A novel mathematical procedure to evaluate the effects of surface topography on the interfacial state of stress. Part II. Verification of the method for scarf interfaces

A mathematical procedure was developed to utilize the complementary energy method, by minimization, in order to obtain an approximate analytical solution to the 3D stress distributions in bonded interfaces of dissimilar materials. The stress solutions obtained predict the stress jumps at the interfaces, which cannot be captured by the current FEA methods. As a novel method, the penalty function is used to enforce the displacement boundary conditions at the interfaces. Furthermore, the mathematical procedure developed enables the integration of different interfacial topographies into the solution procedure. In order to incorporate the effects of surface topography, the interface is expressed as a general surface in Cartesian coordinates, i.e. F(x, y, z) = 0. In this paper, the scarf interface problem, i.e. y = x/2 surface is considered for verification of the method by comparison with finite element analysis (FEA) results. Comparison of the results reveals our new mathematical procedure to be a promising and efficient method for optimizing interface topographies.     

Delamination Mechanics of a Clamped Rectangular Membrane in the Presence of Long-Range Intersurface Forces: Transition from JKR to DMT Limits

A 1-dimensional rectangular freestanding membrane clamped at opposite ends adheres to the planar surface of a rectangular punch. A tensile load applied to the punch causes the membrane to deform and gradually delaminate from the substrate. At equilibrium, the applied load is balanced by the disjoining pressure at the membrane-punch interface with range, y, and magnitude, p. Applying the Dugdale-Barenblatt-Maugis cohesive zone approximation, the disjoining pressure is taken to be uniform and confined to a finite cohesive length at the contact edge. For a fixed adhesion energy, γ = p y, we investigate the following: (i) the Derjaguin-Muller-Toporov (DMT) limit where y → ∞ and p → 0, (ii) the Johnson-Kendall-Roberts (JKR) limit where y → 0 and p → ∞, and (iii) the general case for intermediate but finite y and p. Delamination continues until the contact area shrinks to a line prior to “pinch-off”. The results are compared with the 2-dimensional axisymmetric membrane counterpart.     

An analytical approach for the adhesion of a semi-infinite elastic body in contact with a sinusoidal rigid surface under zero external pressure

An analytical approach for the adhesion of a semi-infinite elastic body in contact with a sinusoidal rigid surface under zero external pressure is presented. Although Johnson (Int. J. Solids Struct. 32, 423 (1995)) has proposed an analytical solution for a slightly wavy surface, while Zilberman and Persson (Solid State Commun. 123, 173 (2002); J. Chem. Phys. 118, 6473 (2003)) have given a numerical solution for a highly wavy surface by considering the curvature of the contact area in the calculation of the interfacial term of the total energy, our solution is not only for small amplitude of roughness (i.e., the slightly wavy surface as Johnson's) but also for large amplitude of roughness (i.e., the highly wavy surface as of Zilberman and Persson). Our solution considers the curvature of the contact area as do Zilberman and Persson. Our results which are obtained for the total energy and equilibrium condition of the system agree with both Johnson's and Zilberman and Persson's results. The effects of the material constants and the surface roughness on the adhesion are clearly expressed and discussed.     

Wettability of Polymeric Solids by Aqueous Solutions of Anionic and Nonionic Surfactant Mixtures

Measurements of the surface tension (γ _LV) and advancing contact angle () on poly(tetrafluoroethylene) (PTFE) and poly(methyl methacrylate) (PMMA) were carried out for aqueous solutions of sodium decyl sulfate (SDS) and p-(1,1,3,3-tetramethylbutyl)phenoxypoly(ethylene glycol) (TX100) and their mixtures. The results obtained indicate that the values of the surface tension and contact angles of solutions of surfactants on PTFE and PMMA surfaces depend on the concentration and composition of the surfactant mixtures. Calculations based on the Lucassen-Reynders equation indicate that for single surfactants and their mixtures at a given concentration in the bulk phase the values of surface excess concentration of surfactants at water–air and PTFE–water interfaces are nearly the same, so the adsorption of the surfactants at water–air and PTFE–water interfaces should also be the same. However, the adsorption of TX100 and its mixtures with SDS at water–air interface is higher than that at PMMA–water interface, which is confirmed by the ratio of absolute values of molecular interaction parameters at these interfaces calculated on the basis of Rosen approach. If we take into account the hydration of the poly(ethylene oxide) chains of TX100 and acid and base parameters of the surface tension of water it appears that the PMMA surface is covered by the 'pure' water molecules from the solution or molecules connected with the chain of nonionic surfactant. On the other hand, the lack of SDS molecules at the PMMA–water interface may result from the formations of its micelles which are connected with the TX100 chain.     

