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TECHNICAL PAPERS

# Average Strain in Fiber Bundles and Its Effect on NCF Composite Stiffness

[+] Author and Article Information
H. David Mattsson

Division of Polymer Engineering, Luleå University of Technology, SE-97187 Luleå, Swedendavid.mattsson@consultant.saab.seU

Janis Varna

Division of Polymer Engineering, Luleå University of Technology, SE-97187 Luleå, Swedenjanis.varna@ltu.se

J. Eng. Mater. Technol 129(2), 211-219 (Jun 27, 2006) (9 pages) doi:10.1115/1.2400266 History: Received September 06, 2005; Revised June 27, 2006

## Abstract

Transverse strain in bundles governs transverse cracking in noncrimp fabric (NCF) composites. Finite element (FE) analysis shows that this strain may be significantly lower than the applied macroscopic strain component in the same direction. This feature is important for damage evolution modeling. The isostrain assumption which in different combinations is widely used in stiffness models is inadequate because the strain in different mesoelements (bundles of different orientation and matrix regions) is assumed the same. Analyzing by FEM the importance of media surrounding the bundle on average transverse strain it was found that an increasing ratio of the bundle transverse stiffness to the matrix stiffness leads to a decrease of the strain in the bundle. An increase of the stiffness in the same direction in adjacent layers leads to an increase of the transverse strain in the bundle. Higher bundle volume fraction in the layer leads to larger transverse strain in the bundle. These trends are described by a power law and used to predict the average strain in bundles. The calculated $H$ matrix which establishes the relationship between strains in the mesoelement and representative volume element strains is used to calculate the “effective stiffness” of the bundle. This effective stiffness is the main element in simple but exact expressions derived to calculate the stiffness matrix of NCF composites. Considering the three-dimensional (3D) FE model as the reference, it was found that all homogenization methods used in this study have sufficient accuracy for stiffness calculations, but only the presented method gives reliable predictions of strains in bundles.

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## Figures

Figure 1

3D model of a NCF composite with layup [0,90]s

Figure 2

Representation of NCF composite layer: (a) homogenization in a layer; (b) simplification of the mesoscale geometry

Figure 3

The schematics of [0,90]s NCF composite meso-scale structure: (a) simplified RVE; (b) a “superelement”; and (c) 2D model consisting of nine “superelements”

Figure 4

2D FE model used for the parametric study of interface distortion between 90deg-bundle and matrix

Figure 5

Effect of mesoparameters on transverse strain in bundles (E90=10GPa): (a) dependence on V90∕(1−V90), E0=150GPa, EM=3GPa; (b) linear dependence on V90∕(1−V90) in logarithmic axes, E0=150GPa, EM=3GPa; (c) effect of E0∕E90, EM=3GPa, L90=8, LM=2, A1=0.96; and (d) effect of EM∕E90, E0=150GPaL90=8, LM=2, A2=0.83

Figure 6

Schematic picture of a cross-ply NCF composite with layup [0,90]s(Vb=0,5) and bundle structure in all layers

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