Elastic and Plastic Deformation in Binary Alloy Crystallization

二元合金结晶中的弹塑性变形

• 批准号: 0413062
• 负责人: Kenneth Elder
• 金额: --
• 依托单位: Oakland University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0413062&HistoricalAwards=false
• 关键词: Elastic; Plastic; Deformation; Binary; Alloy

This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. A phase field crystal (PFC) model has been developed to study elastic behavior in the crystallization of pure materials. This was achieved by modeling the mass density on diffusive time and atomic length scales. The PFC approach naturally incorporates elastic and plastic deformations, multiple crystal orientations and free surfaces and was used to study grain boundary energy, liquid phase epitaxial growth and the yield strength of nano-crystalline solids. One ingredient not included in the original work was concentration which is particularly important since most materials contain at least two elements and the relative concentration of the elements can significantly impact the non-equilibrium processes and resulting microstructures. In addition, since all elements have different lattice structures and sizes, elastic and plastic deformations are strongly influenced by concentration. The goal of the proposed research is to develop a computationally efficient model of microstructure formation and stability in binary alloy crystallization phenomena and to use this model to study technologically important applications such as dendritic growth, eutectic crystallization and liquid phase epitaxial growth in binary alloys. The model will be developed by introducing a density field for each element, constructing an appropriate free energy functional F of these fields and assuming the dynamics are dissipative and driven to minimize F. The PI has extensive experience in constructing such models and has developed, in collaboration with others, models of eutectic solidification, driven charge density waves, polymorphic crystallization and imbibition. For the purposes of this research the PI has developed a preliminary model of binary alloy crystallization that includes elastic and plastic deformation. This model combines the PFC approach with a model of eutectic solidification. Initial calculations indicate that this preliminary model incorporates the generic features of a eutectic phase diagram and many of the typical patterns observed in non-equilibrium phenomena such as dendrites and eutectic crystallites with lamellar structures. In addition to these standard features the model includes all the elastic behavior incorporated in the original PFC model discussed above and was designed so that the concentration dependence of the lattice and elastic constants can be easily adjusted. While this preliminary model may need to be fine tuned, these initial calculations indicate a high likelihood that the PI will accomplish the primary goals of this project. The research will have broad impact on both fundamental and applied science. Undergraduate students will be involved in the projects.%%% This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. A new model has been developed to describe microstructural evolution of binary alloys that also includes their elastic and plastic behavior as a function of their relative concentration. The research will have broad impact on both fundamental and applied science. Undergraduate students will be involved in the projects.***

该奖项由材料研究和数学科学的分区共同资助，在NSF范围内的数学科学优先领域的保护下。 已经开发了相位场晶体（PFC）模型来研究纯材料结晶中的弹性行为。 这是通过对扩散时间和原子长度尺度上的质量密度进行建模来实现的。 PFC方法自然结合了弹性和塑性变形，多个晶体取向和游离表面，并用于研究晶界能量，液相外延生长以及纳米晶体固体的屈服强度。 原始工作中未包含的一种成分是浓度，这一点尤其重要，因为大多数材料至少包含两个元素，并且元素的相对浓度可以显着影响非平衡过程和所得的微观结构。 此外，由于所有元素具有不同的晶格结构和大小，因此弹性和塑性变形受浓度的强烈影响。 拟议的研究的目的是开发一种在二元合金结晶现象中的微观结构形成和稳定性的计算有效模型，并使用该模型来研究二进制合金中的技术重要应用，例如树突状生长，共晶结晶和液相相位相位的二进制合金生长。 The model will be developed by introducing a density field for each element, constructing an appropriate free energy functional F of these fields and assuming the dynamics are dissipative and driven to minimize F. The PI has extensive experience in constructing such models and has developed, in collaboration with others, models of eutectic solidification, driven charge density waves, polymorphic crystallization and imbibition. 出于这项研究的目的，PI开发了一种二元合金结晶的初步模型，其中包括弹性和塑性变形。 该模型将PFC方法与共晶固化模型相结合。 最初的计算表明，该初步模型结合了共晶相图的通用特征，以及在非平衡现象中观察到的许多典型模式，例如树突和层状结构，具有层状结构。 除这些标准功能外，该模型还包括上面讨论的原始PFC模型中纳入的所有弹性行为，并被设计为以便可以轻松调整晶格和弹性常数的浓度依赖性。 虽然可能需要对此初步模型进行微调，但这些初始计算表明PI很有可能实现该项目的主要目标。这项研究将对基本科学和应用科学产生广泛的影响。 本科生将参与项目。%%％该奖项由NSF范围内数学科学优先领域的材料研究和数学科学的分区共同资助。 已经开发了一个新模型来描述二元合金的微观结构演化，这也包括它们的弹性和塑性行为作为其相对浓度的函数。 这项研究将对基本科学和应用科学产生广泛的影响。 本科生将参与项目。***