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Archive of Applied Mechanics

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28-09-2018 | Original

Inter-relationships among stiffness matrix components for general laminates with transverse cracks in oblique plies

Authors: N. D. Barulich, L. A. Godoy, P. M. Dardati

Published in: Archive of Applied Mechanics | Issue 2/2019

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Abstract

In this paper, nine inter-relationships linking the stiffness matrix components of symmetrical or unsymmetrical laminates having transverse matrix cracks in some of the off-axis plies is presented. The crack closure condition under membrane and bending deformations is established and used to obtain the inter-relationships. The derived crack closure conditions and inter-relationships are validated using a numerical model based on previous work by the authors. These inter-relationships include the eighteen stiffness matrix components and are exact within the assumptions made in the classical lamination theory. When using a two-scale finite element-based model, six loading cases would be needed to obtain the complete stiffness matrix. With the obtained inter-relationships, only four loading cases would be needed, thus saving a third of the total amount of information and computing time.

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Barbero, E.J.: Introduction to Composite Materials Design, 3rd edn. CRC, Boca Raton (2018)

McCartney, L.N.: Microlevel approaches to the modelling of damage in composite materials: generalised plane strain analysis. In: Talreja, R., Varna, J. (eds.) Modelling Damage, Fatigue and Failure of Composite Materials, pp. 289–327. Woodhead Publishing, Cambridge (2016)CrossRef

Varna, J.: Thermoelastic constants of damaged laminates: COD- and CSD-based methods. In: Talreja, R., Varna, J. (eds.) Modelling Damage, Fatigue and Failure of Composite Materials, pp. 243–287. Woodhead Publishing, Cambridge (2016)CrossRef

Zhuang, L., Talreja, R., Varna, J.: Transverse crack formation in unidirectional composites by linking of fibre/matrix debond cracks. Compos. A Appl. Sci. Manuf. 107, 294–303 (2018). https://doi.org/10.1016/j.compositesa.2018.01.013 CrossRef

Barbero, E.J., Cabrera Barbero, J.: Determination of material properties for progressive damage analysis of carbon/epoxy laminates. Mech. Adv. Mater. Struct. (2018). https://doi.org/10.1080/15376494.2018.1430281

Dvorak, G.J., Laws, N., Hejazi, M.: Analysis of progressive matrix cracking in composite laminates I. Thermoelastic properties of a ply with cracks. J. Compos. Mater. 19(3), 216–34 (1985). https://doi.org/10.1177/002199838501900302 CrossRef

Li, S., Reid, S.R., Soden, P.D.: A finite strip analysis of cracked laminates. Mech. Mater. 18(4), 289–311 (1994). https://doi.org/10.1016/0167-6636(94)90041-8 CrossRef

Adolfsson, E., Gudmundson, P.: Thermoelastic properties in combined bending and extension of thin composite laminates with transverse matrix cracks. Int. J. Solids Struct. 34(16), 2035–2060 (1997). https://doi.org/10.1016/S0020-7683(96)00156-4 CrossRefMATH

Adumitroaie, A., Barbero, E.J., Schagerl, M.: Matrix cracking in non-symmetric laminates under combined membrane and flexural loading. Int. J. Mater. Mech. Man. 4, 223–231 (2016). https://doi.org/10.18178/ijmmm.2016.4.4.261

10.

Adumitroaie, A., Barbero, E.J.: Intralaminar damage model for laminates subjected to membrane and flexural deformations. Mech. Adv. Mater. Struct. 22(9), 705–716 (2015). https://doi.org/10.1080/15376494.2013.796541 CrossRef

11.

Schmitz, A., Horst, P.: A finite element unit-cell method for homogenised mechanical properties of heterogeneous plates. Compos. A. Appl. Sci. Manuf. 61, 23–32 (2014). https://doi.org/10.1016/j.compositesa.2014.01.014 CrossRef

12.

Hajikazemi, M., Sadr, M.H., Varna, J.: Analysis of cracked general cross-ply laminates under general bending loads: a variational approach. J. Compos. Mater. 51(22), 3089–3109 (2017). https://doi.org/10.1177/0021998316682364 CrossRef

13.

