Bimaterial Interface Cracks Research Articles

Application of J-integral to adhesive contact under general plane loading for rolling resistance

In the present work, a mechanical model for two-dimensional non-slipping adhesive contact between dissimilar elastic solids under general loading, namely, normal forces, tangential forces and moments is proposed. The general solutions are obtained analytically with the stresses at the contact edges exhibiting oscillatory singularity, similar to those at a bimaterial interface crack. The well-known J-integral under the current context is analyzed. Its application under the selected integration contour readily gives the relationship between the stress intensity factors and energy release rates at the contact edges. With the results rolling adhesion between two solids with parabolic profiles is considered further. The applied moment can be directly determined by the difference in energy release rates at the trailing and leading edges and hence the rolling resistance even for adhesive contact with cohesive zones. These results provide the foundation for understanding some tribological phenomena associated with adhesion.

Instantaneous thermal fracture behaviors of a bimaterial with a penny-shaped interface crack via generalized fractional heat transfer

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to pronounced thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model.

A novel strength-energy criterion for bimaterial interface crack propagation

This paper aims to propose a novel fracture criterion to predict complex propagation behaviors of a bimaterial interface crack, either delaminating along the interface or kinking out of the interface into one of the adjoining materials. A strength-based criterion is used to predict the crack deflection, and an energy-based criterion is adopted to assess delamination along the interface. To determine the competition between these two cracking modes, a competing strategy is developed by comparing the strength-based and energy-based criteria. This coupled strength-energy fracture criterion eliminates the disadvantages arising from a criterion based solely on strength or energy, and is convenient to be calculated and embedded into numerical models. As practice, we embed the criterion into a homemade extended finite element model to simulate bimaterial interface crack propagation. Several numerical examples are performed to verify the effectiveness and accuracy of the developed model. Finally, this model is applied to simulate an interface crack propagation in a sandwich structure that has a specially designed peel-stopper. Parametric studies reveal that the material and interface toughness as well as geometrical dimensions of the structure have significant effects on the propagation mode of the interface crack. The results provide practical suggestions on the optimal design of peel-stopper in sandwich structures.

Interface crack analysis in 2D bounded dissimilar materials using an enriched physics-informed neural networks

This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples.

Application of a hierarchical quadrature element method to interface crack analysis in bi-material systems

This paper presents an extension of the hierarchical quadrature element method (HQEM) with p-convergence to evaluating fracture mechanical parameters of bi-material interface cracks. The numerical implementation of HQEM in combination with the virtual crack closure method (VCCM) is comprehensively illustrated, and the formulas for calculating the strain energy release rate (SERR) are rederived. The relationship between components of SERR and the complex stress intensity factors (SIFs) is established. In addition, the effectiveness of an auxiliary parameter related to the dual energy release rates in measuring the accuracy of the present method is examined.The feasibility of applying HQEM to the interface crack problems is demonstrated by investigating the benchmark problem of an infinite bi-material plate with a central interface crack. Two loading cases are considered, including pure tensile loading and mixed tensile-shear loading. The influence of the crack tip element size Δa on the convergence characteristics and computational accuracy of fracture parameters is quantitatively investigated to provide guidance for choosing the most reasonable value of Δa. Numerical results show that even with very coarse meshes, together with a virtual crack extension consisting of only one element, HQEM yields highly accurate results for the total SERR and the complex SIFs, making it suitable for complex, large-scale interface crack problems in dissimilar media.

Modelling and Investigation of the Dynamic Behavior of a Penny-Shaped Interface Crack in Piezoelectric Bimaterials

In this section, the dynamic propagation behavior of a penny-shaped interface crack in piezoelectric bimaterials is analyzed. The objective of this paper is to use the boundary conditions of the penny-shaped interface crack to study the dynamic propagation of the crack under the action of load, so as to provide some valuable implications for the fracture mechanics of the piezoelectric bimaterials and simulate the interface crack between piezoelectric bimaterials, it is necessary to establish a suitable model and give appropriate boundary conditions according to the actual situation. The elastic displacement and potential equations are constructed according to the structural characteristics of the circular crack. In the case of a given displacement or stress, the Laplace transform and Hankel transform are used to simplify the problem into an integral equation with unknown functions. According to the boundary conditions, the corresponding unknowns are obtained, and the closed solution is derived. The results show that the fracture toughness of a penny-shaped interface crack in piezoelectric bimaterials is related to the thickness of the material, the impact time, the material characteristics, and the electric field. At the same time, it can be found that different materials have different roles in the crack propagation, so it is very important to study the crack opening displacement (COD) intensity factor of the crack for safety design.

Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method

This paper presents a new extended isogeometric boundary element method (XIGABEM) for the analysis of cracks in two-dimensional bimaterial interfaces. The classical NURBS approximations used in isogeometric formulations are augmented with functions based on the first two terms of the crack-tip stress and displacement series expansions. The first term is related to the complex stress intensity factor (SIF) and allows the numerical method to capture the singular and oscillatory near-tip behaviour, while the second accounts for the T-stress contribution to the solutions. The proposed enrichment strategy only introduces three additional degrees of freedom per crack tip, which are accommodated in a square linear system by a crack tip tying constraint and a novel condition on the stress parallel to the tip. These supplementary relations also cause the enrichment parameters to become proxies for the SIFs and T-stress. Therefore, the crack-tip factors can be obtained directly from the solution vector given by XIGABEM, eliminating the need for costly computational post-processing techniques. Several benchmark examples, including both straight and curved cracks, are presented to demonstrate the accuracy and convergence of the proposed method. The direct XIGABEM solutions for the SIFs and T-stress compare favourably against those from the literature.

A hierarchical quadrature element method for energy release rate calculation in combination with the virtual crack closure technique

In this paper, the virtual crack closure technique (VCCT) is combined with a hierarchical quadrature element method (HQEM) with p-convergence for the evaluation of strain energy release rate (SERR) for the first time. A universal SERR formula suitable for HQEM is proposed, regardless of the node arrangements and the number of nodes per element boundary. The validity of the present formula is evaluated by the typical cases of mode I and II fracture of homogeneous materials, as well as the bimaterial interface crack problem. A comprehensive comparison with several widely-acknowledged h-version elements shows that the present approach can significantly improve the accuracy and efficiency of SERR calculation even with a relatively coarse mesh and thus be readily used as a viable and effective tool for fracture analysis.

Propagating Schallamach-type waves resemble interface cracks.

Intermittent motion, called stick-slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick-slip arises due to the propagation of slow detachment waves at the interface. Here we analyze two distinct detachment waves moving parallel (Schallamach wave) and antiparallel (separation wave) to applied remote sliding. Both waves cause slip in the same direction, travel at speeds much lesser than any elastic wave speed, and are therefore describable using the same perturbative elastodynamic framework with identical boundary conditions. A numerical scheme is used to obtain interface stresses and velocities for arbitrary Poisson ratio, along with closed-form solutions for incompressible solids. Our calculations reveal a close correspondence between moving detachment waves and bimaterial interface cracks, including the nature of the singularity and the functional forms of the stresses. Based on this correspondence, and coupled with a fracture analogy for dynamic friction, we develop a phase diagram showing domains of possible occurrence of stick-slip via detachment waves vis-á-vis steady interface sliding. Our results have interesting implications for sliding and stick-slip phenomena at soft interfaces.

An efficient meshless method for bimaterial interface cracks in 2D thin-layered coating structures

The interface crack problems in thin-layered coating/substrate structures are analyzed by using the generalized finite difference method, a recently developed meshless collocation method. Since the method is meshless, no element connectivity is needed and the burdensome remeshing of the domain similar to the finite element method is avoided. The multi-domain technique is employed to handle the non-homogeneity of the composite materials. The complex stress intensity factors of the bimaterial interface cracks are computed by using the displacement extrapolation method. Accurate and reliable numerical results with only a small number of degrees of freedom can be obtained for relatively small layer-to-substrate thicknesses. Numerical results calculated by using the boundary element method are also given for the purpose of comparison.

Analysis of bimaterial interface cracks using the localized method of fundamental solutions

This short communication makes the first attempt to apply the localized method of fundamental solutions (LMFS), a newly-developed meshless collocation method, for fracture mechanics analysis of bimaterial interface crack problems. The asymptotic crack-tip field for bimaterial interface cracks exhibits an oscillatory behavior which is quite different from that for in-plane cracks in homogeneous materials. This paper describes an enriched LMFS approach whereby a set of enrichment functions are embedded in the classical LMFS approximation to account for the presence of interface cracks. This method automatically incorporates the oscillatory behavior of the near-tip fields and thus the complex stress intensity factors (SIFs) can be solved accurately with no or very little remeshing. The results presented show excellent accuracy for a range of two-dimensional (2D) bimaterial with interface cracks, where the complex SIFs for interface cracks are computed with relatively errors less than 0.6 per cent.

