A Novel Technique for the Determination of Surface Biaxial Stress under External Confinement Using Raman Spectroscopy

Bi-axial compressive stress induced as a result of mechanical confinement within a zirconium diboride-silicon carbide (ZrB₂-SiC) ceramic composite has been quantified using micro Raman spectroscopy and then validated using two independent experimental methods. First a relationship relating the Raman peak-shift on a confined silicon carbide (SiC) particle to magnitude of imposed confinement stress was developed by utilizing phonon deformation potentials for 3C-SiC diamond and zinc-blende crystal structures. ZrB₂-5wt%SiC samples, prepared using spark plasma sintering were subjected to different confinement pressure on the lateral surface by thermal shrink fitting metallic sleeves. The relationship between Raman peak-shift and confinement stress was then verified by comparing the measured stress in this method with that calculated from analytical expressions readily available for thick walled cylinders. The relationship was further validated independently using digital image correlation (DIC) by measuring the displacements for unknown levels of progressively increasing confinement stress induced by a shaft-collar ring on similar specimens. The Raman peak-shift relation derived for SiC phase also correctly predicted process-induced residual stresses due to a mismatch in coefficient of thermal expansion between the matrix phase and SiC particles. The derived Raman peak-shift relationship can also be generalized and can be a valuable tool to experimentally determine unknown bi-axial stress in a Raman active structure.     

Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

Thermal fracture of a functionally graded/homogeneous bimaterial with system of cracks

The thermal fracture of a bimaterial consisting of a homogeneous material and a functionally graded material (FGM) with a system of internal cracks and an interface crack is investigated. The bimaterial is subjected to a heat flux. The thermal properties of FGM are assumed to be continues functions of the thickness coordinate, while the elastic properties are constants. The method of the solution is based on the singular integral equations. For a special case where the interface crack is much larger than the internal cracks in the FGM the asymptotic analytical solution of the problem is obtained as series in a small parameter (the ratio between sizes of the internal and interface crack) and the thermal stress intensity factors (TSIFs) are derived as functions of geometry of the problem and material characteristics. A parametric analysis of the effects of the location and orientation of the cracks and of the inhomogeneity parameter of FGM’s thermal conductivity on the TSIFs is performed. The results are applicable to such kinds FGMs as ceramic/ceramic FGMs, e.g., TiC/SiC, MoSi₂/Al₂O₃ and MoSi₂/SiC, and also some ceramic/metal FGMs.     

Optimal design of functionally graded plates with thermo-elastic plastic behaviourConfiguration optimale des plaques fonctionnellement graduées à plasticité thermo-élastique

The thermo-elastic plastic behaviour of functionally graded plates under extremal thermal loading at different boundary conditions is considered. The plates consist of two phases – ZrO₂ ceramics and Ti₆Al₄V alloy. The layers are distributed exponentially through the thickness. The mechanical and thermal properties of both materials strongly depend on temperature. The stress–strain behaviour is investigated by the FEM. To predict the stable state of the structures of interest, several failure criteria are applied. Two cost functions are introduced to optimize the design of the plate. The main results are discussed and graphically illustrated. To cite this article: L. Parashkevova et al., C. R. Mecanique 332 (2004).     

Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients

In this work, a self-consistent constitutive framework is proposed to describe the behaviour of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading. Analytical and semi-analytical solutions are obtained to describe the thermo-elastic and thermo-elastoplastic behaviour of a three-layered system consisting of a metallic and a ceramic layer joined together by an FGM layer of arbitrary composition profile. Solutions for the stress distributions in a generic FGM system subjected to arbitrary temperature transient conditions are presented. The homogenisation of the local elastoplastic FGM behaviour in terms of the properties of its individual phases is performed using a self-consistent approach. In this work, power-law strain hardening behaviour is assumed for the FGM metallic phase. The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found throughout. Solutions are also given for the critical temperature transients required for the onset of plastic deformation within the three-layered systems.     

