A micro-mechanical model of reinforced polymer failure with length scale effects and predictive capabilities. Validation on carbon fiber reinforced high-crosslinked RTM6 epoxy resin
NOTICE: this is the author’s version of a work that was accepted for publication in Mechanics of Materials. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mechanics of Materials, 133 (2019), 193-213 DOI: 10.1016/j.mechmat.2019.02.017
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[en] We propose a micro-mechanical numerical model able to predict the nonlinear behavior and failure of unidirectional fiber reinforced high-crosslinked epoxy subjected to transverse loading conditions. Statistical microstructural volume elements (SMVE) of a realistic composite material are generated from the statistical characterization of the fibers distribution and fiber radius estimated from SEM images of a similar material system. The fibers are assumed to be transversely hyperelastic isotropic and the matrix obeys a hyperelastic viscoelastic-viscoplastic constitutive model enhanced by a multi-mechanism nonlocal damage model. This polymer model captures the pressure dependency and strain rate effects. Besides, it also accounts for size
effects through its internal length scales, allowing capturing, with the same unique set of parameters, the behaviors of the epoxy as pure material as well as matrix phase in composites, which are experimentally observed to be different. Additionally, since fiber/matrix interfaces of the considered composite material are categorized as strong ones, the true underlying failure mechanism is located in the matrix close to the fibers, and the interface does not need to be explicitly introduced in the model. The model prediction is found to be in good agreement with experimental results in terms of the global nonlinear stress-strain curves over various strain rates and pressure conditions, on the one hand for pure matrix samples, and on the other hand
for the composite coupons, making the proposed framework a predictive virtual testing facility for material design. Finally, using this model, we study the localization behavior in order to characterize the post-failure behavior of the composite material: the cohesive strength is given by the stress-strain curve peak stress while the critical energy release rate is estimated by evaluating the dissipated energy accumulated during the post-peak localization stage. Finally, different SMVE realizations are considered allowing assessing the discrepancy in the failure characteristics of composites.
Nguyen, Van Dung ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Wu, Ling ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
A micro-mechanical model of reinforced polymer failure with length scale effects and predictive capabilities. Validation on carbon fiber reinforced high-crosslinked RTM6 epoxy resin
Publication date :
June 2019
Journal title :
Mechanics of Materials
ISSN :
0167-6636
Publisher :
Elsevier, Netherlands
Volume :
133
Pages :
193-213
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
The authors gratefully acknowledge the financial support from F.R.S-F.N.R.S. under the project number PDR T.1015.14. Computational resources have been provided by the supercomputing facilities of the Consortium des Equipements de Calcul Intensif en Fédération Wallonie Bruxelles (CECI) funded by the Fonds de la Recherche Scientifique de Belgique (FRS-FNRS).
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE] CÉCI - Consortium des Équipements de Calcul Intensif [BE]
Bonet, J., Burton, A.J., A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations. Comput. Methods Appl. Mech. Eng. 162:1–4 (1998), 151–164, 10.1016/S0045-7825(97)00339-3.
Chevalier, J., Camanho, P., Lani, F., Pardoen, T., Multi-scale characterization and modelling of the transverse compression response of unidirectional carbon fiber reinforced epoxy. Compos. Struct. 209 (2019), 160–176, 10.1016/j.compstruct.2018.10.076.
Chevalier, J., Morelle, X., Camanho, P., Lani, F., Pardoen, T., On a unique fracture micromechanism for highly cross-linked epoxy resins. J. Mech. Phys. Solids 122 (2019), 502–519, 10.1016/j.jmps.2018.09.028.
Coenen, E., Kouznetsova, V., Geers, M., Novel boundary conditions for strain localization analyses in microstructural volume elements. Int. J. Numer. Methods Eng. 90:1 (2012), 1–21, 10.1002/nme.3298.
González, C., LLorca, J., Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: microscopic mechanisms and modeling. Compos. Sci. Technol. 67:13 (2007), 2795–2806, 10.1016/j.compscitech.2007.02.001.
Gudimetla, M.R., Doghri, I., A finite strain thermodynamically-based constitutive framework coupling viscoelasticity and viscoplasticity with application to glassy polymers. Int. J. Plast. 98 (2017), 197–216, 10.1016/j.ijplas.2017.08.001.
Hobbiebrunken, T., Hojo, M., Adachi, T., Jong, C.D., Fiedler, B., Evaluation of interfacial strength in CF/epoxies using FEM and in-situ experiments. Compos. Part A Appl. Sci. Manuf. 37:12 (2006), 2248–2256, 10.1016/j.compositesa.2005.12.021 The 11th US-Japan Conference on Composite Materials.
Lemaitre, J., Chaboche, J.-L., Mechanics of Solid Materials. 1994, Cambridge University Press.
Matouš K., Geers, M.G., Kouznetsova, V.G., Gillman, A., A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J. Comput. Phys. 330 (2017), 192–220, 10.1016/j.jcp.2016.10.070.
May, S., Vignollet, J., de Borst, R., A new arc-length control method based on the rates of the internal and the dissipated energy. Eng. Comput. (Swansea) 33:1 (2016), 100–115, 10.1108/EC-02-2015-0044.
Melro, A., Camanho, P., Pinho, S., Generation of random distribution of fibres in long-fibre reinforced composites. Compos. Sci. Technol. 68:9 (2008), 2092–2102, 10.1016/j.compscitech.2008.03.013.
Melro, A., Camanho, P., Pires, F.A., Pinho, S., Micromechanical analysis of polymer composites reinforced by unidirectional fibres: part ii - micromechanical analyses. Int. J. Solids Struct. 50:11 (2013), 1906–1915, 10.1016/j.ijsolstr.2013.02.007.
Mesarovic, S.D., Padbidri, J., Minimal kinematic boundary conditions for simulations of disordered microstructures. Philos. Mag. 85:1 (2005), 65–78, 10.1080/14786430412331313321.
Morelle, X.P., Chevalier, J., Bailly, C., Pardoen, T., Lani, F., Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin. Mech. Time-Depend. Mater. 21:3 (2017), 419–454, 10.1007/s11043-016-9336-6.
Nguyen, V.-D., Béchet, E., Geuzaine, C., Noels, L., Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation. Comput. Mater. Sci 55:0 (2012), 390–406, 10.1016/j.commatsci.2011.10.017.
Nguyen, V.-D., Lani, F., Pardoen, T., Morelle, X., Noels, L., A large strain hyperelastic viscoelastic–viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers. Int. J. Solids Struct. 96 (2016), 192–216, 10.1016/j.ijsolstr.2016.06.008.
Nguyen, V.-D., Wu, L., Noels, L., Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method. Comput. Mech. 59:3 (2017), 483–505, 10.1007/s00466-016-1358-z.
Nguyen, V.P., Lloberas-Valls, O., Stroeven, M., Sluys, L.J., On the existence of representative volumes for softening quasi-brittle materials - a failure zone averaging scheme. Comput. Methods Appl. Mech. Eng. 199:45–48 (2010), 3028–3038, 10.1016/j.cma.2010.06.018.
Nguyen, V.P., Lloberas-Valls, O., Stroeven, M., Sluys, L.J., Computational homogenization for multiscale crack modeling. implementational and computational aspects. Int. J. Numer. Methods Eng. 89:2 (2012), 192–226, 10.1002/nme.3237.
Peerlings, R., Massart, T., Geers, M., A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking. Comput. Methods Appl. Mech. Eng. 193:30–32 (2004), 3403–3417, 10.1016/j.cma.2003.10.021 Computational Failure Mechanics.
Peerlings, R.H.J., De Borst, R., Brekelmans, W.A.M., De Vree, J.H.P., Gradient enhanced damage for quasi-brittle materials. Int. J. Numer. Methods Eng. 39:19 (1996), 3391–3403.
Perzyna, P., Thermodynamic Theory of Viscoplasticity Advances in Applied Mechanics, 11, 1971, Elsevier, 313–354, 10.1016/S0065-2156(08)70345-4.
Poh, L.H., Sun, G., Localizing gradient damage model with decreasing interactions. Int. J. Numer. Methods Eng. 110:6 (2017), 503–522, 10.1002/nme.5364 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.5364.
Vigueras, G., Sket, F., Samaniego, C., Wu, L., Noels, L., Tjahjanto, D., Casoni, E., Houzeaux, G., Makradi, A., Molina-Aldareguia, J.M., Vázquez, M., Jérusalem, A., An XFEM/CZM implementation for massively parallel simulations of composites fracture. Compos. Struct. 125 (2015), 542–557, 10.1016/j.compstruct.2015.01.053.
Wu, L., Chung, C.N., Major, Z., Adam, L., Noels, L., From SEM images to elastic responses: a stochastic multiscale analysis of UD fiber reinforced composites. Compos. Struct. 189 (2018), 206–227, 10.1016/j.compstruct.2018.01.051.
Wu, L., Tjahjanto, D., Becker, G., Makradi, A., Jérusalem, A., Noels, L., A micro meso-model of intra-laminar fracture in fiber-reinforced composites based on a discontinuous Galerkin/cohesive zone method. Eng. Fract. Mech. 104 (2013), 162–183 https://doi.org/10.1016/j.engfracmech.2013.03.018.
Xie, D., Waas, A.M., Discrete cohesive zone model for mixed-mode fracture using finite element analysis. Eng. Fract. Mech. 73:13 (2006), 1783–1796, 10.1016/j.engfracmech.2006.03.006.