Fracture mechanics analysis of bimaterial interface cracks using an enriched method of fundamental solutions: Theory and MATLAB code

In this paper we study the application of the method of fundamental solutions (MFS) to interface crack analysis in linear elastic bimaterial fracture mechanics. Such problem presents some modelling difficulties because of the oscillatory behavior of the local asymptotic fields in the neighborhood of the interface crack-tip. The present approach is based on the combination of the classical MFS approximation for linear elasticity problems and a set of enrichment functions that take into account the asymptotic behavior of the near-tip displacement and stress fields. The enriched MFS technique automatically incorporates the oscillatory crack-tip behavior and thus can significantly improve the computational accuracy of the displacements and stresses in the vicinity of the crack-tip, even with a relatively coarse MFS model. A multi-domain MFS technique and the displacement extrapolation method (DEM) are used to compute the complex stress intensity factor (SIF) of the cracked bimaterials. Several benchmark numerical examples are presented to illustrate the accuracy and efficiency of the present method. Results calculated by using the boundary element (BEM) method are also given for the purpose of comparison.

Jordan-form special solutions corresponding to arbitrary anti-plane shear forces in polynomial forms imposed on bimaterial interfacial crack surfaces

Bimaterial anti-plane interfacial crack problems with arbitrary distributed forces applied on crack surfaces are numerically investigated. The problems are in essence a kind of boundary value problems about Laplace's equations. Previous work of using Symplectic analytical singular element (SASE) with high-order accuracy and other singular finite elements for calculating mode III stress intensity becomes invalid when the distributed forces on each surface are different. In this paper, Jordan-form special solutions (JFSS) are proposed for the first time. We derive the JFSS for present problems and use them to improve displacement modes of SASE. The distributed forces are therefore converted into equivalent nodal forces of the nodes around SASE. The new SASE is found to be directly and conveniently used for cases where the two distributed forces are either equal (even both zero) or not equal. Numerical examples are provided to demonstrate the effectiveness and accuracy of the present method. The necessity and effectiveness of the JFSS is also validated. Moreover, the JFSS can be applied to some other physical problems represented by the Laplace's equation.

Numerical investigation of bimaterial interfacial crack with interaction of voids and inclusions using XFEM

This article is presented to investigate the influence of several discontinuity like interfacial-crack, void and inclusion in the bimaterial plate, to analyze the normalized mixed-mode stress intensity factor (NMMSIFs) using XFEM under the uniaxial tensile load with considering the several numerical problems. It is investigated the normalized stress intensity factors (NSIFs) for an isotropic bimaterial plate and NMMSIFs for an isotropic-orthotropic bimaterial plate through varying the single-multi voids/inclusions position while its above, aligned and away from the interfacial edge crack and center crack of the bimaterial plate. It is also analyzed the void/inclusion several shape influence in the bimaterial plate. It is observed higher and fluctuating SIFs obtained with more number of voids/inclusions, influence of elliptical and diamond shape of void/inclusion is higher.

Analysis of the Bimaterial Interface Cracks Based on Configurational Forces

Abstract In this paper, an innovative interface fracture criterion is proposed based on the concept of configurational forces in material space. In this criterion, the crack-tip configurational forces as the driving force are introduced to describe the interface crack evolution under mixed-mode loading conditions. And it assumes that the interface crack propagates due to the competition of resultant configurational forces with interface fracture toughness. The analytical expression of the configurational forces is obtained by differentiating the elastic strain energy density and conservative integral for interface cracks. And the relation of interface crack-tip configurational forces with classical complex intensity factors is obtained through strict mathematical deduction. The interface crack-tip configurational forces are evaluated for a classic interface crack problem covering a wide range of bimaterial oscillation indexes. The configurational forces-based interface fracture criterion is validated through series interface fracture experiments. The proposed criterion may provide a novel framework for the analysis of interface fracture under complex loading conditions.

