[en] This paper presents an extension of the so-called incremental-secant mean-field homogenisation (MFH) formulation accounting for fibre bundle failure and matrix cracking in Unidirectional (UD) composites. First a model for fibre bundle failure is developed bth failure probability of the carbon fibre described by a Weibull distribution. This fibre bundle failure model is then framed in a damage model of embedded bundles in a matrix by considering an exponential relation to describe the longitudinal stress build-up profile experimentally observed during failure of embedded fibre bundles. Cracking of the matrix in UD composites is accounted for through an anisotropic non-local damage model, which allows capturing the so-called 0∘ splits experimentally observed during the longitudinal tension of UD plies. A Mean Field Homogenisation (MFH) model is then extended to account for these damage models as component behaviours of the 2-phase composite material. A finite element multi-scale simulation of a notched laminate shows that the intra-laminar failure modes observed by an in situ experiment reported in the literature are well captured by the damage variables related to the matrix and fibre bundle failure processes. Inter-laminar failure is also captured by an extrinsic cohesive law introduced between the plies.
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Beyerlein, I.J., Phoenix, S.L., Statistics for the strength and size effects of microcomposites with four carbon fibers in epoxy resin. Compos Sci Technol 56:1 (1996), 75–92, 10.1016/0266-3538(95)00131-X.
Blassiau S, Thionnet A, Bunsell A. Micromechanisms of load transfer in a unidirectional carbon fibre-reinforced epoxy composite due to fibre failures. Part 1: Micromechanisms and 3d analysis of load transfer: The elastic case. Compos Struct 2006;74(3)303–18. doi: 10.1016/j.compstruct.2005.04.013.
Swolfs, Y., Gorbatikh, L., Verpoest, I., Stress concentrations in hybrid unidirectional fibre-reinforced composites with random fibre packings. Compos Sci Technol 85 (2013), 10–16, 10.1016/j.compscitech.2013.05.013.
St-Pierre, L., Martorell, N.J., Pinho, S.T., Stress redistribution around clusters of broken fibres in a composite. Compos Struct 168 (2017), 226–233, 10.1016/j.compstruct.2017.01.084.
van den Heuvel, P., Peijs, T., Young, R., Failure phenomena in two-dimensional multifibre microcomposites: 3. a raman spectroscopic study of the influence of inter-facial debonding on stress concentrations. Compos Sci Technol 58 (1998), 933–944.
van den Heuvel P, Goutianos S, Young R, Peijs T. Failure phenomena in fibre-reinforced composites. part 6: a finite element study of stress concentrations in unidirectional carbon fibre-reinforced epoxy composites. Compos Sci Technol 2004;64(5):645–56. doi: 10.1016/j.compscitech.2003.06.003.
Scott, A., Mavrogordato, M., Wright, P., Sinclair, I., Spearing, S., In situ fibre fracture measurement in carbon-epoxy laminates using high resolution computed tomography. Compos Sci Technol 71:12 (2011), 1471–1477, 10.1016/j.compscitech.2011.06.004.
Guerrero, J., Mayugo, J., Costa, J., Turon, A., A 3d progressive failure model for predicting pseudo-ductility in hybrid unidirectional composite materials under fibre tensile loading. Compos Part A Appl Sci Manuf 107 (2018), 579–591, 10.1016/j.compositesa.2018.02.005.
Okabe, T., Sekine, H., Ishii, K., Nishikawa, M., Takeda, N., Numerical method for failure simulation of unidirectional fiber-reinforced composites with spring element model. Compos Sci Technol 65:6 (2005), 921–933, 10.1016/j.compscitech.2004.10.030.
Tavares, R.P., Otero, F., Turon, A., Camanho, P.P., Effective simulation of the mechanics of longitudinal tensile failure of unidirectional polymer composites. Int J Fract 208:1 (2017), 269–285.
