Substrate constraint and adhesive thickness effects on fracture toughness of adhesive joints

The adhesive thickness effect on fracture behaviour of adhesive joints has been studied using the boundary effect model recently developed for specimen size effect on fracture properties of concrete, and the essential work of fracture model for ligament (uncracked region) effect on largescale yield of bulk metals and polymers. The leading common mechanism responsible for the nonlinear elastic fracture mechanics behaviours, such as adhesive thickness effect of adhesive joints, specimen size effect of brittle heterogeneous materials and notch dependence of deeply notched metal and polymer specimens, is discussed. These two fracture mechanics models show that the height variation of a fracture process zone (FPZ) or a plastic zone is directly responsible for any change in fracture energy measurements such as the specific fracture energy G _f and the critical strain energy release rate G _c. Both models show that G _f is rapidly reduced when the crack-tip approaches the back-face boundary of a specimen because only a limited FPZ or plastic zone height h _FPZ can be developed in the boundary region. In the case of a thin adhesive joint, the development of a plastic zone height is limited by the thickness of the adhesive sandwiched between the upper and lower adherends or substrates. Consequently, a linear relationship between the adhesive joint toughness and adhesive thickness is established. Test results on adhesive joints from the literature are analysed and compared with the new adhesive joint failure model based on the two well-established fracture mechanics models developed for other material systems.     

Influence of fracture process zone height on fracture energy of concrete

The implication of modelling concrete fracture with a fictitious crack of zero fracture process zone (FPZ) height is addressed because FPZ height, in reality, is not zero and is bound to vary during crack growth. The ligament effect on fracture energy G_F is explained by the nonuniform distribution of a local fracture energy g_f showing the influence of specimen boundary and variation of FPZ height. The nonuniform g_f distribution is then used to determine the size-independent G_F. The recent boundary-effect model based on a bilinear g_f function is confirmed by the essential work of fracture (EWF) model for the yielding of deeply notched polymer and metal specimens. The EWF model provides a theoretical basis for the bilinear g_f distribution. The principal rationale of the boundary-effect model, the influence of FPZ height on fracture energy, is supported by experimental observations of thickness effect on fracture toughness of thin polymeric adhesives between metals.     

CONTRIBUTIONS OF T. K. SHERWOOD AND ASSOCIATES TO THE FIELD OF DRYING (Part 3, Final)

ABSTRACT

Any nonuniformity in local moisture content of paper which develops during drying because of locally nonuniform drying rates provides a driving force for in-plane diffusion of moisture, which in turn acts to reduce this moisture nonuniformity. As no data have appeared for the in-plane diffusivity of moisture during desorption from paper over the range of conditions existing during papermachine drying, an investigation was undertaken to obtain this information.

Moisture diffusivity was determined to he a very strong function of the extent and state of water in the sheet, increasing exponentially with paper moisture content. The presence or absence of liquid water at the sheet boundary would effect moisture difiusivity when there is water in the pores but the direction of moisture transport in paper was found to be of overriding importance. In-plane moisture diffusivity is very much greater than that in the thickness direction, indicating that the non-isotropic nature of paper structure is a key factor. A microscale view of the mechanism of moisture transport in the thickness and in-plane directions was developed, consistent with the enormous difference in effect of moisture content on diffusivity in the two directions.     

Determination of size-independent specific fracture energy of concrete mixes by the tri-linear model

The methods proposed by Elices and co-workers [1], [2], [3] and by Hu and Wittmann [4] are commonly used to determine the size-independent specific fracture energy (G_F) of concrete by correcting the size-dependent specific fracture energy (G_f) measured by the RILEM work-of-fracture method. In the boundary effect model of Hu and Wittmann [4], the change in the local fracture energy (g_f) is approximated by a bilinear function, whereas the method of Elices et al. [1] consists in determining the non-measured work-of-fracture by adjusting the tail of the P-δ curve that corresponds to the final part of the test. Acoustic emission (AE) experiments on notched specimens (Muralidhara et al. [5], [6]) have revealed that under loading the AE events follow approximately a tri-linear distribution; initially the number of events increases almost linearly reaching an extended plateau when the number of events remains nearly constant and eventually the number reduces as the crack approaches the back stress free boundary of the specimen, reminiscent of the development of R-curve in a finite size specimen. This paper exploits this observation and proposes a tri-linear model for the determination of the size-independent specific fracture energy for three different concrete mixes ranging in compressive strength from 57 to 122 MPa. Remarkably, it is found that the resulting size-independent specific fracture energy G_F determined by this tri-linear model and by the bi-linear model of Hu and Wittmann [4] is very nearly the same and independent of the size of the specimen.     

