Average Stress In Matrix Research Articles

Creep of particle and short fibre reinforced polyurethane rubber

Tensile stress–strain testing and creep testing have been carried out on a polyurethane rubber, at three temperatures, with and without either particulate or short fibre alumina reinforcement. A previous paper reported concerning composites with particulate reinforcement and the present work is focused on the effect of the fibres. The samples were made via a blending and extrusion process that produced a certain degree of fibre alignment (along the direction of loading). Prior milling procedures were used to produce fibres with two different ranges of aspect ratio (with averages about 10 and 16). When expressed as true stress–strain relationships, all materials exhibit approximately linear responses. The dependence of stiffness on the volume fraction and aspect ratio of the reinforcement was found to conform well to the Eshelby model predictions. Moreover, the creep behaviour of all of the materials can be captured well by a Miller–Norton formulation, using the average matrix stress predicted by the Eshelby model. A striking conclusion is that it is both predicted and observed that short fibres are much more effective in reducing the creep rate than is the case with particles.

Dynamic compression behavior of glass filled epoxy composites: Influence of filler shape and exposure to high temperature

The effect of filler shape, volume fraction and high temperature cycle on the dynamic compression behavior of rigid particle filled polymer composite is demonstrated by performing experiments using split-Hopkinson pressure bar (SHPB) setup. Two glass filler variants, spherical particles and milled fibers, are reinforced into epoxy matrix upto 10% volume fraction. Two sets of test specimens are prepared; room temperature cured (RTC) and high temperature exposed (HTE) - the ones prepared by subjecting RTC composites to a temperature cycle beyond their glass transition temperature (Tg). The yield stress of milled fiber composites which are consistently higher in HTE cases increases with increasing filler volume fraction whereas it remains nearly constant in all spherical particle composites. While RTC materials exhibit strain softening characteristics, the post-yield strain hardening behavior of HTE composites is attributed to the increased cross-link density of epoxy matrix. Debonded fillers and their foot-prints on the crushed surfaces of HTE composites indicate the relaxation of residual stresses, developed at the filler/matrix interface during curing process. Computational analyses suggest that the average matrix stress in composites remains unaffected by the shape of the inclusions whereas comparatively higher inclusion stresses indicate that slender fillers provide better resistance to deformation when compared to the circular ones. Near constant stresses in circular inclusions at low volume fractions is attributed to the large inter-particle separation. Computational results complement experimental observations where the milled fiber composites consistently exhibited higher yield stress when compared the spherical particle counterparts.

Prediction of the effective Young’s modulus of a particulate composite containing fractured particles

This paper considers the problem of prediction of the effective Young’s modulus of a particulate composite material containing fractured particles. It treats the general case in which some particles are fractured while others remain intact. The reinforcing particles are assumed to be spherical. The Mori–Tanaka model is extended to formulate the method of solution. The resulting auxiliary problem of a single fractured particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method. The predictions are compared with the exact results of Young’s modulus for particulate composites with body-centered cubic packing arrangement and experimental results of Young’s modulus for particulate composites containing fractured particles.

A multiscale modeling approach to analyze filament-wound composite pressure vessels

A multiscale modeling approach to analyze filament-wound composite pressure vessels is developed in this article. The approach, which extends the Nguyen et al. [Prediction of the elastic-plastic stress/strain response for injection-molded long-fiber thermoplastics. J Compos Mater 2009; 43: 217–246.] model developed for discontinuous fiber composites to continuous fiber ones, spans three modeling scales. The microscale considers the unidirectional elastic fibers embedded in an elastic–plastic matrix obeying the Ramberg–Osgood relation and J2 deformation theory of plasticity. The mesoscale behavior representing the composite lamina is obtained through an incremental Mori–Tanaka [Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 1973; 21: 571–574.] type model and the Eshelby [The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc R Soc Lond, Ser A 1957; 241: 376–396.] equivalent inclusion method. The implementation of the micro–meso constitutive relations in the ABAQUS® finite element package (via user subroutines) allows the analysis of a filament-wound composite pressure vessel (macroscale) to be performed. Failure of the composite lamina is predicted by a criterion that accounts for the strengths of the fibers and of the matrix as well as of their interface. The developed approach is validated in the analysis of an aluminum liner – T300 carbon/epoxy pressure vessel to predict the burst pressure. The predictions compare favorably with the numerical and experimental results by Lifshitz and Dayan [Filament-wound pressure vessel with thick metal liner. Compos Struct 1995; 32: 313–323]. The approach will be further demonstrated in the study of the effects of the lamina thickness, helical angle, and fiber–matrix material combination on the burst pressure.