Tavares, R.P., Otero, F., Baiges, J., Turon, A., Camanho, P.P., A dynamic spring element model for the prediction of longitudinal failure of polymer composites. Comput Mater Sci 160 (2019), 42–52, 10.1016/j.commatsci.2018.12.048.
Pimenta, S., Pinho, S.T., Hierarchical scaling law for the strength of composite fibre bundles. J Mech Phys Solids 61:6 (2013), 1337–1356, 10.1016/j.jmps.2013.02.004.
Nguyen, T.-T., Waldmann, D., Bui, T.Q., Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures. J Comput Phys 386 (2019), 585–610, 10.1016/j.jcp.2019.02.022 https://www.sciencedirect.com/science/article/pii/S0021999119301391.
Zhang, P., Yao, W., Hu, X., Bui, T.Q., 3d micromechanical progressive failure simulation for fiber-reinforced composites. Compos Struct, 249, 2020, 112534, 10.1016/j.compstruct.2020.112534 https://www.sciencedirect.com/science/article/pii/S0263822319348421.
Tavares, R.P., Melro, A.R., Bessa, M.A., Turon, A., Liu, W.K., Camanho, P.P., Mechanics of hybrid polymer composites: analytical and computational study. Comput Mech 57:3 (2016), 405–421, 10.1007/s00466-015-1252-0.
Dean A, Asur Vijaya Kumar P, Reinoso J, Gerendt C, Paggi M, Mahdi E, Rolfes R. A multi phase-field fracture model for long fiber reinforced composites based on the puck theory of failure. Compos Struct 2020;251:112446. doi:https://doi.org/10.1016/j.compstruct.2020.112446. http://www.sciencedirect.com/science/article/pii/S0263822320307078.
Zhang, P., Hu, X., Bui, T.Q., Yao, W., Phase field modeling of fracture in fiber reinforced composite laminate. Int J Mech Sci, 161–162, 2019, 105008, 10.1016/j.ijmecsci.2019.07.007 https://www.sciencedirect.com/science/article/pii/S0020740318341729.
Zhang, P., Yao, W., Hu, X., Bui, T.Q., An explicit phase field model for progressive tensile failure of composites. Eng Fract Mech, 241, 2021, 107371, 10.1016/j.engfracmech.2020.107371 https://www.sciencedirect.com/science/article/pii/S0013794420309516.
Bui, T.Q., Hu, X., A review of phase-field models, fundamentals and their applications to composite laminates. Eng Fract Mech, 248, 2021, 107705, 10.1016/j.engfracmech.2021.107705.
Beyerlein, I.J., Phoenix, S., Stress concentrations around multiple fiber breaks in an elastic matrix with local yielding or debonding using quadratic influence superposition. J Mech Phys Solids 44:12 (1996), 1997–2039, 10.1016/S0022-5096(96)00068-3.
Wu, L., Sket, F., Molina-Aldareguia, J., Makradi, A., Adam, L., Doghri, I., Noels, L., A study of composite laminates failure using an anisotropic gradient-enhanced damage mean-field homogenization model. Compos Struct 126 (2015), 246–264, 10.1016/j.compstruct.2015.02.070.
Ponte Castañeda, P., Willis, J., The effect of spatial distribution on the effective behavior of composite materials and cracked media. J Mech Phys Solids 43:12 (1995), 1919–1951, 10.1016/0022-5096(95)00058-Q.
Wu, L., Noels, L., Adam, L., Doghri, I., A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models. Comput Methods Appl Mech Eng 233–236 (2012), 164–179, 10.1016/j.cma.2012.04.011.
Wu, L., Noels, L., Adam, L., Doghri, I., An implicit-gradient-enhanced incremental-secant mean-field homogenization scheme for elasto-plastic composites with damage. Int J Solids Struct 50:24 (2013), 3843–3860, 10.1016/j.ijsolstr.2013.07.022.
Peerlings, R., de Borst, R., Brekelmans, W., Ayyapureddi, S., Gradient-enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39 (1996), 3391–3403.