A model for the self-heating reaction of coal and char

A mathematical model of the self-heating reaction of coal or char in bulk has been developed. The model takes into account a local oxidation reaction which depends on temperature and the concentrations of unreacted and reacted oxygen. The transport processes of diffusion and convection take the mobile reactant, oxygen, from the boundary to the distributed reaction where heat energy is released, and then convey the latter back to the boundary. The equations of the model are evaluated numerically and results are in general agreement with those predicted by the Theory of Thermal Explosions appropriate to the assumptions of the model. Various situations arise in the heating regime, depending on whether the conversion reaction is controlled by thermal conduction, reactant diffusion, reactant convection, or thermal convection where no distinct separation exists between the various cases. Some guidelines emerge for evaluating safe storage conditions for coal or char where the criterion of safety has to be specified for different materials, probably as a maximum safe temperature and maximum time of storage.     

In-Plane Diffusivity of Moisture in Paper

Any nonuniformity in local moisture content of paper which develops during drying because of locally nonuniform drying rates provides a driving force for in-plane diffusion of moisture, which in turn acts to reduce this moisture nonuniformity. As no data have appeared for the in-plane diffusivity of moisture during desorption from paper over the range of conditions existing during papermachine drying, an investigation was undertaken to obtain this information.

Moisture diffusivity was determined to he a very strong function of the extent and state of water in the sheet, increasing exponentially with paper moisture content. The presence or absence of liquid water at the sheet boundary would effect moisture difiusivity when there is water in the pores but the direction of moisture transport in paper was found to be of overriding importance. In-plane moisture diffusivity is very much greater than that in the thickness direction, indicating that the non-isotropic nature of paper structure is a key factor. A microscale view of the mechanism of moisture transport in the thickness and in-plane directions was developed, consistent with the enormous difference in effect of moisture content on diffusivity in the two directions.     

Charpy tests on brittle polymers

This paper describes a simple miss-spring model of Charpy's classical impact bending test. In this model, the mass represents the striker, and the spring the bent specimen. The stiffness of the latter is calculated from the formulas for static bending. The model has been tested by experiments on polymethyl methacrylate at room temperature. First, it is shown that the model correctly describes the effect of the dimensions of the specimen (span, width and thickness) on the fracture impact energy Secondly it is shown, that the fracture energy calculated from the measured fracture time agrees with the fracture energy determined experimentally. Third it has been found that the fracture energy in impact can be predicted by extrapolation of the results of slow bending tests at various deformation rates. Lastly, it has been proven experimentally that any stress waves generated by the impact of the striker have little effect on the measured fracture energy.     

Evaluation of Mode-II Fracture Energy of Adhesive Joints with Different Bond Thickness

A study on the mode-II edge-sliding fracture behaviour of aluminium-adhesive joints was carried out. Compact pure shear (CPS) adhesive joints of different bond thickness were produced using a rubber-modified epoxy resin as the adhesive. An analytical model was developed to calculate the stress distribution along the bond line of the joint. A crack-closure technique was used to evaluate the mode-II strain energy release rate. G_II, as a function of the adhesive bond thickness. The results indicated that for a given applied load, G_II increased gradually with the bond thickness. A finite element model (FEM) was also developed to evaluate the stress state along the bond line and the strain energy release rate of the CPS specimens. Consistent results were obtained between the theoretical model and finite element analysis. Scanning electron micrographs of the fracture surface illustrated a mainly interfacial fracture path between the adherends and the adhesive for all adhesive joint specimens. The critical fracture load increased very rapidly with bond thickness in the range 0.02 mm to 0.1 mm but remained constant thereafter. However, the mode-II critical fracture energy rose more gradually as the bond thickness was increased.     

