Bimaterial Systems Research Articles

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.

A re-usable negative stiffness mechanical metamaterial composed of Bi-material systems for high energy dissipation and shock isolation

Mechanical metamaterials with negative stiffness (NS) effects are able to dissipate mechanical energy repeatedly according to the “snap-back” strategy. Nevertheless, the strategy is merely efficient when a plethora of NS cells are lined together in series. Limitations of the strategy bring challenges to ameliorate the capacity of energy dissipation for the NS. In the present research, an unique re-usable NS mechanical metamaterial made up of Bi-material systems was suggested and fabricated, which is able to dissipate energy even supposing such metamaterial was merely made up of a single unit. To get a thorough knowledge of the metamaterial’s quasi-static mechanical characteristics, a combination of loading-unloading experiments and finite element method (FEM) has been conducted. The effects of structural arguments on the mechanical characteristics were then revealed employing the experimentally authenticated numerical model. The metamaterial possesses outstanding re-usability and a large capacity for energy dissipation, according to the findings of quasi-static tests. Finally, plate-impact tests were executed to explore the cushion performances of this metamaterial. The presented Bi-material NS mechanical metamaterial demonstrated notable potential in energy dissipation and shock isolation.

Numerical simulation of interfacial and subinterfacial crack propagation by using extended peridynamics

The interaction between crack propagation and interfaces is one of the critical problems in bimaterial systems. In this paper, interfacial and subinterfacial fracture behaviors are simulated to investigate this interaction. The modeling approach for bimaterial structures is first introduced, where the extended bond-based peridynamic model is adopted. Then a convergence study is carried out with a bimaterial plate containing two asymmetric inclusions under tensile load. The comparison with the finite element solution validates the proposed modeling approach. Subsequently, several interfacial and subinterfacial fracture cases are considered to pinpoint the influence of interfaces on crack propagation. The numerical results show that the proposed method can satisfactorily capture the interplay between interfaces and crack propagation. Furthermore, in the subinterfacial fracture case, an equilibrium state of mode-I crack growth is successfully obtained, implying that a specific loading condition can counteract the effect of the interface.

Recent Development Strategies for Bismuth-Driven Materials in Sustainable Energy Systems and Environmental Restoration.

Bismuth(Bi)-based materials have gained considerable attention in recent decades for use in a diverse range of sustainable energy and environmental applications due to their low toxicity and eco-friendliness. Bi materials are widely employed in electrochemical energy storage and conversion devices, exhibiting excellent catalytic and non-catalytic performance, as well as CO2 /N2 reduction and water treatment systems. A variety of Bi materials, including its oxides, chalcogenides, oxyhalides, bismuthates, and other composites, have been developed for understanding their physicochemical properties. In this review, a comprehensive overview of the properties of individual Bi material systems and their use in a range of applications is provided. This review highlights the implementation of novel strategies to modify Bi materials based on morphological and facet control, doping/defect inclusion, and composite/heterojunction formation. The factors affecting the development of different classes of Bi materials and how their control differs between individual Bi compounds are also described. In particular, the development process for these material systems, their mass production, and related challenges are considered. Thus, the key components in Bi compounds are compared in terms of their properties, design, and applications. Finally, the future potential and challenges associated with Bi complexes are presented as a pathway for new innovations.

Stress intensity factors for micro- and macroscale bimaterial cantilevers and bend specimens

Bilayered materials with different properties play an important role in several fields of engineering to improve the mechanical, thermal, electrical, magnetic characteristics of structures. In order to determine the fracture toughness of such bimaterials, experimental measurements must be combined with numerical calculations, which is a tremendous effort. Therefore, a procedure is presented which enables a simple determination of the (critical) stress intensity factor for bimaterial bend specimens. The procedure is applicable for nano- to macroscale cantilevers and three-point bend specimens consisting of linear-elastic or elastic-plastic film and substrate materials. By finite element computations, the procedure is verified for a wide range of Young's moduli combinations, layer heights, and crack lengths. Possible limitations of the procedure are worked out. Practical applications for concrete bimaterial systems are presented, as well as the usage as a failure assessment tool.

