Novel rheological modelling of thermosets and unidirectional monotropic fibre-reinforced thermoset matrix composites

• Autorzy: Klasztorny Marian , Nycz Daniel B.
• Języki publikacji: EN

Abstrakty

EN

A refined, fully analytical rheological modelling of thermosetting polymers and unidirectional monotropic fibre-reinforced thermoset matrix (UFRT) composites is presented. New polymers and composites under normal conditions, fully relaxed from curing and post-curing stresses, are modelled. The theory includes quasi-static short-term/medium-term/long-term reversible rheological processes. Thermosets are isotropic materials exhibiting linearly viscoelastic shear strains and linearly elastic bulk strains. Fibres are monotropic (transversely isotropic) and linearly elastic materials. A generic function well reproducing the viscoelastic characteristics of thermosets and UFRT composites is a Mittag-Leffler fractional exponential function in an integral form. Coupled/uncoupled standard/inverse constitutive equations of linear rheology are formulated for thermosets and UFRT composites. The equations are mutually analytically transformable. New rheological models (coded H-R/H) for thermosets and UFRT composites are described by the smallest possible number of material constants. The thermoset is described by two independent elastic constants and three independent viscoelastic constants. The homogenized UFRT composite is described by five independent elastic constants and four independent viscoelastic constants, whereby two visco-elastic constants are common to the matrix and the composite. An improved homogenization theory of UFRT composites, based on analytical solutions of the selected tasks of the theory of linear elasticity, is formulated for monotropic fibres and positively validated experimentally. The viscoelastic constants of the thermoset are calculated analytically in an iterative loop using a long-term unidirectional tension creep experimental test. The viscoelastic constants of the UFRT composite are calculated analytically employing H-R/H shear/quasi-shear storage compliances and VECP (the viscoelastic-elastic correspondence principle) shear/quasi-shear storage compliances. The H-R/H rheological model was validated numerically for selected UFRT composites. The validation tests were performed on the enhanced reliability UFRT composites reported by Soden, Hinton, and Kaddour (Composites Science and Technology, 1998, 2002).

Słowa kluczowe

EN

thermoset; monotropic fibre-reinforced thermoset matrix composite; elasticity; rheology; homogenization; fractional exponential generic function; material modelling; identification; simulation; validation

PL

monotropowy kompozyt termoutwardzalny wzmocniony włóknami; sprężystość; reologia; homogenizacja; ułamkowa wykładnicza funkcja generyczna; modelowanie materiałów; identyfikacja; symulacja; walidacja

• Wydawca: Polskie Towarzystwo Materiałów Kompozytowych
• Czasopismo: Composites Theory and Practice
• Rocznik: 2023
• Tom: R. 23, nr 1
• Strony: 3--21
• Opis fizyczny: Bibliogr. 38 poz., rys., tab.

Twórcy

autor

Klasztorny Marian

• Institute of Technology, Jan Grodek State University in Sanok, ul. A. Mickiewicza 21, 38-500 Sanok, Poland

autor

Nycz Daniel B.

• Institute of Technology, Jan Grodek State University in Sanok, ul. A. Mickiewicza 21, 38-500 Sanok, Poland

Bibliografia

• [1] Klasztorny M., Nycz D.B., Bogusz P., Rheological effects in in-plane shear test and in-plane shear creep test on glass-vinyl-ester lamina, Composites Theory and Practice 2020, 20, 1, 35-42. https://kompozyty.ptmk.net/pliczki/pliki/1338_2020t01_marian-klasztorny-daniel-b-.pdf.
• [2] Klasztorny M., Nycz D.B., Modelling of linear elasticity and viscoelasticity of thermosets and unidirectional-fibre-reinforced thermoset-matrix composites – Part 1: Theory of modelling, Composites Theory and Practice 2022, 22, 1, 3-15. https://kompozyty.ptmk.net/pliczki/pliki/1382_2022t01_marian-klasztorny-daniel-b-.pdf.
• [3] Rabotnov J.N., Creep of elements of structures [in Russian], Nauka Press, Moscow 1966.
• [4] Schapery R.A., On the characterization of nonlinear visco-elastic materials, Polymer Engineering Science 1969, 9, 295-310.
• [5] Aboudi J., Micromechanical characterization of the non-linear viscoelastic behaviour of resin matrix composites, Composites Science and Technology 1990, 38, 4, 371-386.
• [6] Papanicolaou G.C., Zaoutsos S.P., Cardon A.H., Further development of a data reduction method for the nonlinear viscoelastic characterization of FRPs, Composites Part A 1999, 30, 7, 839-848, DOI: 10.1016/S1359-835X(99)00004-4.
• [7] Haj-Ali R., Muliana A., A micro-to-meso sublaminate model for the viscoelastic analysis of thick-section multi- layered FRP composite structures, Mechanics of Time-Dependent Materials 2008, 12, 1, 69-93, DOI: 10.1007/s11043-007-9041-6.
• [8] Falahatgar S.R., Salehi M., Nonlinear viscoelastic response of unidirectional polymeric laminated composite plates under bending loads, Applied Composite Materials 2011, 18, 6, 471-483, DOI: 10.1007/s10443-011-9212-0.
• [9] Jeon J., Kim J., Muliana A., Modeling time-dependent and inelastic response of fiber reinforced polymer composites, Computational Materials Science 2013, 70, 37-50, DOI: 10.1016/j.commatsci.2012.12.022.
• [10] Nunes S.G., Saseendran S., Joffe R. et al., On temperature- related shift factors and master curves in viscoelastic constitutive models for thermoset polymers, Mechanics of Composite Materials 2020, 56, 5, 573-590, DOI: 10.1007/s11029-020-09905-2.
• [11] Kontou E., Tensile creep behavior of unidirectional glass-fiber polymer composites, Polymer Composites 2005, 26, 3, 287-292, DOI: 10.1002/pc.20098.
• [12] Starkova O., Aniskevich A., Limits of linear viscoelastic behavior of polymers, Mechanics of Time-Dependent Materials 2007, 11, 2, 111-126, DOI: 10.1007/s11043-007-9036-3.
• [13] Muliana A.H., Sawant S., Responses of viscoelastic polymer composites with temperature and time dependent constituents, Acta Mechanica 2009, 204, 3, 155-173. DOI: 10.1007/s00707-008-0052-4.
• [14] Ascione L., Berardi V.P., D'Aponte A., A viscoelastic constitutive law for FRP materials, International Journal of Computational Methods in Engineering Science and Mechanics 2011, 12, 5, 225-232, DOI: 10.1080/15502281003660211.
• [15] Zhang X., Huang Q., Chen J. et al., Prediction of viscoelastic behavior of unidirectional polymer matrix composites, Journal of Wuhan University of Technology: Materials Science Edition 2016, 31, 3, 695-699, DOI: 10.1007/s11595-016-1431-7.
• [16] Kotelnikova-Weiler N., Baverel O., Ducoulombier N. et al., Progressive damage of a unidirectional composite with a viscoelastic matrix, observations and modelling, Composite Structures 2018, 188, 297-312, DOI: 10.1016/j.compstruct.2017.12.067.
• [17] Cardoso D.C.T., Harries K.A., A viscoelastic model for time-dependent behavior of pultruded GFRP, Construction and Building Materials 2019, 208, 63-74, DOI: 10.1016/j.conbuildmat.2019.02.155.
• [18] Berardi V.P., Perrella M., Armentani E. et al., Experimental investigation and numerical modeling of creep response of glass fiber reinforced polymer composites, Fatigue Fract. Eng. M 2021, 44, 4, 1085-1095, DOI: 10.1111/ffe.13415.
• [19] Di Gennaro L., Daghia F., Olive M. et al., A new mechanism-based temperature-dependent viscoelastic model for unidirectional polymer matrix composites based on Cartan decomposition, European Journal of Mechanics A – Solids 2021, 90, 104364, DOI: 10.1016/j.euromechsol.2021.104364.