A New Micromechanical Elasto-Plastic Constitutive Model for Fiber-Reinforced Composite Laminates

A micromechanical elastic-plastic bridging constitutive model is developed in this paper for accurate representation of material behavior of fiber-reinforced composite laminates. In the bridging constitutive model, elastic behavior is represented by bridging matrix elements and interaction between the average stresses in matrix with those in fibers are included. A transient plastic bridging matrix is developed to describe accurately the elastic-plastic material properties of the fiber reinforced composites, and the effects of the material parameters of matrix and fiber on the bridging matrix elements have been accounted for. The proposed constitutive model is validated against experiment investigation.

Probing deformation of double-walled carbon nanotube (DWNT)/epoxy composites using FTIR and Raman techniques

Two of the limitations of carbon nanotube (CNT) polymer composites have been the low volume fraction of nanotubes and inadequate load transfer from the polymer to the stiff CNT. Here, we have utilized functionalized mats of double-walled nanotubes (DWNT) to obtain 10 wt.% DWNT in an epoxy matrix, with strength approaching those of quasi-isotropic carbon fiber composites. We used the transmission FTIR technique with in situ loaded specimens to monitor spectral shift per unit applied stress for understanding load transfer behavior at the nanotube–epoxy interface. Tests show that in most cases a tensile stress causes negative FTIR peak shift in the neat epoxy, but this behavior is not always observed for the epoxy matrix in the composite. The FTIR data can be used successfully to estimate the average matrix stress in the composite and thereby the average stress in the nanotubes. In situ Raman studies using the G′ peak are also conducted to obtain complementary information on average tensile stress in the DWNT in the loading direction. The shift response is found to be ∼37 cm −1/GPa.

Stiffness properties of particulate composites containing debonded particles

This paper considers the problem of determining the nonlinear bimodular stiffness properties, i.e., the tensile and compressive Young’s moduli and Poisson’s ratios, and the shear modulus, of particulate composite materials with particle–matrix interfacial debonding. It treats the general case in which some of the particles are debonded while the others remain intact. The Mori–Tanaka approach is extended to formulate the method of solution for the present problem. The resulting auxiliary problem of a single debonded particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method accounting for the particle–matrix separation and contact at the debonded particle–matrix interface. Because of the nonlinear nature of the problem, an iterative process is employed in calculating the stiffness properties. The predicted stiffness properties are compared to the exact solutions of the stiffness properties of particulate composites with body-centered cubic packing arrangement.

Internal stress evolution in a random-planar short fiber aluminum composite

The evolution of deviatoric matrix stresses during in-situ compression tests was studied on a two-dimensional random short fiber-reinforced aluminum/Saffil® composite using neutron diffraction. Under a uniaxial load, the average matrix stress is triaxial and evolves as predicted by a simple Eshelby model.

The connections between the double-inclusion model and the Ponte Castaneda–Willis, Mori–Tanaka, and Kuster–Toksoz models

In this paper, it is shown that the double-inclusion model (Hori, M., Nemat-Nasser, S., 1993. Double-inclusion model and overall moduli of multi-phase composites. Mech. Mater. 14, 189–206) carries more theoretical connections with other micromechanical models than what is presently realized. In the past, only connections with the Mori–Tanaka (MT) model (Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574) and the self-consistent model (Hill, R., 1965. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222; Budiansky, B., 1965. On the elastic moduli of some heterogeneous material. J. Mech. Phys. Solids, 13, 223–227) for aligned inclusions have been established. By choosing the shape and the relative orientation of the inclusion and the matrix judiciously, the double-inclusion model can produce results for a two-phase composite containing randomly oriented ellipsoidal inclusions for the Ponte Castaneda–Willis (PCW) model (Ponte Castaneda, P., Willis, J.R., 1995. The effect of spatial distribution on the effective behavior of composite materials and cracked media. J. Mech. Phys. Solids 43, 1919–1951), MT model, and Kuster–Toksoz (KT) model (Kuster, G.T., Toksoz, M.N., 1974. Velocity and attenuation of seismic waves in two-phase media: I Theoretical formulation. Geophysics, 39, 587–606). These connections have also shed some light into the possible microgeometries for the MT and KT models. The microstructure for the PCW model is already known, and it is now established that the outer shape and orientation of the double inclusion is exactly the spatial distribution ellipsoid of the PCW model. The result also proves that the KT model, widely used in the geophysics community, actually provides a result that is identical to the PCW model and, thus, has a well-defined microstructure that was previously said to be non-existent.