Thermal shock resistance behavior of a functionally graded ceramic: Effects of finite cooling rate

This work presents a semi-analytical model to explore the effects of cooling rate on the thermal shock resistance behavior of a functionally graded ceramic (FGC) plate with a periodic array of edge cracks. The FGC is assumed to be a thermally heterogeneous material with constant elastic modulus and Poisson's ratio. The cooling rate applied at the FGC surface is modeled using a linear ramp function. An integral equation method and a closed form asymptotic temperature solution are employed to compute the thermal stress intensity factor (TSIF). The thermal shock residual strength and critical thermal shock of the FGC plate are obtained using the SIF criterion. Thermal shock simulations for an Al₂O₃/Si₃N₄ FGC indicate that a finite cooling rate leads to a significantly higher critical thermal shock than that under the sudden cooling condition. The residual strength, however, is relatively insensitive to the cooling rate.     

Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure

The propagation behavior of Love waves in a layered piezoelectric structure with an initial stress is investigated in this article. It involves a thin piezoelectric layer bonded perfectly to an elastic substrate. Solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate by solving the coupled electromechanical field equations. The phase velocity equations of the Love wave propagation and the stress fields in the layered piezoelectric structure are obtained for electrical open and short cases on the free surface, respectively. The effect of the initial stress on the phase velocity, the stress fields and the coupled electromechanical factor are discussed, respectively. Three sets of piezoelectric layer–elastic substrate systems are considered, i.e. BaTiO₃ ceramic layer–borosilicate glass substrate, PZT-5H ceramic layer–borosilicate glass substrate, and PZT-5H ceramic layer–SiO₂ glass substrate. It is seen that the phase velocity of the Love wave propagation decreases with the increase of the magnitude of the initial stress. The coupled electromechanical factor increases remarkably, as the magnitude of the initial the stress is greater than 100 MPa. This is useful for the design of acoustic surface wave devices.     

Residual Stress-Related Common Intersection Points in the Mechanical Behavior of Ceramic Matrix Composites Undergoing Cyclic Loading

The mechanical response of SiC-fiber reinforced barium osumilite ceramic matrix composites tested in tension with unloading/reloading cycles was very recently reported to exhibit self-assembling common intersection points (CIP) of unloading/reloading loops in the tensile domain which relate exactly to the thermal residual stress state of reinforcing fibers in a matrix of a lower coefficient of thermal expansion (Dassios et al. Compos A: Appl Sci Manuf 44:105–113, 2013). Knowledge of the experimentally-exact residual stress state enables, herein, examination of the validity of the conventional compliance-based methodology for indirectly calculating residual stresses from projected/extrapolated CIPs. The efficiency of two prominent residual stress prediction models is also tested across the experimentally-established value of thermal residual stress (TRS). The significance of the CIP as the TRS-free origin of the stress-strain curve is discussed in view of the importance in calculating accurate material property values from mechanical testing data of materials under residual stress.     

Stress intensity factors and crack initiation directions for ceramic/metal joint

Four points bending tests for Si₃N₄/Cu/S45C joint specimen showed that the bending strengths depend on the residual stresses that originated from joining process. The residual thermal stresses caused an edge sub-interface crack to initiate in the ceramic. The stress intensity factors (SIFs) of the edge sub-interface crack located at distance h from the interface with or without interlayer metal were calculated by the Green's function obtained from a finite element analysis. The crack path at the joint specimen under four points bending loading with the influence of residual stresses was also evaluated by the maximum tensile stress criterion. Finally the effect of residual stress on the crack path was found numerically; the interlayer metal decreases the deflection angle of crack from interface by reducing the residual stress.     