An oblique circular cylinder element for 3D interfacial cracks in composites

This study further extends a developed symplectic analytical singular element (SASE) library to include three-dimensional (3D) cracks in dissimilar materials. We construct a trial symplectic eigen solution for 3D bimaterial interfacial cracks and use it as the crack tip enrichment to define the interior displacement field of a new singular element. The symplectic approach is applied for the numerical modelling of 3D bimaterial cracks for the first time. In the derivation, a non-standard shape of the 3D crack-tip element, i.e., a cylinder with two oblique ends with arbitrary orientations, is considered to better fit the mesh of curved 3D cracks. It is proven that the proposed 3D element has improved the accuracy and is still convenient to use. The present contribution has provided a new insight for choosing effective and efficient crack tip enrichments of 3D interfacial cracks, and is also an important step forward of the SASE library.

Joule heating effect on thermal stress for a bi-material interface crack

The electric-induced Joule heat plays a dominant role for the fracture and failure in electronic devices, particularly in those with bi-material interfaces, yet the effect of Joule heat on temperature elevation and thermal stress for a bi-material interface crack remains incompletely understood. To this end, we develop a coupled electro-thermo-mechanical model for the bi-material interface crack using the extended finite element method. A novel near-tip asymptotic function is introduced as the enrichment field in the finite element approximations of electrical potential and temperature, which well reproduces the singularities of electric current and heat flux near the bi-material interface crack. Using the domain form of the interaction integral, the complex stress intensity factors and energy release rate are evaluated for bi-material interface cracks. The results of several benchmarking tests demonstrate the accuracy and robustness of the proposed model. The effects of the Joule heat and the mismatch of material properties on the stress intensity factors and energy release rate at the interfacial crack tip are investigated. The results not only reveal the significant contribution of the Joule heating effect on temperature elevation, thermal stress, and energy release rate for a bi-material interface crack, but also provide practical suggestions on the optimal design of multilayered electronic devices to reduce thermal stress and prevent crack propagations.

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.

Orthogonalized Generalized Iso-Geometric Analysis (OGIGA) and its applications to problems of fracture mechanics

Ill conditioning of system matrices is one of the drawbacks of Generalized/eXtended IsoGeometric Analysis (GIGA/XIGA), which results in increase in computational cost in the case of iterative solvers or erroneous results in the case of direct solvers. Linear dependency between the basis functions which can be measured in terms of smallest angle among all the bases is one of the attributes of ill conditioning in XIGA. In the present study, a simplified method to find the smallest angle among all the bases is introduced. Also to reduce the problem of ill conditioning, Orthogonalized Generalized IsoGeometric Analysis (OGIGA) is proposed in which the standard and the corresponding enriched basis functions are orthogonalized. In order to study the performance of present method, various fracture mechanics problems like 2-D homogenous cracks, bi-material interface cracks, inclined cracks and 3-D crack problems are chosen. The effect of crack position and the radius of enrichment zone on accuracy, scaled condition number and smallest angle among all the bases is studied. The results obtained from the proposed OGIGA method are compared with results obtained from standard XIGA and XIGA with enrichment function orthogonalization (OE-XIGA) (Agathos et al., 2019). In all the cases considered, the conditioning of system matrices is significantly improved by employing present methodology and it can be easily extended to wide variety of problems.

Novel special crack-tip elements for interface crack analysis by an efficient boundary element method

This paper presents a new set of novel special crack-tip elements for analysis of interface cracks in linear elastic composite bimaterials by using the boundary element method (BEM). Such interface crack problems present some simulation difficulties based on the conventional numerical methods because the asymptotic crack-tip fields in this case exhibit an oscillatory behavior which is quite different from that in a cracked homogeneous material. The novel special crack-tip elements developed in this study contain the correct local asymptotic behavior of the displacement and stress fields at the tip of an interface crack, and can thus appropriately describe the oscillatory near-tip displacement and stress fields for cracked composite bimaterials. The novel special crack-tip elements are implemented into a BEM, which can significantly improve the computational accuracy of the complex stress intensity factor (SIF) for an interface crack even with a relatively coarse mesh. The proposed computational strategy for interface crack analysis based on the novel special crack-tip elements also enables a direct and accurate evaluation of the complex SIF at the collocation point extremely close to the crack-tip. Several numerical examples are presented and discussed to demonstrate that the present method based on the novel special crack-tip elements is pretty simple, highly accurate, and relatively robust with respect to the size of the used crack-tip elements.