Finite element analysis for the flow characteristics along the thickness direction in injection molding

A numerical simulation of the filling stage along the thickness direction is proposed by combining the free-surface boundary condition with the relevant governing equations. The mathematical model is based on the equations of continuity, momentum, and energy along with the inelastic power-law model and relevant boundary conditions. Because of the significant implications for microstructure development in the product, the fountain effect at the advancing free surface is explicitly taken into consideration in the simulation. The model yields data on free-surface shape and velocity, pressure, temperature, and shear stress distributions within the mold cavity. The rearrangement of the velocity and temperature profiles in the vicinity of the melt front is considered in detail.     

Evaluation of Mode-II Fracture Energy of Adhesive Joints with Different Bond Thickness

A study on the mode-II edge-sliding fracture behaviour of aluminium-adhesive joints was carried out. Compact pure shear (CPS) adhesive joints of different bond thickness were produced using a rubber-modified epoxy resin as the adhesive. An analytical model was developed to calculate the stress distribution along the bond line of the joint. A crack-closure technique was used to evaluate the mode-II strain energy release rate. G _II, as a function of the adhesive bond thickness. The results indicated that for a given applied load, G _II increased gradually with the bond thickness. A finite element model (FEM) was also developed to evaluate the stress state along the bond line and the strain energy release rate of the CPS specimens. Consistent results were obtained between the theoretical model and finite element analysis. Scanning electron micrographs of the fracture surface illustrated a mainly interfacial fracture path between the adherends and the adhesive for all adhesive joint specimens. The critical fracture load increased very rapidly with bond thickness in the range 0.02 mm to 0.1 mm but remained constant thereafter. However, the mode-II critical fracture energy rose more gradually as the bond thickness was increased.     

Influence of panel/back thickness on impact damage behavior of alumina/aluminum armors

Using modified SHPB device, damage behaviors of alumina/aluminum armors under impact load were studied. The influences of panel/back thickness on the target damage characteristics were investigated. The transmitted stress wave increased and the reflected stress wave decreased distinctly with the increase of back thickness, while the panel thickness variation had little influence on the stress wave propagation features. The vertex angle of ceramic inverted cone increased with the increase of back thickness and decrease of panel thickness, but the number of radial cracks reduced with the increase of back thickness and the decrease of panel thickness. Furthermore, the failure mechanism of the ceramic panels, including the cone and radial cracks formation mechanism was analyzed. A “composite beam” model has been established to estimate the local bending stress. The model calculation showed that the local bending stress is related to the panel thickness, back thickness and the panel/back moduli ratio.     

New observations of the fiber orientations effect on machinability in grinding of C/SiC ceramic matrix composite

In this paper, the effect of machining parameters on cutting force, force ratio, 3D surface roughness was studied, and the surface formation mechanism was deeply analyzed in view of the position relation between machining directions and fiber orientations. New observations of the fiber orientation effect on machinability are attempted to obtain in grinding of 2D C/SiC ceramic matrix composite with electroplated diamond grinding tool. Two machining directions (A and B) on one surface are taken into account to study the effect of fiber orientation on the grinding process. The results indicate that the cutting forces obtained in machining direction of A are greater than that in machining direction of B under all experimental conditions. However, the tangential force is greater than the normal force, which is different from grinding ordinary material. Whether in the machining direction of A or direction of B in grinding C/SiC composite, on the whole the surface roughness values (Sa and Sq) decrease as the feed rate increases. As depth of cut increasing, the surface roughness values in the machining direction of A and B come out inconsistency. At different feed rates, the surface roughness values in the machining direction of A and B also represent inconsistency with the change of cutting speed. The theoretical model of undeformed cutting thickness is unfit for evaluating its effect on the surface roughness. After analyzing of the surface formation, except for some fibers forming extruding fault and fracture, being pulled out, and fracture or broken, a new phenomenon that some fibers forming extruding fault and fracture is observed.     

