Two Constitutive Models Based on the Unified Shear Curve to Predict a Nonlinear Response of Fabric Carbon Fibre-Reinforced Plastics in the 2D Stress State
Source abstract
Abstract
Abstract In some case, polymer composites can exhibit a significantly nonlinear deformation behavior. The conventional approach to estimating the strength of a composite structure, in which the material is considered linearly elastic up to failure, can lead to significant errors and overloading. In this work, we examine the effectiveness of two relatively simple models taking into account the nonlinear deformation of the fabric composite with a thermosetting matrix. Both models are based on the assumption that the shear stress–strain curve is independent of the 2D stress state. On the one hand, this significantly simplifies the process of determining model parameters, because only standard tensile and shear tests are used. On the other hand, it is necessary to clearly understand the applicability limits of such models. Verification of deformation models was carried out based on the results of off-axis tensile tests on carbon fabric-reinforced composite specimens as well as composite specimens with the ±15° and ±30° lay-ups of the carbon fabric. Comparison of the calculated and experimental stress–strain curves shows that this approach can be successfully used in the analysis of the nonlinear mechanical behavior of fabric composites made of thermosetting polymers under shear strains up to 5% without significant errors.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Mechanical Behavior of Composites · Fiber-reinforced polymer composites · Natural Fiber Reinforced Composites
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (44)
Show source-provided references
1. Barbero, E.J., Introduction to Composite Materials Design, Boca Raton: CRC Press, 2011. https://doi.org/10.1201/978143989413210.1201/9781439894132 ↗
2. Mishnaevsky, Jr.L., Current Challenges of Wind Energy Development: Materials Science Aspects, Phys. Mesomech., 2021, vol. 24(5), pp. 533–540. https://doi.org/10.1134/S102995992105004010.1134/S1029959921050040 ↗
3. Harussani, M.M., Sapuan, S.M., Nadeem, G., Rafin, T., and Kirubaanand, W., Recent Applications of Carbon-Based Composites in Defence Industry: A Review, Def. Technol., 2022, vol. 18(8), pp. 1281–1300. https://doi.org/10.1016/j.dt.2022.03.00610.1016/j.dt.2022.03.006 ↗
4. Mallick, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Boca Raton: CRC Press, 2007. https://doi.org/10.1201/978142000598110.1201/9781420005981 ↗
5. Fallahi, H., Taheri-Behrooz, F., and Asadi, A., Nonlinear Mechanical Response of Polymer Matrix Composites: A Review, Polym. Rev., 2020, vol. 60(1), pp. 42–85. https://doi.org/10.1080/15583724.2019.165623610.1080/15583724.2019.1656236 ↗
6. David Müzel, S., Bonhin, E.P., Guimarães, N.M., and Guidi, E.S., Application of the Finite Element Method in the Analysis of Composite Materials: A Review, Polymers, 2020, vol. 12, p. 818. https://doi.org/10.3390/polym1204081810.3390/polym12040818 ↗
7. Volegov, P.S., Gribov, D.S., and Trusov, P.V., Damage and Fracture: Classical Continuum Theories, Phys. Mesomech, 2017, vol. 20(2), pp. 157–173.10.1134/S1029959917020060 ↗
8. Hahn, H.T., Nonlinear Behavior of Laminated Composites, J. Compos. Mater., 1973, vol. 7(2), pp. 257–271. https://doi.org/10.1177/00219983730070020910.1177/002199837300700209 ↗
9. Chang, F.K. and Chang, K.Y., A Progressive Damage Model for Laminated Composites Containing Stress Concentrations, J. Compos. Mater., 1987, vol. 21(9), pp. 834–855. https://doi.org/10.1177/0021998387021009010.1177/00219983870210090 ↗
10. Lomakin, E.V. and Fedulov, B.N., Nonlinear Anisotropic Elasticity for Laminate Composites, Meccanica, 2015, vol. 50, pp. 1527–1535. https://doi.org/10.1007/s11012-015-0104-510.1007/s11012-015-0104-5 ↗
11. McCarthy, C.T., O’Higgins, R.M., and Frizzell, R.M., A Cubic Spline Implementation of Non-Linear Shear Behaviour in Three-Dimensional Progressive Damage Models for Composite Laminates, Compos. Struct., 2010, vol. 92, pp. 173–181. https://doi.org/10.1016/j.compstruct.2009.07.02510.1016/j.compstruct.2009.07.025 ↗
