Dissimilar Elastic Materials Research Articles

A Fully Coupled Normal and Tangential Contact Model to Investigate the Effect of Surface Roughness on the Partial Slip of Dissimilar Elastic Materials

By adopting a global search method for all shear tractions in the contacting area and using an alternative convergence criterion regarding load balance in the lateral direction, the newly developed algorithm provides stable solutions to partial-slip problems of elastically dissimilar materials. The model is validated via the comparison between the simulation and literature results for a sphere-on-flat problem under fully coupled conditions. It is then employed to investigate the influence of surface roughness parameters including the root mean square (RMS) roughness and RMS slope on partial-slip solutions under coupled conditions. Since the gross sliding condition is modified under coupling effects, the relationship between the ratio of the stick area to the contacting area (stick ratio) and tangential load in the coupled case, unlike that in the uncoupled one, becomes non-linear for all tested rough surfaces. Under low or medium tangential loads, the surface with a higher RMS gradient or a lower RMS roughness experiences more stick regions within the contacting area. This trend then becomes irregular at higher tangential loads.

On the effective property of a micro-cracked and a microscopically curved interface between dissimilar materials

Two different types of imperfect interfaces between dissimilar elastic materials under antiplane deformations are studied using micromechanics concepts. Interfaces containing interfacial micro-cracks and those that are microscopically wavy (sinusoidal) are modeled as spring-like and membrane-like respectively at the macroscopic level. The strain energy in the microscopic configuration is equated to that in the macroscopic configuration in order to estimate the effective properties of the imperfect interfaces. The boundary value problems for computing the strain energy at the microscopic level are formulated and solved by using boundary integral equations.

Ellipsoidal inhomogeneity with anisotropic incoherent interface. Multipole series solution and application to micromechanics

The ellipsoidal inhomogeneity with transversely isotropic incoherent interface is considered in the conductivity and elasticity context. The general imperfect interface is modeled by the first order approximation of thin transversely isotropic interphase layer. This model expands the Gurtin et al. (1998) theory of curved deformable interfaces in solids with a nanometer-scale microstructure to the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface moduli. The rigorous analytical solution to the conductivity and elasticity problems has been obtained by the multipole expansion method in terms of ellipsoidal solid harmonics. An accurate fulfillment of the imperfect interface conditions reduces the model boundary value problem to the linear algebraic system for multipole strengths. These results apply equally to the inhomogeneities with anisotropic interphases and nano level incoherent interfaces. The obtained solutions are valid for the non-uniform far loading and are readily incorporated in the many-particle (finite cluster or representative unit cell) model of heterogeneous solid with anisotropic incoherent interface. The tensors of effective conductivity and elastic stiffness of composite with ellipsoidal inhomogeneities are evaluated using Maxwell homogenization scheme. The obtained accurate numerical data indicate that the effective properties of composite may vary widely due to shape of inhomogeneities and the interface anisotropy ratio. Taking the incoherency of interface into account may increase reliability of predicting the behavior of nanostructured solids.

Elastic equilibrium of spherical particle composites with transversely isotropic interphase and incoherent material interface

The rigorous analytical solution to the unit cell model of spherical particle composite with transversely isotropic interphase and incoherent material interface has been obtained by the multipole expansion method. To this end, a general expression of the displacement vector in spherical transversely isotropic solid in terms of the vector spherical harmonics has been derived. By accurate fulfillment of the contact conditions, the model boundary value problem is reduced to the linear algebraic system. The anisotropic interface model has been developed as the first order approximation of the transversely isotropic interphase. Relevance of this model to the theory of material interfaces and its applicability in the nanomechanics context is discussed. The developed model expands the theory of curved deformable interfaces of Gurtin et al. [Phil. Mag. A 78 (1998) 1093] on the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface elastic moduli. Taking incoherency of the nano level interfaces into account enables more realistic models and thus increases the predictive power the homogenization theory of nanostructured solids. The obtained accurate numerical data discover a significant effect of the interphase/interface anisotropy on the local stress and effective stiffness of spherical particle composite.

Fracture mechanics analysis of bimaterial interface cracks using the generalized finite difference method

This paper makes the first attempt to apply the generalized finite difference method (GFDM), a recently developed meshless collocation method, for fracture mechanics analysis of dissimilar elastic materials with interfacial cracks. The main idea of the GFDM is to divide the entire computational domain into a set of overlapping small subdomains in which the local Taylor series expansion and moving-least square approximation are employed for generating the local systems of linear equations. Since the method is meshless and no element connectivity is needed, the burdensome remeshing procedures associated with the finite element method (FEM) is avoided. The multi-domain GFDM technique is used to handle the non-homogeneity of the cracked dissimilar materials. The displacement extrapolation method (DEM), which avoids the direct calculation of the oscillatory near-tip displacement and stress fields, is employed to compute the complex stress intensity factors (SIFs) for cracked composite bimaterials. Several representative numerical examples are presented and discussed to demonstrate that the present method is highly accurate and relatively robust for interface crack analysis of composite bimaterials.

