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

金属过去的变形方式会影响它未来的变形和潜在的失效。这种变形的历史对金属的性能有显著的影响。目前预测性能的理论非常复杂，要么依赖于复杂的方法，要么依赖于跟踪许多没有内存路径的描述符。这些先前的方法对于工业应用来说是不切实际的。该奖项支持基础研究，通过开发使用分数阶微分方程预测金属合金性能的新公式来改变这种范式。在这个新公式中，材料的历史与描述材料演化过程的方程的基本结构密切相关。简化的数学描述使其具有广泛采用的吸引力。合金建模的这种范式转变将通过减少寿命预测的不确定性和可持续性来提高安全性，因为组件可以放心地使用更长时间。重要的是，该奖项还包括旨在鼓励神经分化学生（自闭症学生）参与STEM的外展活动。这将通过参与以自闭症为重点的学校和教育大学教师来实现，以建立对自闭症学生的认识和更大的接受度。准确的性能（机械响应和寿命）预测能力只有通过考虑遗传效应才能实现。尽管如此，目前的模型，如使用边界面理论或大量的内部状态变量（isv），与一阶常微分方程，在预测金属和合金的历史（遗传）效应方面存在不足。原因有两个：1)缺乏对遗传效应机制的理解，2)迄今为止ISV理论使用的数学框架采用一阶常微分方程，这些方程是点函数，因此没有记忆路径。这种协同实验和建模方法将通过确定长度尺度遗传变形的表现和开发分数-微积分晶体塑性公式来填补这一知识空白，该公式具有取决于激活体积的材料通知顺序参数。这种分数微积分公式自然地将遗传效应纳入进化方程的结构中，而不是直接通过isv。分数阶晶体塑性建模将与最先进的原位实验相结合，即高温透射电子显微镜和高能x射线衍射显微镜，以统一塑性变形的数学和物理。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.