Propagation of conductive crack along interface of piezoelectric/piezomagnetic bimaterials

This paper investigates the fracture characteristics of a Yoffe conductive crack moving along the interface of piezoelectric (PE)/piezomagnetic (PM) bimaterials. By assuming that the tangential electric- and magnetic-fields along the crack surface are zero and that the speed of the moving crack is lower than the minimum shear wave speed of the bimaterial system, the considered problem can be transformed into a Riemann–Hilbert boundary value problem of vector form. Then, the singularity parameters are exactly solved for different speed regions. In contrast to the anti-plane moving crack model including impermeable and permeable crack-face assumptions along the interface of magnetoelectroelastic (MEE) bimaterials studied before, which shows inverse square-root singularity, three novel kinds of singularities are found as the speed of the moving crack is varied for the present PE/PM interface model, which can be defined as δ1,2 = − 1/2 ± ie (Case 1), δ1,2 = − 1 ± ie (Case 2) and δ1,2 = − 1/2 ± κ (Case 3), and the third parameter δ3 = − 1/2 always holds true for all three cases. Two bimaterial combinations, i.e., BaTiO3/CoFe2O4 and BaTiO3/Terfenol-D, are numerically examined. Different from the piezoelectric case, Case 3 does not appear for BaTiO3/CoFe2O4 bimaterial combination. Above all, the singularity parameters significantly depend on the speed of the moving crack and the material properties of bimaterial systems.

Adhesion of three-dimensional printing on textile fabrics: Inspiration from and for other research areas

Combining textile fabrics with three-dimensional printed items can be a good approach to save time and money as compared with purely three-dimensional printed large-scale objects, to reach desired position-dependent mechanical properties, for design and technological purposes. The main challenge in such bi-material systems is the adhesion between both partners of the composites. Although some experimental research on this topic has been performed during the last years, only few theoretical investigations exist which may support striving for material combinations with higher adhesion. Here, we give an overview of the recent state of experimental research on adhesion in textile/polymer composites as well as of theoretical investigations on adhesion inside the three-dimensional printed part. Combining both topics, we suggest further research approaches to increase the textile/polymer adhesion.

Elastic field at a rugous interface of a bimaterial with surface effects

The two-dimensional problem of elasticity incorporating surface effect at a rugous interface of bimaterial is considered. The current study is directed towards developing the theoretical model for analysing the stress distribution along nanosized interface irregularities of isotropic bimaterial systems, as the fracture of heterogeneous materials is strongly influenced by the stress concentrations around topological defects in an interface region. Based on the simplified Gurtin-Murdoch model of surface elasticity and the boundary perturbation method combined with the complex variable technique, the original boundary value problem is reduced to the sequence of hypersingular integral equations for any-order approximation. For the first-order approximation and periodic shape of the interface, the solution is obtained in an explicit form of Fourier series. The closed form expression for the hoop stress at the interface is derived in the case of the harmonic shape of the interface. Some detailed numerical investigations of the influence of mechanical characteristics of the interface, the shape and the size of interface asperities, and the elastic properties of the bimaterial components on the hoop stress and stress concentration are presented. It is shown that the incorporation of an interfacial energy exhibits properties that cannot be obtained using classical approach. For instance, the size effect is revealed, namely, the stress concentration depends on the deviation amplitude of the interface undulation at the nanoscale when the ratio of this amplitude to the period is constant; allowing for the interface elasticity reduces the concentration of the hoop stresses if the interface tension is neglected; if external loading is absent or relatively small, the elastic field at the interphase region is determined by the value of the interface tension and depends on geometric and elastic properties of the interface.

Homogenization of Random Porous Materials With Low-Order Virtual Elements

A fast statistical homogenization procedure (FSHP) based on virtual element method (VEM)—previously developed by the authors has been successfully adopted for the homogenization of particulate random composites, via the definition of the representative volume element (RVE), and of the related equivalent elastic moduli. In particular, the adoption of virtual elements of degree one for modeling the inclusions provided reliable results for materials with low contrast, defined as the ratio between mechanical properties of inclusions and matrix. Porous media are then here described as bimaterial systems in which soft circular inclusions, with a very low value of material contrast, are randomly distributed in a continuous stiffer matrix. Several simulations have been performed by varying the level of porosity, highlighting the effectiveness of FSHP in conjunction with virtual elements of degree one.