Surface Segmental Mobility and Adhesion—Effects of Filler and Molecular Mass

The adhesion of thin films of poly(methyl acrylate) (PMA) on glass slides in contact with tape has been measured as a function of thickness, molecular mass, and amount of silica-based filler. In all cases studied the polymer thin-film, tape-peel tests resulted in linear force-velocity plots. The best-fit lines were extrapolated to find the fracture energies at zero velocity. For thin layers of rubbery PMA on glass slides the PMA-tape fracture energies were found to decrease (from 55-20 J/m²) with increasing PMA thickness (50-1000 nm). Thin films made from glassy poly(methyl methacrylate) (PMMA) were found to have no thickness dependence and much higher fracture energies (∼ 140 J/m²). The effect of PMA molecular mass was found to be smaller than the effect of film thickness. Including silica in the films at low levels dramatically increased the fracture energies, with a maximum (182 J/m²) found with 5.2% silica. With larger amounts of silica, the fracture energy declined significantly.     

Mode II fracture energy in the adhesive bonding of dissimilar substrates: carbon fibre composite to aluminium joints

The end-notched flexure (ENF) test calculates the value of mode II fracture energy in adhesive bonding between the substrates of same nature. Traditional methods of calculating fracture energy in the ENF test are not suitable in cases where the thickness of the adhesive is non-negligible compared with adherent thicknesses. To address this issue, a specific methodology for calculating mode II fracture energy has been proposed in this paper. To illustrate the applicability of the proposed method, the fracture energy was calculated by the ENF test for adhesive bonds between aluminium and a composite material, which considered two different types of adhesive (epoxy and polyurethane) and various surface treatments. The proposed calculation model provides higher values of fracture energy than those obtained from the simplified models that consider the adhesive thickness to be zero, supporting the conclusion that the calculation of mode II fracture energy for adhesives with non-negligible thickness relative to their adherents should be based on mathematical models, such as the method proposed in this paper, that incorporate the influence of this thickness.     

考虑局部非热平衡的流体层流横掠多孔介质中恒热流平板的传热分析

对流体层流横掠多孔介质中恒热流加热的平板,应用Brinkman-Forchheime-extended Darcy流动模型和流体与多孔介质之间局部非热平衡理论建立守恒方程组,应用数量级分析和积分法,得出了速度边界层厚度、热边界层厚度、壁面黏性摩擦系数和对流传热系数、流体与多孔介质之间局部温差的计算公式。结果表明,速度边界层与光板时明显不同,其在平板前端迅速增长,之后越来越平坦,趋于一个恒定值;而热边界层则沿着流动方向不断增长,类似于光板时的情况;局部的表面对流传热系数在平板前端达最大值,之后逐渐减小,也类似于光板时的情况;多孔介质与流体间的局部温差在平板前端达最大值,之后呈现沿着流动方向逐渐减小的变化趋势。     

Finite element analysis of composite T-joints used in wind turbine blades

Abstract

This paper presents a finite element (FE) analysis of the fracture behaviour of composite T-joints with various fibre reinforcement architectures subjected to pull-out loading. The FE model accounts for the effect of interface strength and interlaminar fracture energy on the ultimate load to failure; a linear softening fracture based law is adopted to describe crack growth in the form of delamination. The numerical simulation shows that the failure load increases with increasing interlaminar strength, which controls delamination initiation. The FE also demonstrates that the failure load increases with increasing interface fracture energy and the delamination propagation depends largely upon the fracture energy, which is enhanced by introducing interlaminar veils or through-thickness tuft yarns (stitching). Predictions were validated using experimental data for E-glass fibre/epoxy T-joints subjected to a tensile pull-out loading. The load–displacement response from the FE analysis is in a good agreement with measurements, illustrating the effectiveness of through thickness tufting that results to progressive, a more ‘ductile’, rather than abrupt catastrophic failure.     

