A theoretical study of a thin-film delamination using shaft-loaded blister test: Constitutive relation without delamination

This paper presents exact solutions for nonlinear large deflection of thin circular membrane loaded by a central point force using blister test with two types of boundary conditions and with or without residual stress cases. A comparison with existing solutions is presented, and a geometrically nonlinear finite element analysis (FEA) is conducted to verify our analytical solutions.     

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.     

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.     

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.     

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 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.     

缝合复合材料层间开裂的试验和数值研究

缝合复合材料层合板中贯穿厚度方向的缝线,能有效增强层合板的抗分层能力。本文对一种碳纤/环氧缝合复合材料层板进行了短梁三点弯试验,测得了压头的载荷-位移曲线,并观察了层间裂纹的扩展,证实了缝线对层间裂纹的阻滞作用。建立了三维有限元模型模拟了上述试验,模型中相邻的铺层之间布置了一层初始无厚度的界面单元,界面单元的失效自然模拟层间开裂,而缝线简化为面积等效的梁单元,数值结果与试验观测吻合。     

Experimental and theoretical/numerical investigations of thin films bonding strength

A laser spallation facility has been developed to measure the strength of planar interfaces between a substrate and a thin coating. This quantity is a central requirement in contemporary thin film and protective coatings technology and its successful measurement should improve the scientific/technological potential for the design of advanced composites, protective coatings of composites that operate in hostile environments, and in joining of dissimilar materials. The technique involves impinging a laser pulse of ultra short duration on the rear surface of the substrate, which is coated by a thin layer of energy absorbing metal such as Sn and Pb. The explosive evaporation of the metallic layer, confined between a fused quartz crystal and the substrate, induces a compressive shock wave, which propagates through the substrate toward the material interface. Upon reflection from the free surface of the coating, the pressure pulse is converted into a tensile wave which, under certain conditions, can lead to spallation at the interface. It is shown by mathematical simulation that atomic bond rupture is the mechanism of separation in this experiment. Since the interaction of laser energy with matter is a complicated, highly non-linear process, our investigations, at first, were based on measurement of the pressure pulse generated by the threshold flux level that leads to spallation, by using a micro-electronics device with a piezo-electric crystal, and on computation of the tensile stress experienced at the material interface, by numerical simulation of the induced stress wave propagation. Several substrate/coating (ceramic/ceramic and ceramic/metal) systems have been investigated such as, 1–15 μm SiC by CVD, 1–4 μm TiC and TiN by PVD coatings on sapphire substrates, as well as 1–2 μm Au, Sn and Ag coatings by sputtering on sapphire, fused quartz and glass substrates. For identically prepared specimens, the measured threshold energy levels are reproducible, thus leading to reproducible bond strength values, while the spall size, as expected, is dependent on the laser pulse energy level. Finally, the bond strength values obtained are in very good agreement with similar data derived by direct experimental techniques based on Laser-Doppler-Interferometry.     

Thin film delamination: A discrete dislocation analysis

Interface delamination during indentation of micron-scale ceramic coatings on metal substrates is modeled using discrete dislocation (DD) plasticity to elucidate the relationships between delamination, substrate plasticity, interface adhesion, elastic mismatch, and film thickness. In the DD method, plasticity in the metal substrate occurs directly via the motion of dislocations, which are governed by a set of physically based constitutive rules for nucleation, motion and annihilation. A cohesive law with peak stress characterizes the traction-separation response of the metal/ceramic interface. The indenter is a rigid flat punch and plane strain deformation is assumed. A continuum plasticity model of the same problem is studied for comparison. For low interface strengths (e.g. ), DD and continuum plasticity results are quantitatively similar, with delamination being nearly independent of interface strength, and easier for thinner, lower-modulus films. For higher interface strengths (), continuum plasticity predicts no delamination up to very high loads while the DD model shows a smooth increase in the critical indentation force for delamination with increasing interface strength. Tensile delamination in the DD model is driven by the accumulation of dislocations, and their associated high stresses, at the interface upon unloading. The DD model is thus capable of predicting the nucleation of cracks, and its dependence on material parameters, in realms of realistic constitutive behavior and/or small length scales where conventional continuum plasticity fails.     

