Rigorous Micro-Macro Estimates For Low-Symmetry Polycrystals

材料工程中的一个基本问题是从组成多晶团聚体的单晶颗粒的微观行为和关于颗粒大小、形状和分布的统计信息来计算多晶团聚体的宏观行为。在G.I.泰勒提出这一概念整整50年后，人们仍然在用均匀应变率近似的方法来实现这一点。虽然泰勒方法适用于高对称性/低各向异性的晶体，如面心立方和体心立方材料，但对于低对称性/高各向异性的多晶体，如HCP和离子材料，泰勒方法是非常不准确的，特别是当独立滑移系的数量不足(少于5个)时。此外，众所周知，泰勒理论导致的纹理预测比实验观察的要敏锐得多。为了克服泰勒模型的这两个长期存在的局限性，我们提出了一种新的非线性均匀化方法(即所谓的二阶方法)，这种方法已经在PI甲醛和其他类型的复合材料中获得了巨大的成功。最终目标是开发用于实现变形加工操作的无限元模拟的本构模型，充分考虑这些材料中的晶体和形态织构的演化。这项研究计划将对改进轻质、高强度结构合金(例如钛)的制造操作产生影响，这些合金在许多行业中都非常重要。

Rigorous micro-macro estimates for low-symmetry polycrystals.A fundamental problem in materials engineering is the computation of themacroscopic behavior of polycrystalline aggregates from the microscopicbehavior of their constituent single-crystal grains and statisticalinformation about the grain size, shape and distribution. Exactly 50 yearssince its introduction by G.I. Taylor, this is still being done by means ofthe uniform strain-rate approximation. While appropriate forhigh-symmetry/low-anisotropy crystals, such as FCC and BCC materials, theTaylor approach is highly inaccurate for low-symmetry/high-anisotropypolycrystals, such as HCP and ionic materials, especially when the numberof independent slip systems is deficient (less than five). In addition, itis well known that the Taylor theory leads to texture predictions that aresignificantly sharper than experimentally observed. To address these twolong-standing limitations of the Taylor model, we propose to implement arigorous nonlinear homogenization method (the so-called second-orderprocedure) that has already been used with great success by the PI formetal-matrix and other types of composites materials. The ultimateobjective is the development of constitutive models for implementation infinite element simulations of deformation processing operations, fullyaccounting for crystallographic and morphological texture evolution inthese materials. This research program will have an impact in thedevelopment of improved manufacturing operations for light-weight,high-strength structural alloys (e.g., titanium), which are of greatimportance in many industries.