Poisson Contraction Research Articles

Coulomb friction controlled bridging stresses and crack resistance of ceramic matrix composites

Bridging stresses in ceramic matrix composites (CMC) are calculated taking into account the effect of Poisson contraction of fibre and matrix during loading and a two parameter Weibull distribution of fibre strength. A parameter study is performed in order to assess the influence of the constituent properties. The bridging stress curve provides the link from the micromechanical analysis to the prediction of macroscopic composite behaviour. The load–deflection behaviour of pre-notched CMC specimens is derived by application of the method of weight functions. The predictions are compared with experimental results giving information about the actual properties of the material.

A model for the transverse strain response of unidirectional ceramic matrix composites during tensile testing

A comprehensive micromechanical model relating the longitudinal stress and transverse strain of unidirectional fibre toughened ceramic matrix composites (CMCs) is presented. The model uses different cylindrical unit-cells to describe the composite throughout a tensile test and considers all relevant damage mechanisms. The proposed model takes into account the Poisson contraction of fibre and matrix, the relief of thermal residual stresses upon damage development, and the build-up of compressive radial stresses at the interface due to mismatch between fibre and matrix after debonding and sliding. Thus the modelled transverse strain response depends on a wide range of microstructural and micromechanical parameters. The approach is checked by comparing the experimentally observed and simulated response of a unidirectional SiC/CAS composite of which all constituent properties were determined experimentally. The agreement between experiment and theory is excellent.

TRANSVERSE STRAIN RESPONSE OF HI-NICALON FIBRE REINFORCED SILICON NITRIDE MATRIX COMPOSITES

The relation between the longitudinal stress {sigma} and the transverse strain {var_epsilon}{sub tr} during monotonic tension testing of unidirectional fiber toughened ceramic matrix composites (UD-CMCs) has been studied experimentally and theoretically by several authors. Matrix cracking and interface debonding generally causes {var_epsilon}{sub tr} to increase or to become positive. Recently, this has been theoretically explained by a model taking into account the Poisson contraction of fiber and matrix, the redistribution of mechanical stress and the relief of residual thermal strain upon damage development, and the built-up of compressive radical stresses at the interface caused by the radial interfacial mismatch after interface debonding and sliding. In this paper, the {var_epsilon}{sub tr} response of a series of Hi-Nicalon (SiC) fiber reinforced silicon nitride matrix composites is reported and described by a previously developed model. This paper focuses on the extension of the model to composites with a radial gap {delta} after interface debonding, which was necessary to model the present CMC materials.

Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites

Potential effects of interfacial roughness in ceramic composites were studied using a model that included the progressively increasing contribution of roughness with relative fiber/matrix displacement during debonding of the fiber/matrix interface. A parametric approach was used to study interfacial roughness in conjunction with other parameters such as the strength, radius, and volume fraction of the fiber. The progressive roughness contribution during initial fiber/matrix sliding caused a high effective coefficient of friction, as well as an increased clamping stress, which led to rapidly changing friction with increasing debond length. Calculated effects implied a potentially significant contribution to the behavior of real composite systems and the necessity for explicit consideration in the interpretation of experimental data to understand composite behavior correctly. In a tension test, the Poisson's contraction of the fiber may negate the effects of roughness, allowing an “effective constant shear stress” (tau) approximation. This was evaluated using a piecewise linear approximation to the progressive roughness model in an analysis of composite stress‐strain behavior; for the Nicalon/SiC system, the effective tau value was lower than the values that would be obtained from fiber pushout tests and/or matrix crack spacings.

The relationship between longitudinal stress and transverse strain during tensile testing of unidirectional fibre toughened ceramic matrix composites

A comprehensive, micromechanical model, relating the longitudinal stress and transverse strain during tensile testing of unidirectional fibre toughened ceramic matrix composites, has been developed. The model uses different unit-cells to describe the composite and considers all relevant damage as it develops throughout a tensile test. Specifically, the proposed model takes into account the Poisson contraction of fibre and matrix, the redistribution of mechanical stress and the relief of thermal stress due to the development of damage, and the build-up of compressive radial stresses at the interface due to the radial mismatch between fibre and matrix after interface debonding and sliding. Consequently, the modelled transverse strain response depends on a wide variety of structural and mechanical parameters. The followed approach has been assessed by comparing the simulated and experimentally observed response of a unidirectional SiC CAS composite. Theory and experiment are in excellent agreement for an experimentally determined set of constituent properties, but a parametric study shows the important effect of some of these, such as the radial interfacial mismatch, which are difficult to determine experimentally.

