Among micro-scale imaging technologies of materials, X-ray micro-computed tomography has evolved as most popular choice, even though it is restricted to limited field-of-views and long acquisition times. With recent progress in small-angle X-ray scattering these downsides of conventional absorption-based computed tomography have been overcome, allowing complete analysis of the micro-architecture for samples in the dimension of centimetres in a matter of minutes. These advances have been triggered through improved X-ray optical elements and acquisition methods. However, it has not yet been shown how to effectively transfer this small-angle X-ray scattering data into a numerical model capable of accurately predicting the actual material properties. Here, a method is presented to numerically predict mechanical properties of a carbon fibre-reinforced polymer based on imaging data with a voxel-size of 100 μm corresponding to approximately fifteen times the fibre diameter. This extremely low resolution requires a completely new way of constructing the material’s constitutive law based on the fibre orientation, the X-ray scattering anisotropy, and the X-ray scattering intensity. The proposed method combining the advances in X-ray imaging and the presented material model opens for an accurate tensile modulus prediction for volumes of interest between three to six orders of magnitude larger than those conventional carbon fibre orientation image-based models can cover.

在材料的微尺度成像技术中，X射线微计算机断层扫描已发展成为最受欢迎的选择，尽管它受到有限的视场和较长的采集时间的限制。随着小角度 X 射线散射的最新进展，传统吸收型计算机断层扫描的这些缺点已被克服，从而可以在几分钟内对厘米尺寸样品的微结构进行完整分析。这些进步是通过改进的 X 射线光学元件和采集方法引发的。然而，目前尚未证明如何有效地将这种小角度 X 射线散射数据转换为能够准确预测实际材料特性的数值模型。在此，提出了一种基于体素尺寸为 100 μm（相当于纤维直径的大约 15 倍）的成像数据对碳纤维增强聚合物的机械性能进行数值预测的方法。这种极低的分辨率需要一种全新的方法来构建基于纤维取向、X 射线散射各向异性和 X 射线散射强度的材料本构定律。所提出的方法结合了 X 射线成像的进步和所提出的材料模型，可以对感兴趣的体积进行精确的拉伸模量预测，比传统的基于图像的碳纤维取向模型可以覆盖的体积大三到六个数量级。