12. Ladeveze, P. and LeDantec, E., Damage Modelling of the Elementary Ply for Laminated Composites, Compos. Sci. Technol., 1992, vol. 43(3), pp. 257–267. https://doi.org/10.1016/0266-3538(92)90097-M10.1016/0266-3538(92)90097-M ↗
13. Matzenmiller, A., Lubliner, J., and Taylor, R.L., A Constitutive Model for Anisotropic Damage in Fiber-Composites, Mech. Mater., 1995, vol. 20(2), pp. 125–152. https://doi.org/10.1016/0167-6636(94)00053-010.1016/0167-6636(94)00053-0 ↗
14. Hochard, C., Aubourg, P.A., and Charles, J.P., Modelling of the Mechanical Behaviour of Woven-Fabric CFRP Laminates up to Failure, Compos. Sci. Technol., 2001, vol. 61(2), pp. 221–230. https://doi.org/10.1016/S0266-3538(00)00199-810.1016/S0266-3538(00)00199-8 ↗
15. Schuecker, C. and Pettermann, H.E., A Continuum Damage Model for Fiber Reinforced Laminates Based on Ply Failure Mechanisms, Compos. Struct., 2006, vol. 76(1-2), pp. 162–173. https://doi.org/10.1016/j.compstruct.2006.06.02310.1016/j.compstruct.2006.06.023 ↗
16. Laux, T., Gan, K.W., Dulieu-Barton, J.M., and Thomsen, O.T., A Simple Nonlinear Constitutive Model Based on Non-Associative Plasticity for UD Composites: Development and Calibration Using a Modified Arcan Fixture, Int. J. Solids Struct., 2019, vol. 162, pp. 135–147. https://doi.org/10.1016/j.ijsolstr.2018.12.00410.1016/j.ijsolstr.2018.12.004 ↗
17. Ogihara, S., Nonlinear Mechanical Response of CFRP Laminates under Off-Axis Tensile Loading, Sci. Eng. Compos. Mater., 2010, vol. 17(2), pp. 133–141. https://doi.org/10.1515/SECM.2010.17.2.13310.1515/SECM.2010.17.2.133 ↗
18. Cho, J., Fenner, J., Werner, B., and Daniel, I.M., A Constitutive Model for Fiber-Reinforced Polymer Composites, J. Compos. Mater., 2010, vol. 44(26), pp. 3133–3150. https://doi.org/10.1177/002199831037154710.1177/0021998310371547 ↗
19. Ogihara, S. and Moriwaki, S., Tensile Creep Deformation in Unidirectional Carbon/Epoxy Laminates under Off-Axis Loading, J. Mater. Sci., 2004, vol. 39(10), pp. 3465–3467. https://doi.org/10.1023/B:JMSC.0000026952.29053.f110.1023/B:JMSC.0000026952.29053.f1 ↗
20. Vyas, G.M., Pinho, S.T., and Robinson, P., Constitutive Modelling of Fibre-Reinforced Composites with Unidirectional Plies Using a Plasticity-Based Approach, Compos. Sci. Technol., 2011, vol. 71(8), pp. 1068–1074. https://doi.org/10.1016/j.compscitech.2011.03.00910.1016/j.compscitech.2011.03.009 ↗
21. Wang, J. and Xiao, Y., Some Improvements on Sun-Chen’s One-Parameter Plasticity Model for Fibrous Composites (Part II: Finite Element Method Implementation and Applications), J. Compos. Mater., 2017, vol. 51(4), pp. 533 – 545. https://doi.org/10.1177/002199831664978010.1177/0021998316649780 ↗
22. Yokozeki, T., Ogihara, S., Yoshida, S., and Ogasawara, T., Simple Constitutive Model for Nonlinear Response of Fiber-Reinforced Composites with Loading-Directional Dependence, Compos. Sci. Technol., 2007, vol. 67(1), pp. 111–118. https://doi.org/10.1016/j.compscitech.2006.03.02410.1016/j.compscitech.2006.03.024 ↗
23. Ogihara, S. and Reifsnider, K.L., Characterization of Nonlinear Behavior in Woven Composite Laminates, Appl. Comp. Mater., 2002, vol. 9(4), pp. 249–263. https://doi.org/10.1023/A:101606922025510.1023/A:1016069220255 ↗
24. Espinosa, H.D., Lu, H.C., Zavattieri, P.D., and Dwivedi, S., A 3D Finite Deformation Anisotropic Visco-Plasticity Model for Fiber Composites, J. Compos. Mater., 2001, vol. 35(5), pp. 369–410. https://doi.org/10.1177/00219980177266215410.1177/002199801772662154 ↗
25. Jang, J., Jeon, S.Y., Choi, J.H., Shim, W., Cho, J.M., Yoon, S.J., and Yu, W.R., Mechanical Analysis of Fiber-Reinforced Plastics Using an Elastoplastic-Damage Constitutive Equation Considering Asymmetric Material Behavior, Compos. Struct., 2021, vol. 272, p. 114268. https://doi.org/10.1016/j.compstruct.2021.11426810.1016/j.compstruct.2021.114268 ↗
26. Sun, C.T. and Chen, J.L., A Simple Flow Rule for Characterizing Nonlinear Behavior of Fiber Composites, J. Compos. Mater., 1989, vol. 23(10), pp. 1009–1020. https://doi.org/10.1177/00219983890230100410.1177/002199838902301004 ↗
27. Hill, R., The Mathematical Theory of Plasticity, vol. 11, Oxford University Press, 1998. https://doi.org/10.1093/oso/9780198503675.001.000110.1093/oso/9780198503675.001.0001 ↗
28. Puck, A. and Schürmann, H., Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models, Compos. Sci. Technol., 2002, vol. 62(12–13), pp. 1633–1662. https://doi.org/10.1016/S0266-3538(01)00208-110.1016/S0266-3538(01)00208-1 ↗
29. Hashin, Z., Fatigue Failure Criteria for Unidirectional Fiber Composites, J. Appl. Mech., 1980, vol. 47(4), pp. 329– 334. https://doi.org/10.1115/1.315774410.1115/1.3157744 ↗
30. Reiner, J., Feser, T., Schueler, D., Waimer, M., and Vaziri, R., Comparison of Two Progressive Damage Models for Studying the Notched Behavior of Composite Laminates under Tension, Compos. Struct., 2019, vol. 207, pp. 385–396. https://doi.org/10.1016/j.compstruct.2018.09.03310.1016/j.compstruct.2018.09.033 ↗
31. Yang, J., Yang, X., Zhu, H., Shi, D., Chen, X., and Qi, H., The Effect of Off-Axis Angles on the Mesoscale Deformation Response and Failure Behavior of an Orthotropic Textile Carbon-Epoxy Composite, Compos. Struct., 2018, vol. 206, pp. 952–959. https://doi.org/10.1016/j.compstruct.2018.08.01010.1016/j.compstruct.2018.08.010 ↗
32. Koohbor, B., Ravindran, S., and Kidane, A., Meso-Scale Study of Non-Linear Tensile Response and Fiber Trellising Mechanisms in Woven Composites, J. Reinf. Plast. Comp., 2016, vol. 35(12), pp. 986–995. https://doi.org/10.1177/073168441663377110.1177/0731684416633771 ↗
33. Tarnopol’skii, Y.M., Zhigun, I.G., and Polyakov, V.A., Spatially Reinforced Composites, CRC Press, 1991.
34. Leshkov, E.V. and Sapozhnikov, S.B., Modeling the Nonlinear Deformation and Damage of Carbon-Aramid Fabric Composites in Tension, Mech. Compos. Mater., 2020, vol. 56, pp. 591–600. https://doi.org/10.1007/s11029-020-09906-110.1007/s11029-020-09906-1 ↗
35. Sapozhnikov, S.B., Guseynov, K.A., and Zhikharev, M.V., Multiphase Fea-Approach for Non-Linear Deformation Prediction and Fibre-Reinforced Plastics Failure, Mech. Compos. Mater., 2023, vol. 59(2), pp. 283–298. https://doi.org/10.1007/s11029-023-10096-910.1007/s11029-023-10096-9 ↗
36. Daniels, H.E., The Statistical Theory of the Strength of Bundles of Threads. I, P. Roy. Soc. Lond. A. Mater., 1945, vol. 183(995), pp. 405–435. https://doi.org/10.1098/rspa.1945.001110.1098/rspa.1945.0011 ↗
37. Totry, E., Molina-Aldareguía, J.M., González, C., and LLorca, J., Effect of Fiber, Matrix and Interface Properties on the In-Plane Shear Deformation of Carbon-Fiber Reinforced Composites, Compos. Sci. Technol., 2010, vol. 70(6), pp. 970–980. https://doi.org/10.1016/j.compscitech.2010.02.01410.1016/j.compscitech.2010.02.014 ↗
38. ASTM D3039/D3039M-17, Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials, 2017.
39. ASTM D5379/D5379M-19e01, Standard Test Method for Shear Properties of Composite Materials by the V-Notched Beam Method, 2019.
40. ISO 527-5:2009, Plastics-Determination of Tensile Properties—Part 5: Test Conditions for Unidirectional FibreReinforced Plastic Composites, 2009.
41. Hufner, D.R. and Accorsi, M.L., A Progressive Failure Theory for Woven Polymer-Based Composites Subjected to Dynamic Loading, Compos. Struct., 2009, vol. 89(2), pp. 177–185. https://doi.org/10.1016/j.compstruct.2008.07.02310.1016/j.compstruct.2008.07.023 ↗
42. Kumosa, M., Odegard, G., Armentrout, D., Kumosa, L., Searles, K., and Sutter, J.K., Comparison of the ±45° Tensile and Iosipescu Shear Tests for Woven Fabric Composite Materials, J. Compos. Tech. Res., 2002, vol. 24(1), pp. 3–16. https://doi.org/10.1520/CTR10892J10.1520/CTR10892J ↗
43. Kawai, M. and Taniguchi, T., Off-Axis Fatigue Behavior of Plain Weave Carbon/Epoxy Fabric Laminates at Room and High Temperatures and Its Mechanical Modeling, Compos. A. Appl. S., 2006, vol. 37(2), pp. 243–256. https://doi.org/10.1016/j.compositesa.2005.07.00310.1016/j.compositesa.2005.07.003 ↗
44. Zhou, G., Sun, Q., Li, D., Meng, Z., Peng, Y., Zeng, D., and Su, X., Effects of Fabric Architectures on Mechanical and Damage Behaviors in Carbon/Epoxy Woven Composites under Multiaxial Stress States, Polym. Test., 2020, vol. 90, p. 106657. https://doi.org/10.1016/j.polymertesting.2020.10665710.1016/j.polymertesting.2020.106657 ↗