Barbero, E.J., Cabrera Barbero, J.: Analytical solution for bending of laminated composites with matrix cracks. Compos. Struct. 135, 140–155 (2016). https://doi.org/10.1016/j.compstruct.2015.09.021 CrossRef

14.

Pupurs, A., Varna, J., Loukil, M., Kahla, H.B., Mattsson, D.: Effective stiffness concept in bending modeling of laminates with damage in surface 90-layers. Compos. A Appl. Sci. Manuf. 82, 244–252 (2016). https://doi.org/10.1016/j.compositesa.2015.11.012 CrossRef

15.

Adolfsson, E., Gudmundson, P.: Matrix crack induced stiffness reductions in \([(0m/90n/+ \theta p/-\theta q)S]M\) composite laminates. Compos. Eng. 5(1), 107–123 (1995). https://doi.org/10.1016/0961-9526(95)93983-3 CrossRef

16.

Li, S., Singh, C.V., Talreja, R.: A representative volume element based on translational symmetries for FE analysis of cracked laminates with two arrays of cracks. Int. J. Solids Struct. 46(7), 1793–1804 (2009). https://doi.org/10.1016/j.ijsolstr.2009.01.009 CrossRefMATH

17.

Barbero, E.J., Cortes, D.H.: A mechanistic model for transverse damage initiation, evolution, and stiffness reduction in laminated composites. Compos. B Eng. 41(2), 124–132 (2010). https://doi.org/10.1016/j.compositesb.2009.10.001 CrossRef

18.

Moure, M.M., Sanchez-Saez, S., Barbero, E., Barbero, E.J.: Analysis of damage localization in composite laminates using a discrete damage model. Compos. B Eng. 66, 224–32 (2014). https://doi.org/10.1016/j.compositesb.2014.05.015 CrossRef

19.

Moure, M.M., García-Castillo, S.K., Sánchez-Sáez, S., Barbero, E., Barbero, E.J.: Influence of ply cluster thickness and location on matrix cracking evolution in open-hole composite laminates. Compos. B Eng. 95, 40–47 (2016). https://doi.org/10.1016/j.compositesb.2016.03.091 CrossRef

20.

Barbero, E.J., Shahbazi, M.: Determination of critical energy release rates for discrete damage mechanics analysis in ANSYS. Theor. Appl. Fract. Mech. 92, 99–112 (2017). https://doi.org/10.1016/j.tafmec.2017.05.016 CrossRef

21.

Carraro, P.A., Quaresimin, M.: A stiffness degradation model for cracked multidirectional laminates with cracks in multiple layers. Int. J. Solids Struct. 58, 34–51 (2015). https://doi.org/10.1016/j.ijsolstr.2014.12.016 CrossRef

22.

Montesano, J., Singh, C.V.: A synergistic damage mechanics based multiscale model for composite laminates subjected to multiaxial strains. Mech. Mater. 83, 72–89 (2015). https://doi.org/10.1016/j.mechmat.2015.01.005 CrossRef

23.

Montesano, J., McCleave, B., Singh, C.V.: Prediction of ply crack evolution and stiffness degradation in multidirectional symmetric laminates under multiaxial stress states. Compos. Part B Eng. 133, 53–67 (2018). https://doi.org/10.1016/j.compositesb.2017.09.016 CrossRef

24.

Hajikazemi, M., McCartney, L.N., Van Paepegem, W., Sadr, M.H.: Theory of variational stress transfer in general symmetric composite laminates containing non-uniformly spaced ply cracks. Compos. A Appl. Sci. Manuf. 107, 374–386 (2018). https://doi.org/10.1016/j.compositesa.2018.01.021 CrossRef

25.

Jagannathan, N., Gururaja, S., Manjunatha, C.M.: Probabilistic strength based matrix crack evolution in multi-directional composite laminates. Compos. B Eng. 87, 263–73 (2016). https://doi.org/10.1016/j.compositesb.2015.09.050 CrossRef

26.

Mohammadi, B., Pakdel, H.: Experimental and variational-based analytical investigation of multiple cracked angle-ply laminates. Eng. Fract. Mech. 190, 198–212 (2017). https://doi.org/10.1016/j.engfracmech.2017.12.003 CrossRef

27.

Varna, J.: Crack separation based models for microcracking. In: Zweben, C.H., Beaumont, P. (eds.) Comprehensive Composite Materials, vol. II, 2nd edn, pp. 192–220. Elsevier, Oxford (2018)CrossRef

28.

