Orthotropic Bimaterials Research Articles

Analysis of Edge Bridged Crack in Bimaterial Anisotropic Half-Space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half- space is analyzed for a general case of elastic anisotropy bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (ψ - integral) is discussed as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM.

The Effect of an Imperfect Interface on the Singular Stress Field of an Orthotropic Bimaterial Wedge

In this analysis, the effect of an imperfect interface on the stress singularity of an orthotropic elastic bimaterial wedge subjected to traction free boundary conditions, is investigated, where the planes of symmetry are aligned, and one symmetry plane is along the interface and another symmetry plane coincides with the cross-sectional plane. The Stroh formalism with the method of separation of variables are used to obtain the relevant expressions for displacements and stresses. At the interface, only the interfacial tractions and the displacement normal to the interface are assumed to be continuous. The imperfect bond is modeled using a local coordinate system, where each tangential traction component in this local coordinate system is directly proportional to the corresponding displacement discontinuity and inversely proportional to the distance from the wedge apex. The order of singularity is computed numerically for graphite/epoxy wedges and presented for various imperfect interface conditions. The numerical results agree with the available results for the fully bonded case. It is expected that when the axes of local and global coordinate systems are aligned, that the in-plane and antiplane problems are uncoupled, and this feature also can be seen in the numerical results.

On interface crack models with contact zones situated in an anisotropic bimaterial

A boundary value problem for two semi-infinite anisotropic spaces with mixed boundary conditions at the interface is considered. Assuming that the displacements are independent of the coordinate x3, stresses and derivatives of displacement jumps are expressed via a sectionally holomorphic vector function. By means of these relations the problem for an interface crack with an artificial contact zone in an orthotropic bimaterial is reduced to a combined Dirichlet-Riemann problem which is solved analytically. As a particular case of this solution, the contact zone model (in Comninou's sense) is derived. A simple transcendental equation and an asymptotic formula for the determination of the real contact zone length are obtained. The classical interface crack model with oscillating singularities at the crack tips is derived from the obtained solution as well. Analytical relations between fracture mechanical parameters of different models are found, and recommendations concerning their implementation are given. The dependencies of the contact zone lengths on material properties and external load coefficients are illustrated in graphical form. The practical applicability of the obtained results is demonstrated by means of a FEM analysis of a finite-sized orthotropic bimaterial with an interface crack.

Fracture along an interlayer

A nonhomogeneous interlayer is introduced between two dissimilar materials to characterize the transition of the elastic moduli across the bimaterial interface. The 1/√r singularity field near the tip of an advancing interlayer crack is related to the remote interface crack tip field for general aligned orthotropic bimaterials. An approximate but explicit relation for the phase shift between the near tip and the remote singularity fields is derived. Comparisons with analytical and numerical solutions show that the relation is fairly accurate. The interlayer model provides insightful interpretations of several important concepts of interface fracture mechanics, such as stress oscillation, near tip contact and mode mixity. For crack tip mode mixity, ψtip, in the range − π/2 < ψtip < π/2, the crack tip is truly open. The crack is partially closed for ψtip = ± π/2. Plasticity effects associated with dislocation emissions from the crack tip are also considered.

Kinking of an interface crack between two dissimilar anisotropic elastic solids

A detailed analysis of kinking of an interface crack between two dissimilar anisotropic elastic solids is presented in this paper. The branched crack is considered as a distributed dislocation.A set of the singular integral equations for the distribution function of the dislocation density is developed.Explicit formulas of the stress intensity factors and the energy release rates for the branched crack are given for orthotropic bimaterials and misoriented orthotropic bicrystals.The role of the stress parallel to the interface, σ0 is taken into account in these formulas.The interface crack can advance either by continued extension along the interface or by kinking out of the interface into one of the adjoining materials. This competition depends on the ratio of the energy release rates for interface cracking and for kinking out of the interface and the ratio of interface toughness to substrate toughness.Throughout the paper, the influences of the inplane stress σ0 on the stress intensity factors and the energy release rates for the branched crack, which can significantly alter the conditions for interface cracking, are emphasized.

Stress intensity factors and energy release rates of delaminations in composite laminates

Due to the oscillatory characteristics of stresses near interface crack tips, the stress intensity factor K i , i = I, II, III, should be modified and the energy release rate G i , i = 1, 2, 3, of each fracture mode calculated by the virtual crack closure method may not exist. Based upon a near-tip solution for interface cracks between dissimilar anisotropic media, a proper definition for the stress intensity factors and energy release rates for general anisotropic bimaterial interface cracks is provided in this paper, which is applicable for the delaminated composites. Moreover, this definition can be reduced to the classical definition for a crack tip in homogeneous media when the two materials become the same. A simple quadratic relation between K i and G i is derived, which is further reduced explicitly for orthotropic bimaterials. The influence of fiber orientation and the coupling among opening, shearing and tearing mode fracture are studied numerically. The results show that the classical stress intensity factors and energy release rates are still the dominant stress intensity and energy release rate of the mixed mode condition induced by the interface.

Crack extension and kinking in laminates and bicrystals

Singular fields at the tip of an interface crack in anisotropic solids are reviewed with emphasis on establishing a framework to quantify fracture resistance under mixed mode conditions. The concepts of mode mixity and surface toughness are unified by using generalized interface traction components. The similarity between the anisotropic theory and existing isotropic theory is shown. Explicit formulae are given for misoriented orthotropic bimaterials with potential applications envisioned including composite laminates and semiconductor crystals. Competition between crack extension along the interface and kinking into the substrate is investigated using a boundary layer formulation. Several case studies reveal the role of anisotropy. An explicit complex variable representation for orthotropic materials and a solution to a dislocation interacting with a crack are presented in two self-contained Appendices.

Mechanics of dynamic debonding

Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined. Emphasis is placed on extending an established frame work for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response. For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity. This simplifies the problem, rendering the Stroh techniques applicable. In general, the singularity oscillates, similar to quasi-static cracks. The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds. In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed. Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials. Implications on crack branching and substrate cracking are discussed. Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol’dshtein and Dugdale problems. Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed.