The compressive failure of long carbon fiber composites is due to complex mechanisms. The knowledge of this material is important for the design of composite structures [1], because the compressive strength and stiffness of laminates is assumed less than their tensile strength. There are many articles in the literature regarding the modeling of composites compressive behavior, particularly the microbuckling phenomenon / local instability. But, only few researchers modeled the mechanism at the structural / mesoscopic scale. For example Drapier, et al. [2], proposed a 2D homogenized model, which takes into account fiber initial alignment defects, matrix plasticity and structural parameters. The model is successful in predicting the elastic microbuckling modes, but the model is 2D and assumes microbuckling is periodic in fiber direction, just one gradient in thickness direction is taken into account. Consequently, not possible to compare test results obtained with real structures. Moreover, the prediction of both the 'distribution' and 'amplitudes' of fiber initial imperfection is still not well known [3]. Few studies give the distribution by X-Ray but this information is not taken into account in a model at the structural scale. Recently, we have developed a simple 3D non-local model called Beam Non-Local (BNL) model in Abaqus to predict the elastic mode of instability in pure compression, bending, compression-torsion and next to the hole in specimen under compressive load. This model is an extension of [4] and can be applied to Unidirectional (UD) plies and laminates. But, this model is limited to particular cases and is not possible to simulate composite structures with a complex microstructure, such as 2D or 3D woven composite. One of the major drawback is that, it is a discontinuous finite element model. 

Although, many nonlocal theories and various FE approaches has been developed over the years to solve the problem at the microscopic/mesoscopic scale, each model is restricted to some limitations and there is no particular model that has been developed to assess the compressive strength (particularly microbuckling phenomenon/local instability) of the carbon/epoxy composite at the structural scale. Hence, a new homogenized nonlocal numerical model is proposed in this article, similar to Mindlin's II gradient theory [5] to grasp well the instabilities. The framework of this nonlocal modeling is more general that of [2] to assess microbuckling phenomenon in UD and woven composites (carbon/epoxy long fiber). The developed nonlocal numerical model has been implemented in User Element (UEL) subroutine (coded in FORTRAN 77) for analysis in Abaqus, which permits to simulate the behavior of 2D and 3D cases. The nonlinearity of the matrix is take into account with a User subroutine (UMAT), which permits to model all family of behavior. The non-local materials properties are obtained by comparison with RVE, defined by the microstructure. The methodology and some results will be presented in the future paper.

Reference

[1] Mechin P.-Y., Keryvin V., Grandidier J.-C., Glehen D., An experimental protocol to measure the parameters of the compressive strength of CFRP with a fiber micro-buckling failure criterion, Composite Structures 211 (2019) 154-162.

[2] Drapier S., Grandidier, J.-C., Potier-Ferry, M., Towards a numerical model of the compressive strength for long fiber composites, European Journal of Mechanics / A Solids 18 (1999) 69-92.

[3] Drapier S., Grandidier, J.-C., Potier-Ferry, M., A structural approach of plastic microbuckling in long fiber composites: comparison with theoretical and experimental results, Composite Science and Technology 38 (2001), 3877 -3904

[4] Wisnom MR Analysis of shear instability in compression due to fiber waviness, Journal of Reinforced Plastic and Composites, Vol.12 No. 11, pp. 1171-1189, 1990.

[5] Mindlin, RD, Microstructure in linear elasticity, Arch. Rat. Mech. Anal 16 (1964) 57-78.