A parametric study of laser induced thin film spallation

We report parametric studies of elastic wave generation by a pulsed laser and associated spalling of thin surface films by the corresponding high stresses. Two different substrate materials, single crystal Si (100) and fused silica, are considered. Spallation behavior of Al thin films is investigated as a function of substrate thickness, film thickness, laser energy, and various parameters governing the source. Surface displacement due to the stress wave is measured by Michaelson interferometry and used to infer the stresses on the film interface. Consistent with previous studies, the maximum stress in the substrate and at the film/substrate interface increases with increasing laser fluence. For many of the conditions tested, the substrate stress is large enough to damage the Si. Moreover, the maximum interface stress is found to increase with increasing film thickness, but decrease with increasing substrate thickness due to geometric attenuation. Of particular significance is the development of a decompression shock in the fused sillica substrates, which results in very high tensile stresses at the interface. This shock enhances the failure of thin film interfaces, especially in thicker samples.     

Poroelastic toughening in polymer gels: A theoretical and numerical study

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.     

A numerical study of the non-absorbable effects on the falling liquid film absorption

A numerical study for the simultaneous heat and mass transfer in a falling liquid film absorption process with the presence of non-absorbable gases is presented. Water vapor mixed with air as the non-absorbables being absorbed into a falling smooth aqueous lithium chloride film flow was chosen as the model problem for the study. The finite difference numerical calculation was proceeded by marching downward from the top end, owing to the parabolic type energy and concentration equations for both liquid and gas phases. The results indicate that the local non-absorbable gas concentration is much higher at the gas-liquid interface than that in the ambient, hence the local vapor pressure is lowered there such that the absorption driving potential of the vapor pressure difference is reduced. The resulting reduction of the absorption rate due to the presence of the non-absorbables suggests that its effect must be carefully considered in the application of absorption heat pump design. The present study can provide some useful information for this purpose.

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Numerische Studie über die Einwirkung von nicht absorbierbaren Stoffen auf die fallende Flüssigkeitsfilmabsorption

Zusammenfassung Hier wurde eine numerische Studie der Wärmeund Stoffübertragung in einem Absorptionsprozeß eines fallenden Flüssigkeitsfilms in Anwesenheit von nicht absorbierbaren Gasen dargestellt. Ein Wasserdampf-Luft-Gemisch, das in Anwesenheit von nicht absorbierbaren Gasen von einer fallenden glatten flüssigen Lithium-Chlorid-Filmströmung absorbiert wird, wurde als das Modellproblem für diese Studie gewählt. Die numerische Berechnung mit dem Finite Differenzenverfahren wurde schrittweise vom obersten Ende nach unten durchgeführt. Die Berechnung bezieht sich auf den parabolischen Typ der Energie- und Konzentrationsgleichungen für die Flüssigkeits- und Gasphasen. Die Ergebnisse weisen darauf hin, daß die lokale nicht absorbierbare Gaskonzentration bei der Gasflüssigkeitsphase sehr viel höher ist als in der Umgebung. Weiter ist der lokale Dampfdruck so erniedrigt worden, daß sich das Absorptionsbewegungspotential des Dampfdruckunterschiedes reduziert. Die resultierende Reduzierung der Absorptionsrate, die auf die Anwesenheit der nicht absorbierbaren Stoffe zurückzuführen ist, verlangt eine sorgfältige Einbeziehung ihere Einflüsse auf die Gestaltung der Absorptionswärmepumpen. Diese Arbeit kann einige nützliche Informationen für diesen Zweck geben.