• [20] Wilczynski A.P., Klasztorny M., Determination of complex compliances of fibrous polymeric composites, Journal of Composite Materials 2000, 34, 1, 2-26, DOI: 10.1177/002199830003400101.
• [21] Klasztorny M., Wilczynski A.P., Constitutive equations of viscoelasticity and estimation of viscoelastic parameters of unidirectional fibrous polymeric composites, Journal of Composite Materials 2000, 34, 19, 1624-1639, DOI: 10.1106/K8KV-7NEN-5Q04-G217.
• [22] Klasztorny M., Wilczynski A.P., Witemberg-Perzyk D., A rheological model of polymeric materials and identification of its parameters, J Theor App Mech-Pol 2001, 39, 1, 13-32. http://www.ptmts.org.pl/jtam/index.php/jtam/issue/view/v39n1.
• [23] Wilczynski A.P., Klasztorny M., Modelling of fibrous polymeric composites in the viscoelastic range [in Polish], Kompozyty (Composites) 2002, 2, 3, 97-102. https://kompozyty.ptmk.net/pliczki/pliki/semVI_16.pdf.
• [24] Klasztorny M., Gieleta R., Modelling of viscoelastic resins as matrices of fibre-reinforced polymeric composites [in Polish], Kompozyty (Composites) 2002, 2, 3, 103-107, https://kompozyty.ptmk.net/pliczki/pliki/semVI_17.pdf.
• [25] Klasztorny M., Gieleta R., The HWKK rheological model for resins, J. Theor. App. Mech.-Pol. 2002, 40, 4, 939-960, http://www.ptmts.org.pl/jtam/index.php/jtam/issue/view/v40n4.
• [26] Klasztorny M., Constitutive modelling of resins in compliance domain, Mechanics of Composite Materials 2004, 40, 4, 349-358, DOI: 10.1023/B:MOCM.0000039751.74145.63.
• [27] Klasztorny M., Constitutive modelling of resins in stiffness domain, Mechanics of Composite Materials 2004, 40, 5, 443-452, DOI: 10.1023/B:MOCM.0000047235.48540.fc.
• [28] Klasztorny M., Numerical simulation of rheological processes in hardening plastics under stress control, Mechanics of Composite Materials 2007, 43, 2, 133-140, DOI: 10.1007/s11029-007-0014-2.
• [29] Klasztorny M., Nycz D.B., Modelling of linear elasticity and viscoelasticity of thermosets and unidirectional-fibre-reinforced thermoset-matrix composites – Part 2: Homogenization and numerical analysis, Composites Theory and Practice 2022, 22, 1, 25-39, https://kompozytyptmk.net/pliczki/pliki/1385_2022t01_marian-klasztorny-daniel-b-.pdf..
• [30] Klasztorny M., Konderla P., Piekarski R., An exact stiffness theory for unidirectional xFRP composites, Mechanics of Composite Materials 2009, 45, 1, 77-104, DOI: 10.1007/s11029-009-9064-y.
• [31] Soden P.D., Hinton M.J., Kaddour A.S., Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates, Composites Science and Technology 1998, 58, 7, 1011-1022, DOI: 10.1016/S0266-3538(98)00078-5.
• [32] Soden P.D., Hinton M.J., Kaddour A.S., Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: failure exercise benchmark data, Composites Science and Technology 2002, 62, 1489-1514, DOI: 10.1016/S0266-3538(02)00093-3.
• [33] Wilczynski A.P., A basic theory of reinforcement for unidirectional fibrous composites, Composites Science and Technology 1990, 38, 4, 327-337, DOI: 10.1016/0266-3538(90)90019-2.
• [34] Wilczynski A.P., Lewinski J., Predicting the properties of unidirectional fibrous composites with monotropic reinforcement, Composites Science and Technology 1995, 55, 2, 139-143, DOI: 10.1016/0266-3538(95)00090-9.
• [35] Klasztorny M., Urbanski A., Application of the finite element method to improve quasi-exact reinforcement theory of fibrous polymeric composites, Mechanics of Composite Materials 2005, 41, 1, 55-64, DOI: 10.1007/s11029-005-0007-y.
• [36] Daniel I.M., Ishai O., Engineering Mechanics of Composite Materials, Oxford University Press, New York-Oxford 1994.
• [37] Klasztorny M., Coupled and uncoupled constitutive equations of linear elasticity and viscoelasticity of orthotropic materials, J. Theor. App. Mech.-Pol. 2008, 46, 1, 3-20, https://www-1webofscience-1com-100003ee80000.han.wat.edu.pl/wos/woscc/full-record/WOS:000258574900001.
• [38] Efunda Engineering Fundamentals. Abscissas and Weights of Gauss-Legendre Integration, https://www.efunda.com/math/num_integration/findgausslegendre.cfm (accessed 15.05.2021).

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).