Keywords: composite, fragmentation, delamination, dissipated energy, plastic microbuckling, kink band, transient dynamic, crash.

The modelling of composites up to failure is an important industrial challenge, especially for crash applications. It implies the treatment of all steps of physical degradations by the use of advanced material models coupled with reasonable CPU cost. It is well known today that delamination is a challenge for crash modelling. In addition to its advantages, delamination can be assimilated to a key driver of the ply fragmentation process occuring in composite absorbers, where the composite is reduced to little fragments. Initiation of fragmentation takes place at the microscale where microscopic buckling of fibres can appear in the longitudinal direction, leading to kink band features. Thanks to many micromechanical studies, a good comprehension of fragmentation initiation processes has been achieved. Nevertheless, fragmentation in composites is not implemented yet in industrial codes due to the numerical difficulties and scale representation. For a reasonable structural calculation, an appropriate numerical approach is needed. The mesomodelling of composites is a good compromise to access the thin phenomena with an accurate representation [1,2,3]. The objective of this work is to study the feasibility of building a mesoscale model for initiation of fragmentation by microbuckling, considering the microparameter influence on the equivalent dissipated energy during fragment creation.

Today it is commonly admitted that under compression loading in the fibre direction, the failure is the consequence of plastic microbuckling phenomenon initiated by the wavy nature of the defects [4,5]. Under compression loading, initially wavy fibres bend and a kink band is suddenly created leading to catastrophic failure. Even if it is well understood that defects are triggers, the material defects influence on dissipative energy is not today clear. We use a well recognized model to describe the different steps of microbuckling leading to fragment creation [6], it involves fibres bending, matrix plasticity and misalignment of fibres in only static load cases. Thanks to this model, the associated dissipative energy from discrete kink band formation with regards to real imperfections range is computed.

The constitutive law for elementary parts is a classical Euler Bernoulli bending law for fibres and for matrix, we assumed a linear elastic-plastic law using an isotropic hardening law. Finte element (FE) simulations are performed with an iterative calculation method. The presence of two non-linear sources implies the use of a Newton iterative algorithm for global equilibrium and a Riks-Crisfield method for peak limitation problem. Results of the simulations show that micro-imperfections have an influence on the peak load, which corresponds to the instability of the behaviour. Nevertheless, it is shown that the dissipated energy during the fragment creation process is relatively independent of microscopic imperfections, which were not clearly identified in the past. Results of fragments lengths are also similar with experimental observations [4]. Thanks to this microscale analysis, which is not conceivable in industrial simulations, we conclude that the mesoscale approach could be a good choice in order to tackle the key mechanism of the fragmentation, without taking into account all imperfection ranges.

Dynamic delamination modelling is also a key point for crash absorber devices. Indeed many years of developments on delamination modelling at mesoscale give rise to robustness [2,3], except for dynamic effects and mesh dependencies issues. In consequence, a great effort has been made to control delamination computation for predictive analyses in the domain of transient dynamics. Furthermore, the competition between delamination and fragmentation are necessary for a good simulation of the degradation scenario appearing in crash absorber devices.

Eventually, we develop a corotational formulation in dynamic which account for total displacement but small deformations in two dimensions [7]. A specific adaptation in the context of transient dynamics has been computed. The future challenge is to build a mesoscale approach considering the above conclusions and in particular to study the delamination-fragmentation interactions within a mesoscale framework and to create dedicated numerical tools.

1

P. Ladevèze, "On the damage mechanics of composites", JNC 5, C. Bathias & Menkès eds, Pluralis Publication, Paris. 667-683, 1986.

2

O. Allix, P. Ladevèze, "Interlaminar interface modelling for the prediction of delamination", Composite Structures. 22(4): 235-242, 1992. doi:10.1016/0263-8223(92)90060-P

3

O. Allix, D. Lévêque, L. Perret, "Interlaminar interface model identification and forecast of delamination in composite laminates", Composite Science & Technology. 58(5): 671-678, 1998. doi:10.1016/S0266-3538(97)00144-9

4

R.R. Effendi, J.J. Barrau, D. Guedra-Degeorges, "Failure mechanism analysis under compression loading of unidrectional carbon/epoxy composites using micromechanical modelling", Composite Structures. 31(2): 87-98, 1995. doi:10.1016/0263-8223(94)00060-3

5

B. Paluch, "Analysis of geometric imperfections in fibres for unidirectional fibre reinforced composites", in La Recherche Aéronautique. 6: 431-448, 1994.

6

N. Fleck, L. Deng, B. Budiansky, "Prediction of kink width in compressed fibre composites", J. of Applied Mechanics. 62: 329-337, 1995. doi:10.1115/1.2895935

7

C.A. Felippa, B. Haugen, "A unified formulation of small-strain corotational finite elements: I. Theory", Comput. Methods Appl. Mech. Engrg. 194, 2285-2335, 2005. doi:10.1016/j.cma.2004.07.035

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