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Nomenclature C absorbent concentration in weight fraction of salt - C _a nonabsorbables concentration in molar fraction - C _a at inlet and infinity - C _in C at film inlet - c _p specific heat of liquid - c _{p g} specific heat of gas - D species diffusivity for LiCl-H₂O - D _g species diffusivity for air-water vapor - g gravity - h _o film thickness - H _a heat of absorption - k thermal conductivity of liquid - k _g thermal conductivity of gas - L transformation constant - water vapor mass absorption rate - P _v water vapor pressure - Re film Reynolds number=V ₀ h ₀/ - T film temperature - T _in film temperature at inlet - T _g gas temperature - T _w wall temperature - T gas temperature at inlet and infinity - u velocity inx-direction - U =1.5V ₀ - V ₀ mean film velocity=g h ₀ ² /3µ - x coordinate parallel to the wall - y coordinate normal to the wall in the film region - y _g coordinate normal to the wall in the gas region - transformedy _g Greek letters dynamic viscosity - liquid density - _g gas density     

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.     

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.     

Two-layer film flow on a rotating disk: A numerical study

Development of thin two-layer film over a uniformly rotating disk is studied numerically under the assumption of planar interface and free surface. Similarity transformation is applied to transform the Navier-Stokes equations into a set of coupled non-linear, unsteady partial differential equations. This set of equations are solved numerically by using the finite-difference technique. It is observed that the rate of film thickness varies at different time zone depending on the rate of rotational speed of the disk. A physical explanation is provided to justify this anomalous behaviour. It is observed that, smaller thickness on the top layer enhance the initial rate of film thinning. But the overall effect of density, viscosity and the initial film thickness ratio are found to be insensitive to the final film thickness at large time.     

Parametric excitation of a thin ring under time-varying initial stress; theoretical and numerical analysis

Initial stress in rings is one of the destructive effects which is almost inevitable due to various reasons such as being subsystems of a shrink-fitted joint, imperfections in the manufacturing, assembly or misalignment of the supporting mounts, and unbalancing in rotating condition. So, in this paper we focus on the effect of the initial stress and its variation with time on the dynamics of the pre-stressed ring. For this purpose, the equation of motion for in-plane bending vibration of a thin ring is derived using Hamilton’s principle. It is assumed that the initial stress is due to the distributed radially time-varying pressure. By representing the dynamic initial stress in the coefficients of the equation of motion; the equation is converted to Mathieu’s equation. The strained parameters method has been used to obtain the stability regions of motion and transition curves. Furthermore, to validate the obtained stability regions, numerical solutions of the equation of motion and Floquet theorem are used in some selected values of the parameters of the initial stress (magnitude of static and dynamic components of the initial stress). The fourth-order Runge-Kutta algorithm is used for numerical analysis of the equation of motion. The results show that the parameters of initial stress have direct impact on the stability of dynamic response. The obtained results from theoretical and numerical methods which are notably consistent with each other demonstrate that the initial stress, which has been almost always neglected in dynamic models of the systems, has a significant effect on the dynamics of the system, and it may even lead to an unstable dynamic response, while the excitation frequency is far enough from resonance region. So this paper can present the other application of modal analysis to non-destructive measure of initial stress.     

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.     

A broad reconsideration of anti-vortex film cooling method using numerical optimization and an improved heat-flux model

This paper represents the detailed results of an evolutionary optimization framework towards the exploration of vortex mechanisms leading to effective anti-vortex film cooling. In this regards, several arrangements of triple cooling holes were studied on flat and curved geometries using differential-evolution optimization algorithm and a modified Reynolds-stress based flow solver. Depending on the flow and geometric parameters, four distinct types of vortex interaction with different cooling mechanisms were identified. The vortex-trapping mechanism, observed in the optimized upstream arrangement acts through imposing a mild downwash over the main counter-rotating vortex pair and provides the best cooling effectiveness for the low injection angle (less than 30°) cases. The vortex-suppression and -balancing are the optimal possible solutions of the adjacent arrangement. The latter is the classic well-known type of anti-vortex cooling, while the former provides a sudden strong controlling potential for high blowing ratios (higher than 1.0) and high injection angle film cooling. For the non-flat surfaces the triple holes effectively perform up to blowing-ratio of 2.0. However, the reverse-vortex-trapping mechanism occurring in the downstream arrangement is recommended for convex surfaces, while the adjacent arrangement is the choice for concave regions. In general, there is a possibility of reducing the coolant consumption about 30% through increasing the pitch-to-diameter ratio, while the values of cooling-effectiveness still remain in an acceptable range.