Processing of interfacial tension data in solvent extraction studies. Interfacial properties of various acidic organophosphorus extractants

Basically, the interfacial tension data can be plotted as a function of logarithm C where C denotes the concentration of any form of the surface active species considered. The various relationships y vs In C are discussed here from a mathematical point of view and it is shown that ambiguities may arise from the use of the interfacial tension curves versus the total extractant concentration for the interfacial tension data interpretation. The method recommended in this work is based on the computation of the whole surface excess curves (Γ vs concentration of individual species). This is achieved by matching various adsorption equations (e.g. Szyszkowski or Temkin relationships) or empirical equations to the interfacial tension data (y vs C). The term dy/dln C can then be analytically calculated and introduced into the Gibbs equation [Γ = ?(1/RT)dy/dln C] to derive mathematical expressions for the surface excess curves. To exemplify our approach, interfacial data are interpreted for dibutylphosphoric acid (HDBP), di(2-ethylhexyl)phosphoric acid (HDEHP), di(hexoxyethyl)phosphoric acid (HDHOEP), 2-ethylhexyl-2-ethylhexylphosphonic acid (HEH[EHP]) and di(2-ethylhexyl)phosphinic acid (H[DEHP]) at various liquid-liquid interfaces.     

J-integral studies of crack initiation and crack tip-blunting of phenolphthalein polyether ketone

The J-integral is applied to characterize the fracture initiation of phenolphthalein polyether ketone (PEK-C) for which the concepts of linear elastic fracture mechanics (LEFM) are inapplicable at high temperatures for reasonably-sized specimens due to extensive plasticity. The multiple-specimen resistance curve technique recommended by the ASTM is the basic method employed. The values of J_IC increase with increasing temperature. The crack tipblunting of PEK-C is observed. The parameters, such as crack opening displacement (COD), δ₀, and the stretching increment Δa_b1 are introduced to describe the blunting phenomenon. The δ₀ increases with increasing temperature, as does Δa_b1. This indicates that the blunting occurs easily as the temperature increases; i.e., as the material's yield stress, σ_y steadily falls. The relationships between δ₀, Δa_b1, and σ_y are also discussed. © 1994 John Wiley & Sons, Inc.     

Non-linear stress and failure analyses of adhesively-bonded joints subjected to a bending moment

In this paper, the mechanical behavior of the Single-Lap Joints (SLJs) bonded with two different adhesives (FM 73 and SBT 9244) under a bending moment was analyzed, both experimentally and numerically. Four-point bending experiments for the joints with different overlap lengths were carried out and fracture surfaces of the SLJs were examined with a Scanning Electron Microscope (SEM). After the stress analysis in the SLJs was performed via a finite element method by considering the material non-linearities of the adhesives and adherend (AA2024-T3), the Finite Element Analysis (FEA) results were compared with experimental results. Finally, the stress analyses and experimental results show that the failure in the SLJs subjected to a bending moment probably initiates from the overlap region on the adhesive–upper adherend interface in tension and propagates towards the centre of the overlap. Also, in the joint subjected to a bending moment, it is seen that the load carried by the SLJ with SBT 9244 adhesive with increasing overlap length is more than that of the SLJ with FM 73 adhesive, although in the bulk form FM 73 adhesive is about three times stronger than SBT 9244 adhesive.     

Interfacial Interactions in Polymers: The Dependence of the Measured Surface Tension of Solid Polymer on the Surface Tension of Wetting Liquid

Careful measurements of the surface tension of solid polymers, y_s , based on the data on contact angles for wetting liquids with various surface tension, y_L , allows one to establish the functional dependence of y_s = f(y_L ). This dependence is divided into three zones: one zone, where there is no dependence of y_s on y_L and two zones where y_s changes linearly with y_L .     

