Non-Additive Morphology Effects in Thermal Expansion of Three-Phase Materials

Abstract

Minerals like talcum or mica have low thermal expansion. One puts them into plastics to reduce the thermal expansion; however, for good toughness one usually also adds some rubber. Rubbers have a higher thermal expansion than plastics, so, based on the additivity premise, it is commonly believed that the addition of rubber in the mineral-reinforced plastics should unavoidably increase the overall thermal expansion. In this work we have conducted direct finite element calculations with three-phase computer models containing several hundred talcum and rubber inclusions. It appears that by adding rubber one can actually reduce the overall thermal expansion. Intrinsically, this non-additive effect has a threephase nature, i.e., one cannot observe it by addressing the three-phase problem as a series of two-phase problems. It seems feasible to employ the non-additive morphology effects to design a new generation of advanced multi-phase materials with application-tailored dimensional stability, not only with respect to temperature changes but also solvent uptake and relaxation of the fabrication stresses.In the search for improved performance, industry is turning increasingly to the use of multi-phase complex-morphology materials. Figure 1 depicts one example, a three-phase talcum-reinforced rubber-toughened polymer-matrix material. Because of its remarkable impact resistance, this and other similar materials have become indispensable today in various applications, including in the automobile industry for the manufacturing of automobile bumpers. Unfortunately, plastics typically have a much larger thermal expansion than steels. As a consequence, upon temperature variations, plastic and steel components change their sizes differently. It would be ideal to reduce the thermal expansion of plastics to approach that of metals and steels.Here, we have studied the thermal expansion of threephase materials numerically for the first time, based on threephase computer models comprised of up to several hundred aligned non-overlapping rubber spheroids and a dozen talcum platelets randomly dispersed in a polymer matrix (see Fig. 2). Periodic morphology-adaptive meshes of up to 10 7 tetrahedra were built with an in-house Delaunay mesh generator. In numerical calculations, we used an iterative conjugate-gradient displacement-based finite-element solver with a diagonal preconditioner. [1] The numerical methodology employed has already been discussed elsewhere, [2,3] see also Gusev et al. [3,4] for experimental validation. Typical properties were assumed for the constituent phases. [5] Figure 3 presents the numerical results obtained. For spherical rubber particles, the predictions are in harmony with the common-sense additivity premise, i.e., the overall thermal expansion gradually increases upon increasing the rubber fraction. However, at quite moderate aspect ratios, a crossover takes place and the overall material behaviour becomes non-additive, i.e., the overall thermal expansion decreases upon increasing the rubber loading. Counte...

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