Quantitative characterization of the interfacial adhesion of Ni thin film on steel substrate: A compression-induced buckling delamination test

A compression-induced buckling delamination test is employed to quantitatively characterize the interfacial adhesion of Ni thin film on steel substrate. It is shown that buckles initiate from edge flaws and surface morphologies exhibit symmetric, half-penny shapes. Taking the elastoplasticity of film and substrate into account, a three-dimensional finite element model for an edge flaw with the finite size is established to simulate the evolution of energy release rates and phase angles in the process of interfacial buckling-driven delamination. The results show that delamination propagates along both the straight side and curved front. The mode II delamination plays a dominant role in the process with a straight side whilst the curved front experiences almost the pure mode I. Based on the results of finite element analysis, a numerical model is developed to evaluate the interfacial energy release rate, which is in the range of 250–315 J/m² with the corresponding phase angle from −41° to −66°. These results are in agreement with the available values determined by other testing methods, which confirms the effectiveness of the numerical model.     

Analysis of delamination in thin film electrodes under galvanostatic and potentiostatic operations with Li-ion diffusion from edge

Progressive delamination driven by Li-ion diffusion in elastic disk-like thin film electrodes of Li-ion batteries is modeled based on the cohesive model. Axisymmetric diffusion model is considered under both galvanostatic and potentiostatic operations. The effect of edge diffusion on the delamination process is evaluated. It is found that the diffusion from edge leads to an earlier delamination initiation. The edge effect is significant for active disks with a small aspect ratio, but negligible for the case of large aspect ratio. The edge diffusion is weaker in the potentiostatic operation than in the galvanostatic operation.     

Two-dimensional analysis of progressive delamination in thin film electrodes

By employing the two-dimensional analysis, i.e., plane strain and plane stress, a semi-analytical method is developed to investigate the interfacial delamination in electrodes. The key parameters are obtained from the governing equations, and their effects on the evolution of the delamination are evaluated. The impact of constraint perpendicular to the plane is also investigated by comparing the plane strain and plane stress. It is found that the delamination in the plane strain condition occurs easier, indicating that the constraint is harmful to maintain the structure stability. According to the obtained governing equations, a formula of the dimensionless critical size for delamination is provided, which is a function of the maximum volumetric strain and the Poisson’s ratio of the active layer.     

Modeling of progressive delamination in a thin film driven by diffusion-induced stresses

A semi-analytical method based on the cohesive model has been developed to investigate the progressive growth of interface delamination in an axisymmetric thin film electrode driven by diffusion-induced stresses under the assumption that the electrode remains elastic during the Li-ion diffusion process. The evolutions of the cohesive zone and debonding zone with respect to charging time have been predicted. The cohesive zone propagates in an accelerating manner and the debonding zone advances in a slowing down manner. The key parameters that control the interfacial stresses and delamination have been identified from the obtained governing equations. And according to the discussions on the key parameters, design insights into the geometry, charging velocity and material properties of the electrode have been provided.     

A multi-scale simulation of tungsten film delamination from silicon substrate

To bridge the different spatial scales involved in the process of tungsten (W) film delaminating from silicon (Si) substrate, a multi-scale simulation procedure is proposed via a sequential approach. In the proposed procedure, a bifurcation-based decohesion model, which represents the link between molecular and continuum scales, is first formulated within the framework of continuum mechanics. Molecular dynamics (MD) simulation of a single crystal W block under tension is conducted to investigate the effect of specimen size and loading rate on the material properties. The proposed decohesion model is then calibrated by using MD simulation of a single crystal W block under tension and using available experimental data, with a power scaling law to account for the size effect. A multi-scale model-based simulation of W film delamination from Si substrate is performed by using the proposed procedure within the framework of the material point method. The simulated results provide new insights into the mechanisms of the film delamination process.     

