Interphase modulus

Evidently, the critical pressure to cause failure decreases with a stiffer interphase modulus, E, or a reduced interlayer thickness, h, or both. This hypothesis has been tested on several simulation systems, which confirm that increased adhesion is possible with a negative transversal modulus gradient at the material interface. 

Experimental data for epoxy resin composite show that the change in the composite moduli with respect to the interphase thickness is the greatest for high fiber volume fraction and the lowest for low fiber volume. This trend is t5rpi-cal, regardless of the ratio of matrix modulus to interphase modulus. The authors believe that the properties of the interfacial region often arise from chemical interaction between the constituents. The resulting interphase me-... 

Folkes and Wong [79], in their study of adhesion between fiber and matrix of thermoplastic composites, noticed that the formation of transcrystalline morphology around glass fibers in polypropylene has an effect on the critical fiber length, probably through the change in local interphase modulus. 

The mechanism of chemical adhesion is probably best studied and demonstrated by the use of silanes as adhesion promoters. However, it must be emphasized that the formation of chemical bonds may not be the sole mechanism leading to adhesion. Details of the chemical bonding theory along with other more complex theories that particularly apply to silanes have been reviewed [48,63]. These are the Deformable Layer Hypothesis where the interfacial region allows stress relaxation to occur, the Restrained Layer Hypothesis in which an interphase of intermediate modulus is required for stress transfer, the Reversible Hydrolytic Bonding mechanism which combines the chemical bonding concept with stress relaxation through reversible hydrolysis and condensation reactions. 

A unique but not yet widespread technique that may influence the interfacial bond quality relies on the localized variation in the polymer modulus normal to the polymer-substrate junction in the composite assembly, as illustrated schematically in Fig. 15 [41,52]. The transversal modulus variation may be accomplished by interposing a tertiary interphase between the substrate and... 

Restrained layers—coupling agents develop a highly crosslinked interphase region with a modulus intermediate between that of the substrate and the polymer. 

In this conceptual framework it is naturally impossible to simulate the effect of the interphases of complex structure on the composite properties. A different approach was proposed in [119-123], For fiber-filled systems the authors suggest a model including as its element a fiber coated with an infinite number of cylinders of radius r and thickness dr, each having a modulus Er of its own, defined by the following equation ... 

When a - 1 ( perfect adhesion) the elasticity modulus of the interphase decreases continuously from the fiber value to the matrix value, the interphase layer modulus being higher than that of the matrix. When a < 1, the interphase layer modulus assumes, some distance off the fiber surface, a minimum value smaller than the matrix value, and then increases tending asymptotically to the matrix modulus. 

The model for a filled system is different. The filler is, as before, represented by a cube with side a. The cube is coated with a polymer film of thickness d it is assumed that d is independent of the filler concentration. The filler modulus is much higher than that of the d-thick coat. A third layer of thickness c overlies the previous one and simulates the polymeric matrix. The characteristics of the layers d and c are prescribed as before, and the calculation is carried out in two steps at first, the characteristics of the filler (a) - interphase (d) system are calculated then this system is treated as an integral whole and, again, as part of the two component system (filler + interphase) — matrix. From geometric... 

For the three-term unfolding model in fiber composites the E (r)-modulus of the interphase is again expressed by relation (22). 

Upon loading a void-containing material, a certain stress distribution in the sample will develop that proceeds and determines the following deformation. Typically the voids (or other dispersed phase) will tend to concentrate stresses to interphases between materials of different modulus. Even though no complete picture exists of what will happen upon deformation, such a stress description may give a better understanding of the relation between stress concentrations in the sample due to the voids and the final fracture behavior. 

The mechanical properties of the blend of silane/size and bulk epoxy matrix (at concentrations representing likely compositions found at the fiber-matrix interface region) also suggest that the interaction of size with epoxy produces an interphase which is completely different to the bulk matrix material (Al-Moussawi et al., 1993). The interphase material tends to have a lower glass transition temperature, Tg, higher modulus and tensile strength and lower fracture toughness than the bulk matrix. Fig. 5.4 (Drown et al., 1991) presents a plot of Tg versus the amount of... 

Cho, C.R. and Jang, J. (1990). Adhesion of ultrasonic high modulus polyethylene fiber-epoxy composite interfaces. In Controlled Interphases in Composite Materials, Prod. ICCI-III, (H. Ishida ed.), Elsevier Sci. Pub., New York, pp. 97 107. 

Jayaraman. K. and Reifsnider, K.L. (1992). Residual stresses in a composite with continuously varying Young s modulus in the fiber/matrix interphase. J. Composite Mater. 26, 770-791. 

Decreased mobility of adsorbed chains has been observed and proved in many cases both in the melt and in the solid state [52-54] and changes in composite properties are very often explained by it [52,54]. Overall properties of the interphase, however, are not completely clear. Based on model calculations the formation of a soft interphase is claimed [51], while in most cases the increased stiffness of the composite is explained by the presence of a rigid interphase [55,56]. The contradiction obviously stems from two opposing effects. Imperfection of the crystallites and decreased crystallinity of the interphase should lead to lower modulus and strength and larger deformability. Adhesion and hindered mobility of adsorbed polymer chains, on the other hand, decrease deformability and increase the strength of the interlayer. 

The thickness of the interphase is a similarly intriguing and contradictory question. It depends on the type and strength of the interaction and values from 10 Ato several microns have been reported in the hterature for the most diverse systems [47,49,52,58-60]. Since interphase thickness is calculated or deduced indirectly from some measured quantities, it depends also on the method of determination. Table 3 presents some data for different particulate filled systems. The data indicate that interphase thicknesses determined from some mechanical properties are usually larger than those deduced from theoretical calculations or from extraction of filled polymers [49,52,59-63]. The data supply further proof for the adsorption of polymer molecules onto the filler surface and for the decreased mobility of the chains. Thermodynamic considerations and extraction experiments yield data which are not influenced by the extent of deformation. In mechanical measurements, however, deformation of the material takes place in all cases. The specimen is deformed even during the determination of modulus. With increasing deformations the role and effect of the immobilized chain ends increase and the determined interphase thickness also increases (see Table 3) [61]. 

The amount of polymer bonded in the interphase depends on the thickness of the interlayer and on the surface area, where the filler and the polymer are in contact with each other. The size of the interface is more or less proportional to the specific surface area of the filler, which is inversely proportional to particle size. In accordance with the above proposed explanation on the relation of the effect of immobilized polymer chains and the extent of deformation, modulus shows only a very weak dependence on the specific surface area of the filler [64]. 

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