Depth-sensitive strain analysis of a W–Ta–W trilayer

The high-resolution X-ray diffraction technique was used to determine the entire strain tensor as a function of X-ray penetration depth in a 400 nm W–Ta–W trilayer, which consisted of 150 nm W, 100 nm Ta, and 150 nm W. The strain tensor was calculated in a laboratory reference frame to determine the variation of in-plane strains, ϵ x x and ϵ y y , and the normal strain ϵ z z , as a function of X-ray penetration depth. Two different methods were then used to determine the strains ϵ x x , ϵ y y , and ϵ z z in each layer of trilayer. The first approach was based on diffraction peak subtraction, and the second on a linear elastic model. Both indicated that the strain states in the W layers were the same, and that the strains ϵ x x and ϵ y y in the W and Ta layer were the same magnitude. The difference between the Ta and W arose with the normal strain ϵ z z , and was due to a Poisson contraction effect. The average residual stresses in the trilayer were determined with the HRXRD data, and also with sin 2 ψ and a substrate curvature technique, double-crystal diffraction topography. All three techniques indicated that the average biaxial stress in the trilayer was ca. 1.0 GPa.

Effect of Interfacial Slippage on Viscoelastic Adhesion

Peeling of a viscoelastic adhesive from a solid substrate poses a wonderful problem of polymer flow. When the adhesive is peeled, it is also stretched in a direction normal to the substrate. The concomitant Poisson contraction creates a pressure gradient and thus induces a shear flow in the adhesive close to the delamination front. Earlier it was pointed out that the strength of viscoelastic adhesion would decrease if the shear stress in the adhesive is relaxed by a slip process at the interface. Here we report experimental results which confirm that viscoelastic adhesives do indeed slip on segmentally mobile organic surfaces at and near the crack tip regions. Evidence of slip was obtained from the interfacial displacements of small fluorescent particles when the adhesive was peeled from various substrates. While on most surfaces the slip distances were about 1−2 μm, a large slip (13 μm) was observed on segmentally mobile tethered chains of polydimethylsiloxanes (silicones). On the latter surface, slippag...

Dimensional Analysis of Bond Modulus in Fiber Pullout

To evaluate the stress-crack opening relationship of fiber-reinforced composites, the properties of the constituents and the fiber-matrix interface should be known. The properties of the fibers and the matrix can fairly easy be determined, whereas those of the interface must be measured indirectly. In several fiber pullout analyses, a linear relationship between the bond shear stress and the slip is assumed in the elastic range. In this paper, the value of the bond modulus is studied using dimensional analysis and the finite element method. The value of the bond modulus was seen to depend on the fiber diameter, fiber volume content, and the modulus of elasticity of the fiber and the matrix. A diagram is shown, from which the values for the bond modulus can be read. The numerical results agree reasonably with the theory by Budiansky et al. However, the results are substantially higher than the limited available experimental data. A possible reason is that the Poisson's contraction can cause the debonding near the fiber free end even with low pullout loads.

Depth-Sensitive Strain Analysis of a W/Ta/W Trilayer

AbstractThe high-resolution x-ray diffraction technique was used to determine the entire strain tensor as a function of x-ray penetration depth in a 400 nm W/Ta/W trilayer, which consisted of 150 nm W, 100 nm Ta, and 150 nm W. The strain tensor was calculated in a laboratory reference frame to determine the variation of in-plane strains, εxx, and εyy, and the normal strain εzz as a function of x-ray penetration depth. Two different methods were then used to determine the strains εxx, εyy, and εzz in each layer of trilayer, and both indicated that the strain states in the W layers were fe same, and that the strains εxx and εyy. in the W and Ta layer were the same magnitude. The difference between the Ta and W arose witK the normal strain, εzz, and was due to a Poisson contraction effect. The average residual stresses in the trilayer were determined with the HRXRD data, and also with sin2ψ and a substrate curvature technique, double-crystal diffraction topography. All three techniques indicated that the average biaxial stress in the trilayer was ∼1.0 GPa.

Investigations of the misfit dislocation structure at a CdTe(001)/ga As(001) interface using Stillinger-Weber potentials and high-resolution transmission electron microscopy

Abstract In this paper, Stillinger-Weber potentials which accurately describe the elastic constants of CdTe and GaAs are developed. These potentials are applied to investigate the misfit dislocation structure at a CdTe(001)/GaAs(001) interface. Based on these calculated structures, simulated high-resolution transmission electron microscopy images are compared with experimentally observed images. It will be shown that, although the exact energetics of the interface are not provided by these potentials, dislocation stand-off is more strongly influenced by the Poisson expansion or contraction of the individual materials. Further, the best agreement between the experimentally observed and simulated images is obtained when the dislocations occur at the interface with no stand-off being exhibited. The calculated structures indicate that the misfit dislocation structure exhibited along the [110] direction is different from that along the [110] direction if the initial monolayer of material, in this case believed...

