A theory for the shock-loading response of an alumina-filled epoxy mixture

Abstract

Alumina‐gilled epoxy is an engineering material which is used as a potting compound in impulsively‐loaded ferroelectric power supplies. It is a composite material composed of tightly packed alumina particles (8 μm in diameter) in an epoxy matrix. No voids are present in the composite.Extensive experimental data characterizing the dynamical response of this material is available. These data include ultrasonic shear and longitudinal wave speeds, large‐amplitude shock and release wave profiles, and a large‐amplitude shear wave profile. From these observations it is clear that contact between neighboring alumina particles significantly influences the behavior of the composite. At low pressures, measured shock velocities are 50 percent greater than predictions which ignore interparticle contact. At high pressures, particle contact results in both large release wave velocities and an enhancement of the effective shear modulus of the composite.The mixture theory of Drumheller and Bedford is used to develop a three‐dimensional model for alumina‐filled epoxy. Interparticle contact is treated by partitioning the bulk strain of the particles between two effects: that due to the loads imposed by the surrounding epoxy; and that due to the loads imposed by contact with neighboring particles.The portion of the confining pressure which arises from interparticle contact results in an enhancement of the shear modulus of the composite. To account for this effect, the shear modulus is assumed to be a linear function of this portion of the confining pressure. Through careful consideration of thermodynamical principles, it is shown that this assumption results in a kinematical constraint on the material response. The material must dilate during pure shearing motion. Schuler has observed this dilatancy phenomenon in static triaxial tests on this material.The available experimental data is sufficient to allow both a unique evaluation of the model constants and an independent evaluation of the predictive capabililty of the model. Good comparisons are achieved for both the loading and unloading behavior of longitudinal and shear waves.