Multiple cracking of elastic coatings under transient thermal load

A periodic array of cracks in an elastic coating bonded to a homogeneous substrate is considered. The medium is subjected to mechanical loads and/or thermal loads. The problem is formulated in terms of a singular integral equation with the crack face displacement as the unknown variable. In addition to the time-varying stress intensity factors and stresses for various parameters of the problem, the effect of periodic cracking on the relaxation of the transient stress on the coating surface is discussed. Solution techniques for a single elastic layer and an elastic coating bonded to an infinite substrate are given. It is found that, if the crack density attains a saturation value, the transient thermal stress in the medium could be released significantly, suggesting that further cracking is difficult.     

Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior

A contact stress analysis is presented for a layered elastic half-space in contact with a rough surface exhibiting self-affine (fractal) behavior. Relationships for the mean contact pressure versus representative strain and the real half-contact width versus elastic properties of the layer and the substrate, asperity radius, layer thickness, and truncated half-contact width were derived from finite element simulations of a layered medium compressed elastically by a rigid cylindrical asperity. These relationships were incorporated in a numerical algorithm that was used to obtain the contact pressure distributions and stresses generated by the asperity contacts formed at the interface of the layered medium and the fractal surface. Analytical solutions illustrate the significance of the elastic material properties, layer thickness, and surface topography (roughness) on global parameters such as normal load and real contact area. Results for the contact pressure distribution and the surface and subsurface stresses provide insight into the initiation of yielding and the tendency for cracking in the layered medium. It is shown that cracking at the surface and the layer/substrate interface is more likely to occur in the case of a stiff layer, whereas surface cracking is more prominent for a relatively compliant layer.     

Fracture mechanics analysis of thin coatings under plane-strain indentation

A combined experimental/analytical work is carried out to elucidate the fracture resistance of a thin, hard coating bonded to a semi-infinite substrate due to indentation by a cylindrical surface. The bending of the coating under the softer substrate induces concentrated tensile stress regions at the lower and upper surfaces of the coating, from which cracks may ensue. The evolution of such damage in a model transparent system (glass/polycarbonate) is viewed in situ from below and from the side of the specimen. The critical load needed to initiate a crack on the lower coating surface generally increase proportionally to the coatings thickness, d. An interesting departure from this trend occurs for thin coatings, where the fracture load, although marred by a large scatter, increases somewhat with decreasing d. The fracture data for the upper coating surface are limited to relatively thick coatings due to the recurrence of premature failure from the coating edges. The behavior in this range is similar to that for the lower surface crack, albeit with an order of magnitude greater fracture resistance.A fracture mechanics analysis in conjunction with FEM is performed to elucidate the stress intensity factors responsible for crack propagation. A crack normal to the coating surface is assumed to emanate either from the lower or upper surface of the coating. A major feature of the solution is the occurrence of a bending-induced compression stress field over a region ahead of the crack tip. This effect, which become more dominant as the ratio between the contact length and the coating thickness is increased, tends to delay the onset of crack propagation, especially for the lower surface crack. Consequently, in applications associated with large indenters, thin and/or tough coatings and stiff substrates, cracking from the upper coating surface may precede that from the lower surface. An interesting feature of this crack shielding mechanism is that when the coating surface contains a distribution of flaws rather than a single crack, small flaws in this population may be more detrimental than large ones. Incorporation of these aspects into the analysis leads to a good correlation with the test results. In the special case of line loading, which constitutes a lower bound for the critical loads, a closed-form, approximate solution for the stress intensity factors or the critical loads are obtained.Plane-strain indentation, although less common than spherical indentation, allows for characterizing the fracture resistance of opaque films through observation from the specimen edge. This approach is not easily implemented to thin films (i.e., less than about a hundred microns), however.     

