X-ray scattering tensor tomography based finite element modelling of heterogeneous materials

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.