A new failure mechanism in thin film by collaborative fracture and delamination: Interacting duos of cracks

When a thin film moderately adherent to a substrate is subjected to residual stress, the cooperation between fracture and delamination leads to unusual fracture patterns, such as spirals, alleys of crescents and various types of strips, all characterized by a robust characteristic length scale. We focus on the propagation of a duo of cracks: two fractures in the film connected by a delamination front and progressively detaching a strip. We show experimentally that the system selects an equilibrium width on the order of 25 times the thickness of the coating and independent of both fracture and adhesion energies. We investigate numerically the selection of the width and the condition for propagation by considering Griffith's criterion and the principle of local symmetry. In addition, we propose a simplified model based on the criterion of maximum of energy release rate, which provides insights of the physical mechanisms leading to these regular patterns, and predicts the effect of material properties on the selected width of the detaching strip.     

A theoretical and numerical study of thin film delamination using the pull-off test

An accurate closed-form analytical solution for the strain energy release rate for a thin rectangular film loaded by a central line force using the pull-off test is derived in the presence of a tensile residual stress. The theoretical constitutive relation and the strain energy release rate agree very well with two-dimensional nonlinear finite element analysis for the entire deformation regime ranging from bending plate to stretching membrane. Fracture modes for this pull-off test are also investigated based upon the finite element analysis, offering additional insights to the interfacial delamination.     

The Mexican hat effect on the delamination buckling of a compressed thin film

Because of the interaction between film and substrate,the film buckling stress can vary significantly,depending on the delamination geometry,the film and substrate mechanical properties.The Mexican hat effect indicates such interaction.An analytical method is presented,and related dimensional analysis shows that a single dimensionless parameter can effectively evaluate the effect.     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

Characterization of the Grain-Level Mechanical Behavior of Eglin Sand by Nanoindentation

Characterization was made on the structure and grain-level mechanical behavior of Eglin sand (Quikrete #1961 sand quarried in Pensacola, FL). The as-received assorted sand was sorted to six grain sizes: 0.60 mm, 0.50 mm, 0.42 mm, 0.30 mm, 0.212 mm, and 0.15 mm. The sand chemical constituents and crystalline structures were determined using energy dispersive X-ray spectroscopy, X-ray diffraction and transmission electron microscopy. The Young’s modulus and hardness were determined using nanoindentation with a Berkovich tip, and the fracture toughness was measured using a cube-corner tip. The median Young’s modulus, hardness and fracture toughness were determined as 90.4 GPa, 12.8 GPa and 2.32 MPa?m^0.5, respectively. The mechanical properties were analyzed statistically and the parameters of the Weibull distribution were determined. The grains show highly ductile behavior under nanoindentation due to confinement by high pressure induced by Berkovich tip. An inverse problem solving approach using finite element method (FEM) with the consideration of the Ramberg-Osgood model was used to determine the stress–strain relationship for individual sand grains.     

Characterization of Stress-Diffusion Coupling in Lithiated Germanium by Nanoindentation

There is currently a growing demand for low-cost, high-performance electrochemical energy storage solutions to consumer electronics, vehicle electrification and stationary power management. The successful development and deployment of such solutions necessitate a fundamental understanding of the mechanical properties of electrochemical materials, as well as the intricate coupling between the electro-chemo-mechanical processes in these materials. In this work, we performed a combined experimental and modelling investigation of the stress-diffusion coupling behavior of lithiated germanium (Ge) for its use in high-performance lithium-ion batteries. Thin films of Ge were fabricated using sputtering deposition and then electrochemically lithiated, after which they were subjected to nanoindentation at varying load levels to study indentation-induced creep deformation. Concurrently, a continuum chemo-mechanical model of the nanoindentation test was developed and used to investigate the fundamental mechanisms underlying the stress-gradient-driven creep deformation. The stress-diffusion coupling coefficient and diffusivity of lithium in Ge were obtained by quantitatively comparing the simulated nanoindentation response with the experimental measurements. This integrative experimental and computation work provides important insights into the chemo-mechanical coupling process in high-performance rechargeable battery electrodes.     

Controlled buckling of thin film on elastomeric substrate in large deformation

Electronic systems with large stretchability have many applications. A precisely controlled buckling strategy to increase the stretchability has been demonstrated by combining lithographically patterned surface bonding chemistry and a buckling process. The buckled geometry was assumed to have a sinusoidal form, which may result in errors to determine the strains in the film. A theoretical model is presented in this letter to study the mechanics of this type of thin film/substrate system by discarding the assumption of sinusoidal buckling geometry. It is shown that the previous model overestimates the deflection and curvature in the thin film. The results from the model agree well with finite element simulations and therefore provide design guidelines in many applications ranging from stretchable electronics to micro/nano scale surface patterning and precision metrology.     

