Time-dependent creep of a dual-phase viscoplastic material with lamellar structure

Exact solutions for the time-dependent creep behavior of a two-phase material with a lamellar microstructure are derived as a function of volume concentration and the properties of its constituents. Each phase is taken to be elastic–viscoplastic, exhibiting work-hardening characteristics. The derivation takes advantage of the condition of interfacial discontinuities over the interfaces, with a result given in a rate form for the general combined loading. Specific overall creep strains are presented along five distinctive loading directions for two kinds of viscoplastic composites: one involving an elastic and a viscoplastic phases and the other with dual viscoplastic phases. In addition to providing insightful information for the overall time-dependent creep, the exact nature of the results can also serve as a bench mark to test the accuracy of the approximate theories. In this light a secant-viscosity approach recently developed for a particle-reinforced solid (Li and Weng (1997). A secant-viscosity approach to the time-dependent creep of an elastic–viscoplastic composite. J. Mech. Phys. Solids, 45, 1069) is extended to a lamellar structure and the results are tested against these exact solutions. Comparison between the two indicates that the secant-viscosity concept is a sufficiently accurate one and it can be applied to composites with other types of microgeometries.