Grain Boundary Film Thicknesses in Superplastically Deformed Silicon Nitride

The thickness of intergranular films in polycrystalline β-Si₃N₄ ceramics, both before and after superplastic deformation, has been systematically investigated using high-resolution transmission electron microscopy. In characterizing the film thickness, care was taken to correlate the grain boundary orientation with the direction of the compressive stress applied during the hot-pressing and the superplastic deformation. The film thickness shows a dependence on the intersection angle between the grain boundary and the applied force direction, typically ranging from around a characteristic value for most of the boundaries to zero for a boundary which has an overall short length and is perpendicular to the applied force direction. The film thicknesses in the deformed material, as compared with those before deformation, are marked by a wider distribution and an increased fraction of boundaries free of films, unequivocally demonstrating that during the superplastic deformation the liquid phase is redistributed within short ranges, a process governed by the local stress level as well as kinetic factors. Possible consequences of the liquid-phase redistribution on the deformation behavior are also discussed.     

Surface Segmental Mobility and Adhesion—Effects of Filler and Molecular Mass

The adhesion of thin films of poly(methyl acrylate) (PMA) on glass slides in contact with tape has been measured as a function of thickness, molecular mass, and amount of silica-based filler. In all cases studied the polymer thin-film, tape-peel tests resulted in linear force-velocity plots. The best-fit lines were extrapolated to find the fracture energies at zero velocity. For thin layers of rubbery PMA on glass slides the PMA-tape fracture energies were found to decrease (from 55–20 J/m²) with increasing PMA thickness (50–1000 nm). Thin films made from glassy poly(methyl methacrylate) (PMMA) were found to have no thickness dependence and much higher fracture energies (～ 140 J/m²). The effect of PMA molecular mass was found to be smaller than the effect of film thickness. Including silica in the films at low levels dramatically increased the fracture energies, with a maximum (182 J/m²) found with 5.2% silica. With larger amounts of silica, the fracture energy declined significantly.     

Fracture behaviour of a rubber nano-modified structural epoxy adhesive: Bond gap effects and fracture damage zone

This paper critically examined the fracture behaviour of a rubber-modified, structural epoxy adhesive with various bond gap thicknesses ranging from 0.05 mm to 6 mm. The main and very novel contribution is direct measurement of the fracture process zone, plastic deformation zone and intrinsic fracture energy dissipated in the fracture process zone. The shape and size of the fracture process zone and plastic deformation zone were identified using scanning electron microscopy, transmission electron microscope and transmission optical microscope. As the bond gap thickness increased, the fracture energy increased steadily from 2365 J/m² for 0.05 mm bond gap thickness to 6289 J/m² of 1.6 mm bond gap thickness, and then plateaued. The thickness and failure strain of the fracture process zone remained essentially constant, being approximately 0.052 mm and 0.55 respectively, for different bond gap thicknesses. The intrinsic fracture energy (dissipated in the fracture process zone) appeared to be a material property, which remained approximately 2738 J/m². The plastic deformation zone extended through the entire bond gap in thickness and occupied a significant length for all bond gap thicknesses. The effect of bond gap thickness on the fracture energy of the adhesive joints is hence directly attributed to the variation of the plastic deformation energy (dissipated in the plastic deformation zone) with bond gap thickness.     

Fracture analysis of rubber‐like materials using global and local approaches: Initiation and propagation direction of a crack

In this work, fracture of elastomers is analyzed using global and local approaches, combining experiments, analytical developments, and finite element calculations. The J‐integral is chosen as a global parameter characterizing crack initiation in such materials. Particular attention is paid to single specimen methods for measuring the fracture surface energy. More precisely, models developed in the literature are summarized and, because of the lack of accuracy of these models, an original pertinent expression of J is proposed by analogy with linear elastic fracture mechanics frameworks. However, the J‐integral is not able to predict the kinetic or the propagation direction of a crack. Thus, some local parameters are examined: principal strains, principal stresses, and the strain energy density (SED) factor. Results revealed that all these parameters represent reasonable indicators of the crack propagation direction in elastomers. Moreover, unlike maximal principal stress and SED factor, maximal principal strain seems to govern the crack initiation in this kind of materials. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers