Representative volume elements for discontinuous carbon fibre composites – Part 2: Determining the critical size

Harper, L.T.; Qian, C.; Turner, T.A.; Li, S.; Warrior, N.A.

doi:10.1016/j.compscitech.2011.11.003

Cited by 72 publications

(29 citation statements)

References 16 publications

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“…Computation time is therefore one of the primary concerns associated with meso-scale FEA models for DFC materials. 2D models are the most computationally inexpensive option, using 1D linear beam elements to represent fibre bundles randomly distributed in 2D space [7,[22][23][24][25][26]. However, this approach overlooks fibre crimping and allows bundle-bundle penetration, as all bundles are deposited on the same plane, reducing accuracy.…”

Section: Introductionmentioning

confidence: 99%

“…RVE size is linked to the fibre length and tow size [7] and can be several orders of magnitude larger than the scale of the reinforcement. Computation time is therefore one of the primary concerns associated with meso-scale FEA models for DFC materials.…”

Section: Introductionmentioning

confidence: 99%

“…DFCs are versatile and their mechanical properties span a wide range [4][5][6], but it is difficult to control the high levels of material variability compared with continuous fibre composites. Due to this, a large number of test specimens is required to achieve suitable confidence in experimental data [7,8]. This is both time consuming and costly, particularly as mechanical properties can also be influenced by size and scale [9][10][11][12][13][14] due to the random heterogeneous nature of the material.…”

Section: Introductionmentioning

confidence: 99%

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3D geometric modelling of discontinuous fibre composites using a force-directed algorithm

Harper

Qian

Luchoo

et al. 2016

Journal of Composite Materials

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A geometrical modelling scheme is presented to produce representative architectures for discontinuous fibre composites, enabling downstream modelling of mechanical properties. The model generates realistic random fibre architectures containing high filament count bundles (>3k) and high (~50%) fibre volume fractions. Fibre bundles are modelled as thin shells using a multi-dimension modelling strategy, in which fibre bundles are distributed and compacted to simulate pressure being applied from a matched mould tool. FE simulations are performed to benchmark the in-plane mechanical properties obtained from the numerical model against experimental data, with a detailed study presented to evaluate the tensile properties at various fibre volume fractions and specimen thicknesses. Tensile modulus predictions are in close agreement (less than 5% error) with experimental data at volume fractions below 45%.Ultimate tensile strength predictions are within 4.2% of the experimental data at volume fractions between 40%-55%. This is a significant improvement over existing 2D modelling approaches, as the current model offers increased levels of fidelity, capturing dominant failure mechanisms and the influence of out-of-plane fibres.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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3D geometric modelling of discontinuous fibre composites using a force-directed algorithm

Harper

Qian

Luchoo

et al. 2016

Journal of Composite Materials

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“…Their proposed methodology was evaluated by Dirrenberger et al [265] to study the size of the RVE for a pathological model of random structures. Harper et al [266] determined the critical size of the RVE for discontinuous fiber composites with increasing fiber length and volume fraction. They evaluated a number of microsamples and confirmed that it is computationally more efficient to study fewer large microsamples rather than many small ones.…”

Section: 22mentioning

confidence: 99%

“…They employed similar criteria as described in Ref. [266] to determine the size of the RRVE for piezoelectric nanocomposites. The influence of the number of realizations of the microstructure on the obtained RVE size has been also studied by Temizer and Zohdi [261].…”

Section: 22mentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

190

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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A dual‐scale homogenization method to study the properties of chopped carbon fiber reinforced epoxy resin matrix composites

Zheng

Qiu

et al. 2022

Polymer Composites

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In this work, a dual‐scale homogenization (DSH) procedures including the representative volume element (RVE) and Unit cell (UC) with Halpin–Tsai models in the UC scale and space direction‐sensitive Hotelling expansion (SDSHE) models in RVE scale separately. These two methods are introduced and implemented to predict the response of effective elastic properties in chopped fiber reinforced epoxy matrix structures. A post‐processing scheme of subdomain in UC scale based on Gauss theorem is proposed in SDSHE method, which is used to extract the average strain and stress in UC three‐dimensional structure. In addition, the X‐ray computed tomography was used to determine the fourth order tensor orientation angle and the probability distribution information of chopped fiber length in testing samples. Homogenization properties in RVE scale, and inclusion volume fraction (VF), thickness of interface and orientation tensors are designed in UC scale and compared. The excellent correlations with experiments prove the effectiveness of the proposed models. Furthermore, the algorithm proposed in this paper realizes the homogenization of the two scales in the process of numerical analysis, and it will effectively take into account many problems that cannot be achieved by other algorithms, such as the path strain of the model, the thickness of the interface, and so on.

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Representative volume elements for discontinuous carbon fibre composites – Part 2: Determining the critical size

Cited by 72 publications

References 16 publications

3D geometric modelling of discontinuous fibre composites using a force-directed algorithm

3D geometric modelling of discontinuous fibre composites using a force-directed algorithm

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

A dual‐scale homogenization method to study the properties of chopped carbon fiber reinforced epoxy resin matrix composites

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