Estimation of Elastic Moduli of Particulate Composites by New Models and Comparison with Moduli Measured by Tension, Dynamic, and Ultrasonic Tests

Abstract

The elastic constants of particulate composites are evaluated employing a theoretical cube-within-cube formation. Two new models of four and five components, respectively, formed by geometrical combination of three-component models existing in the literature, are used as Representative Volume Elements. Using the governing stress and strain equations of the proposed models, two new equations providing the static elastic and shear moduli of particulate composites are formulated. In order to obtain the dynamic elastic and shear moduli, the correspondence principle was applied successively to components connected in series and/or in parallel. The results estimated by the proposed models were compared with values evaluated from existing formulae in the literature, as well as with values obtained by tensile, dynamic, and ultrasonic experiments in epoxy/iron particulate composites. They were found to be close to values obtained by static and dynamic measurements and enough lower compared with values obtained from ultrasonic experiments. The latter is attributed to the high frequency of ultrasonics. Since measurements from ultrasonic's and from dynamic experiments depend on the frequency, the modulus of elasticity estimated by ultrasonic's is compared with that (storage modulus) estimated by dynamic experiments.

Analytic approximations for the elastic moduli of two-phase materials

“…Consequently, the actual value for the E modulus of the composite must be located between these two bounds, as pointed out by previous studies [17,18]. For the numerical example above and using only a single set of joining operation, either PS or SP, bounds of 107.3 and 115.3 GPa are obtained and the difference between them becomes E = 8 GPa [ Fig.…”

“…Several models and theories have been proposed to estimate the Young's modulus for composites of mutually surrounding phases [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The utilized methods are mainly based upon derivations from elasticity theory [9][10][11][12][13][14][15][16], considerations on the arrangement of the phases, and the sequence of their connection [17][18][19] or empirical curve fitting to experimental data [20], which lead to either complicated formulae (e.g., requiring summation of determinants) [10][11][12][13], or to improved upper and lower * zjzhang@imr.ac.cn † zhfzhang@imr.ac.cn.…”

“…bounds only [14][15][16][17][18], or to equations containing parameters that are hard to be determined [20]. Of all these models, the Hashin and Shtrikman bounds (HS bounds) [14], derived from variational principles of elasticity, are broadly accepted to be the most accurate one in describing experimental data [21].…”

“…The entire derivation is based on similar connection sequences as used in previous studies for deriving the upper and lower bounds [17,18]. The important innovation of the present study is to introduce an integration step in the derivation process so that the number of dismounting and joining steps of the unit cell of the composite is increased from the two or four steps used in previous studies [17,18] to infinity.…”

“…The important innovation of the present study is to introduce an integration step in the derivation process so that the number of dismounting and joining steps of the unit cell of the composite is increased from the two or four steps used in previous studies [17,18] to infinity. In this manner, specific values of the elastic properties are obtained rather than limiting bounds.…”