Geers M. Experimental analysis and computational modelling of damage and fracture. Ph.D. thesis, University of Technology, Eindhoven (Netherlands); 1997.
de Borst R, Verhoosel CV. Gradient damage vs phase-field approaches for fracture: similarities and differences. Comput Methods Appl Mech Eng 2016;312:78–94, phase Field Approaches to Fracture. doi: 10.1016/j.cma.2016.05.015. http://www.sciencedirect.com/science/article/pii/S0045782516303796.
Steinke, C., Zreid, I., Kaliske, M., On the relation between phase-field crack approximation and gradient damage modelling. Comput Mech 59:5 (2017), 717–735, 10.1007/s00466-016-1369-9.
Leclerc, J., Wu, L., Nguyen, V.D., Noels, L., A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous galerkin-cohesive band model framework. Int J Numer Methods Eng 113:3 (2018), 374–410.
van der Meer, F., Sluys, L., Continuum models for the analysis of progressive failure in composite laminates. J Compos Mater 43:20 (2009), 2131–2156, 10.1177/0021998309343054.
Zhao, Y., Weng, G., Transversely isotropic moduli of two partially debonded composites. Int J Solids Struct 34:4 (1997), 493–507, 10.1016/S0020-7683(96)00027-3.
Jain, A., Abdin, Y., Paepegem, W.V., Verpoest, I., Lomov, S.V., Effective anisotropic stiffness of inclusions with debonded interface for eshelby-based models. Compos Struct 131 (2015), 692–706, 10.1016/j.compstruct.2015.06.007.
Hobbiebrunken T, Hojo M, Adachi T, Jong CD, Fiedler B. Evaluation of interfacial strength in cf/epoxies using fem and in-situ experiments. Compos Part A Appl Sci Manuf 2006;37(12):2248–56, the 11th US-Japan Conference on Composite Materials. doi: 10.1016/j.compositesa.2005.12.021. http://www.sciencedirect.com/science/article/pii/S1359835X06000066.
Nguyen, V.-D., Wu, L., Noels, L., 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. Mech Mater 133 (2019), 193–213, 10.1016/j.mechmat.2019.02.017.
Cox, H.L., The elasticity and strength of paper and other fibrous materials. British J Appl Phys 3:3 (1952), 72–79, 10.1088/0508-3443/3/3/302.
van den Heuvel, P., Wubbolts, M., Young, R., Peijs, T., Failure phenomena in two-dimensional multi-fibre model composites: 5. A finite element study. Compos Part A Appl Sci Manuf 29:9 (1998), 1121–1135, 10.1016/S1359-835X(98)00089-X.
Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc London Ser A Math Phys Sci 1957;241(1226):376–96.
Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 1973;21(5):571–4, cited By (since 1996) 1814.
Berveiller, M., Zaoui, A., An extension of the self-consistent scheme to plastically-flowing polycrystals. J Mech Phys Solids 26:5–6 (1978), 325–344, 10.1016/0022-5096(78)90003-0.
Hill, R., Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids 13:2 (1965), 89–101, 10.1016/0022-5096(65)90023-2.
Pettermann, H.E., Plankensteiner, A.F., Böhm, H.J., Rammerstorfer, F.G., A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori-Tanaka approach. Comput Struct 71:2 (1999), 197–214, 10.1016/S0045-7949(98)00208-9.
Doghri, I., Ouaar, A., Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms. Int J Solids Struct 40:7 (2003), 1681–1712, 10.1016/S0020-7683(03)00013-1.
Doghri, I., Tinel, L., Micromechanical modeling and computation of elasto-plastic materials reinforced with distributed-orientation fibers. Int J Plast 21:10 (2005), 1919–1940, 10.1016/j.ijplas.2004.09.003 http://www.sciencedirect.com/science/article/pii/S0749641904001706.
Pierard, O., Doghri, I., Study of various estimates of the macroscopic tangent operator in the incremental homogenization of elasto-plastic composites. Int J Multiscale Comput Eng 4 (2006), 521–543.
Molinari, A., Canova, G., Ahzi, S., A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall 35:12 (1987), 2983–2994.
Masson, R., Bornert, M., Suquet, P., Zaoui, A., An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals. J Mech Phys Solids 48 (2000), 1203–1227.
Zaoui A, Masson R. Modelling stress-dependent transformation strains of heterogeneous materials. In: Bahei-El-Din YA, Dvorak GJ, Gladwell GML, editors. IUTAM symposium on transformation problems in composite and active materials, vol. 60 of Solid mechanics and its applications. Springer, Netherlands; 2002. p. 3–15. doi:10.1007/0-306-46935-9z_1.
Molinari, A., El Houdaigui, F., Tóth, L., Validation of the tangent formulation for the solution of the non-linear eshelby inclusion problem. Int J Plast 20:2 (2004), 291–307, 10.1016/S0749-6419(03)00038-X.
Mercier, S., Molinari, A., Homogenization of elastic-viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes. Int J Plast 25:6 (2009), 1024–1048, 10.1016/j.ijplas.2008.08.006 http://www.sciencedirect.com/science/article/pii/S0749641908001290.
Chaboche, J., Kanouté, P., Roos, A., On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites. Int J Plast 21:7 (2005), 1409–1434, 10.1016/j.ijplas.2004.07.001.
Wu, L., Noels, L., Adam, L., Doghri, I., A combined incremental–secant mean–field homogenization scheme with per–phase residual strains for elasto–plastic composites. Int J Plast 51 (2013), 80–102, 10.1016/j.ijplas.2013.06.006.
Suquet, P., Overall properties of nonlinear composites: A modified secant moduli theory and its link with ponte castañeda's nonlinear variational procedure. CR Acad Sci 320 (1995), 563–571.
Ponte Castañeda, P., Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J Mech Phys Solids 44:6 (1996), 827–862, 10.1016/0022-5096(96)00015-4.
Doghri, I., Brassart, L., Adam, L., Gérard, J.S., A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites. Int J Plast 27:3 (2011), 352–371, 10.1016/j.ijplas.2010.06.004.
Wu, L., Adam, L., Doghri, I., Noels, L., An incremental-secant mean-field homogenization method with second statistical moments for elasto-visco-plastic composite materials. Mech Mater 114 (2017), 180–200, 10.1016/j.mechmat.2017.08.006.
Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I - theory. J Mech Phys Solids 2002;50(4):737–57. doi:10.1016/S0022-5096(01)00099-0.
Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: II - applications. J Mech Phys Solids 2002;50(4):759–82. doi:10.1016/S0022-5096(01)00098-9.
Ponte Castañeda, P., A new variational principle and its application to nonlinear heterogeneous systems. SIAM J Appl Math 52:5 (1992), 1321–1341.
Lahellec N, Suquet P. On the effective behavior of nonlinear inelastic composites: I. incremental variational principles. J Mech Phys Solids 2007;55(9):1932–63. doi:10.1016/j.jmps.2007.02.003.
Lahellec N, Suquet P. On the effective behavior of nonlinear inelastic composites: II. a second-order procedure. J Mech Phys Solids 2007;55(9):1964–92. doi:10.1016/j.jmps.2007.02.004.
Brassart, L., Stainier, L., Doghri, I., Delannay, L., A variational formulation for the incremental homogenization of elasto-plastic composites. J Mech Phys Solids 59:12 (2011), 2455–2475, 10.1016/j.jmps.2011.09.004.
Brassart, L., Stainier, L., Doghri, I., Delannay, L., Homogenization of elasto-(visco) plastic composites based on an incremental variational principle. Int J Plast 36 (2012), 86–112, 10.1016/j.ijplas.2012.03.010.