Analysis of the effect of interfacial roughness on fiber debonding and sliding in brittle matrix composites

Previous analyses of the relation between the force and displacement during fiber sliding (pushing or pulling) are extended to include effects of interfacial roughness. Analytical solutions are obtained for a linear roughness profile over the range of displacements that are smaller than the dominant half-wavelength of the roughness. With the equations expressed in normalized form, a convenient friction parameter, which defines the roles of the friction coefficient and the roughness angle, has been defined. For certain values of the friction parameter, the effect of the roughness negates the Poisson's contraction during fiber pulling, giving solutions that are very close to the response of a system with a constant frictional stress at the interface.

Pull-out of a ductile fibre from a brittle matrix

Pull-out of a ductile fibre from a brittle matrix has been analysed using a shear lag model. Debonding at the fibre-matrix interface and yielding of the fibre occurred during the pull-out process. Both Poisson's contraction of the fibre and Coulomb friction of the debonded interface were considered. The debond length, which consists of an elastic zone length and a plastic zone length, was also analysed. When the fibre has a finite embedded length, it was found that necking prior to full pull-out of the fibre was required to optimize the toughening of a brittle matrix due to plastic deformation of the fibres. The essential material properties to achieve this are addressed.

Analysis of the single-fibre pull-out test by the use of Raman spectroscopy. Part I: pull-out of aramid fibres from an epoxy resin

Raman spectroscopy has been used to analyse the distribution of fibre strain in the single-fibre pull-out test by mapping the variation of strain along an aramid fibre undergoing pull-out from an epoxy resin matrix. Both sized and de-sized aramid fibres have been used in room-temperature and high-temperature cured resins. At low strains the behaviour follows conventional shear-lag analysis but as the fibre strain is increased yielding can take place in the matrix at the fibre/matrix interface. It is found that failure eventually takes place by either fibre/matrix de-bonding or fibre fracture outside the resin matrix. The presence of radial stresses at the interface has been found to be important. They are induced by thermal shrinkage upon cooling the hot-cured resin to room temperature and can also be caused by Poisson contraction during the pull-out process. They result in the measured values of interfacial shear stress being significantly different from those found for fully-embedded fibres.

Buckling of a coating bonded to a round bar subjected to axial extension

Initial buckling of an elastic coating perfectly bonded to a circular-section prismatic bar subjected to axial extension is investigated analytically. The phenomenon is associated with the substrate Poisson contraction. Two different models of the coating are used: the first is based on classical thin-shell theory and the other is based on first-order shear-deformation shell theory. The results for typical examples are compared and used to explain cracking of the coating previously observed experimentally.

Computer simulation of the surface topology of (001) silicon resulting from the termination of [formula omitted] edge dislocations with Burgers vectors parallel to the surface

The Stillinger-Weber interatomic potential for silicon was used to simulate the atomic arrangement at the emergence points of a/2〈110〉 perfect edge dislocations at a free surface. Results indicate step heights are comparable in magnitude vectors parallel to the surface can produced steps at the surface. The resulting step heights are comparable in magnitude with the steps which would be created if these dislocations were dissociated into Shockley partials. As a result, step source activation from these dislocations is possible without dissociation. The origin of the steps can be rationalized in terms of the Poisson expansion and contraction owing to relaxation of the compressive and tensile stress fields of the edge dislocations at a free surface.

Micromechanical characterisation of fibre/matrix interfaces

Theoretical analyses for the single fibre pull-out and push-out models under monotonic loading are given which are based on a shear-lag analysis in a fracture mechanics approach considering non-constant friction at the debonded interface as a result of fibre Poisson contraction (or expansion). The solutions allow the determination of typical fibre/matrix interfacial properties such as the interfacial fracture toughness, G ic, the coefficient of friction, μ, and the residual clamping stress, q 0. Under cyclic loading the interfacial properties are expected to degrade as a result of repetitive abrasion, and a power law function is assumed between μ and the number of elapsed cycles, N. However, G ic is assumed to be unaffected and a fracture mechanics based debond criterion is derived for the relationship between the external applied stress, the debond length and the reduced friction coefficient for both fibre pull-out and fibre push-out. In addition, the relative displacements between the free fibre end and the matrix top are obtained for cyclic fatigue when the fibre is loaded and unloaded. A relationship obtained for the protrusion (or intrusion) length in fibre pull-out (or push-out) experiments allows the severity of the interface frictional degradation to be evaluated and characterised. Similarities and differences in the frictional degradation behaviour between fibre pull-out and push-out are also identified.

