Thermal expansion coefficient of composites

Schapery, R.A. (1968). Thermal expansion coefficients of composite materials based on energy principles. J. Composite Mater. 2, 380-404. 

Still another approach to predicting the thermal expansion coefficient of composites has been taken by Wang and Kwei (1969), who derived expressions to account for deviations from a simple additivity rule due to the development of thermal stresses. Such stresses will arise in practice if a composite is cooled from its fabrication temperature and if the components have different coefficients of expansion. They obtained the following equations to give the linear coefficient of expansion of the composite 5 ... 

Ucj/ = in-plane thermal expansion coefficient of composite laminate Uf = thermal expansion coefficient of fiber... 

Several kinds of mixing rules are presented in Table 2-6 regarding the thermal expansion coefficient of composites. By predicting the thermal expansion coefficient using these equations, and by controlling material composition and formulation, it is possible to approach the desired values. 

Table 2-6 Mixture rules for thermal expansion coefficients of composites.

By the same approach, the thermal expansion coefficient of the composite is evaluated ... 

Relation (18) correlates Tgc with the thermal properties of matrix and mesophase. Obviously, more accurate expressions for the thermal expansion curves, or the thermal expansion coefficient of the composite may provide a better approach to Tgc than the above formula. However, in many cases, it was found that this relation applies with satisfactory accuracy. 

An additional check is the almost coincidence of the linear thermal expansion coefficients of the composite in the glassy region. Theory yields acl = 48.20 x 10-6 °C whereas experiment gives ac, = 48.00x 10 6 °C 1. This coincidence does not hold beyond glass transition. Indeed it was found that ot = 122.90 x 10-6 °C, whereas the experiment gave a 2 = 158 x 10"6 °C 1. 

Sideridis, E. (1994). Thermal expansion coefficients of fiber composites defined by the concept of the interphase. Composites Sci. Technol. 51, 301-317. 

Thermal expansion differences exist between the tooth and the polymer as well as between the polymer and the filler. The tooth has a thermal expansion coefficient of 11 x 10-6/°C while conventional filled composites are 2-4 times greater [63, 252], Stresses arise as a result of these differences, and a breakdown between the junction of the restoration and the cavity margin may result. The breakdown leads to subsequent leakage of oral fluids down the resulting marginal gap and the potential for further decay. Ideal materials would have nearly identical thermal expansion of resin, filler, and tooth structure. Presently, the coefficients of thermal expansion in dental restorative resins are controlled and reduced by the amount and size of the ceramic filler particles in the resin. The microfilled composites with the lower filler loading have greater coefficient of thermal expansions that can be 5-7 times that of tooth structure. Acrylic resin systems without ceramic filler have coefficients of thermal expansion that are 9 times that of tooth structure [202-204, 253],... 

The same models of mechanical conpling can be used to predict the coefficient of linear thermal expansion in the composite, ai, based on the moduli, and thermal expansion coefficients of the fiber and matrix, a/ and a, respectively ... 

When a composite is subjected to external forces, the energy of the matrix is only transferred to the fibres when there is question of a proper attachment. For that reason fibres are some-times provided with a layer of another material. An example boron fibres in an aluminium matrix are provided with a silicon carbide coating and as a result the fibres are called borsic fibres. The thermal expansion coefficient of a fibre and its matrix must correspond. Figure 14.9 is a representation of what takes place when a crack in a fibre-reinforced matrix grows. 

The coefficient of thermal expansion (CTE) of composite materials usually follows the simple rule of mixtures (or more complex models), based on the CTE of the respective components, their volume fraction and the volume fraction of interfacial phases. Based on these models, a Si3N4-Si3N4(w) composite should possess a similar CTE to monolithic Si3N4 ceramic (3.2 x 10 6/°C). obviously, the chemical composition of the sintering additive will have a certain influence but should remain within the variations observed for monolithic Si3N4. 

The above discussion pertains to unidirectional composites that are initially free of matrix cracking examples would include Nicalon SiCf/CAS, Nicalon SiQ/1723 glass, Nicalon SiQ/LAS, and SCS-6 SiQ/HPSN. For composites such as Cf/borosilicate, where the thermal expansion coefficient of the matrix is substantially greater than that of the fiber, microcracks can develop in the matrix during fabrication. These composites do not exhibit a linear stress-strain response (Stage I), even for small applied loads. 

Another explanation for an abnormal increase in Tgl in polymer blends has been proposed by Manabe, Murakami, and Takayanagi 125). They used a three-layered shell model, which accounts for interaction between the dispsersed and continuous phases of the blend. Abnormal increases in the glass transition of polystyrene in blends with various rubbers were explained by thermal stresses which arise from the difference in thermal expansion coefficients of the component polymers. However shifts in the glass transition temperatures of the SIN s do not appear to arise from differences in the expansion coefficients of the components because samples with the same overall composition and almost identical microstructures have significantly different glass transition temperatures. 

Thermal expansion is an important property of transition metal carbides. " They are practically never used in pure form but mostly in composite materials with matrices of other materials (metals). Upon thermal load, the difference in the thermal expansion coefficients of the carbide phase and the matrix may cause degradation of the composite. Generally, the thermal expansion of transition metal carbides is higher than that of the pure metal component. Table 1 gives average thermal expansion coefficients of various carbides. For WC, the thermal expansion has even been measured at various pressures. ... 

---