Strip-electromechanical model solution for piezoelectric plate cut along two semi-permeable collinear cracks

A strip electric saturation and mechanical yielding model solution is proposed for a piezoelectric plate cut along two equal collinear semi-permeable mode-I cracks with electrical polarization reaching a saturation limit and normal stress reaching a yield stress along a line segment in front of the cracks. By using Stroh formalism and complex variable technique, we derived the analytical solution for the field quantities. Three different situations are investigated when developed electrical saturation zone is bigger/smaller or equal to the developed mechanical yield zone. Numerical results show that the effect of different electric boundary conditions on the crack opening displacement and crack opening potential drop is significant and should not be ignored. The influence of electric load displacement on the energy release rate is also investigated for PZT-4, PZT-5H and BaTiO₃ ceramics, and it may assists for the correct choosing of ceramic for specific job.     

The flow of polymer thickened motor oils in convergent jet thrust nozzles

Jet nozzles are described in which liquids are subjected to uniaxial and biaxial stretching motions, shear also being present near the nozzle walls. Jet thrust measurements show that the behaviour of polymer-thickened oils can best be studied by comparison with the behaviour of Newtonian base oils at equivalent Reynolds numbers. These data compare well with measurements previously made in long, straight tubes.Jet thrusts for polymer-thickened oils are lower than those of base oils and show evidence of a threshold point at which the two forms of behaviour deviate. The axial stress in the oil is almost independent of the strain rate, at high strain rates, but is related to axial strain in a simple manner. For 3.5 per cent polymer dissolved in Iranian light base oil, the axial stress is shown to be τ₁₁ = 2000 γ_G dyn cm^?2 for uniaxial strain and τ₁₁ = 2800 γ^1.30_G dyn cm^?2 for biaxial strain, where γ_G is the measure of strain defined by Green. For a standard Shell Multigrade 20W/50 motor oil the equivalent equation for biaxial strain is τ₁₁ = 3200 γ^1.02_G dyn cm^?2. The stresses developed during biaxial extension are higher than those developed during uniaxial extension.The presence of fully elastic behaviour in polymer-thickened oils at extensional strain rates of the order 500 s^?1 and principal extension ratios of only 8 is of potential significance to lubrication technology. The stress rises with the square of the extension ratio and should become large as lubricated surfaces approach. Polymer degradation will commence as the stress rises; it is suggested that further tests be carried out at higher stresses and temperatures.     

Numerical Investigation on the Hydrogen-Assisted Start-Up of Methane-Fueled, Catalytic Microreactors

The hydrogen-assisted start-up of methane-fueled, catalytic microreactors has been investigated numerically in a plane-channel configuration. Transient 2-D simulations have been performed in a platinum-coated microchannel made of either ceramic or metallic walls. Axial heat conduction in the solid wall and surface radiation heat transfer were accounted for. Simulations were performed by varying the inlet pressure, the solid wall thermal conductivity and heat capacity, and comparisons were made between fuel mixtures comprising 100% CH₄ and 90% CH₄?C10% H₂ by volume. A significant reduction in the ignition (t _ig) and steady-state (t _st) times was evident for microreactors fed with hydrogen-containing mixtures in comparison to pure methane-fueled ones, for all pressures and reactor materials investigated, with hydrogen having a direct thermal rather than chemical impact on catalytic microreactor ignition. The positive impact of H₂ addition was attenuated as the pressure (and the associated CH₄ catalytic reactivity) increased. Reactors with low wall thermal conductivity (cordierite material) benefited more from hydrogen addition in the fuel stream and exhibited shorter ignition times compared to higher thermal conductivity ones (FeCr alloy) due to the creation of spatially localized hot spots that promoted catalytic ignition. At the same time, the cordierite material required shorter times to reach steady state. Microreactor emissions were impacted positively by the addition of hydrogen in the fuel stream, with a significant reduction in the cumulative methane emissions and no hydrogen breakthrough. Finally, gas-phase chemistry was found to elongate the steady-state times for both ceramic and metallic materials.     