Effect of Interfacial Properties on Fracture Toughness in Fiber-Reinforced Ceramic Composites

Enhancement of fracture toughness increment by fiber bridging in fiber-reinforced composites was theoretically predicted in the case of small scale bridging conditions. This calculation was based on the stress field analysis of fiber pull-out which takes account of the interfacial bond, interfacial residual clamping stress and the Poisson's contraction of fibers induced by applied tensile loads. Fracture toughness tests of unidirectionally SiC fiber-reinforced glass composites were also performed. The fracture toughness increment observed in the experiment was in good agreement with the present theoretical prediction. The optimum interfacial properties to maximize the fracture toughness in steady-state as well as the relationship between the interfacial debonding behavior and fracture toughness were addressed.

Interfacial debonding and fiber pull-out stresses of fiber-reinforced composites Part VI. Interpretation of fiber pull-out curves

The stress-displacement relationship of the fiber during the fiber pull-out process in a fiber-reinforced composite ( i.e. the fiber pull-out curve) is considered. Understanding of both interfacial debonding and friction at the debonded interface is essential in interpreting the fiber pull-out curve. The behavior of interfacial debonding, which can be unstable, partially stable or stable, is characterized in the present study. The debonded interface can be either subjected to Coulomb friction, or free of friction which is contingent upon the comparison between the residual clamping stress and the interfacial radial tension induced by Poisson's contraction of the axially tensile-loaded fiber. The important parameters controlling the characteristics of interfacial debonding and friction are studied, and various fiber pull-out curves are elucidated.

Interfacial Sliding Friction in Silicon Carbide–Borosilicate Glass Composites: A Comparison of Pullout and Pushout Tests

Interfacial sliding friction stress (τf) was assessed using both pushout and pullout tests on SiC‐borosilicate glass composite specimens. Single‐filament composite specimens were fabricated by heating to 950°C in argon borosilicate glass rods with fine‐diameter (250‐μm) capillary in which SiC filaments were inserted. The composite specimens prepared in this manner showed only frictional bonding. The maximum frictional sliding loads for pushout and the initial frictional sliding loads in pullout were measured as functions of the embedded length of the filament in the glass rods. The nonlinear variations of the frictional loads were analyzed using shear‐lag models that include corrections for the effects of Poisson expansion or contraction on the sliding friction stress. It is shown that under identical conditions of composite fabrication the two tests give nearly identical properties for the interfaces. Pushout tests on hotpressed bulk composite specimens, however, showed both chemical bonding and a higher sliding friction stress relative to the single‐filament capillary specimens. The presence of compressive residual stress on the filaments was independently confirmed by evidence of stress‐induced birefringence.

A compressibility-based derivation of simple expressions for the transverse Poisson's ratio and shear modulus of an aligned long fibre composite

There is continuing interest in the elastic behaviour of long fibre composites. This concerns not only the axial and transverse Young's moduli, but also the shear moduli and Poisson's ratios. As an example of the significance of such parameters, interlaminar coupling stresses in a composite laminate may be influenced by the transverse Poisson's ratios of the individual plies: in a cross-ply laminate the through-thickness Poisson contraction of the transverse ply will tend to be much greater than that of the axial ply (i.e. 1'23 >~> v21 , where 1 is the fibre axis direction), which can be relevant for calculation of the coupling stresses. Unfortunately, analysis becomes complex when transverse stresses, which are very inhomogeneously distributed, are significant. Advanced laminate stress analysis is routinely carried out, requiring as input data the elastic constants of an individual lamina. These are obtained by use of: (i) equations derived from the convenient but very crude "slab" or "sandwich" model [1-3], (ii) equations derived from some attempt to analyse the transverse stress distribution [4], or at least to represent its effect by a semi-empirical approach [5], or (iii) accurate but complex models which do not lead to simple analytical equations. This last group may be subdivided into numerical methods [6, 7] and complex analytical approaches, notably the Eshelby equivalent homogeneous inclusion analysis [8, 9], in which the effect of a reinforcement with different elastic constants from those of the matrix can, for the case of an ellipsoidal shape, be predicted after replacing it with matrix which has first been subjected to an appropriate "stress-free" or ' transformation" strain. The analysis is mathematically exact only for a single inclusion in an infinite matrix [10], but it can also be used to predict elastic constants and other thermophysical properties [11, 12] of a real composite (with short or long fibres), providing a suitable assumption is made about how the matrix and the reinforcement sample the mean stress. The mean field model [13] is now commonly employed and has been used to produce the predictions reported below. Calculations are normally made on the basis of both constituents being themselves elastically isotropic. The slab model is quite widely used, where f is the volume fraction of fibre although it is accurate only for the axial Young's modulus, El, and, to a good approximation, for the axial Poisson's Ratio, vii, of a long fibre composite.