On the thermomechanical behavior of two-dimensional foam/metal joints with shear-deformable adherends: Model validation with FE analysis

The stress distributions in metal/adhesive/foam planar joints subjected to biaxial tensile load and thermal load was investigated through a semi-analytical model. The shear deformation of adherends was accounted for according to a linear law in order to obtain closed-form solutions. For the model validation, a comparative study with a finite element (FE) simulation was carried out. A 2D behavior of stress fields is observed due especially to the Poisson's ratio effects and the biaxial nature of loads. The through thickness shear stresses are comparable to normal stresses; therefore, the adherend shear deformation must be accounted for correct failure prediction. According to the comparison with FE results, the normal stress distributions at any location in the foam and the shear stresses in the foam regions close to the adhesive surface can be well predicted by the proposed model. The through thickness shear stresses, however, showed to vary according to a cubic law rather than a linear law.     

Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints

This research investigates the use of a meshless smoothed particle hydrodynamics (SPH) method for the prediction of failure in an adhesively bonded single lap joint. A number of issues concerning the SPH based finite element modelling of single lap joints are discussed. The predicted stresses of the SPH finite element model are compared with the results of a cohesive zone based finite element model. Crack initiation and crack propagation in the adhesive layer are also studied. The results show that the peel stresses predicted by the SPH finite element model are higher and the shear stresses are lower than those predicted by the cohesive zone finite element model. The crack initiation and propagation response of the two models is similar, however, the SPH finite element model predicted a lower failure load than the cohesive zone finite element model. It is concluded that the current implementation of SPH method is a promising method for modelling cohesive failure in bonded joins but requires further development to allow for interfacial crack growth and better stress prediction under tensile loading to compete with existing methods.     

Multiple cohesive cracking during nanoindentation in a hard W-C coating/steel substrate system by FEM

Stress evolution and subsequent cohesive cracking in the hard and stiff W-C coating on steel substrate during nanoindentation have been investigated using finite element modelling (FEM) and eXtended FEM (XFEM). The FEM simulations showed that the maximum principal stresses in the studied system were tensile and always located in the coating. They evolved in several stages. At indentation depths below 15% of the relative indentation depth, the maximum principal tensile stresses of ∼3 GPa developed at the top surface of the coating along the indenter/coating interface. At relative depths range 15–60%, the maximum tensile stresses of ∼6–8 GPa concentrated under the indenter tip in the coating along the interface with the substrate. At relative depths exceeding 60%, the maximum stresses gradually increased up to 10 GPa and they were located in the sink-in zone outside the indent as well as below the indenter tip. The first and subsequent cohesive cracks developed when the maximum tensile stresses in the sink-in zone at the top surface of the coating (and at the coating/substrate interface under the indenter) repeatedly reached the ultimate tensile strength of the coating. The hardness profile as well as cohesive cracking is controlled by the deformation of the substrate defined by the ration of the yield stresses of the coating and substrate. Very good correlation between the experimentally obtained cracks and multiple cracks predicted by XFEM confirmed the ability of the applied modelling in the prediction of fracture behavior of the studied coating/substrate system.     

Finite element simulation of straight plunge grinding for advanced ceramics

The objective of this work is to model the grinding forces and the associated stress and deformation fields generated in a ceramic workpiece during plunge surface grinding. A two-dimensional finite element model is constructed with the grinding parameters and the mechanical properties of the workpiece as input variables. The size of the geometric model is several times larger than the size of the cutting zone, using approximately 5200 rectangular solid elements with a finer mesh in the cutting zone and with fixed remote boundaries. The loading in the cutting zone is imposed by displacement vectors proportional to the local undeformed chip thickness, which is a function of grinding parameters. For a given set of inputs, the model predicts the normal and tangential forces generated by the grinding wheel, as well as the deformation and the stress fields within the workpiece. As an example, the simulation is applied to a silicon nitride workpiece. Analysis of the stress fields developed in this material suggests that shear failure within the cutting zone is the dominant mode of subsurface failure, which could lead to the formation of shear micro- cracks at the grain interfaces. The depth of the subsurface shear failure zone increases with an increase in maximum undeformed chip thickness or the wheel depth of cut. The resulting local grinding force vectors, maximum stresses and damage zone sizes are predicted as a function of maximum undeformed chip thickness (or the wheel depth of cut).     