Effects of inserts on the injection molding process

Injection molds often contain blocks of dissimilar material for improved cooling; they may also contain blocks of movable metal as a means of ejecting large parts from the mold. In this case, the blocks of metal are made of the same material, but the resistance at the interface between them has a marked influence on the cooling in the local area near the interface. In many other cases, inserts may be required because of wear in a particular mold section, or because efficient mold design is needed to produce similar parts. Hence, any mathematical model for analysis of heat transfer in injection molds must be general enough to apply to interfaces with and without gaps (i.e., with and without resistance to the flow of heat at the interface) for similar, as well as dissimilar, materials. A new and accurate model for prediction of heat transfer in heterogeneous (zoned) molds is presented in this paper. Through the solution of real problems with this model, the effects of differing material properties and interfacial thermal resistance are studied and the results are reported. It is observed that inserts have both local and global effects on the injection molding process; the overall ejection time for a part may be shortened, and the surface appearance of a part may be improved by correct placement of inserts.     

Catalytic and Heating Behavior of Nanoscaled Perovskites under Microwave Radiation

Perovskite powders of the types La_0.5Ca_0.5Al_yM_1–yO_3–δ (y = 0–0.8), M = Fe, Cr, Mn, Co and La_xSr_1–xMn_yCo_1–y (x = 0.5–1, y = 0–1) were prepared via a sol‐gel route according to the modified Pechini method. Incineration of the resins was performed before final sintering at 1000 °C for 6 h. The phase composition of the samples was established by X‐ray powder diffraction analysis, and the lattice parameters were calculated using Rietveld analysis. The shape and size of the particles were determined via scanning electron microscopy and the specific surface area of the powder perovskites was established by the BET method. The principal particles were ca. 100 nm in size and formed agglomerates larger than 1.0 μm. The composition of the perovskites was established by EDX analysis. Following this, the catalytic behavior was tested by means of total oxidation of propane. The catalytic performance was measured at atmospheric pressure with 3 g of catalyst in a fixed‐bed quartz reactor (i.d. = 18 mm) under thermal‐assisted and microwave‐assisted conditions. Initial results show a strong dependence of the catalytic and heating behavior on the nature of the M‐atom and its number of unpaired d‐electrons as well as on the particle size and its specific surface area. No significant difference in the results could be detected from comparison of the two heating methods.     

Wetting Behavior of Aqueous Solutions of Binary Surfactant Mixtures to Poly(tetrafluoroethylene)

Measurements of the surface tension (γ _LV) and advancing contact angle () on poly(tetrafluoroethylene) (PTFE) were carried out for aqueous solutions of cetyltrimethylammonium bromide (CTAB), cetylpyridynium bromide (CPyB), sodium decylsulfate (SDS), sodium dodecylsulfate (SDDS), p-(1,1,3,3-tetramethylbutyl) phenoxypoly(ethylene glycol)s, Triton X-100 (TX100) and Triton X-165 (TX165) and their mixtures. The results obtained indicate that the values of the surface tension and wettability of PTFE depend on the concentration and composition of the surfactants mixture. In contrast to Zisman finding, there was no linear dependence between cos and the surface tension of aqueous solutions of surfactants and their mixtures for all studied systems, but a linear dependence existed between the adhesional tension and solution surface tension for PTFE in the whole concentration range, the slope of which was –1, indicating that the surface excess concentration of surfactant at the PTFE–solution interface was the same as that at the solution–air interface for a given bulk concentration. It was also found that the work of adhesion of aqueous solutions of surfactants and their mixtures to PTFE surface did not depend on the type of surfactant, its concentration and composition of the mixture. This means that for the studied systems the interaction across PTFE–solution interface was constant, and it was largely of Lifshitz–van der Waals type. On the basis of the surface tension of PTFE and the Young equation and thermodynamic analysis of the work of adhesion of aqueous solutions of surfactants to the polymer surface it was found that in the case of PTFE the changes of the contact angle as a function of the total mixture concentration in the bulk phase resulted only from changes of the polar component of the solution surface tension.     

