Rational design of low fatigue phase-transforming Cu-based alloys

In this study, we introduce a novel material descriptor and corresponding mechanical criteria to guide the development of low-fatigue shape memory alloys. Our approach synergistically combines compatibility theories, crystallographic algorithms, and micromechanical experiments to optimize materials through a two- parameter compositional tuning strategy. We demonstrate this method on a series of CuAlx₁Mnx₂ alloys, where the atomic composition vector x = (x₁, x₂) ∈ [0.17, 0.22] × [0.09, 0.11]. By employing a scalar-valued function to index the functional fatigue property based on cofactor conditions, we analyze the continuity and extremes with respect to compositional variables. Through just three iterative development steps, we identify the composition CuAl_20.2Mn_11.3, achieving a reduction in thermal hysteresis by a factor of 2 and enhancing mechanical reversibility up to 1000 cycles. This result underscores the potential of mathematical methods in designing complex materials with desirable mechanical properties. Our findings not only provide a theoretical framework for the design of shape memory alloys but also highlight the importance of integrating theoretical and experimental techniques to achieve optimal material properties.