Modeling of coating separation under thermomechanical loading in the beam approximation

The beam approximation is developed to solve some problems of fracture mechanics concerning the formation of separation of thin elastic coatings with allowance for the constraints acting on the connection boundaries and the influence of unsteady temperature actions.The separation end region is modeled by an elastic beam loaded by an external bending moment and by force factors from the connection with the base. This region is subjected to thermoelastic stresses caused by a sudden variation in the temperature of the surface or the adhesive layer. We estimate how the effective fracture strength of the adhesive joint varies for various modes of application of affecting factors, including variations in material properties with temperature and across the coating thickness; we also study buckling phenomena and the kinetics of local fracture processes in the end region. The results can be used when choosing the parameters of an adhesive joint so as to ensure a given effective adhesion fracture strength of the joint.     

Combined analysis of fracture under stresses acting along cracks

A joint approach to the study of two non-classical fracture mechanisms, namely fracture of cracked materials with initial (residual) stresses acting along the crack planes and fracture under compression along parallel cracks, is considered in the framework of three-dimensional linearized solid mechanics. Mathematical statements of problems for pre-stressed solids that contain interacting circular cracks are given. Problems for an infinite solid containing two parallel co-axial cracks and for a space with the periodical set of co-axial parallel cracks as well as for a half-space with near-the-surface crack are solved. Several patterns of loading on the crack faces (normal loading, radial shear and torsion) are considered. The effects of initial stresses on stress intensity factors are analyzed for highly elastic materials with some types of elastic potentials. Formulation of fracture criteria accounting effect of initial (residual) stresses is given. Critical parameters of fracture of solids containing interacting cracks under compression along the cracks are calculated. The influence of geometrical parameters of the problems as well as physical and mechanical properties of materials on these critical parameters is analyzed.     

石英添加量对搪瓷涂层微观结构及摩擦磨损性能的影响

采用一次浸搪法制备石英添加量为0%、4%、8%和12%的搪瓷涂层,通过HSR-2M型高速往复摩擦试验机测试涂层摩擦学性能,SEM和EDS分别表征涂层微观组织和磨损形貌,并分析磨损机理. 结果表明:搪瓷涂层中石英添加质量分数为0%和4%时,涂层气孔率大、气孔密度低,摩擦时形成的微裂纹易沿着气孔间最短距离方向扩展,硬质磨屑转移至摩擦对偶表面而使涂层磨痕底部形成尖锐的凹槽,磨损形式主要为磨粒磨损和脆性断裂. 而石英添加质量分数为8%和12%的涂层气孔率小、气孔密度高,其中8%添加量涂层的孔径分布更加均匀,磨损率及磨痕深度仅为未添加涂层的1/3. 摩擦过程中孔径均匀的小尺寸气孔增大了裂纹扩展时所需的能量势垒而阻碍裂纹扩展,磨屑被气孔拦截后在磨损表面形成密实的堆积层,避免了摩擦对偶与涂层的直接接触而起到减摩作用,磨损形式主要为磨粒磨损.      

Modeling the contact wear fracture of a two-layer basement

We develop a method for calculating the kinetics of fatigue fracture of a two-layer elastic basement by a periodic system of indenters sliding on the surface and modeling the surface microroughness. The method is based on solving the contact problem for a periodic system of indenters and a two-layer elastic basement, determining the internal stresses with friction forces taken into account, and constructing the damage function in the two-layer basement. We calculate the kinetics of the fatigue fracture of the surface layer (the coating) and find the characteristics of the process depending on the strength and mechanical properties of the coating and basement materials, the loading and geometric characteristics of the system, and the friction coefficient.     

Fretting contact of two elastic solids with graded coatings under torsion

In this paper, the fretting contact problem for two elastic solids with graded coatings is investigated. We assume a conventional axisymmetric Hertzian contact takes place between two elastic solids under the action of the normal pressure. The application of the torque produces an annulus of slip. It is assumed that the surface shear traction within the contact area is limited by Coulomb’s friction law and the torsion angel was produced within the central adhesion zone as a rigid body. The linear multi-layer model is used to model the functionally graded coating with arbitrarily varying shear modulus. This model divides the coating into a series of sub-layers with the elastic modulus varying linearly in each sub-layer and continuous on the sub-interfaces. By using the transfer matrix method and Hankel integral transform technique, this problem is formulated as the solution of the Cauchy singular integral equations. The contact tractions are calculated by solving the equations numerically. The results show that the appropriate gradual variation of the shear modulus can significantly alter the contact tractions. Therefore, graded coatings may have potential applications in improving the resistance to fretting contact damage at the contact surfaces.     

