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

合作研究：通过分数阶微积分状态变量公式嵌入材料丰富的历史

• 批准号: 2345437
• 负责人: Jean-Briac le Graverend
• 金额: $ 35.41万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-06-01 至 2027-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2345437&HistoricalAwards=false
• 关键词: Collaborative; Research; Embedding; Material; Informed

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.

过去如何变形金属会影响其将来的变形和潜在失败。这种变形史对金属的性能有重大影响。当前的预测性能的理论是高度复杂的，依靠复杂的方法或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是不切实际的。该奖项支持基本研究，通过开发一种新的配方，用于使用分数阶微分方程来预测金属合金性能。在这个新的公式中，材料的历史与描述材料进化过程的方程式的基础结构紧密相连。简化的数学描述使其对广泛采用有吸引力。合金建模的这种范式转变将通过减少生活预测和可持续性的不确定性来提高安全性，因为组件可以保持更长的保障服务。重要的是，该奖项还包括旨在鼓励神经分散的学生（自闭症频谱中的学生）参与的外展活动。这将通过参与以自闭症为中心的学校和大学教师的教育来实现这一目标，以提高自闭症学生的意识和更高的接受。预测能力的绩效（机械响应和终生）只能通过会计遗传性效应来实现。尽管如此，当前使用的模型，例如，使用界面表面理论或具有一阶普通微分方程的大量内部状态变量（ISV），在金属和合金中预测历史（遗传性）效应方面缺乏。原因是双重的：1）缺乏对负责遗传效应的机制的理解，2）到目前为止，用于ISV理论的数学框架采用了一阶普通微分方程，这些方程是点函数，因此没有内存路径。这种协同的实验和建模方法将通过确定长度尺度的遗传变形表现出来并根据激活量取决于材料信息的阶阶参数来填补这一知识差距。这种分数表述自然将遗传效应纳入了进化方程的结构，而不是直接通过ISV。分分级晶体塑性模型将与最新的原位实验相结合，即高温传播电子显微镜和高能量X射线衍射显微镜统一数学和物理学，以统一数学和塑性变形的物理。这些奖项反映了NSF的构建范围，并具有范围的构建范围。影响审查标准。