Improved mechanical performance: Shear behaviour of strain-hardening cement-based composites (SHCC)

The retardation of moisture and gas ingress associated with important degradation mechanisms in cement-based composites in general and reinforced concrete or prestressed concrete in particular is an ongoing research focus internationally. A dense outer layer is generally accepted to significantly enhance durability of structural concrete. However, cracking leads to enhanced ingress, unless the cracks are restricted to small widths. Strain-hardening cement-based composites (SHCC) make use of fibres to bridge cracks, whereby they are controlled to small widths over a large tensile deformation range. In this paper, SHCC shear behaviour is studied, verifying that the cracks which arise in pure shear are also controlled to small widths in these materials. The design of an Iosipescu shear test setup and specific SHCC geometry is reported, as well as the results of a test series. A computational model for SHCC, based on finite element theory and continuum damage mechanics, is elaborated and shown to capture the shear behaviour of SHCC.     

Contact-Induced Transverse Fractures in Brittle Layers on Soft Substrates: A Study on Silicon Nitride Bilayers

An analysis of transverse cracks induced in brittle coatings on soft substrates by spherical indenters is developed. The transverse cracks are essentially axisymmetric and geometrically conelike, with variant forms dependent on the location of initiation: outer cracks that initiate at the top surface outside the contact and propagate downward; inner cracks that initiate at the coating/substrate interface beneath the contact and propagate upward; intermediate cracks that initiate within the coating and propagate in both directions. Bilayers consisting of hard silicon nitride (coating) on a composite underlayer of silicon nitride with boron nitride platelets (substrate), with strong interfacial bonding to minimize delamination, are used as a model test system for Hertzian testing. Test variables investigated are contact load, coating/substrate elastic-plastic mismatch (controlled by substrate boron nitride content), and coating thickness. Initiation of the transverse coating cracks occurs at lower critical loads, and shifts from the surface to the interface, with increasing elastic-plastic mismatch and decreasing coating thickness. This shift is accompanied by increasing quasi-plasticity in the substrate. Once initiated, the cracks pop in and arrest within the coating, becoming highly stabilized and insensitive to further increases in contact load, or even to coating toughness. A finite element analysis of the stress fields in the loaded layer systems enables a direct correlation between the damage patterns and the stress distributions: between the transverse cracks and the tensile (and compressive) stresses; and between the subsurface yield zones and the shear stresses. Implications of these conclusions concerning the design of coating systems for damage tolerance are discussed.     

Prediction of edge and tunnelling crack formation in layered ceramics using a stress-energy fracture criterion

A coupled stress-energy criterion is utilized to predict initiation of both edge and tunnelling cracks in layered ceramics containing thermal residual stresses. Edge (surface) cracks may originate in layers having high compressive in-plane stresses while tunnelling (internal) cracks may form in layers with high tensile in-plane stresses. This work investigates the influence of both the residual stresses magnitude and layer thickness on the formation of surface cracks and provides a design map defining safe regions where no cracks will be present in the sintered multilayer architecture upon reaching the room temperature. Necessary stress and energy inputs to evaluate the coupled criterion are calculated using the finite element method. Simulation results are validated with experimental observations on sample architectures fabricated with layers of various thicknesses and in-plane thermal residual stresses. The good agreement demonstrates the potential of the stress-energy coupled criterion for designing crack-free multi-layered ceramic architectures.     

Densification effects on the fracture in fused silica under Vickers indentation

This study investigates the effects of densification on the deformation and fracture in fused silica under Vickers indentation by both the finite element analysis (FEA) and experimental tests. A refined elliptical constitutive model was used, which enables us to investigate the effects of the evolution of yield stress under pure shear and elastic properties with densification. The densification distribution was predicted and compared with experiments. The plastic deformation and indentation stress fields were used to analyze the initiation and morphology of various crack types. The formation mechanism of borderline cracks was revealed for the first time. This study reveals that the asymmetry of the densification distribution and elastic-plastic boundary significantly influences the cracking behavior. Under the Vickers indentation, conical cracks have the largest penetration depth. When these cracks emerge from a region far from the impression, they extend with constant radii to form circles on the sample surface. Otherwise, they tend to be initiated at the centers of the indenter-material contact edges before propagating towards the impression corners with increasing radii. Therefore, the borderline cracks consisting of successive partial conical cracks can form at a low load and makes them the first type of crack to appear.     

Elastic analysis and engineering design formulae for bonded joints

The general elastic plane strain problem of adhesively bonded structures which consist of two different adherends is considered. To facilitate a truly general approach the adhesive joint is modelled as an adherend-adhesive sandwich with any combination of tensile, shear and moment loading being applied at the ends of both adherends. A full elastic analysis is presented which calculates the adhesive shear and tensile stresses in the overlap region, this analysis has been validated for a range of load cases using a finite element program. Basic design approaches are outlined and explicit expressions are developed which enable the simple evaluation of the stress distributions in the adhesive overlap. Simplified two parameter design formulae are also produced which accurately describe the peak stresses at the ends of the adhesive overlap in both the transverse and longitudinal shear directions. In all of the analyses the adherends are assumed to behave as linear elastic cylindrically bent plates with the adhesive forming an elastic interlayer between them. In the simplified analyses only one component of adhesive stress is considered, while in the full elastic analysis two components of stress are considered with a consequent increase in the complexity of the required solution method, but also an increase in accuracy over the simplified analyses for a wider range of joint configurations.     

