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

技术摘要：该项目的目标是用直接基于位错的建模取代在三维多晶塑性模拟中使用塑性变形的经验本构描述。我们将以Lebensohn及其同事介绍的先前开发的快速傅立叶变换（FFT）多晶塑性公式为基础。FFT方法的关键特征是任何特征应变都可以包含在计算过程中而不发生实际变化。从位错的角度看，特征应变只是塑性变形张量，反映了位错引起的滑移。因此，用更直接的位错微观结构演变计算取代塑性的本构模型是很简单的，给出了一种模拟位错的方法。我们将基于基于位错密度演变的连续级模型来开展多晶塑性的初步工作，该模型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行为与多晶材料行为的宏观级描述之间的差距，从而更好地理解和新的预测能力，如塑性变形，蠕变，疲劳等基本材料特性。这个项目的成功完成将导致一种新的方法，在多晶塑性框架内耦合粗粒度和离散位错建模。该方法将允许在晶粒尺度上模拟塑性变形的非均匀性，包括位错流动的影响。因此，我们期望提高多晶塑性计算的能力，以模拟局部、晶内取向变化和应变，这些目前还没有很好地捕获。更具体地说，这种新的能力将是离散位错模拟的一个进步，因为它包括了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积累的建模成为可能。将该方法应用于一系列具体问题，并将结果与实验和现有建模能力进行比较。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，而是由随机取向的晶体组成，称为晶粒。这些多晶材料是我们当前许多技术的基础，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构成多晶的单晶晶粒的性能，还取决于这些晶粒的尺寸和取向的分布。新的实验方法对局部晶体取向的三维分布提供了详细的观察，具有无损和时间函数的新兴能力，对不同负载条件下多晶体的演变结构产生了前所未有的看法。多晶力学行为的计算建模已经成为变形研究的一个标准部分，例如用于汽车耐撞性设计。目前，大多数模型将多晶内部各晶粒的变形视为均匀的，从实验中我们知道这是不准确的。该项目的目标是在建模中更好地描述材料在每个颗粒中的变形。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，这是一种重要的现象，可能导致材料随着时间的推移而失效（断裂）。

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.