A sub-interface thermal crack problem for bonded dissimilar plates with interfacial thermal resistance

The present work aims to investigate the effect of interfacial thermal resistance on thermal fracture behavior of bonded and composite materials. We consider a sub-interface crack parallel to the interface between two semi-infinite dissimilar plates subjected to remote heat flux thermal loading. A constant thermal resistance is assumed to exist along the interface. The temperature distribution along the crack, the thermal stress intensity factors (TSIFs), and the crack opening/sliding displacements (COD/CSD) are obtained using an integral transform/superposition method. The numerical results for Al2O3/Si3N4 bimaterial systems show that the magnitude of the mode I TSIF generally decreases with increasing thermal resistance of the interface but increases with increasing thermal resistance for cracks that are very close to the interface. On the other hand, the model II TSIF increases with increasing thermal resistance if the crack is in the Al2O3 semi-infinite plate, and decreases if the crack is in the Si3N4 semi-infinite plate. The COD/CSD are also significantly influenced by the thermal resistance of the interface.

Failure characterization of solid structures based on an equivalence of cohesive zone model

Cohesive zone models have been widely used to model interface crack initiation and propagation both in single-material media and bi-material systems. For single-material media with cohesive elements inserted into interface among segments, in order to ensure that the introduction of interface cohesive zone models does not affect the mechanical properties of single-material media before the softening stage of cohesive zone models, a selection criterion of stiffness of cohesive elements is proposed theoretically firstly based on the properties’ equivalence. Taking the softening stage into account, the mechanical responses of the overall stress-strain relationship of single-material media, for the cases of stable increase of strain and snap-back instability of strain, are both obtained, and the related energy mechanism are investigated. For bi-material systems with cohesive elements at interface between two materials, the thickness-dependent failure characteristics of systems in uniaxial tension are found, which is attributed to the difference of the releasing rate of elastic strain energy in the materials with different thicknesses. Furthermore, as a more complex application of cohesive elements, based on the selection criterion proposed, failure behaviors of the ceramic coating/substrate systems under three-point bending are modeled by finite element method and inserting cohesive elements into the coating segments and the coating/substrate interface simultaneously. The simulation results indicate the transition of dominated failure mode from coating cracking to interface delamination with increasing coating thickness, and show faster damage of thick coating systems, agreeing with experimental results. The effects of interface strength and toughness of cohesive elements on failure are also revealed. These results can provide guidance for the application of cohesive elements, and help us better understand the overall failure behaviors of interface systems.

Design of composite systems for rotary wear applications

Due to the prevalence of sliding interfaces in mechanical assemblies, fast and reliable wear prediction capabilities are imperative for system design and analysis. This study investigates the rotary wear of multi-material composite systems that have thrust washer geometries. An analytical rotary wear model is developed to predict the rotary wear performance based on Archard's wear law and a Pasternak elastic foundation model. Numerical methods are used to track the evolution of key wear parameters including surface profile, contact pressure distribution, volume loss and composite wear rate during both run-in and steady-state wear regimes. A direct method is also developed to determine the steady-state characteristics from just the initial conditions and configurations of a given composite system. Optimal designs and design guidelines for several wear objectives are identified. Initial optimal material distributions for target steady-state surface profiles are determined. In addition, the steady-state composite wear rate is minimized to reduce material loss for bi-material systems with prescribed volume fractions. It is found that the optimal material configuration for this objective is counterintuitive. Wear tests are conducted to evaluate the proposed models and optimal design solutions. Results obtained from the wear models agree well with the experimental measurements.