An energy-based failure criterion for delamination initiation in electronic packaging

The significance of interfacial delamination as a crucial failure mechanism in electronic packaging has been documented in many papers. A number of failure criteria have been used to solve the problems with a pre-crack at the interface. However, in real electronic packages, the size and location of the cracks or/and delamination cannot be predicted. It is not easy to use the traditional fracture criteria to deal with more complicated 3D delamination problems. The epoxy molding compound (EMC)/copper leadframe interface was selected in this study. A series of button shear tests were conducted to evaluate the interfacial adhesion between the EMC and copper. In each test, the failure load acting on the EMC of the button shear sample was measured at different shear angles and a finite element model was used to evaluate the stresses at the EMC/copper interface. In this paper, an energy-based failure criterion is proposed using both the interfacial distortional and hydrostatic strain energy densities as two failure parameters. Stresses were extracted from the numerical simulation in order to calculate the interfacial distortional strain energy density, U _d, and the interfacial hydrostatic strain energy density, U _h, related, respectively, to the shear and tensile modes. U _d and U _h were averaged within a selected region of the finite element model where it exhibits high interfacial strain energy density values.     

A Comparison of Numerous Lap Joint Theories for Adhesively Bonded Joints

Numerous authors have investigated the state of stress in the adhesive of adhesively bonded joints. They have made various assumptions concerning the behavior of the adhesive and adherends to yield tractable differential equations which remove the stress singularities which occur at the edges of the bi-material interfaces. By examining several test problems, this paper investigates the effect of these assumptions on predicted adhesive stress. It was found that predicted maximum adhesive shear stress is insensitive to underlying assumptions and that maximum adhesive peel stress is relatively unaffected by most assumptions except that neglecting shear deformation of the adherends can affect results by as much as 30%. Peel stresses from the well known theory of Goland and Reissner which neglects shear deformation of the adherends and makes several inconsistent assumptions vary as much as 30% from stresses from a consistent lap joint theory which considers shear deformation of the adherends. However, in most cases the effects of the inconsistencies cancel the effects of neglecting the shear deformation of the adherends and the variation is less than 15%. This paper points out that finite element analyses of bonded joints where one layer of 4 node isoparametric elements are used to model the adhesive give results very close to those from consistent lap joint theories.     

Compressive Surface Layer to Avoid Edge Cracking in Laminar Ceramic Composite

Previous work has shown that layers within ceramic laminates that contain biaxial compressive stresses will also contain tensile stresses where the layer intercepts the surface. It has also been shown that when the thickness of the layer exceeds a critical value, the tensile stresses at and near the surface can produce a centerline crack that extends along the surface to a depth corresponding to the thickness of the compressive layer. The current work explores the concept of preventing the occurrence of surface cracks with a thin layer of material that places the entire external surface in compression. A recent finite element analysis by Monkowski and Beltz showed that when the external surface layer material was identical to the compressive layers, the tensile stresses at the surface could be reduced to zero when the thickness of the surface layer was 0.6 of the thickness of the compressive layer. In addition, they determined the stress intensity factor function for a surface crack and showed that surface cracking could be avoided when the thickness of the surface layer was ≥0.25 times the thickness of the compressive layer. The experimental results presented here show that a thin compressive layer will prevent surface cracks from forming in the compressive layers; the results also appear to confirm the predictions of Monkowski and Beltz.     

Comprehensive dynamic failure mechanism of thermal barrier coatings based on a novel crack propagation and TGO growth coupling model

Comprehensive understanding of failure mechanism of thermal barrier coatings (TBCs) is essential to develop the next generation advanced TBCs with longer lifetime. In this study, a novel numerical model coupling crack propagation and thermally grown oxide (TGO) growth is developed. The residual stresses induced in the top coat (TC) and in the TGO are calculated during thermal cycling. The stresses in the TC are used to calculate strain energy release rates (SERRs) for in-plane cracking above the valley of undulation. The overall dynamic failure process, including successive crack propagation, coalescence and spalling, is examined using extended finite element method (XFEM). The results show that the tensile stress in the TC increases continuously with an increase in an undulation amplitude. The SERRs for TC cracks accumulate with cycling, resulting in the propagation of crack toward the TC/TGO interface. The TGO cracks nucleate at the peak of the TGO/bond coat (BC) interface and propagate toward the flank region of the TC/TGO interface. Both TC cracks and TGO cracks successively propagate and finally linkup leading to coating spallation. The propagation and coalescence behavior of cracks predicted by this model are in accordance with the experiment observations. Therefore, this study proposed coating optimization methods towards advanced TBCs with prolonged thermal cyclic lifetime.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

