Development of modelling and homogenisation procedures for stochastic tape-based discontinuous composites

Abstract

Conventional laminated composites have, due to their high stiffness- and strength-to-weight ratios, shown to be a viable alternative to metals in applications where lightweight structures are of essence. However, the current reach of conventional laminated composites is limited to certain industries and high-end products as a result of their high manufacturing cost. As a way to reduce cost while maintaining high performance, stochastic tape-based discontinuous composites (STBDCs) have emerged, offering a middle ground between the easy manufacturing of short fibre composites and high performance of continuous fibres composites. The irregular mesostructure and high interest from industries have increased the demand for efficient and predictive models (analytical and numerical) describing the mechanical response of this class of material. As a response to the increased interest, this project aimed to develop a method to predict the elastic properties of STBDCs, based on the mesostructural configuration and constituent properties (impregnated tapes and pure matrix). To replicate the complex material structure, a modular MATLAB code was developed as the core of the project. The MATLAB code takes the tape and plate dimensions, material properties, voxel resolution, etc, as inputs, then builds the material layer-by-layer by placing tapes at random positions and angles until the desired plate thickness has been reached. The developed algorithm allows tapes to form around each other (drape) to replicate the compression part of the real manufacturing process. The outputs of the code are, among other visualisations, a 3D-image of the material structure and Abaqus input files for the coming analysis. Based on the generated material structures, smaller statistical volume elements (SVEs) were extracted and used for the analysis. Nearly 400 SVEs of different dimensions from different samples were extracted and analysed to have a large enough sample size to account for the variability of the material. Computational homogenisation was used to determine the volume averaged in-plane elastic parameters. The homogenisation process was carried out by applying periodic boundary conditions (PBCs) to the SVEs using the Abaqus plug-in EasyPBC. The computational homogenisation was initially focused on a full 3D-model but as a subsequent step, the full 3D-model was reduced to a 2D-model by an intermediate analytical homogenisation process using classical laminate theory. A full 3D- and reduced 2D-model were generated for each SVE sample to allow a comparative analysis. Finally, experimental data of manufactured STBDCs plates was used as a comparison to verify the results of the numerical model. The study found that the voxel-based 3D-model and the developed methodology can be used to accurately evaluate the elastic properties of STBDCs. More specifically, the generated material samples and methodology used provided reliable results for all studied SVE dimensions, converging to elastic properties within one standard deviation compared to experimental tests. Furthermore, the reduced 2D-model showed a similar accuracy compared to the 3D-model while also requiring significantly less computational power, indicating that this is a reasonable simplification to make. It should be noted that the developed model is not a perfect representation of reality, simplifications had to be made to stay within the limitations of the project. As a consequence, the fibre volume fraction (FVF) of experimental data could not be reached, making the model slightly under-predict the elastic properties. With further improvements to raise the FVF, the data indicates that the model would produce more accurate results compared to experimental tests, thus being a reliable source material for future industrial use.