Extending Dislocation Dynamics with FFT to Address Dislocation Patterning and Slip Band Formation

技术摘要本项目的目标是用直接的基于位错的建模来代替在多晶塑性的三维模拟中使用的塑性变形的经验本构描述。我们将基于Lebensohn及其同事先前开发的多晶塑性的快速傅立叶变换（FFT）公式进行工作。 FFT方法的主要特点是在计算过程中不发生真实的变化，可以包括任何本征应变。 从位错的角度来看，本征应变就是塑性变形张量，反映了位错引起的滑移。 因此，用更直接的位错微结构演化计算代替塑性本构模型是简单的，给出了一种模拟位错的方法。 我们将根据最初的工作多晶塑性使用的连续水平模型的基础上位错密度的演变，这将部分基于离散位错模拟的结果。 因此，我们的目标是弥合离散位错的行为与多晶材料行为的宏观水平描述之间的差距，从而能够更好地理解和新的预测能力，如塑性变形，蠕变，疲劳，等。成功完成这个项目将导致一个新的方法，夫妇粗-多晶塑性框架内的晶粒和离散位错建模。 该方法将允许模拟的非均匀性的塑性变形在晶粒尺度，包括位错流动的影响。 因此，我们希望提高多晶塑性计算的能力，以模拟局部，晶粒内取向的变化和应变，这是目前没有很好地捕捉。 更具体地说，这种新的能力将是离散位错模拟的一个进步，包括各向异性弹性和局部晶格旋转的能力。 多晶塑性的新能力将使位错运动与晶粒结构和取向的耦合以及局部位错含量的积累的建模成为可能。 该方法的应用将作出一系列的具体问题，比较结果与实验和现有的建模能力。 非技术总结：在大多数基于金属系统的技术应用中，金属不是单晶，而是由随机取向的微晶组成，称为晶粒。 这些多晶材料是我们目前大部分技术的基础，毫无疑问，在未来也将发挥类似的作用。 它们的力学性能不仅取决于组成多晶的单晶颗粒的性质，而且还取决于这些颗粒的尺寸和取向的分布。 新的实验方法提供了对局部晶体学取向的三维分布的详细观察，并具有非破坏性和作为时间函数的新兴能力，从而产生了各种载荷条件下多晶体演变结构的前所未有的视图。多晶体力学行为的计算建模已成为变形研究的标准部分，例如，在汽车耐撞性的设计中。 目前，大多数模型将多晶内单个晶粒的变形视为均匀的，这是不准确的。 该项目的目标是在建模中更好地描述每个晶粒内材料的变形。 该项目的成功将使我们能够更准确地模拟变形中的许多重要问题，包括疲劳，这是一种随着时间的推移可能导致材料失效（断裂）的重要现象。

Technical SummaryThe goal of this project is to replace the use of empirical constitutive descriptions of plastic deformation in three-dimensional simulations of polycrystal plasticity with direct dislocation-based modeling. We will base the work on a previously-developed fast-Fourier transform (FFT) formulation of polycrystal plasticity introduced by Lebensohn and colleagues. The key feature to the FFT approach is that any eigenstrain can be included with no real change in the calculational procedure. From a dislocation perspective, the eigenstrains are just the plastic distortion tensor, which reflects the slip caused by the dislocation. Thus, replacing a constitutive model for plasticity with a more direct calculation of dislocation microstructure evolution is straightforward, given a way to model the dislocations. We will base the initial work on polycrystalline plasticity on the use of a continuum-level model based on dislocation density evolution, which will be based in part on results from discrete dislocation simulations. Our goal is thus to bridge the gap between the behavior of discrete dislocations and macroscopic-level descriptions of the behavior of polycrystalline materials, enabling a better understanding of, and new predictive capabilities for, such fundamental materials properties as plastic deformation, creep, fatigue, etc.Successful completion of this project will lead to a new methodology that couples coarse-grained and discrete dislocation modeling within a polycrystal plasticity framework. The method will allow for simulation of the heterogeneity of plastic deformation at the grain scale that includes the effects of dislocation flow. We thus expect to improve on the ability of polycrystal plasticity calculations to model local, intragrain orientation changes and strain, which currently are not well captured. More specifically, this new capability will be an advance for discrete dislocation simulations by including the ability to include anisotropic elasticity and local lattice rotations. The new capabilities for polycrystal plasticity will enable the modeling of the coupling of dislocation motion with grain structure and orientation and the accumulation of localized dislocation content. Application of the method will be made to a series of specific problems, comparing results with both experiments and existing modeling capabilities. Non-technical summary:In most technological applications based on metallic systems, the metals are not single crystals, but rather are made up of randomly-oriented crystallites, called grains. These polycrystalline materials serve as the basis for much of our current technology and will undoubtedly serve a similar role in the future. Their mechanical properties depend not only on the properties of the single-crystal grains that make up the polycrystal, but also on the distribution of size and orientation of those grains. New experimental methods are providing a detailed look at the three-dimensional distribution of local crystallographic orientations, with an emerging ability to do so non-destructively and as a function of time, yielding unprecedented views of the evolving structure of polycrystals under various loading conditions.Computational modeling of the mechanical behavior of polycrystals has become a standard part the study of deformation, used, for example, in the design of the crash-worthiness of automobiles. Currently, most models treat the deformation individual grains within the polycrystal as being uniform, which we know from experiment is not accurate. The goal of this project is to incorporate within the modeling a better description of the deformation of the material within each grain. Success of this project will enable us to more accurately model numerous important problems in deformation, including fatigue, an important phenomenon that can lead to the failure (breaking) of the material over time.