A mass transfer model for the autocatalytic dissolution of a rotating copper disc in oxygen saturated ammonia solutions

A mathematical model of mass transfer processes during autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique is presented. The model is based on the equations of steady state convective diffusion with volumetric mass generation terms and boundary conditions of the third kind, in more generalized form, at the disc surface and of the first kind in the bulk solution. The boundary value problem was solved numerically using the finite difference method with variable mesh spacing. Comparison of calculated and experimental results indicates that the model quantitatively represents the measurements. The rate of the reaction Cu(II)+Cu2Cu(I) determines the overall rate of the process.Nomenclature A rotating disc surface area, (cm²) - B dimensionless constant,B=k ₃ c ₁ ^{0 –1} - c _i concentration of speciesi, c _i=c _i(y) (mol cm^–3) - c _i ⁰ concentration of species i in the bulk of solution,c _i ⁰ =c _i ⁰ (t) (mol cm^–3) - c _{i, 0} concentration of species i at the disc surface,c _i,0=c _i (y=0) (mol cm^–3) - C _i concentration ratio,C _i=c _i/c _i ⁰ ,C _i=C _i() - C _i ⁰ concentration ratio (in the bulk of solution),C _i=c _i ⁰ /c _i ⁰ - C _i,0 concentration ratio (at the disc surface),C _i,0=c _i,0/c _i ⁰ - D _i molecular diffusivity of species i (cm² s^–1) - h space increment,h==(/v)^1/2y, dimensionless - j _i mass flux of species i (mol cm^–2 s^–1) - k _i first-order reaction rate constant (cm s^–1 or cm³ mol^–1 s^–1) - K _i,j diffusivity ratio,K _i,j=D _i/D _j, dimensionless - M number of space increments - n _i total number of moles of Cu(II) entering the bulk of solution referred to the unit disc surface area (mol cm^–2) - rate of production of species i by the chemical reaction (mol cm^–3 s^–1) - Sc _i Schmidt number,Sc _i=v _i/D _i - t time, (s) - t time increment (s) - v fluid velocity vectorv=(u, v, w) (cm s^–1) - V volume of solution (cm³) - W ₁,W ₂ dimensionless group,W ₁=(K _3,2/D ₁) (v/)^1/2,W ₂ = (K _1,2/D ₂(v/)^1/2 - x ₁ coordinates,l=1, 2, 3 - y axial coordinate (perpendicular to the disc surface) - y space increment (cm) Greek letters nabla operator - kinematic viscosity of solution (cm² s^–1) - _i stoichiometric coefficients - disc angular velocity (s^–1) - dimensionless axial coordinate, =(/v)^1/2 y - dimensionless space increment, =(/v)^1/2y     

The diffuse interface phase-field model for in situ interlayer phase formations in low-temperature reaction bonding of alumina laminates—A theoretical and experimental comparison

A diffuse interface phase-field model is developed to study alumina seamless laminate composites formation via reaction interlayer diffusion bonding. The model was designed to indicate the important role of interface on phase transition and interfacial chemical reactions. The model has indicated the interfacial reactions, phase transitions, and phase evolution along the alumina/reaction layer interface. The theoretical results were assessed, validated, and confirmed by experimental data at similar bonding conditions via targeted diffusion bonding in aluminum-alkaline earth hydride and alanate interlayer systems Me (Me: Mg–Sr). The alanates and hydrides dissociations left pockets of intermetallic phases at interlayer as bonding constituents. The solid-state bonds have formed by diffusion bonding at laminate interfaces and partial oxidations. The elemental analysis showed the alkaline earth rich zones at interlayer and near interfaces. The crystalline composition of the interlayer materials was combinations of polycrystalline mixed oxide layers, formed due to different oxidation kinetics and diffusion rates. Interlayer oxidation products were combination of complex oxides with Sr_uMg_xAl_yO_z (u: 0.8–1, x: 0.7–1, y: 2–10, z: 4–17) stoichiometry.     

Adsorption of some anionic surfactants on barite and at solution/Air interfaces

The adsorption behavior of synthesized anionic surfactants with the chemical structure RO-Ph-N=N-Ph-SO₃Na, where R is an octyl, dodecyl, or cetyl group, was analyzed by using a modified version of the Frumkin adsorption isotherm. The values of thermodynamic parameters (including free energy of micellization, ΔG _mic, and of adsorption, ΔG _ads) at the solution/air interface and the solid/liquid interface were calculated, and the relation between the adsorption of the surfactants at these interfaces was investigated. Studies of the surface properties of these synthetic surfactants showed that the length of the hydrocarbon chain of these surfactants plays a major role in determining their surface and thermodynamic properties and that there is a good relationship between the effectiveness of adsorption of the surfactant and its efficiency as a collector.     

