A One-Dimensional Model of a Shape Memory Alloy Fiber Reinforced Aluminum Metal Matrix Composite

A one-dimensional model of a shape memory alloy fiber reinforced aluminum metal matrix composite is developed based on a linearized shape memory alloy constitutive model. The requirements of stress equilibrium and strain compatibility within the composite couple the constitutive variables of the shape memory alloy reinforcement. The shape memory alloy reinforcement's state trajectory resulting from a particular external thermal-mechanical process is therefore sensitive to the external process, the constitutive properties of the composite matrix, and fiber volume fraction. Three distinct thermal-mechanical processes are treated in this paper; the first is an isothermal tensile loading-unloading process at the stress free martensitic transformation start temperature; the second is an external stress free thermal process to a temperature above that required for the shape memory alloy reverse transformation; and, the final process is an isothermal loading at the thermal process finish temperature. The model predicts that the composite will exhibit a large longitudinal compressive strain during the heating process, and will retain a large matrix residual compressive stress at the end of the heating process. The model also predicts that the composite elevated temperature flow strength will be significantly higher than that of the unreinforced matrix alloy.