The effect of microstructural morphology on the elastic,inelastic, and degradation behaviors of aluminum–alumina composites

Micromechanical models with idealized and simplified shapes of inhomogeneities have been widely used to obtain the average (macroscopic) mechanical response of different composite materials. The main purpose of this study is to examine whether the composites with irregular shapes of inhomogeneities, such as in the aluminum–alumina (Al–Al₂O₃) composites, can be approximated by considering idealized and simplified shapes of inhomogeneities in determining their overall macroscopic mechanical responses. We study the effects of microstructural characteristics, on mechanical behavior (elastic, inelastic, and degradation) of the constituents, and shapes and distributions of the pores and inclusions (inhomogeneities), and thermal stresses on the overall mechanical properties and response of the Al–Al₂O₃ composites. Microstructures of a composite with 20% alumina volume content are constructed from the microstructural images of the composite obtained by scanning electron microscopy (SEM). The SEM images of the composite are converted to finite element (FE) meshes, which are used to determine the overall mechanical response of the Al–Al₂O₃ composite. We also construct micromechanics model by considering circular shapes of the inhomogeneities, while maintaining the same volume contents and locations of the inhomogeneities as the ones in the micromechanics model with actual shapes of inhomogeneities. The macroscopic elastic and inelastic responses and stress fields in the constituents from the micromechanics models with actual and circular shapes of inhomogeneities are compared and discussed.     

Thermo–elasto–plastic stresses in functionally graded materials under consideration of the fabrication process

Summary  The present study analyzes elasto–plastic thermal stresses in some particle-reinforced functionally graded material plates (FGP) by taking into consideration residual stresses of the fabrication process. For the FGP, the region near the cooling metal surface consists of distributed ceramic particles in a metal matrix, while the region near the heating ceramic surface contains distributed metal particles in a ceramic matrix. We use the thermo–elasto–plastic constitutive equation of a particle-reinforced composite, taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Elasto–plastic thermal stresses are discussed here with the goal of reducing the thermal stresses. Two kinds of particle-reinforced FGP are considered: the first kind (FGP1) represents distributed ceramic particles in the metal matrix, and the second one (FGP2) represents distributed metal particles in the ceramic matrix. We modify the thermo–elasto–plastic constitutive equation of a particle-reinforced composite for the FGP2 by taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Using the temperature-dependent material properties, three cases of temperature conditions are studied. The first one is the cooling from the fabrication temperature to the room temperature, the second one is the heating from the room temperature, and the last one is the heating after cooling from the fabrication temperature. The particle volume fraction is assumed to vary according to a power function in the thickness direction of the FGPs. Using the finite element method, the effects of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix and the stress in the particle in the FGPs are discussed. Also, the effects of the particle volume fraction and the fabrication temperature on the maximum tensile matrix stress are discussed. Received 22 November 2000; accepted for publication 24 April 2001     

Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading

Thermo-mechanical analysis of functionally graded hollow sphere subjected to mechanical loads and one-dimensional steady-state thermal stresses is carried out in this study. The material properties are assumed to vary non-linearly in the radial direction, and the Poisson’s ratio is assumed constant. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the analysis presented here, the effect of non-homogeneity in FGM thick sphere was implemented by choosing a dimensionless parameter, named β _i (i = 1, . . . , 3), which could be assigned an arbitrary value affecting the stresses in the sphere. It is observed that the solution process for β _i (i = 3) = −1 are different from those obtained for other values of β _i (i = 1, . . . , 3). Cases of pressure, temperature, and combined loadings were considered separately. It is concluded that by changing the value of β _i (i = 1 . . . 3), the properties of FGM can be so modified that the lowest stress levels are reached. The present results agree well with existing results. Using FEM simulations, the analytical findings for FGM spheres under the influence of internal pressure and temperature gradient were compared to finite element results.     

Stress relaxation,creep, and internal stresses in high density polyethylene filled with calcium carbonate

The effect of filling high density polyethylene (HDPE) with calcium carbonate (up to 50% by weight) on the stress relaxation and the creep in uniaxial extension at room temperature was investigated. The addition of CaCO₃ was found to have a strong influence on the flow behaviour of HDPE. In particular, it was observed that the internal stress level, calculated from relaxation data, increased markedly with the filler content. The reduction in creep rate of the filled samples suggested that the CaCO₃-particles induce a change in the structure of the HDPE-interphase close to the filler surface. This was supported by dynamic mechanical measurements performed at low temperatures on swollen HDPE-CaCO₃ samples.     