Peridynamic modeling of bonded-lap joints with viscoelastic adhesives in the presence of finite deformation

This study concerns damage initiation and its progression in bonded-lap joints with adhesives under quasi-static loading conditions. The weak form of peridynamic (PD) equilibrium equation is derived based on the nonlinear response of elastic adherends and viscoelastic adhesives. The peridynamic deformation gradient tensor is evaluated in the bond-associated domain of interaction using the PD differential operator. The fidelity of this approach is established in the absence of failure by comparison with benchmark solutions for relaxation and creep response under simple loading conditions. Subsequently, the PD predictions in a domain of two dissimilar elastic and viscoelastic materials are verified against the finite element predictions. Finally, a double-lap and a single-lap joint are considered for failure initiation and growth. The PD predictions successfully capture the deformation response and damage initiation sites and propagation paths.

Near-tip singular fields for an interface anticrack between dissimilar anisotropic elastic materials

We study the near-tip singular fields for an interface anticrack between dissimilar anisotropic elastic materials using the sextic Stroh formalism. The stress and strain fields exhibit an oscillatory singularity and a square root singularity at the anticrack tip. A complex and a real strain/rotation intensity factors are introduced to scale, respectively, the two singularities. An explicit expression for the negative anticrack contraction force is obtained in terms of the proposed intensity factors. We illustrate our results using an example in which the bimaterial is orthotropic. In this typical case, a complex stress intensity factor can also be defined to replace the complex strain/rotation intensity factor.

The two-dimensional fretting contact with a bulk stress. Part II – Loading history and dissimilar elastic materials

The contact model for similarly elastic materials advanced in the companion paper is enhanced to account for the more general case of contacting bodies with different elastic properties. The latter contact model, involving dissimilarly elastic bodies under partial slip, is particularly difficult to solve due to the mutual interaction between the normal and the shear tractions. As opposed to the contact of similar elastic materials, pressure is affected by the shear tractions and vice versa. Therefore, the contact submodels in the normal and in the tangential direction are not independent. The connection can only be overcome in an iterative manner, by adding a new external loop to the contact algorithm, in which the solutions of the systems in the normal and in the tangential directions are mutually adjusted by successively solving both systems until convergence is reached. Moreover, with friction being a dissipative process, any state depends upon the process path, i.e., on all previous states attained during the loading history. The contact model is solved as a series of quasi-static states that are expected to replicate the loading path. Two levels of iterations are added to the model of similarly elastic materials, described in the companion paper, to account for the dissimilarity in the elastic properties. The contact process is reproduced on a prolonged loading history, consisting in the first fretting loops. The distributions of contact tractions are obtained using a technique for the fast computation of convolutions involving the fast Fourier transform. The conducted simulations prove the method robustness and its application in the modelling of the fretting processes.

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

The current work models a weak (soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micro-crazed interface can be readily computed. The effective stiffness is an important quantity needed for expressing the interfacial conditions in the spring-like macro-model of soft interfaces. Specific case studies are conducted to gain physical insights into how the effective stiffness of the interface may be influenced by the details of the interfacial micro-crazes.

Nonmonotonicity of the Frictional Bimaterial Effect

AbstractSliding along frictional interfaces separating dissimilar elastic materials is qualitatively different from sliding along interfaces separating identical materials due to the existence of an elastodynamic coupling between interfacial slip and normal stress perturbations in the former case. This bimaterial coupling has important implications for the dynamics of frictional interfaces, including their stability and rupture propagation along them. We show that while this bimaterial coupling is a monotonically increasing function of the bimaterial contrast, when it is coupled to interfacial shear stress perturbations through a friction law, various physical quantities exhibit a nonmonotonic dependence on the bimaterial contrast. In particular, we show that for a regularized Coulomb friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is a nonmonotonic function of the bimaterial contrast and provides analytic insight into the origin of this nonmonotonicity. We further show that for velocity‐strengthening rate‐and‐state friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is also a nonmonotonic function of the bimaterial contrast. Results from simulations of dynamic rupture along a bimaterial interface with slip‐weakening friction provide evidence that the theoretically predicted nonmonotonicity persists in nonsteady, transient frictional dynamics.

On Solvability of the BVP Formulated in Terms of Displacement Orientations on the Interface Between Dissimilar Elastic Materials

On Solvability of the BVP Formulated in Terms of Displacement Orientations on the Interface Between Dissimilar Elastic Materials

Boundary integral formulation for interfacial cracks in thermodiffusive bimaterials

An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight function matrices are used together with a generalized Betti's reciprocity theorem in order to derive a system of integral equations that relate the applied loading, the temperature and mass concentration fields, the heat and mass fluxes on the fracture surfaces and the resulting crack opening. The obtained integral identities can have many relevant applications, such as for the modelling of crack and damage processes at the interface between different components in electrochemical energy devices characterized by multi-layered structures (solid oxide fuel cells and lithium ions batteries).

