Multiscale modelling of the compressive behaviour of long-fibre composites

12 April 2016, 2.00 PM - 12 April 2016, 3.00 PM

Olivier Allix, LMT-Cachan / Institut Universitaire de France

Faculty Board Room, Queen's Building, University of Bristol

The intensive use of Carbon Fibres Reinforced Plastics in aeronautics implies to master the prediction of the behaviour of composite up to final failure and if one consider energy absorption even further. The so-called virtual testing approach supports this goal and relies on the use of robust models keeping the key physical mechanisms into account.

An important aspect of the response of composite is compression, which involve a particular mode of deterioration the kinking of fibres. In dynamics it can lead to a large amount of dissipated energy thanks to the fragmentation of the whole structure. Thanks to many works the physics of formation of kinking is today relatively well understood at the scale of the fibres, the one of the energy dissipated in the process far less. Moreover, its modeling at the meso-scale and its interaction with delamination is still a challenging issue.

Preliminary studies focus on quasi-static loadings of relatively small samples. A micro model of a representative unit cell incorporating carbon fibres in an epoxy matrix has been developed to account for the main degradation mechanisms associated to kinking. It is based on Fleck & Budiansky’s kinking theory [1]. This micro model has been used to extract the most important characteristics (strength, dissipated energy, kink band size) [2-3] and the associated scattering mainly due to the statistical waviness of the fibres. From that point on, a ply-scale model has been improved to account for compressive loadings [4]. The chosen representative volume element relies on the fragment size at the micro scale. An approximate potential form has been proposed and the associated state and evolution laws are identified using an energy equivalence principle between the scales – and models. The kink band size plays the role of a localization limiter. This constitutive law is parameterized by the fibre waviness angle and is able to represent material and geometrical nonlinearities under multi-axial loadings.

This work can be divided in three parts. The first one describes the kinking micro model and the main associated results. The second part focuses on the construction of a homogenized constitutive law at the mesoscale. The third part features an application of the strategy to the modelling of the degradation of holed plates in compression. For this purpose, the meso-scale model has been implemented in the virtual material model developed by Ladevèze [5]. This hybrid description strategy allows the interaction between the micro buckling mechanism (kinking) and other classical degradation mechanisms, such as delamination and transverse cracking [6], to take place for any configuration. The discussion of the relevance of the approach using qualitative comparisons between simulation [7] and experiments from the literature [8-9] will be discussed.

References

[1] B. Budiansky and N. A. Fleck, N. Compressive failure of fibre composites. Journal of the Mechanics and Physics of Solids, 41(1):183-211, 1993.
[2] J.M. Guimard, O. Allix, N. Pechnik, and P. Thévenet. Energetic analysis of fragmentation mechanisms and dynamic delamination modelling in {CFRP} composites. Computers and Structures, 87(15):1022-1032, 2009.
[3] N. Feld, O. Allix, E. Baranger, and J.M. Guimard. Micro-mechanical prediction of UD laminates behavior under combined compression up to failure: influence of matrix degradation. Journal of Composite Materials, 45(22):2317-2333, 2011.
[4] N. Feld, O. Allix, E. Baranger, and J. M. Guimard. A micromechanics-based mesomodel for unidirectional laminates in compression up to failure. Journal of Composite Materials, 46(23):2893-2909, 2012.
[5] P. Ladevèze, G. Lubineau, and D. Violeau. A computational damage micromodel of laminated composites. International Journal of Fracture, 137(1):139-150, 2006.
[6] C. S. Yerramalli and A. M. Waas. A failure criterion for fiber reinforced polymer composites under combined compression-torsion loading. International journal of solids and structures, 40(5):1139-1164, 2003.
[7] Allix, O., Feld, N., Baranger, E., Guimard, J.M., Ha-Minh, C. The compressive behaviour of composites including fiber kinking: modelling across the scales. Meccanica. Vol 49. Num 11. Pages 2571-2586. 2014
[8] Soutis C, Fleck NA (1990) Static compression failyre of 943 carbon fibre T800/924C composite plate with a single hole. 944, J Compos Mater 24:536–558
[9] Lee J, Soutis C (2008) Measuring the notched compressive strength of composite laminates: specimen size effects. Compos Sci Technol 68:2359–236

Contact information

For further information please contact Jo Hickey-Hall

Professor Olivier Allix

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