Role of inclusion stiffness and interfacial strength on dynamic matrix crack growth: An experimental study

Experimental simulations of dynamic crack growth past inclusions of two different elastic moduli, stiff (glass) and compliant (polyurethane) relative to the matrix (epoxy), are carried out in a 2D setting. Full-field surface deformations are mapped in the crack–inclusion vicinity optically. The crack growth behavior as a function of inclusion–matrix interfacial strength and the inclusion location relative to the crack is studied under stress-wave loading conditions. An ultra high-speed rotating mirror-type digital camera is used to record random speckle patterns in the crack–inclusion vicinity to quantify in-plane displacement fields. The crack-tip deformation histories from the time of impact until complete fracture are mapped and fracture parameters are extracted. The crack front is arrested by the symmetrically located compliant inclusion for about half the duration needed for complete fracture event. The dynamically propagating crack is attracted and trapped by the weakly bonded inclusion interface for both stiff and compliant symmetrically located inclusion cases, whereas it is deflected away by the strongly bonded stiff inclusion and attracted by strongly bonded compliant inclusion when located eccentrically. The crack is arrested by a strongly bonded compliant inclusion for a significant fraction of the total dynamic event and is longer than the one for the weakly bonded counterpart. The compliant inclusion cases show higher fracture toughness than the stiff inclusion cases. Measured crack-tip mode-mixities correlate well with the observed crack attraction and repulsion mechanisms. Macroscopic examination of fracture surfaces reveals much higher surface roughness and ruggedness after crack–inclusion interaction for compliant inclusion than the stiff one. Implications of these observations on the dynamic fracture behavior of micron size A-glass and polyamide (PA6) particle filled epoxy is demonstrated. Filled-epoxy with 3% V_f of PA6 filler is shown to produce the same dynamic fracture toughness enhancement as the one due to 10% V_f glass.     

Quantitative assessment of the surface crack density in thermal barrier coatings

In this paper, a modified shear-lag model is developed to calculate the surface crack density in thermal barrier coatings（TBCs）. The mechanical properties of TBCs are also measured to quantitatively assess their surface crack density. Acoustic emission（AE） and digital image correlation methods are applied to monitor the surface cracking in TBCs under tensile loading. The results show that the calculated surface crack density from the modified model is in agreement with that obtained from experiments. The surface cracking process of TBCs can be discriminated by their AE characteristics and strain evolution. Based on the correlation of energy released from cracking and its corresponding AE signals, a linear relationship is built up between the surface crack density and AE parameters, with the slope being dependent on the mechanical properties of TBCs.     

Cracking in thin multi-layers with finite-width and periodic architectures

Many applications involve thin multi-layers comprised of repeating patterns of different material sections, notably interconnect–dielectric structures in microelectronics. This paper considers a variety of failure scenarios in systems with periodically arranged features within a single layer. Crack driving forces are presented for (i) debonding between alternating material sections in a thin film (i.e. channel and tunnel cracking at material junctions), and (ii) channel cracking in a thin uniform coating above a layer comprised of alternating sections of different materials. The effects of elastic mismatch, feature spacing, crack spacing and residual stress are illustrated for a wide range of parameters. The results presented here illustrate that residual stresses in intact sections can strongly promote cracking in adjacent layers, which is in contrast to analyses of blanket film multi-layers which predict that residual stress in adjacent layers has no effect. An important finding is that decreasing the relative size of low-modulus sections significantly increases the crack driving force in adjacent layers. The implications of these results are discussed in the contexts of critical feature spacing and the impact of incorporating low elastic-modulus sections (such as polymer dielectrics) on thermo-mechanical reliability.     