A review of theoretical analysis techniques for cracking and corrosive degradation of film-substrate systems

Abstract This paper contains a review of the most vital concepts regarding the analysis and design of film systems. Various techniques have been presented to analyse and predict the failure of films for all common types of failure: fracture, delamination, general yield, cathodic blistering, erosive and corrosive wear in both organic and inorganic films. Interfacial fracture or delamination is the loss of bonding strength of film from substrate, and is normally analysed based on the fracture mechanics concepts of bi-material systems. Therefore, keeping the focus of this review on bonding strength, the emphasis will be on the interfacial cracking of films and the corresponding stresses responsible for driving the delamination process. The bi-material characteristics of film systems make the nature of interfacial cracks as mixed mode, with cracks exhibiting various complex patterns such as telephone cord blisters. Such interfacial fracture phenomenon has been widely studied by using fracture mechanics based applicable analysis to model and predict the fracture strength of interface in film systems. The incorporation of interfacial fracture mechanics concepts with the thermodynamics/diffusion concepts further leads to the development of corrosive degradation theories of film systems such as cathodic blistering. This review presents suggestions for improvements in existing analysis techniques to overcome some of limitations in film failure modelling. This comprehensive review will help researchers, scientists, and academics to understand, develop and improve the existing models and methods of film-substrate systems.

A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics

In this study, a finite element (FE) framework for the analysis of the interplay between buckling and delamination of thin layers bonded to soft substrates is proposed. The current framework incorporates the following modeling features: (i) geometrically nonlinear solid shell elements, (ii) geometrically nonlinear cohesive interface elements, and (iii) hyperelastic material constitutive response for the bodies that compose the system. A fully implicit Newton–Raphson solution strategy is adopted to deal with the complex simultaneous presence of geometrical and material nonlinearities through the derivation of the consistent FE formulation. Applications to a rubber-like bi-material system under finite bending and to patterned stiff islands resting on soft substrate for stretchable solar cells subjected to tensile loading are proposed. The results obtained are in good agreement with benchmark results available in the literature, confirming the accuracy and the capabilities of the proposed numerical method for the analysis of complex three-dimensional fracture mechanics problems under finite deformations.

Interface traction stress of 3D dislocation loop in anisotropic bimaterial

By applying discrete Fast Fourier Transformation (FFT), semi-analytical solutions are developed to calculate the interface elastic fields of anisotropic bimaterial systems with perfect bonding, dislocation-like, force-like and linear spring-like interface models. Interface elastic fields are the linear superimposition of bulk stress, free surface relaxation image stress and interface traction stress (ITS) fields. Interface image energy of perfect bonding bimaterials can be solved through area integral over the interface plane, including the contribution of several componential stress fields. Calculation examples on dislocation loops within Cu–Nb bimaterial are performed to demonstrate the efficiency of such approaches. Effects of Ku=[kiju] for the dislocation-like, Kt=[kijt] for the force-like and Ks=diag[KT,KN] for the linear spring-like imperfect interface models are investigated. Differences between perfect bonding and imperfect interface models, isotropic and anisotropic models are also studied. It is found that interface conditions and anisotropy have drastic effects on the interface elastic fields.

The Evolution of Carbon Nanotube Network Structure in Unidirectional Nanocomposites Resolved by Quantitative Electron Tomography.

Carbon nanotube (CNT) reinforced polymers are next-generation, high-performance, multifunctional materials with a wide array of promising applications. The successful introduction of such materials is hampered by the lack of a quantitative understanding of process-structure-property relationships. These relationships can be developed only through the detailed characterization of the nanoscale reinforcement morphology within the embedding medium. Here, we reveal the three-dimensional (3D) nanoscale morphology of high volume fraction (V(f)) aligned CNT/epoxy-matrix nanocomposites using energy-filtered electron tomography. We present an automated phase-identification method for fast, accurate, representative rendering of the CNT spatial arrangement in these low-contrast bimaterial systems. The resulting nanometer-scale visualizations provide quantitative information on the evolution of CNT morphology and dispersion state with increasing V(f), including network structure, CNT alignment, bundling and waviness. The CNTs are observed to exhibit a nonlinear increase in bundling and alignment and a decrease in waviness as a function of increasing V(f). Our findings explain previously observed discrepancies between the modeled and measured trends in bulk mechanical, electrical and thermal properties. The techniques we have developed for morphological quantitation are applicable to many low-contrast material systems.