Effects in Surface Free Energy of Sputter-Deposited VNx Films

Vanadium nitride (VN _x ) thin films have attracted much attention for semiconductor integrated circuit (IC) packaging molding dies, and forming tools due to their excellent hardness and, thermal stability. VN _x thin films with VN_0.45, VN_0.83, VN_1.22, VN_1.73, VN_2.06 were prepared using a radio frequency (RF) sputter technique. The experimental results showed that the contact angle at 20°C increases with increasing nitrogen content of the VN _x films, to 101.4° corresponding to VN_1.73 and then decreased. In addition, the contact angles decreased with increasing surface temperature, because an increase of the surface temperature disrupts the hydrogen bonds between water and the films and the water gradually vaporizes. The total surface fee energy (SFE) at 20°C decreased with nitrogen content of the VN _x films to 29.8 mN/m (VN_1.73) and then increased. This is because a larger contact angle means weaker hydrogen bonding which results in a lower SFE. The polar SFE component had the same trend as the total SFE, but the dispersive SFE component had the opposite trend. The polar SFE component is also lower than the dispersive SFE component. This is because hydrogen bonds are polar. The total SFE, dispersive SFE and polar SFE of the VN _x films all decrease with increasing surface temperature. This is because with increasing temperature, water evaporates from the surface, disrupting hydrogen bonds and hence increasing surface entropy. The film roughness has an obvious effect on the SFE and there is tendency for the SFE to increase with increasing film surface roughness. As a result the SFE and surface roughness can be expressed in terms of a simple ratio function.     

A model of the electrochemical behaviour within a stress corrosion crack

A mathematical model of the electrochemical behaviour within a stress corrosion crack is proposed. Polarization field, crack geometry, surface condition inside the crack, electrochemical kinetics, solution properties and applied stress can be represented by the polarization potential and current, the electrochemical reactive equivalent resistance of the electrode, the change in electrolyte specific resistance and surface film equivalent resistance, respectively. The theoretical calculated results show that (i) when anodic polarization potential is applied, the change in the crack tip potential is small; (ii) when cathodic polarization potential is applied, the crack tip potential changes greatly with the applied potential; (iii) the longer the crack, the smaller the effect of the applied potential on the crack tip potential in both anodic polarization and cathodic polarization conditions. The calculated results are in good agreement with previous experimental results.Notation coordinate, from crack mouth (on the metal surface) to crack tip (cm) - y y = s _L L/(s ₀ – s _L) + L – , function of (cm) - y ₀ y ₀ = s _L L/(s ₀ – s _L) + L (cm) - V polarization potential (V) - galvanic potential of electrode (V) - ₁ galvanic potential of electrolyte (V) - t sample thickness (cm) - w sample width (cm) - S _L crack tip width (cm) - S _o crack mouth width (cm) - L crack length (cm) - s() crack width at position (cm) - _lo specific resistance of electrolyte, as a constant ( cm) - _s specific resistance of metal ( cm) - (, y) specific resistance of electrolyte, varies with potential and crack depth ( cm) - R _b (, y) electrochemical reactive equivalent resistance of electrode, varies with potential and crack depth () - R ₁ electrolyte resistance () - R _s metal resistance () - r(, y) surface film equivalent resistance, varies with potential and crack depth () - r _o surface film equivalent resistance, as a constant () - I _o total polarization current (A) - I net polarization current from integrating 0 to in Fig. 2 (A) - polarization overpotential (V) - _a anodic polarization overpotential (V) - _c cathodic polarization overpotential (V) - Euler's constant     

EXAFS and FTIR characterization of tetrarhodium carbonyl clusters attached on tris-(hydroxymethyl)phosphine grafted silica catalytically active for olefin hydroformylation

A series of perovskites of the formula Ca_1–x Sr _x Ti_1–y M _y O_3–, M=Fe, Co, Cr or Ni,x = 0–1,y = 0–0.6, has been synthesized by a modified sol-gel method using citrate. Several of these materials were proved to be stable under operating conditions in reducing atmospheres of air and hydrocarbons. An outline of the synthesis procedure is given, together with the results of XRD, SEM, BET, TG, DTA and IR characterization before and after catalytic testing. The solubility of Ni and Cr in this perovskite was very limited, and the solubility of Co decreased abruptly above 1173 K. The solubility range of Ca and Sr on alkaline earth sites is 100%.     

