Determination of the material and geometrical contributions in the non-linear elastic behaviour of unidirectional CFRP laminates from experimental and numerical procedure
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Kylian MAHÉ-FLAHAUT (FRANCE), Vincent KERYVIN (FRANCE), Cédric BERNARD , Tom ALLEN (NEW ZEALAND), Jean-Claude GRANDIDIER , Adrien MARCHANDISE (FRANCE)Abstract :
Unidirectional (UD) carbon fibre-reinforced polymers (CFRP) exhibit a non-linear elastic behaviour (NLEB), characterised by a stiffening under tension and a softening under compression [6]. In the context of structural design, not taking this NLEB into account could lead to dramatic consequences in the case of structures subjected to compression, such as sailing yachts masts. Even if the NLEB of carbon fibres has been known for decades [1], the physical origin of the NLEB of UDs has yet to be properly addressed. A previous study [4] showed that the contribution of fibre waviness in the NLEB of UDs was negligible. However, this was for a restricted strain range of [0-0.5%] and with the elastic behaviour of the matrix assumed to be purely linear.
The goal of this study is to precisely determine the contributions of the constituents (defined as “material” contribution) and of the fibre waviness (“geometrical” contribution) in the global NLEB of UDs. To broaden the strain range compared to the study performed by Keryvin et al. [4], only standard (SM) and intermediate modulus (IM) CFRPs were studied as they exhibit a higher failure strain than high modulus CFRPs.
Firstly, experimental work at different scales was conducted. Single fibre tensile tests and micro-pillar compression tests were performed. Uniaxial tensile and compressive tests were also undertaken on the cured epoxy resin matrix. These tests were used to characterise the NLEB of the constituents considered independently, hence the purely material contribution. Then, uniaxial tensile and Combined Loading Compression (CLC) according to ASTM D6641/6641M-23 tests were performed on thin UD laminates to characterise the NLEB at ply scale i.e. considering both contributions. Eventually, four-point bending (4PB) testing on thick laminates was undertaken, exhibiting a shift of the neutral axis position which is an indicator of the NLEB [5].
Secondly, numerical simulations were conducted to determine the contribution of the fibre waviness. Two different modelling strategies were used: a classical micromechanics model and the Beam Non-Local model (BNL) of Grandidier et al. [3]. Both feature a 1° initial misalignment of fibres – as measured by Grabow [2] using the Yurgartis’ method [7] – and the non-linear behaviour of the matrix. Both achieved similar results.
Finally, a numerical model of the 4PB test was developed and fed using both the NLEB of constituents determined experimentally and the NLEB rising from fibre waviness determined numerically. The shift of the neutral axis position was compared to the experimental one. Good correlation was achieved.
The study showed that, in this strain range, the contribution of fibre waviness is not negligible. However, the main contributor in the NLEB of CFRP UDs remains the fibre material behaviour.
The goal of this study is to precisely determine the contributions of the constituents (defined as “material” contribution) and of the fibre waviness (“geometrical” contribution) in the global NLEB of UDs. To broaden the strain range compared to the study performed by Keryvin et al. [4], only standard (SM) and intermediate modulus (IM) CFRPs were studied as they exhibit a higher failure strain than high modulus CFRPs.
Firstly, experimental work at different scales was conducted. Single fibre tensile tests and micro-pillar compression tests were performed. Uniaxial tensile and compressive tests were also undertaken on the cured epoxy resin matrix. These tests were used to characterise the NLEB of the constituents considered independently, hence the purely material contribution. Then, uniaxial tensile and Combined Loading Compression (CLC) according to ASTM D6641/6641M-23 tests were performed on thin UD laminates to characterise the NLEB at ply scale i.e. considering both contributions. Eventually, four-point bending (4PB) testing on thick laminates was undertaken, exhibiting a shift of the neutral axis position which is an indicator of the NLEB [5].
Secondly, numerical simulations were conducted to determine the contribution of the fibre waviness. Two different modelling strategies were used: a classical micromechanics model and the Beam Non-Local model (BNL) of Grandidier et al. [3]. Both feature a 1° initial misalignment of fibres – as measured by Grabow [2] using the Yurgartis’ method [7] – and the non-linear behaviour of the matrix. Both achieved similar results.
Finally, a numerical model of the 4PB test was developed and fed using both the NLEB of constituents determined experimentally and the NLEB rising from fibre waviness determined numerically. The shift of the neutral axis position was compared to the experimental one. Good correlation was achieved.
The study showed that, in this strain range, the contribution of fibre waviness is not negligible. However, the main contributor in the NLEB of CFRP UDs remains the fibre material behaviour.