Crack propagation in anisotropic composite structures

A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053-1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures.

Mode III crack propagation in a bimaterial plane driven by a channel of small line defects

We consider the quasi-static propagation of a Mode III crack along the interface in a bimaterial plane containing a finite array of small line defects (microcracks and rigid line inclusions). The microdefects are arranged to form a channel around the interface that can facilitate (or prevent) the crack propagation. The two dissimilar elastic materials are assumed to be weakly bonded, so that there is no kinking of the main crack from the straight path. On the basis of asymptotic formulae obtained by the authors, the propagation is analysed as a perturbation problem and the incremental crack advance is analytically derived at each position of the crack tip along the interface relative to the position of the defects. Numerical examples are provided showing potential applications of the proposed approach in the analysis of failure of composite materials. Extension to the case of infinite number of defects is discussed.

Investigation of the Initial Stage of Kinking of an Interface Crack at an Angular Point of the Interface of Two Media

We present the solution of the problem of initial process zone under the conditions of plane deformation in the vicinity of an angular point on the interface of two dissimilar elastic materials playing the role of the origin of an interface crack. We study the dependences of orientation, length, and crack opening displacement on the external load, opening angle of the interface, and the elastic parameters of the joined materials. The conditions of crack initiation are analyzed by using the deformation criterion.

Perturbation analysis of Mode III interfacial cracks advancing in a dilute heterogeneous material

The paper addresses the problem of a Mode III interfacial crack advancing quasi-statically in a heterogeneous composite material, that is a two-phase material containing elastic inclusions, both soft and stiff, and defects, such as microcracks, rigid line inclusions and voids. It is assumed that the bonding between dissimilar elastic materials is weak so that the interface is a preferential path for the crack. The perturbation analysis is made possible by means of the fundamental solutions (symmetric and skew-symmetric weight functions) derived in Piccolroaz et al. (2009). We derive the dipole matrices of the defects in question and use the corresponding dipole fields to evaluate “effective” tractions along the crack faces and interface to describe the interaction between the main interfacial crack and the defects. For a stable propagation of the crack, the perturbation of the stress intensity factor induced by the defects is then balanced by the elongation of the crack along the interface, thus giving an explicit asymptotic formula for the calculation of the crack advance. The method is general and applicable to interfacial cracks with general distributed loading on the crack faces, taking into account possible asymmetry in the boundary conditions. The analytical results are used to analyse the shielding and amplification effects of various types of defects in different configurations. Numerical computations based on the explicit analytical formulae allows for the analysis of crack propagation and arrest.

Fracture Analyses for Interface Corners in Elastic Materials Subjected to Thermal Loading

By employing the Stroh formalism for two-dimensional anisotropic thermoelasticity, fracture analyses of interface corners between two dissimilar anisotropic elastic materials under thermal loadings are considered in this paper. It was proved that the consideration of thermal effects will not influence the stress singularity but will induce heat flux singularity if the singularity of the temperature field is not permissible. To calculate the stress intensity factors via path independent H-integral, it was found that the one proposed previously for the mechanical loading conditions should be modified by adding an additional surface integral accounting for the thermal effects. Two examples considering cracks and corners in isotropic plates are presented to show the correctness and validity of the modified H-integral.

Interfaces Between two Dissimilar Elastic Materials

Due to the mismatch of elastic properties, stress singularity usually occurs near the tips of interface corners/cracks between two dissimilar materials, which may initiate failure of materials and structures. The singular order of stresses near the interface corners/cracks is a good index for the understanding of failure initiation. However, in engineering applications one usually feels only the knowledge of singular orders is not enough for the prediction of failure initiation since it only reflects the local combination and is nothing to do with the far-field environment and the external loading condition. These global influential factors are reflected through another important parameter – stress intensity factor. Therefore, for interface problems it is important to know the singular orders as well as their associated stress intensity factors. However, due to the complexity of stresses near the tip of interface corners/cracks, most of the existing calculation methods will encounter the problems of accuracy and convergency. With this understanding, recently several works regarding the interfaces between two dissimilar elastic materials are studied in our research group. One is devoted in the improvement of boundary element method by including the fundamental solution of bimaterials, and the other is the improvement of the computational method for stress intensity factors by establishing a path independent H-integral for general interface problems.

Modeling of Cracks Crossing an Interface between Dissimilar Elastic Anisotropic Materials

Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimilar elastic anisotropic materials. The link to the configurational forces approach is suggested.

The Effect of Frequency in the Problem of Interface Crack Under Harmonic Loading

The influence of the frequency of harmonic loading on displacements and tractions at the penny-shaped interface crack between two dissimilar elastic materials is studied. The problem is solved by the boundary integral equations method.