基于球压应力应变测量的单晶体弹性参数估计的贝叶斯框架
A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters from Spherical Indentation Stress-Strain Measurements
摘要：
本文提出了一个两步贝叶斯框架的内在单晶弹性刚度参数的估计从多晶样品，其晶格取向已使用电子背散射衍射技术测量的多个单独的晶粒的球形压痕应力-应变响应的测量。第一步需要建立的功能依赖的压痕弹性模量给定的晶格取向和固有的单晶弹性刚度参数。以前的这一步骤的努力需要一个计算昂贵的有限元（FE）模拟的大型数据库，以建立具有足够的精度这个功能。在本文中，它表明，引入贝叶斯框架可以大大减少建立这个功能所需的模拟的数量，同时引入实际有用的不确定性措施，可以指导选择特定的额外的模拟，预计最好地提高预测精度的功能。第二步涉及马尔可夫链蒙特卡罗（MCMC）采样的单晶弹性刚度参数的可能值的分布的基础上一组给定的实验测量的弹性压痕模量在不同的晶格取向的个别晶粒。第二步是通过将可用的实验数据校准到第一步中建立的函数来完成的。这种新的框架，并证明在本文中为铸态立方多晶Fe-3%Si样品和六方多晶商业纯钛（CP-Ti）样品。
英文摘要：
This paper presents a two-step Bayesian framework for the estimation of the intrinsic single crystal elastic stiffness parameters from the measurements of spherical indentation stress-strain responses in multiple individual grains of a polycrystalline sample, whose crystal lattice orientations have been measured using electron back-scattered diffraction technique. The first step requires the establishment of the functional dependence of the indentation elastic modulus given the lattice orientation and the intrinsic single crystal elastic stiffness parameters. Previous efforts for this step required a large database of computationally expensive finite element (FE) simulations in order to establish this function with adequate accuracy. In this paper, it is shown that the introduction of a Bayesian framework can greatly reduce the number of simulations necessary to establish this function, while introducing practically useful measures of uncertainty which can guide the selection of specific additional simulations that are expected to best improve the predictive accuracy of the function. The second step involves a Markov Chain Monte-Carlo (MCMC) sampling of the distribution of possible values for the single crystal elastic stiffness parameters based on a given set of experimentally measured elastic indentation moduli in individual grains of different lattice orientations. This second step is accomplished by calibrating the available experimental data to the function established in the first step. This novel framework is presented and demonstrated in this paper for an as-cast cubic polycrystalline Fe-3% Si sample and a hexagonal polycrystalline commercially pure (CP-Ti) titanium sample.
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