Direct Measurement of Longitudinal Strains and Stresses within Single Lap Shear Adhesive Joints Using Neutron Diffraction

The neutron diffraction technique has been used to investigate the longitudinal stresses in the adherend produced as a result of cure and due to the application of a tensile load in a single lap shear joint. A comparison has also been made between the stress distributions in loaded “aged” and “unaged” joints. The neutron diffraction technique is the only viable method of investigating these stresses within metal adherends and enables comparisons between predicted and measured stresses to be made. The results of these experiments cast doubt on some of the predictions from finite element modelling of adherend stress levels.     

Evolution of internal cracks and residual stress during deposition of TBC

Thermal barrier coating (TBCs) are ceramic coatings that are deposited on metallic substrates to provide high thermal resistance. Residual stress is among the critical factors that affect the performance of TBCs. It evolves during the process of coating deposition and in-service loading. High residual stresses result in significant cracking and premature delamination of the TBC layer. In the present study, a hybrid computational approach is used to predict the evolution of internal cracks and residual stress in TBC. Smooth particle hydrodynamics (SPH) is first used to model the deposition of yttria-stabilized zirconia (YSZ) layer that contains various interfaces and micropores on a steel substrate. Then, three-dimensional (3D) finite element analysis is utilized to predict the evolution of internal cracks and residual stress in the ceramic coating layer. It is found that multiple cracks emerge during the solidification of the coating layer due to the development of high tensile (quenching) stresses. The cracking density is higher at regions near the coating interface. It is also found that compressive (residual) stresses are developed when the deposited coating is cooled to room temperature. The residual stress state is equibiaxial and nonlinear across the thickness/width of the TBC layer. The residual stress profile predicted compares well with that of hole drilling experiments.     

Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate

The paper presents the results of an analytical and numerical solution for interfacial stresses in carbon fiber reinforced plastic (CFRP)–reinforced concrete (RC) hybrid beams studied by the finite element method. The analytical analysis is based on the deformation compatibility approach where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the concrete beam and the bonded plate. In numerical analysis, the mesh sensitivity test shows that the finite element results for interfacial stresses are not sensitive to the finite element mesh. The finite element analysis then is used to calculate the interfacial stress distribution and evaluate the effect of the structural parameters on the interfacial behavior. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions. We can conclude that this research is helpful for the understanding the mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

Surface Cracking in Layers Under Biaxial, Residual Compressive Stress

Thin two-phase, Al₂O₃/ t -Zr(3Y)O₂ layers bounded by much thicker Zr(3Y)O₂ layers were fabricated by co-sintering powders. After cooling, cracks were observed along the center of the two-phase, Al₂O₃/ t -Zr(3Y)O₂ layers. Although the Al₂O₃/ t -Zr(3Y)O₂ layers are under residual, biaxial compression far from the surface, tensile stresses, normal to the center line, exist at and near the surface. These highly localized tensile stresses can cause cracks to extend parallel to the layer, to a depth proportional to the layer thickness. A tunneling/edge cracking energy release rate function is developed for these cracks. It shows that for a given residual stress, crack extension will take place only when the layer thickness is greater than a critical value. A value of the critical thickness is computed and compared with an available experimental datum point. In addition, the behavior of the energy release rate function due to elastic mismatch is calculated via the finite element method (FEM). It is also shown how this solution for crack extension can be applied to explain cracking associated with other phenomena, e.g., joining, reaction couples, etc.     

Stresses developed in reaction-bonded ceramics

A physical model is presented that predicts the stress distribution created in a particle during its reaction with a surrounding reactant to form a uniform layer of reaction product on its surface, when the reaction involves a volume change. The results of the model are applied specifically to the case of silicon reacting with nitrogen to form Si₃N₄. The model predicts the generation of a high, tensile hydrostatic stress in the Si core as well as high tensile radial stress and compressive tangential stress in the nitride layer. Although the model is restricted to elastic deformation only and therefore predicts unrealistically high stresses in some cases, the results are anyway of relevance in the consideration of possible non-elastic processes such as creep and fracture and also in assessing the possible effect of stress on the reaction equilibrium. It is predicted that the nitride reaction layer would fracture during the nitridation process. A second model is also presented predicting the residual stresses arising during cooling of a partially reacted particle as a result of the difference in thermal expansion of the reactant core and the reaction product layer. In the case of the reaction of silicon to silicon nitride these thermal expansion mismatch stresses are significant but small compared to the stresses due to the chemical reaction. ©