Systematic Identification of Constitutive Parameters for Crystal Plasticity Models of Non-Cubic Metal Alloys

构成我们日常生活基础设施（交通、发电等）的大多数材料主要是多晶和金属，如钢、铝、镁或铜。多晶性是指材料中的所有原子排列在一个规则的网格上，并且网格的方向在相邻的体积（称为“颗粒”或“晶体”）中是不同的。为了掌握制造步骤并预测这些结构重要材料的使用性能，工程师们利用描述这些材料力学行为的模型。这样的模型有相当数量的可调参数，这些参数对每种材料都是不同的，需要对每种材料进行量化。这种参数识别非常复杂，特别是对于具有复杂原子排列的金属，例如钛、镁或锡。在本研究项目中，pi取代了传统的通过观察难以获得的样品的变形来进行参数识别的方法，采用了一种新的方法，用特殊形状的针进行小印痕。拥有这样一种具有成本效益的方法来建立材料模型，将大大节省整个制造链的时间、能源和材料成本，并改进对最终材料性能的预测。该计划还将通过让学生在多个层次上接触科学和工程，包括研究生和本科生的教育和培训，为国家的智力基础设施做出贡献，从而带来广泛的好处。由于潜在的缩短开发时间、节约成本和提高可靠性，计算建模集成到工艺开发和设计中继续加速。在基本层面上，结构金属力学行为的控制因素是位错对滑移的阻力，即位错运动的临界分解剪应力，以及同时发生的结构演变（例如加工硬化）。因此，为了准确地描述构成结构部件的多晶阵列的变形、可能的损伤成核和断裂行为，有必要建立一个包含物理变形过程的健全模型，并为进入该模型的可调参数提供准确的值。虽然这些本构参数可以很容易地确定许多立方金属使用完善的单晶方法，他们很难确定许多非立方金属。这是因为即使在可以获得合适的单晶的情况下，不同滑移体系类型的激活应力差异很大，这使得在单晶的标准单轴试验中不可能选择性地激活某些（一组）滑移体系。多相材料带来了进一步的挑战，历史上很难在不受相邻相影响的情况下对单个相进行分析。如果所选本构模型的可调参数可信，则任意变形路径（例如，在金属成形中发生）的全场或平均场晶体塑性模拟可以用于理解和预测非立方金属的各向异性变形和损伤成核。提出的研究应用了一种新开发的方法，以相对快速和经济有效的方式确定本构描述的参数，以许多不同的单相和双相合金。在这种技术中，球-锥形纳米压痕被用来连续询问多晶样品表面足够多的不同晶体取向。然后使用原子力显微镜来测量这些凹痕周围的地形，这是晶体取向和不同滑移系统的特定局部活性的强烈函数。然后在不同的本构参数下进行压痕过程的晶体塑性有限元模拟，直到在不同取向/形貌的晶体上的几个不同压痕中，测量和模拟的形貌之间达到最优匹配。这种方法是有效的，因为轴对称的球-圆锥压痕几何形状导致许多不同的滑移系统以不同的速率运行，并沿着不同的应变路径运行，这取决于压痕下方的材料位置。在本研究中，该方法将用于确定一系列含六方相和体心立方相的钛基合金以及纯度为99%的四边形锡的本构参数。为商业上重要的合金确定的本构参数将对跨各种长度尺度开发集成计算材料工程（ICME）数据和模型的能力产生直接影响。这将大大节省时间、能源和材料成本。总体而言，材料加工能够可靠地预测非均质变形是非常重要的，这是在基于物理的置信度预测性能或可靠性之前所需要的。

Non-Technical SummaryMost of the materials that make up our daily-life infrastructure (transportation, power generation, etc.) are predominantly polycrystalline and metallic, such as steel, aluminum, magnesium, or copper. Polycrystallinity means that all atoms in the material are arranged on a regular grid and the grid orientation is different in neighboring volumes (which are termed "grains" or "crystallites"). To master the manufacturing steps and predict the in-service performance of such structurally important materials, engineers make use of models that describe the mechanical behavior of these materials. Such models have a fair number of adjustable parameters, which are different for each material and need to be quantified for each of them. This parameter identification is quite involved, particularly for metals that have complicated atomic arrangements, such as, for instance, titanium, magnesium, or tin.In this research project, the PIs replace the traditional way of parameter identification done by observing the deformation of difficult to obtain samples, by a new method that puts small impressions with a specially shaped needle. Having such a cost-effective means to establish the material model will lead to substantial savings in time, energy, and material cost across the manufacturing chain and improved prediction of final material properties. This program will also have broad benefits by exposing students at multiple levels to science and engineering, including the education and training of both graduate and undergraduate students to contribute to the nation's intellectual infrastructure.Technical SummaryThe integration of computational modeling into process development and design continues to accelerate due to the potential shortened development times, cost savings, and enhanced reliability. At the fundamental level, the controlling factors in the mechanical behavior of structural metals are the resistance of dislocations to slip, i.e. the critical resolved shear stress for the motion of dislocations, and the concurrent structural evolution (e.g. work hardening). Thus, in order to accurately describe the deformation, possible damage nucleation, and fracture behavior of the polycrystalline arrays that make up structural components, it is necessary to have a sound model with physical deformation processes involved and accurate values for the adjustable parameters that enter such models. While these constitutive parameters can be readily determined for many cubic metals using well established single crystal methods, they are much more difficult to ascertain in many non-cubic metals. This is because even in cases when suitable single crystals can be obtained, the large differences in activation stress for different slip system types can make it impossible to selectively activate some (set of) slip systems in standard uniaxial tests of single crystals. Multiphase materials pose a further challenge, where historically it has been very difficult to carry out analysis on the individual phases without the influence of neighboring phases. Provided that adjustable parameters of a selected constitutive model are available with confidence, full or mean field crystal plasticity simulations of arbitrary deformation paths (occurring, for instance, in metal forming) can then be used to understand and predict the anisotropic deformation and damage nucleation in non-cubic metals.The proposed research applies a newly developed approach to determine parameters of the constitutive description in a relatively rapid and cost-effective manner to a number of different single and dual phase alloys. In this technique, sphero-conical nano-indentation is used to serially interrogate a sufficiently large number of different crystal orientations at the surface of polycrystalline samples. Atomic force microscopy is then used to measure the topography around these indents, which is a strong function of the crystal orientation and the specific local activity of different slip systems. Crystal plasticity finite element (CPFE) simulation of the indentation process is then carried out with varying constitutive parameters until an optimal match is achieved between the measured and simulated topographies in several different indents on crystals with different orientations/topographies. This method is effective because the axisymmetric sphero-conical indentation geometry causes many different slip systems to operate at different rates and along different strain paths depending on the material location beneath the indent. In the present study this approach will be used to determine the constitutive parameters in a range of titanium-based alloys containing hexagonal and body-centered cubic phases as well as in tetragonal tin of 99% purity.The constitutive parameters identified for the commercially important alloys will have a direct effect on the ability to develop integrated computational materials engineering (ICME) data and models across a variety of length scales. This will lead to substantial savings in time, energy, and material cost. Overall it is very important for materials processing to be able to reliably predict heterogeneous deformation, which is required before prediction of performance or reliability can be made with physically-based confidence.