Lahellec N, Suquet P. Effective response and field statistics in elasto-plastic and elasto-viscoplastic composites under radial and non-radial loadings. Int J Plast doi:10.1016/j.ijplas.2012.09.005.
Boudet, J., Auslender, F., Bornert, M., Lapusta, Y., An incremental variational formulation for the prediction of the effective work-hardening behavior and field statistics of elasto-(visco)plastic composites. Int J Solids Struct 83 (2016), 90–113, 10.1016/j.ijsolstr.2016.01.003 www.sciencedirect.com/science/article/pii/S0020768316000068.
Lemaitre, J., Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng 51:1–3 (1985), 31–49, 10.1016/0045-7825(85)90026-X.
Doghri, I., Numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage. Int J Numer Methods Eng 38:20 (1995), 3403–3431, 10.1002/nme.1620382004.
Peerlings, R., de Borst, R., Brekelmans, W., Geers, M., Gradient-enhanced damage modelling of concrete fracture. Mech Cohesive-Frictional Mat 3 (1998), 323–342.
Peerlings, R., Geers, M., de Borst, R., Brekelmans, W., A critical comparison of nonlocal and gradient-enhanced softening continua. Int J Solids Struct 38 (2001), 7723–7746.
Wu L, Zhang T, Maillard E, Adam L, Martiny P, Noels L. Per-phase spatial correlated damage models of ud fibre reinforced composites using mean-field homogenisation; applications to notched laminate failure and yarn failure of plain woven composites. Comput Struct.
Herráez, M., Fernández, A., Lopes, C.S., González, C., Strength and toughness of structural fibres for composite material reinforcement. Philos Trans A Math Phys Eng Sci 374:2071 (2016), 1–11, 10.1098/rsta.2015.0274.
Pinho, S., Iannucci, L., Robinson, P., Formulation and implementation of decohesion elements in an explicit finite element code. Compos Part A Appl Sci Manuf 37:5 (2006), 778–789, 10.1016/j.compositesa.2005.06.007.
Arteiro, A., Catalanotti, G., Melro, A., Linde, P., Camanho, P., Micro-mechanical analysis of the in situ effect in polymer composite laminates. Compos Struct 116 (2014), 827–840, 10.1016/j.compstruct.2014.06.014.
Hexcel Corporation. HexTowAS4, Carbon Fiber, Product Data Sheet; 2018.
Lucas, V., Golinval, J.-C., Paquay, S., Nguyen, V.-D., Noels, L., Wu, L., A stochastic computational multiscale approach; application to MEMS resonators. Comput Methods Appl Mech Eng 294 (2015), 141–167, 10.1016/j.cma.2015.05.019.
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, 2018, 1, 10.1016/j.compstruct.
Riks E. On formulations of path-following techniques for structural stability analysis. NASA STI/Recon Technical Report N 931 (1992) 16346–+.
Geers MGD. Enhanced solution control for physically and geometrically non-linear problems. part ii-comparative performance analysis. Int J Numer Methods Eng 1999;46(2):205–30. doi:10.1002/(SICI)1097-0207(19990920)46:2<205::AID-NME669>3.0.CO;2-S.
Wu, L., Becker, G., Noels, L., Elastic damage to crack transition in a coupled non-local implicit discontinuous galerkin/extrinsic cohesive law framework. Comput Methods Appl Mech Eng 279 (2014), 379–409, 10.1016/j.cma.2014.06.031 http://www.sciencedirect.com/science/article/pii/S0045782514002175.
Leclerc, J., Nguyen, V.-D., Pardoen, T., Noels, L., A micromechanics-based non-local damage to crack transition framework for porous elastoplastic solids. Int J Plast, 127, 2020, 102631, 10.1016/j.ijplas.2019.11.010.
Doghri, I., Mechanics of Deformable Solids- Linear, Nonlinear, Analytical and Computational Aspects. 2000, Springer-Verlag, Berlin.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.