Collaborative Research: Embedding Material-Informed History through Fractional Calculus State Variable Formulation

How a metal has been deformed in the past influences how it will deform and potentially fail in the future. This history of deformation has significant effects on the performance of metals. Current theories to predict performance are highly complex, relying either on intricate approaches or tracking of many descriptors that have no memory path. These prior approaches are impractical for industrial applications. This award supports fundamental research to change this paradigm by developing a new formulation for predicting metallic alloy performance using fractional-order differential equations. In this new formulation, the history of the material is intimately intertwined with the underlying structure of the equations describing the material evolution process. The simplified mathematical description makes it attractive for widespread adoption. This paradigm shift in alloy modeling will improve safety by decreasing uncertainty in life predictions and sustainability as components can stay in service longer with confidence. Importantly, this award also includes outreach activities designed to encourage the participation of neuro-divergent students - students on the autistic spectrum - in STEM. This will be accomplished through involvement in autism-focused schools and education of college faculty to build awareness and greater acceptance for autistic students.Accurate performance (mechanical response and lifetime) predicting capabilities will only be achieved by accounting for hereditary effects. Nonetheless, current models using, e.g., bounding surface theory or a large numbers of internal state variables (ISVs), with first-order ordinary differential equations, fall short in predicting history (hereditary) effects in metals and alloys. The reason is twofold: 1) there is a lack of understanding of the mechanism responsible for hereditary effects, and 2) the mathematical framework used so far for ISV theory employs first-order ordinary differential equations that are point functions and have, therefore, no memory path. This synergistic experimental and modeling approach will fill this knowledge gap by determining at which length scale hereditary deformation manifests and developing a fractional-calculus crystal-plasticity formulation with a material-informed order parameter depending on an activation volume. This fractional calculus formulation naturally incorporates hereditary effects into the structure of the evolution equations rather than directly through ISVs. The fractional-order crystal-plasticity modeling will be combined with state-of-the-art in situ experiments, i.e., high-temperature transmission electron microscopy and high-energy X-ray diffraction microscopy, to unify the mathematics and the physics of plastic deformation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.