Channel cracking in inelastic film/substrate systems

Studies on channel cracking are generally limited to elastic films on elastic or inelastic substrates. There are important applications were the cracking process involves extensive plasticity in both the film and substrate, however. In this work steady-state channel cracking in inelastic thin-film bilayers undergoing large-scale yielding from thermal or mechanical loading is studied with the aid of a plane-strain FEA. The plasticity of the film and substrate, represented by a Ramberg–Osgood constitutive law, each increases the energy release rate (ERR) relative to the linearly-elastic case. This effect is more pronounced under mechanical loading where the entire bilayer undergoes large-scale yielding. To help assess the analytic approach some fragmentation tests are performed using a well-bonding epoxy/aluminum system. The analysis reproduced well the observed dependence of crack initiation strain on film thickness.Ultra-thin films may be well represented by an elastic-perfectly plastic response. For such films on a flexible support the ERR remains fixed as the applied strain exceeds the yield strain of the film. Accordingly, a critical coating thickness exists below which no channel cracking is possible. The explicit relations and graphical data presented may be used for optimal design of such structures against premature failure as well as for determining fracture energy of ductile thin films.     

Debonding of graded coatings under in-plane compression

Graded materials are multiphase composites with continuously varying thermophysical properties. The concept provides material scientists and engineers with an important tool to develop new materials tailored for some specific applications. One such application of this new class of materials is as top coats or interfacial regions in thermal barrier systems. A widely observed failure mode in these layered materials is known to be interfacial cracking that leads to spallation. In many cases it is the buckling instability of coating under mechanically or thermally induced compressive stresses that triggers spallation. Under in-plane loading since the linear elastic small deformation theory gives only a trivial solution, in this study the plane strain interface crack problem for a graded coating bonded to a homogeneous substrate is formulated by using a kinematically nonlinear continuum theory. Both the instability and the postbuckling problems are considered. The main objective of the study is the investigation of the influence of material nonhomogeneity, kinematic nonlinearity and plate approximation on the critical instability load and on such fracture mechanics parameters as strain energy release rate, stress intensity factors and crack opening displacements.     

Edge-cracked bimaterial systems under thermal heating

The problem of thermoelastic edge-cracking in two-layered bimaterial systems subjected to convective heating is considered. The medium is assumed to be insulated on one surface and exposed to sudden convective heating on another surface containing the edge crack. It is known that, when a bimaterial system’s surface is heated, compressive stresses arise near the heating surface, forcing the crack surfaces together over a certain cusp-shaped contact length. It is also known that, for a cooled bimaterial systems surface, tensile stresses take place close to the cooling surface and tend to open the crack. So, the edge cracked heating surface problem is treated as an embedded crack with a smooth closure condition of the crack surfaces, with the crack contact length being an additional unknown variable. Superposition and uncoupled quasi-static thermoelasticity principles are adopted to formulate the problem. By using a Fourier integral transform technique, the mixed boundary value problem is reduced to a Cauchy type singular integral equation with an unknown function as the derivative of the crack surface displacement. The numerical results of the stress intensity factors for an edge crack and a crack terminating at the interface, are calculated and presented as a function of time, crack length, heat transfer coefficient, and thickness ratio for two different bimaterial systems, namely a stainless steel layer welded on ferritic steel and a ceramic layer coating on ferritic steel.     

