A GENERALIZED LAW OF MIXTURES

The mechanical properties of two-phase composites are predicted using a rigorous continuum mechanics analysis and an equivalent microstructu ral transformation approach. This leads to a generalized law of mixtur es which is contrasted with the classical linear law of mixtures which requires some explicit assumptions. The generalized law of mixtures e nables prediction of a variety of mechanical properties of a two-phase composite with any volume fraction, grain shape and phase distributio n. It is shown that the classical linear law of mixtures is a specific case of the generalized law of mixtures. Examples are given from cont inuous Cu-W composites, the particulate Co-WC system, Al/SiC(p) compos ites, alpha-beta Ti Mn alloys and alpha-beta Cu Zn alloys for the pred ictions of properties such as Young's modulus, yield strengths, flow s tresses, the overall friction stresses and the overall Hall-Petch coef ficients. It is shown that the theoretical predictions by the generali zed law of mixtures are in very good agreement with the corresponding experimental results drawn from the literature, for both continuous fi bre composites and particulate reinforced systems.