Development of modelling and homogenisation procedures for stochastic tape-based discontinuous composites
Typ
Examensarbete för masterexamen
Program
Applied mechanics (MPAME), MSc
Publicerad
2022
Författare
Sjöberg, Jacob
Haglund Nilsson, Olle
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Stochastic Tape Based Discontinuous Composite , Periodic Boundary Condition , Statistical Volume Element , Voxel , Chopped Fibre Composite , Tow , Homogenisation