粗糙面在梯度表面层上滑动接触的应力分布

对粗糙面在梯度表面层上的滑动过程进行应力分布研究,以模拟实际摩擦过程中,考虑塑性变形情况下,梯度覆层体中的应力分布规律,同时与均质体及单覆层体进行比较研究,分析了在表面载荷相同时滑动接触的应力分布。结果表明覆层体出现塑性变形后,在接触表面上的压力分布与弹性变形时有很大变化,在界面处梯度层的应力分布比单层膜更为理想,其应变梯度也较小;受相同表面载荷作用下产生塑性变形时,梯度层膜在基体产生塑性变形较小     

Dynamic torsion testing of nanocrystalline coatings using high-speed photography and digital image correlation

The strength and ductility of microcrystalline and nanocrystalline tungstsen carbide-cobalt (WC-Co) cermets have been evaluated by employing a stored energy Kolsky bar apparatus, high-speed photography and digital image correlation. The test specimens were thin-walled tubular AI7075-T6 substrates 250 μm thick, coated with a 300 μm thick microcrystalline or nanocrystalline WC-Co layer with an average grain size of about 3 μm and 100 nm, respectively. Dynamic torsion experiments reported in this paper reveal a shear modulus of 50 GPa and a shear strength of about 50 MPa for both microcrystalline and nanocrystalline WC-Co coatings. The use of high-speed photography along with digital image correlation has shown that damage to the coating coincides with a significant softening on the stress-strain curve. The coating failed in mode III, and strong interactions between the crack faces were probably responsible for the increase in load after failure of the coating. The overall failure of the coating-substrate system was not brittle but rather progressive and controlled by the ductility of the aluminum substrate. A methodology for investigating damage kinetics and failure has been established. This methodology can be applied to examine the behavior of other advanced materials that can be manufactured as coatings on ductile substrates. Manufacturing coatings free of initial microcracks remains a significant challenge. Research on optimization of the spray deposition parameters should be pursued to produce high-quality nanostructured coatings that can fully exploit the benefits of nano-size grains.     

Buckling of an orthotropic graded coating with an embedded crack bonded to a homogeneous substrate

To simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an orthotropic stress–strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the critical buckling strain. The Finite Element Method was additionally used to model the crack problem. The main objective of the paper is to study the influence of material nonhomogeneity on the buckling resistance of the graded layer for various crack positions, coating thicknesses and different orthotropic FGMs.     

Effect of rising elastic modulus in surface layer on stress intensity and gradient

The relaxation element method is applied to obtain the stress field around a crack under normal tension. A surface layer is assumed to surround the crack periphery taken to be in the shape of a narrow ellipse. The elastic modulus within this layer increases from zero to the bulk value of the medium outside. Calculations show that the stresses are finite at the crack tip; they reach a maximum in the layer and then decay to the well known solution of Griffith outside the layer. The influence of plastic deformation on the crack front stresses can also be simulated by the surface layer model. Stress concentration at the crack front is found to be lower when plastic deformation takes place. Sharp decay of stress next to the crack is accompanied by increase of local stress gradients. Severity of the local stress fluctuation depends on the width of the crack surface layer.     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

Effects of multiple cracking on the residual strength behavior of thermally shocked functionally graded ceramics

When subjected to severe thermal shocks a functionally graded ceramic (FGC) suffers strength degradation due to the thermally-induced damages in the material. Multiple surface cracking has been observed as one of the dominant defects/damages affecting the thermal shock behavior of ceramics. This paper presents a thermo-fracture mechanics model to investigate the thermal shock residual strength behavior of elastically homogeneous but thermally graded FGCs undergoing multiple surface cracking. We consider an FGC plate with an array of parallel edge cracks at the thermally shocked surface. A Fourier transform/superposition method is used to derive the singular integral equation of the thermal shock crack problem. The critical thermal shock that causes crack propagation and thermal shock damage are determined using linear elastic fracture mechanics. The thermal shock residual strength of the FGC as a function of thermal shock severity and crack density (crack spacing) is subsequently evaluated. Numerical calculations are carried out for two FGC materials, i.e., Al₂O₃/Si₃N₄ and TiC/SiC FGCs, to illustrate the effects of crack density (crack spacing) and material gradation on the thermal shock strength behavior of FGCs. It is found that a higher crack density (lower crack spacing) together with appropriately graded material properties significantly enhances the residual strength of the thermally shocked FGCs.