basic theories of interface fracture mechanics, the interfacial fracture of jointed rock mass was analyzed, and one new criterion of interfacial crack initiation for jointed rock mass is proposed. Moreover, based on the proposed interfacial crack initiation criterion, the effect of main influence factors on the interfacial crack initiation of jointed rock mass was analyzed comprehensively. At last, by using the triaxial compression numerical tests on a jointed rock mass specimen with interfacial crack, the theoretical studies were verified.

The present study analyzes the fundamental properties of a rate-dependent cohesive model applied to the description of dynamic mode-II crack propagation. To make a semi-analytical treatment possible, the idealised problem of a crack along the interface between a semi-infinite elastic layer and a rigid substrate is considered. Solutions corresponding to the propagation of the crack tip at a constant speed are constructed. Using asymptotic properties of the solution far from the crack tip allows obtaining the complete solution of the boundary value problem by direct integration without iterations, using a specific form of the shooting method. By conversion of the problem to dimensionless variables, the behavior of the system for all possible crack velocities and arbitrary combinations of material and geometric parameters can be characterized. The dependence of fracture energy and other important characteristics on model parameters and the crack speed can then be analyzed. Even if the approach is applied to a specific form of damage rate dependence and motivated by the analysis of delamination propagation, the same technique could be used for other classes of interfacial cohesive rate-dependent models.

This paper focuses on the interfacial characteristics of dissimilar Ti6Al4V/AA6060 lap joint produced by pulsed Nd:YAG laser beam welding. The process-sensitivity analysis of welding-induced interface joining quality was performed by using the orthogonal design method. Microstructural tests such as scanning electron microscopy and energy dispersive X-ray spectroscopy were used to observe the interfacial characteristics. The mechanism of interfacial crack initiation, which is an important indicator of joint property and performance, was assessed and analyzed. The preferred propagation paths of welding cracks along the interfaces of different intermetallic layers with high dislocation density were analyzed and discussed in-depth. The results indicate that discontinuous potential phases in the micro-crack tip would mitigate the mechanical resistance or performance of the welded joint, while the continuous intermetallic layer can lead to a sound jointing performance under pulsed Nd:YAG laser welding process.

Nanocomposites were prepared by adding graphene nanoplatelets (GNP) into epoxy with a variety of loadings. The thickness of GNPs used in this study was in a range of 1 nm to 10 nm. Nanocomposite film was deposited on the aluminum (Al) substrate via a spinning coating process. Tensile tests were carried out to determine the elastic modulus, ultimate strength and fracture strain of the nanocomposites. Theoretical prediction of the fracture toughness of the film/substrate composite structure with an interfacial crack under mode I loading was derived utilizing linear elastic fracture mechanics theory. Four-point bending tests were performed to evaluate the mode I fracture toughness. It was observed that the performance of the nanocomposite, such as elastic modulus, ultimate strength, and fracture toughness, were significantly enhanced by the incorporation of GNPs and increased with the increase in GNP concentration. The elastic modulus and mode I fracture toughness of the epoxy reinforced with 1 wt.% of GNPs were increased by 42.2% and 32.6%, respectively, in comparison with pure epoxy. Dispersion of GNPs in the epoxy matrix was examined by scanning electron microscope (SEM). It can be seen that GNPs were uniformly dispersed in the epoxy matrix, resulting in the considerable improvements of the ultimate strength and fracture toughness of the nanocomposite.

This paper presents an analysis of symmetric and skew-symmetric weight functions for in-plane interfacial crack problems in piezoelectric bimaterials. The symmetric weight function matrix is obtained by means of the solution of a Wiener–Hopf functional equation and the skew-symmetric weight function matrix is developed by the construction of a corresponding full field solution. The explicit expressions for the symmetric and skew-symmetric weight functions are given and applied to in-plane deformation problems for a semi-infinite crack between two dissimilar piezoelectric materials. The validity of the present method in the determination of the field intensity factors is demonstrated by illustrative examples, in which both piezoelectric bimaterials and piezoelectric/elastic bimaterials are considered. It is shown that, for the present interfacial crack problem, both symmetric and skew-symmetric weight function matrices are necessary in the general integral formula for the evaluation of field intensity factors, and that the contribution of the skew-symmetric element of the applied load is not negligible in fracture analysis.

This paper investigated the performance of single-lap joints with interfacial crack through the finite element method. The finite element method was validated by the G-R solutions at first. And then the influence of geometric parameter of the joint as well as the length of the interfacial crack were discussed. Results showed that the presence of a spew fillet can reduced the stress intensity factors (SIF).The relationship of the crack length ratio and SIF, adhesive thickness ratio and SIF were built.