Several series of heterogeneous materials composed of conducting carbon particles randomly dispersed inside a polymeric matrix have been prepared. The particles are a carbon black and short graphite fibers. The polymers are epoxy resins and a silicon elastomer. In each series of materials an insulator-to-conductor transition is evidenced in agreement with percolation theory as the volume-particle concentration is varied. The piezoresistive effects of the materials are investigated under hydrostatic and uniaxial pressures. It is shown that the piezoresistance depends on materials composition, pressure, and carbon concentration. In each series, the piezoresistance increases rapidly as the concentration decreases towards the conductivity threshold. The range of pressure values over which the piezoresistance varies faster depends on the elastic properties of the matrix and on whether the applied pressure is hydrostatic or uniaxial. All these behaviors are accounted for by an extension of percolation theory involving volume-particle concentration changes under pressure. It is then demonstrated that the piezoresistance arises mostly from the heterogeneity of the materials, and to a lesser extent to geometrical changes of the samples under pressure. In conclusion, we examine the practical interest of designing composite materials for making strain or pressure gauges with desired sensitivity, resistivity, and useful pressure range given appropriate choices of the polymeric matrix and of the conducting particles concentration.

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We present an experimental realization with electrical composites of the thermal fuse model [D. Sornette and C. Vanneste, Phys. Rev. Lett. 68, 612 (1992)], proposed as a paradigm of dynamical rupture in heterogeneous media. An isolating polymer matrix is filled with conducting particles, and the particle-particle contacts evolve due to thermal expansion of the matrix as a function of the applied current I. Above a critical current, the electric resistance R increases as a power law of time to rupture R ϳ ͑t r 2 t͒ 2a , with a Ӎ 0.65, and the breakdown time t r scales as t r ϳ I 22 in agreement with the model. [S0031-9007(96)01260-4] PACS numbers: 62.20.Mk