Optimum Polymer - Solid Interface Design for Adhesion Strength: Carboxylation of Polybutadiene and Mixed Silanes Surface Modification of Aluminum Oxide

To understand the optimum design of polymer-solid interfaces for adhesion strength, model polymer-solid interfaces of carboxylated polybutadiene(cPBD) adhered to mixed silane modified Al₂O₃ surfaces were examined. The cPBD, having various ?COOH sticker group concentration φ(X) (0 ～ 10 mol%), was synthesized through high-pressure carboxylation of PBD, while Al₂O₃ surfaces were modified to have various -NH₂ density, φ(Y) (0 ～ 100 mol%), using self-assembly of mixed amine- and methyl-terminated silanes. The coadsorption kinetic model of the two silanes was analyzed through X-ray photoelectron spectroscopy (XPS), atomic force microscope (AFM), and dynamic contact angle (DCA), which gave the capability of controlling the receptor concentration of aluminum oxide surfaces. The polymer surface chain responses after exposure to various media were understood by measuring contact angle changes of various probe liquids. T-peel tests of the model polymer–solid interfaces, as a function of time and sticker and receptor group concentrations showed much longer time dependence than the characteristic time of a bulk polymer chain. Additionally, the classical equation of interface failure was re-examined to see the effects of deformation rate, annealing temperature, and annealing time. A simple scaling analysis of free energy of an adsorbed polymer on a solid surface was extended to predict the adhesion potential of the model polymer–solid interfaces. From the experiments and theory of adhesive vs. cohesive failure, it was found that there existed an optimum product value r* = φ(X)φ(Y)χ of sticker concentration φ(X), receptor concentration φ(Y), and their interaction strength χ, which was approximately 150 cal/mol for this polymer–solid interface. Below or above this optimum product value r*, the fracture energy of polymer-solid interfaces, G _IC, was less than its optimal value, G _lc*.     

Insight into the wetting and interfacial behavior of Cu-Ti/ZrB2 system: A combined experimental and DFT calculation

The wetting of ZrB₂ ceramic by molten pure Cu, Cu-(20, 30, 40, 50 at.%)Ti alloys were performed by the sessile drop method under vacuum of ∼4 × 10⁻⁴ Pa in the 1030−1070 °C temperature range. The wetting and interfacial behaviors of Cu-Ti/ZrB₂ systems were analyzed and discussed. Furthermore, the work of adhesion and electronic properties of the Cu(1 1 1)/ZrB₂(0 0 0 1) and Ti(0 0 0 1)/ZrB₂(0 0 0 1) atomic interfaces were quantitatively evaluated by first-principles method. The wettability is significantly improved with the Ti concentration or wetting temperature increasing as a result of the formation of (Ti) solid solution at interface. The calculated results show that the B-terminated ZrB₂ (0 0 0 1) surface is preferable to bond with Ti(0 0 0 1) surface, and the electronic structure reveals that the dominant interfacial bonding is the Ti-B ionic bond for the Ti/B-terminated ZrB₂ interface.     

Welding of polymer interfaces

Studies of strength development at polymer-polymer interfaces are examined and applications to welding of similar and dissimilar polymers are considered. The fracture properties of the weld, namely, fracture stress, σ, fracture energy, G_Ic, fatigue crack propagation rate da/dN, and microscopic aspects of the deformation process are determined using compact tension, wedge cleavage, and double cantilever beam healing experiments. The mechanical properties are related to the structure of the interface via microscopic deformation mechanisms involving disentanglement and bond rupture. The time dependent structure of the welding interface is determined in terms of the molecular dynamics of the polymer chains, the chemical compatibility, and the fractal nature of diffuse interfaces. Several experimental methods are used to probe the weld structure and compare with theoretical scaling laws, Results are given for symmetric amorphous welds, incompatible and compatible asymmetric amorphous welds, incompatible semicrystalline and polymer-metal welds. The relevance of interface healing studies to thermal, friction, solvent and ultrasonic welds is discussed.