Finite Element Computations of Complex Stress Intensity Factor Magnitude of Interfacial Crack in Bi-Material Composites

Composite structures are distinguished by interfaces separating their different layers. These interfaces represent region of mismatches in mechanical and thermal properties of the adjacent layers. These regions are rich in cracks which are laying either on or sub- the interface in a direction parallel or perpendicular to it. In bi-material composites, interfacial crack is under mixed loading mode and stress intensity factor is a complex number even if the opening mode loading is applied. This paper solves for energy release rates and the magnitude of complex intensity factor of interfacial cracks using the classical stiffness finite element method. The path-independent integral is used to calculate the energy release rate during crack extension in the elastic plane strain deformation field. In this work, the crack tip region is meshed with fan-shaped non-singular four nodes isoparametric quadrilateral elements. In addition, a conical shape of function is employed in the numerical implementation of the equivalent energy domain integral. Realization of all numerical computations and demonstration of results are completely composed and written in MATLAB language. Meshing the computational domains and crack tip region are performed by a free downloadable program AUTOMESH-2D. Numerical results of stress intensity factor are found to be very close to the analytical and referenced values in both cases of bi-material and single layer systems. Furthermore, numerical values of -integral contours are very close to interfacial fracture energy measured experimentally between a hard film and a soft substrate.

Simulation-based Study of Layered Aluminum Crystal Microstructures Subjected to Shock Loading

A one-dimensional finite difference method allowing for anisotropic deformation is used in conjunction with a nonlinear thermoelastic-viscoplastic material model to compute the shock response of various microstructural instantiations of pure aluminum at peak stresses exceeding the Hugoniot Elastic Limit (HEL). Single crystals and layered bi-materials consisting of grains with alternating orientations relative to the direction of shock propagation -- specifically [100], [111], or low-symmetry orientations -- are impacted to peak shock stresses on the order of 5GPa. The [111] orientation [111] is observed to be stiffest both plastically and elastically, while the [100] orientation is found to be most compliant. Layered bi-materials that only demonstrate pure longitudinal waves exhibit average shock stresses, entropy production, and internal energy in between values computed for their single crystal constituents. Layered bi-materials that generate both quasi-longitudinal and quasi-transverse waves results in lower peak stresses and higher internal energy than their single crystal constituents. In bi-material systems, stress fluctuations decrease in frequency with increasing layer thickness, and peak stress amplitudes increase with layer thickness. Average dissipation depends on orientation but is relatively insensitive to layer thickness. Results of the computational method may ultimately be used to guide design of metallic systems with microstructures tailored for optimal impact resistance.

Infrared detection based on localized modification of Morpho butterfly wings.

Inspired by butterflies an advanced detection and sensing system is developed. The hierarchical nanoarchitecture of Morpho butterfly wings is shown to facilitate the selective modification of such a structure, which results in a sensitive infrared response. These findings offer a new path both for detecting infrared photons and for generating nanostructured bimaterial systems for high-performance sensing platforms.

Correlation between the viscoelastic properties and cracking potential of engineered cementitious composites

Although Engineered Cementitious Composites (ECC) offer a number of advantages over ordinary and fiber reinforced concrete in many respects, it is not cost-effective to build a whole structure with ECC, currently. Thus, ECC can potentially be used in repair systems or in bi-material systems which require it to be used together with a dimensionally stable material. High shrinkage, together with the restraining effect brings about cracking a critical phenomenon for ECC. In this study, along with the mechanical properties of ECC, viscoelastic properties like autogenous shrinkage, drying shrinkage and tensile creep which were used to calculate ECC’s cracking potential were studied. At the same time, the tendency of ECC mixtures to crack under restrained shrinkage conditions was also investigated using restrained shrinkage rings. It was concluded that creep, elastic properties, and shrinkage data should be together used to evaluate the dimensional compatibility.