CNFC materials

The major difference between NFC and CNFC materials is that the later composite does not exhibit directionality. It behaves predominantly like isotropic material, meaning that the stiffness and elongation-to-failure are the same in all directions.

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5.2.2.1 Evolution of surface strain ratios

(a)

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(c)

(d)

Figure 5.14: Evolution of contours of surface strain ratio (deformation mode) and FLD. (a) U200; (b) U100; (c) U70; and (d) U25.

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Similar to NFC materials, strain ratio information of CNFC specimens is calculated by the python script created in this work. Figure 5.14 above shows the surface contour of strain ratio for each sample, as well as the FLDs at the end of each stage. The amount of strain deformation is very small at the edges of surface contours, leading to some extremely negative strain ratios. In the pre-stretch stage, all specimens (except the full circle sample which exhibits a major deformation mode of biaxial stretch) experience negligible minor strain, suggesting unequal restriction in the longitudinal and transverse directions. These samples are pulled at both edges in the pre-stretch stage, leading to a deformation mode of in between uniaxial tension and plane strain. As lateral restriction increases with wider samples, the major deformation mode moves towards plane strain (as observed in U70 and U100), suggesting that the lateral direction remains unstrained while both edges are pulling away from each other. Equal amounts of force are applied to the U200 sample from every direction, resulting in a major deformation mode close to biaxial-stretch. In addition, none of the samples exhibits a major deformation mode of pure shear due to the predominantly isotropic nature of CNFC materials. Observations of FLDs at the end of the first stage show a clear trend of lowered maximum strain deformation as sample width increases.

For the full circle sample or the U200 specimen, the composite exhibits a major deformation mode of biaxial stretch during forming, since the entire sample edge is completely fixed during forming. Therefore, unlike other geometries which have three separate stages, the UF200 specimen has only two stages (stage 1 and stage 3). For the U70 and U100 specimens, the pole and its nearby regions shift from the negative minor strain region to the positive minor strain region in the biaxial stretch behaviour. Similar behaviour is not obvious for the U25 sample, which can be attributed to the fact that the biaxial stretch behaviour disappears very quickly due to a small sample width. In the

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third stage, specimens exhibit their major deformation mode which is influenced by the sample geometry.

Unlike NFC materials, CNFC materials could not exhibit pure shear behaviour during stretch forming experiments, which is attributed to the fibre reinforcement nature of CNFC samples. The lack of deformation mode of pure shear also results in larger amount of strains acting on the fibres, leading to lower deformation depths. The application of short chopped fibres would help recycle composites at the end of its use- life, and it seems that a trade-off needs to be made between ease for recycling and better formability.

5.2.2.2 Constructing the FLC

The construction of the FLC of the CNFC is based on the principal strain values provided by the ARAMIS™ system. Line fractures in CNFC materials can be narrowed down to short segments where the failure initiates, and this is achieved by setting the frame rate of the ARAMIS™ system to its maximum of 15 images per second. Principal strains of these small segments at the stage just prior to failure are used to construct the FLC, as shown in Figure 5.15. Note that the surface point experiencing strain deformation above the FLC is considered failure. Using FLC to describe failure behaviour provides a quantitative measure for defining the limiting major strains as a function of minor strain, and such mathematical relations can be implemented in FEA models through a user-defined material subroutine.

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Figure 5.15: FLC of the CNFC materials obtained from stretch forming tests.

Similar to the procedure used to construct the FLC for the untreated specimens, the water-treated as well as the redried samples were cut into hourglass shapes (with varying middle sectional widths) and then formed into a hemispherical dome. Significantly improved elongation-to-failure has been noticed in the water-treated CNFC materials. Figure 5.16 shows that the increased elongation-to-failure can be translated to an increased forming envelope. Numerically, FLCs in different conditions of water treatment can be expressed in the following equations 5.21-5.23. It is not surprising that the redried composite has very similar forming limits to the untreated composite, as ductility has been largely returned to the untreated level when drying from the wet condition. Compared to these two dry conditions, the CNFC exhibits a significantly expanded forming envelope in the water-treated conditions, such that the limiting major strains are increased by 61% in biaxial stretch, and 92.8% in plane strain.

113 For the untreated composite:

𝛆_𝟏′ = { −𝟕𝟖. 𝟔𝟗 ∗ 𝛆𝟐

𝟐_{+ 𝟏. 𝟕𝟗 ∗ 𝛆}

𝟐+ 𝟎. 𝟎𝟑 𝟎% < 𝛆𝟐 < 𝟐%

−𝟏𝟑𝟗 ∗ 𝛆_𝟐𝟐− 𝟏. 𝟔𝟕 ∗ 𝛆_𝟐+ 𝟎. 𝟎𝟑 − 𝟎. 𝟔% < 𝛆_𝟐 < 𝟎% (5. 21)

For the water-treated composite:

𝛆𝟏′= {

𝟎. 𝟎𝟔𝟕𝟓 𝟎% < 𝛆𝟐< 𝟑%

−𝟏𝟖𝟑 ∗ 𝛆_𝟐𝟐_{− 𝟐. 𝟎𝟏 ∗ 𝛆}

𝟐+ 𝟎. 𝟎𝟔𝟕𝟓 − 𝟎. 𝟕% < 𝛆𝟐< 𝟎%

(5. 22)

For the redried composite:

𝛆_𝟏′ _{= {}−𝟐𝟓. 𝟗𝟔 ∗ 𝛆𝐌𝐢𝐧𝐨𝐫𝟐+ 𝟎. 𝟕𝟑 ∗ 𝛆𝐌𝐢𝐧𝐨𝐫+ 𝟎. 𝟎𝟑𝟓 𝟎% < 𝛆𝐌𝐢𝐧𝐨𝐫 < 𝟐. 𝟏%

−𝟐𝟓𝟎 ∗ 𝛆_{𝐌𝐢𝐧𝐨𝐫}𝟐_{− 𝟑. 𝟓 ∗ 𝛆}

𝐌𝐢𝐧𝐨𝐫+ 𝟎. 𝟎𝟑𝟓 − 𝟎. 𝟓𝟓% < 𝛆𝐌𝐢𝐧𝐨𝐫 < 𝟎%

(5. 23) where 𝜀_{𝑀𝑎𝑗𝑜𝑟}′ is limiting major strain; and 𝜀_{𝑀𝑖𝑛𝑜𝑟} is minor strain.

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5.3 FEA simulations