Composite stress models

FIGURE 123 Composite stress models (a) Voight or isostiain (h) Reuss or isostiess. Arrows indicate tension force direction. 

Recently, stress analysis has been carried out for the determination of stress distribution around inclusions in particulate filled composites. A model based on the energy analysis has led to the determination of debonding stress [8]. This stress, which is necessary for the separation of the matrix and filler, was shown to depend on the reversible work of adhesion (see Eq. 16) and it is closely related to parameter B. 

The quasielastic method as developed by Schapery [26] is used in the development of the viscoelastic residual stress model. The use of the quasielastic method is motivated by the fact that the relaxation moduli are required in the viscoelastic analysis of residual stresses, whereas the experimental characterization of composite materials is usually in terms of the creep compliances. An excellent account of the development of the quasielastic method is given in [27]. The underlying restriction in the application of the quasielastic method is that the compliance response of the material shows little curvature when plotted versus log time [28]. Harper [27] shows excellent agreement between the quasielastic method and direct inversion for AS4/3510-6 graphite/epoxy composite. For most graphite/thermoset systems, the restrictions imposed by the quasielastic method are satisfied. 

In a version of the Mileiko18 model in which it is assumed that each of six neighboring fibers has a break somewhere within the span of the length of a given fiber, but that the location of those breaks is random within the span, the relationship between the steady-state creep rate and the composite stress is... 

A. Saigal, E.R. Fuller, S. Jahanmir, Modeling of Residual Stresses and Mechanical Behavior of Glass-Infiltrated Spinel Ceramic Composites, Computational Modelling of Materials, Minerals and Metals Processing, (ed M. Cross, J.W. Evans and C. Bailey), TMS, (2001). 

No.22, 1997, p.5699-702 EFFECTIVE WIDTH OF INTERFACE IN A STRESSED MODEL POLYMER COMPOSITE MEASURED BY MICRO-FTIR... 

Transient Stresses During Sintering 11.4.2.1 Composite Sphere Model... 

Scherer also considered a self-consistent model in which a microscopic region of the matrix is regarded as an island of sintering material in a continuum (the composite) that contracts at a slower rate (34). The mismatch in sintering rates causes stresses that influence the densification rate of each region. It is found that the equations for the self-consistent model differ from those of the composite sphere model only in that the shear viscosity of the matrix Gm is replaced by the shear viscosity of the composite Gc. Taking Eq. (11.33), the corresponding equation for the self-consistent model is therefore... 

Using Eqs. (11.34) and (11.37), the ratio AGJ3K can be calculated in terms of the relative density of the matrix and this ratio can be substituted into Eqs. (11.28), (11.29), and (11.35) to calculate the stresses and densification rates for the composite sphere model. Alternatively, for the self-consistent model, Gc can be found from Eq. (11.36), and the same procedure repeated to determine the stresses and strain rates. Figure 11.20 shows the predicted values for tjt as a function of the relative density of the matrix for the composite sphere and self-consistent models. For v less than 20 vol%, the predictions for the two models are almost identical, but they deviate significantly for much higher values of V,-. When v is less than —10-15 vol%, the predicted values of tJtT are not... 

In the section, a viscoelastic constitutive model for rPET polymer concrete is discussed. To model the mechanical response of polymers is difficult because of resin composition, stress level, temperature sensitivity and other factors. For a composite mixture of recycled polymers, the situation is more complicated than for virgin polymer concrete. Due to these factors, empirical formulae developed from the curve fitting of experimental data are most suitable for predicting the creep response of rPET polymer concrete. 

When applied to partide-reinforced polymer composites, micromechanics models usually follow certain basic assumptions linear elasticity of fillers and polymer matrix the fillers are axisymmetric, identical in shape and size, and can be characterized by parameters such as aspect ratio well-bonded filler-polymer interface, so no interfacial slip is considered filler-matrix debonding and matrix microcraddng. Further details of some important preliminary concepts such as hnear elastidty, average stress and strain, composites average properties, and the strain concentration and stress concentration tensors can be found in preview literature [48-50]. 

ELEMENTARY FAILURE MECHANISMS IN THERMALLY STRESSED MODELS OF FIBER REINFORCED COMPOSITES... 

Herrmann, K.P. and Ferber, F., Numerical and experimental investigations of branched thermal crack systems in self-stressed models of unidirectional ly reinforced fibrous composites. In Computational Mechanics 88, eds. S.N. Atiuri and G. Yagawa, Springer Verlag, Berlin/Heidelberg/New York, 1988, 8.V.1-8.V.4. 

Interpretation of test results of the actual composite (stress-strain curves and crack spacing) to determine the interfacial shear strength values indirectly using analytical models which accounted for the composite behaviour in tension and flexure. Results of such interpretations will be discussed separately in Section 4.5. 

Toutanji, H., Dempsey, S., 2001. Stress modeling of pipelines strengthened with advanced composite materials. Thin-WaUed Structures 39, 153—165. 

Nassehi, V., Kinsella, M. and Mascia, 1.., 1993b. Finite element modelling of the stress distribution in polymer composites with coated fibre interlayers. J. Compos. Mater. 27, 195-214. 

Boltzmann s constant, and T is tempeiatuie in kelvin. In general, the creep resistance of metal is improved by the incorporation of ceramic reinforcements. The steady-state creep rate as a function of appHed stress for silver matrix and tungsten fiber—silver matrix composites at 600°C is an example (Fig. 18) (52). The modeling of creep behavior of MMCs is compHcated because in the temperature regime where the metal matrix may be creeping, the ceramic reinforcement is likely to be deforming elastically. 

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