Buckling of a stiff thin film on a pre-strained bi-layer substrate

Controlled buckling can impart stretchable mechanics to brittle materials when integrated as thin films on soft, elastomeric substrates. Typical elastomers are permeable to fluids, however, and therefor unable to provide robust barriers to entry of water, for instance, into devices built with the supported thin films. In addition, the mechanical strength of a system dominated by a soft substrate is often unsatisfactory for realistic applications. We show that introduction of a bi-layer substrate yields a robust, high strength system that maintains stretchable characteristics, with a soft layer on top of a relatively stiff layer in the substrate. As a mechanical protection, a soft encapsulation layer can be used on top of the device and the stretchability of the encapsulated system is smaller than that of the system without encapsulation. A simple, analytic model, validated by numerical analysis and FEA, is established for stiff thin films on a bi-layer substrate, and is useful to the design of stretchable systems.     

NANOINDENTATION OF THIN-FILM-SUBSTRATE SYSTEM： DETERMINATION OF FILM HARDNESS AND YOUNG’S MODULUS

In the present paper, the hardness and Young‘s modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates, i.e. glass and silicon, are studied. Nanoindentation XP Ⅱ and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young‘s modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young‘s modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, φ, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.     

Mechanics of shaft-loaded blister test for thin film suspended on compliant substrate

Based on the von Kármán plate theory, the mechanics of a shaft-loaded blister test for thin film/substrate systems is studied by considering elastic substrate deformations and residual stresses in these films. In testing, films are attached to a substrate provided with a circular hole, through which loading is applied to the film by a flat-ended shaft of circular cross-section. The effect of substrate deformation on the deflection of the loaded film is taken into account by using a line spring model. For small deflections, an analytical solution is derived, while for large deflections a numerical solution is obtained using the shooting method. The resulting load-shaft displacement relation, which is essential in blister tests, compares favorably with finite element analysis.     

Mixed-mode interfacial adhesive strength of a thin film on an anisotropic substrate

The mixed-mode interfacial adhesion strength between a gold (Au) thin film and an anisotropic passivated silicon (Si) substrate is measured using laser-induced stress wave loading. Test specimens are prepared by bonding a fused silica (FS) prism to the back side of a 〈1 0 0〉 Si substrate with a thin silicon nitride (Si_xN_y) passivation layer deposited on the top surface. A high-amplitude stress wave is developed by pulsed laser ablation of a sacrificial absorbing layer on one of the lateral surfaces of the FS prism. Due to the negative non-linear elastic properties of the FS, the compressive stress wave evolves into a decompression shock with fast fall time. Careful selection of the incident angle between the pulse and the FS/Si interface generates a mode-converted shear wave in refraction, subjecting the Si_xN_y/Au thin film interface to dynamic mixed-mode loading, sufficient to cause interfacial fracture. A detailed analysis of the anisotropic wave propagation combined with interferometric measurements of surface displacements enables calculation of the interfacial stresses developed under mixed-mode loading. The mixed-mode interfacial strength is compared to the interfacial strength measured under purely tensile loading.     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

Modelling of the interface between a thin film and a substrate within a strain gradient plasticity framework

Interfaces play an important role for the plastic deformation at the micron scale. In this paper, two types of interface models for isotropic materials are developed and applied in a thin film analysis. The first type, which can also be motivated from dislocation theory, assumes that the plastic work at the interface is stored as a surface energy that is linear in plastic strain. In the second model, the plastic work is completely dissipated and there is no build-up of a surface energy. Both formulations introduce one length scale parameter for the bulk material and one for the interface, which together control the film behaviour. It is demonstrated that the two interface models give equivalent results for a monotonous, increasing load. The combined influence of bulk and interface is numerically studied and it is shown that size effects are obtained, which are controlled by the length scale parameters of bulk and interface.     

Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.