Model-neutron diffraction strain measurement comparisons for steady state creep of metal matrix composites

Mori and coworkers have developed a model for the prediction of the steady state creep rate of discontinuous composites based on the Eshelby model. This model recognizes that matrix creep can only achieve steady state creep when relaxation processes at the inclusion/matrix interface balance the rate of build up of internal stress. In this paper we follow through the implications of this model for the level of the average matrix stress attained in the steady state as a function of the applied load. We compare the predictions with direct measurements of the matrix stress by neutron diffraction. The model indicates that the composite creep exponent should be less than the creep exponent of the unreinforced matrix provided neither debonding nor inclusion cracking occurs. This is observed experimentally for the composites under the conditions studied.

Stress–strain fields and the effectiveness shear properties for three-phase composites with imperfect interface

Based on the ‘average stress in the matrix’ concept of Mori and Tanaka (Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusion. Acta Metall. 21, 571–580) a micromechanical model is presented for the prediction of the elastic fields in coated inclusion composites with imperfect interfaces. The solutions of the effective elastic moduli for this kind of composite are also obtained. In two kinds of composites with coated particulates and fibers, respectively, the interface imperfections are taken to the assumption that the interface displacement discontinues are linearly related to interface tractions like a spring layer of vanishing thickness. The resulting effective shear modulus for each material and the stress fields in the composite are presented under a transverse shear loading situation.

Boundary stress and its effect on toughness in thin boundary layered and particulate composites: model analysis and experimental test on Y-TZP-based ceramic composites

The average thermal residual stress in continuous boundary phase of polycrystalline ceramic composites was calculated with a simple thin boundary layer model and a criterion for the self-cracking of the boundary phase was derived under a certain assumption. From the proposed model, the toughness of the materials can be increased by both tensile and compressive stress at boundaries when the crack propagates transgranularly; and will be increased when the stress at boundary is compressive for intergranular fracture mode. The maximum increase is predicted to be achieved at the boundary phase content not higher than 33%. The experimental results with Y-TZP doped with different kinds of grain boundary phase show a qualitative agreement with the prediction by the model but the toughness increase is largely dependent on the distribution feature of glass phases. From the ideal particle-in-infinite matrix model, the average stress in matrix and in particle for possible practical system was estimated and compared with the thin boundary layer model. The criterion for the self-cracking in matrix and in particle or at the particle–matrix interface was derived with stress intensity factor approach. From the existing periodic stress field model for particulate composite, the toughness increase is found not to increase monotonously with the content of second phase. Alternatively a maximum toughness increase is found, which is predicted to be achieved at the particulate phase content of 14·3 vol%. The experimental results on Y-TZP/Al 2O 3 composites were compared with the prediction of the model.

Calculated elastic constants of alumina-mullite ceramic particles

Using two theoretical models, we estimated the isotropic elastic constants of an alumina-mullite ceramic composite. The alumina phase, 20% by volume, consisted of brickshaped particles with a 4:1 aspect ratio embedded in a mullite matrix (mullite = 3Al2O3·2SiO2). We took alumina elastic-constant values from the literature, and we measured mullite's elastic constants using a megahertz-frequency pulse-echo method. The two theoretical models, Datta-Ledbetter and Mori-Tanaka, proceed from very different viewpoints. The Datta-Ledbetter model uses the long-wavelength limit of a scattered plane wave ensemble-average approach. The model estimates the speed of a plane harmonic wave, averages the scattered field by the Waterman-Truell procedure and uses Lax's quasicrystalline approximation to sum over pairs. The Mori-Tanaka method proceeds by estimating the average matrix stress in a material containing ellipsoidal inclusions. For randomly oriented ellipsoids, it extends Eshelby's solution for a single ellipsoidal inclusion. Both models lack adjustable parameters. Surprisingly, the two models with different physical approaches give practically identical results. A rough check on our estimates is that they lead to correct predictions of the elastic constants of an alumina-mullite-particle aluminium-matrix composite.

Average stress in matrix and average elastic energy of materials with misfitting inclusions

Having noted an important role of image stress in work hardening of dispersion hardened materials, (1,3) the present paper discusses a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain. It is shown that the average stress in the matrix is uniform throughout the material and independent of the position of the domain where the average treatment is carried out. It is also shown that the actual stress in the matrix is the average stress plus the locally fluctuating stress, the average of which vanishes in the matrix. Average elastic energy is also considered by taking into account the effects of the interaction among the inclusions and of the presence of the free boundary.