Hashin, Z.: Analysis of cracked laminates: a variational approach. Mech. Mater. 4(2), 121–136 (1985). https://doi.org/10.1016/0167-6636(85)90011-0 CrossRef

29.

McCartney, L.N.: Stress transfer based models for microcracking in laminates. In: Zweben, C.H., Beaumont, P. (eds.) Comprehensive Composite Materials, vol. II, 2nd edn, pp. 167–191. Elsevier, Oxford (2018)CrossRef

30.

Whitney, J.M.: Effective thermo-elastic constants angle-ply laminates containing 90 degree ply cracks. J. Compos. Mater. 35(15), 1373–91 (2001). https://doi.org/10.1106/RA4L-4FC2-LQX8-LF5J

31.

McCartney, L.N.: Predicting transverse crack formation in cross-ply laminates. Compos. Sci. Technol. 58(7), 1069–1081 (1998). https://doi.org/10.1016/S0266-3538(96)00142-X CrossRef

32.

McCartney, L.N.: Physically based damage models for laminated composites. Proc. Inst. Mech. Eng. L J. Mater. Des. Appl. 217(3), 163–199 (2003). https://doi.org/10.1177/146442070321700301

33.

McCartney, L.N.: Derivations of energy-based modelling for ply cracking in general symmetric laminates. J. Compos. Mater. 47(20–21), 2641–2673 (2013). https://doi.org/10.1177/0021998313492359 CrossRef

34.

McCartney, L.N., Blazquez, A., Paris, F.: Energy-based delamination theory for biaxial loading in the presence of thermal stresses. Compos. Sci. Technol. 72(14), 1753–1766 (2012). https://doi.org/10.1016/j.compscitech.2012.06.015 CrossRef

35.

Barulich, N.D., Godoy, L.A., Dardati, P.M.: Evaluation of cross-ply laminate stiffness with a non-uniform distribution of transverse matrix cracks by means of a computational meso-mechanic model. Compos. Struct. 185, 561–572 (2018). https://doi.org/10.1016/j.compstruct.2017.11.063 CrossRef

36.

Petracca, M., Pelà, L., Rossi, R., Oller, S., Camata, G., Spacone, E.: Multiscale computational first order homogenization of thick shells for the analysis of out-of-plane loaded masonry walls. Comput. Methods Appl. Mech. Eng. 315, 273–301 (2017). https://doi.org/10.1016/j.cma.2016.10.046 MathSciNetCrossRefMATH

37.

Barbero, E.J., Cosso, F.A., Campo, F.A.: Benchmark solution for degradation of elastic properties due to transverse matrix cracking in laminated composites. Compos. Struct. 98, 242–252 (2013). https://doi.org/10.1016/j.compstruct.2012.11.009 CrossRef

38.

Abaqus v. 6.7: Dassault Systèmes, Providence (2009)

39.

Piezel, B., Mercatoris, B.C., Trabelsi, W., Laiarinandrasana, L., Thionnet, A., Massart, T.J.: Bending effect on the risk for delamination at the reinforcement/matrix interface of 3D woven fabric composite using a shell-like RVE. Compos. Struct. 94(8), 2343–2357 (2012). https://doi.org/10.1016/j.compstruct.2012.03.015 CrossRef

40.

Otero, F., Oller, S., Martinez, X., Salomón, O.: Numerical homogenization for composite materials analysis. Comparison with other micro mechanical formulations. Compos. Struct. 122, 405–416 (2015). https://doi.org/10.1016/j.compstruct.2014.11.041 CrossRef

41.

de Souza Neto, E.A., Feijóo, R.A.: On the equivalence between spatial and material volume averaging of stress in large strain multi-scale solid constitutive models. Mech. Mater. 40(10), 803–811 (2008). https://doi.org/10.1016/j.mechmat.2008.04.006 CrossRef

Title: Inter-relationships among stiffness matrix components for general laminates with transverse cracks in oblique plies
Authors: N. D. Barulich
L. A. Godoy
P. M. Dardati
Publication date: 28-09-2018
Publisher: Springer Berlin Heidelberg
Published in: Archive of Applied Mechanics / Issue 2/2019
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-018-1470-y

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