In this paper, the application of a recently formulated two-step Bayesian framework to the estimation of effective anisotropic elastic constants of single plies within a multi-laminate polymer matrix composite is demonstrated, while using previously reported spherical indentation measurements within singular plies. Experimental spherical indentation measurements within the epoxy/fiber plies are inherently noisy due to local variation of the fiber volume fraction underneath the indenter. This paper demonstrates that the usage of a two-step Bayesian framework enables the extraction of reliable point estimates (and associated distributions) for the effective elastic constants from indentation modulus measurements conducted within single plies at different angles to the fiber orientations. The first step of the two-step Bayesian framework establishes the effective elastic indentation modulus of a single ply as a function of its intrinsic elastic stiffness parameters and the angle between the indentation direction and the fiber orientation using a database of suitable finite element simulations. The second step involves the calibration of the indentation measurements from a given set of multi-laminate samples to the reduced-order model established in the first step. The second step is accomplished by sampling the posterior distribution of the single ply elastic parameters via Monte Carlo Markov Chain methods. This new framework is demonstrated in this study for an IM7/977-3 carbon fiber/epoxy multi-laminate sample.

中文翻译：

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从多层聚合物基质纤维增强复合材料样品上的球形凹痕对单层各向异性弹性常数的贝叶斯估计

在本文中，展示了最近制定的两步贝叶斯框架在多层聚合物基复合材料内单层有效各向异性弹性常数的估计中的应用，同时使用先前报道的单层内的球形压痕测量。由于压头下方纤维体积分数的局部变化，环氧树脂/纤维层内的实验性球形压痕测量具有固有的噪声。本文展示了两步贝叶斯框架的使用能够从与纤维取向不同角度的单层内进行的压痕模量测量中提取有效弹性常数的可靠点估计（和相关分布）。两步贝叶斯框架的第一步使用合适的有限元模拟数据库建立单层的有效弹性压痕模量，作为其固有弹性刚度参数和压痕方向与纤维取向之间的角度的函数。第二步涉及将一组给定的多层样品的压痕测量校准到第一步中建立的降阶模型。第二步是通过蒙特卡罗马尔可夫链方法对单层弹性参数的后验分布进行采样来完成的。这项新框架在本研究中针对 IM7/977-3 碳纤维/环氧树脂多层样品进行了演示。