Static and dynamic compaction of ceramic powders

The static and dynamic compaction of ceramic powders was investigated experimentally using a high-pressure friction-compensated press to achieve static stresses of 1.6 GPa and with a novel gas gun setup to stresses of 5.9 GPa for a tungsten carbide powder. Experiments were performed in the partial compaction region to nearly full compaction. The effects of variables including initial density, particle size distribution, particle morphology, and loading path were investigated in the static experiments. Only particle morphology was found to significantly affect the compaction response. Post-test examination of the powder reveals fracture of the grains as well as breaking at particle edges. In dynamic experiments, steady structured compaction waves traveling at very low velocities were observed. The strain rate within the compaction waves was found to scale nearly linearly with the shock stress, in contrast with many fully dense materials where strain rate scales with stress to the fourth power. Similar scaling is found for data from the literature on TiO₂ powder. The dynamic response of WC powder is found to be significantly stiffer than the static response, probably because deformation in the dynamic case is confined to the relatively narrow compaction wave front. Comparison of new static powder compaction results with shock data from the literature for SiO₂ also reveals a stiffer dynamic response.     

Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: A three-dimensional theory based on thermodynamics with internal state variables

In the vicinity of the glass transition, glass-forming materials exhibit pronounced frequency-dependent changes in the mechanical material properties, the thermal expansion behaviour and the specific heat. The frequency dependence becomes apparent under harmonic stress, strain or temperature excitations. The Prigogine-Defay ratio is a characteristic number which connects the changes in magnitude of these quantities at the glass transition. In order to represent the thermoviscoelastic properties of glass-forming materials in continuum mechanics, a three-dimensional approach which is based on the Gibbs free energy as thermodynamic potential is developed in this article. The Gibbs free energy depends on the stress tensor, the temperature and a set of internal variables which is introduced to take history-dependent phenomena into account. In the vicinity of an equilibrium reference state, the specific Gibbs free energy is approximated up to second order terms. Evaluating the Clausius-Duhem inequality, the constitutive relations for the strain tensor, the entropy and the internal variables are derived. In comparison with other approaches, the entropy, the strain tensor and the internal variables are functionals not only of the stress tensor but also of the temperature. Applying harmonic temperature- or stress-controlled excitations, complex frequency-dependent relations for the specific heat under constant stress, for the thermal expansion coefficients as well as for the dynamic mechanical compliance are obtained. The frequency-dependence of these quantities depicts the experimentally observed behaviour of glass-forming materials as published in literature. Under the assumption of isotropic material behaviour, it is shown that the developed theory is compatible with the Prigogine-Defay inequality for arbitrary values of the material parameters.     

Determination of the effective elastic–plastic response of metal–ceramic composites

The mechanical response of metal–ceramic composites is analysed through a homogenization model accounting for the mechanical behaviour of the constituent materials. In order to achieve this purpose a nonlinear homogenization method based on the phase field approach has been suitably implemented into a numerical code. A prescribed homogenized strain state is applied to a unit volume element of a metal–ceramic composite with proportional loading in which all components of the strain tensor are proportional to one scalar parameter. The mechanical response of the material has been modeled by considering a von Mises plasticity model for the metal phase and a Drucker–Prager associative elastic–plastic material model for the ceramic phase. A two stages plasticity has been obtained in which inelastic strain develops in the metal phase followed by a fully plastic response. A comparison with a finite element model of the stress–strain response of an axisymmetric unit cell has been carried out with the purpose to validate the homogenization based modeling presented in the paper. Plastic parameters of a Drucker–Prager yield surface for the homogenized composite have been calculated at different materials compositions. Associative Drucker–Prager plasticity has been found to be accurate for high ceramic content.