Matrix shrinkage

The radial (compressive) stress, qo, is caused by the matrix shrinkage and differential thermal contraction of the constituents upon cooling from the processing temperature. It should be noted that q a, z) is compressive (i.e. negative) when the fiber has a lower Poisson ratio than the matrix (vf < Vm) as is the normal case for most fiber composites. It follows that q (a,z) acts in synergy with the compressive radial stress, 0, as opposed to the case of the fiber pull-out test where the two radial stresses counterbalance, to be demonstrated in Section 4.3. Combining Eqs. (4.11), (4.12), (4,18) and (4.29), and for the boundary conditions at the debonded region... 

Fig. 7.24. Predicted fracture toughness of carbon and glass fiber-polymer matrix composites (CFRP and GFRP) with varying matrix shrinkage stress, n. After Piggott (1981).

Lam P.K. and Piggoll M.R. (1989a). The durability of controlled matrix shrinkage composites Part 1. Mechanical properties of resin matrices and their composites, J. Mater. Sci. 24, 4068-4075. 

Lim J.T., Piggoll M.R. and Bailey W.J. (1984), Toughness of fiber compo,sites with controlled matrix shrinkage. SAMPE Quarterly 15, 25-30. 

Pekot, L. J Reeves, S.R 2003. Modeling the effects of matrix shrinkage and differential swelling on coalbed methane recovery and carbon sequestration. Proceedings of the 2003 International Coalbed Methane Symposium. University of Alabama, 0328. 

Further development of this model incorporating diffusion, bulk flow, transmembrane flux, and matrix shrinkage [42-44] showed that the cell membrane is the main barrier to mass transfer only for single cells or thin slices of tissue. When the thickness of the sample increases, the extracellular space may become the limiting factor [45]. 

An HT fiber composite was found to be dimensionally and structurally unstable well below the maximum fiber processing temperature of 1400 C. The fiber shrank (the frozen in process stress relaxes) at temperatures as low as 850°C. The shrinkage of the fiber bundle embedded in phenolic resin during the carbonization process was influenced by matrix shrinkage stresses and pyrolysis products. Above 1000°C, the HTA carbon fiber in carbon-carbon bundles continuously changed its structure. After heat treatment at a temperature of 2800°C, the structure (lattice distance, orientation of the crystallites, crystallite size) was very similar to that of HM fibers. 

Fibre-matrix adhesive strength is unimportant for the modulus of compounds, which is determined by the volume fraction of fibres, the moduli of fibres and matrix, the fibre aspect ratio and the fibre orientation. The modulus is a small-strain property and the matrix shrinkage is usually sufficiently high to ensure the modulus increase desired without any true adhesion [4]. 

It has been shown that the peak positions of the Raman-active bands of carbon fibres are strain-sensitive and that Raman Microscopy can be used to follow the deformation of carbon fibres both in air and in a thermoplastic PEEK matrix. It has been demonstrated that the fibres near the surface in the carbon-fibre/PEEK composite examined are subject to a residual compressive strain of the order of 0.287o which is of the same order as that expected (19) from matrix shrinkage due to crystallisation and thermal contraction on cooling from the processing temperature. It is found that when the composite is subject to an externally-applied tensile deformation then, as expected, the change in fibre strain is similar to the applied strain as expected from simple composite theory. 

Pinchin and Tabor [21,22] studied the effect of normal stresses (confining pressures) on pull-out specimens. The effect ofthe level of normal stress was evaluated, up to a maximum of 28.5 N/mm. They calculated a fibre-matrix radius misfit value. So, to be about -0.2/u.m (Eq. 3.20), in the case of steel FRC specimens. Obviously, this value would be sensitive to matrix shrinkage, which is dependent on its composition and curing. The absolute misfit value was found to decrease during pull-out, which was suggested to be the result of local matrix compaction in the vicinity ofthe pulled-out fibre. 

Some of the differences in the values in Table 3.2 may be explained on the basis of environmental conditions. The higher bond values calculated by Laws [15] for air-cured specimen may be the result ofthe matrix shrinkage, which leads to higher normal compressive stresses across the interface, and higher shear resistance. Yet, this may not be always the case Pinchin and Tabor [32] obtained lower pull-out loads in sealed specimens that underwent some shrinkage, compared to water-cured specimens which had swelled. They suggested that microcracking, which... 

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