Abstract
A modeling method of variable stiffness composite structures (VSCSs) with curved fiber trajectories has been developed. The fiber trajectories are aligned in the direction of maximum principal stress, and the VSCSs with variable fiber orientation and the variable fiber volume fraction are modeled on the basis of these trajectories. A material property degradation method taking into account the heterogeneity of material properties of the VSCSs is used to predict the ultimate load and model the progressive failure for a composite plate with a hole under tensile loading. It is shown that a transition from rectilinear reinforcement to curvilinear results in an increase in the ultimate load of the plate. The opportunity for simulation of a continuous fiber path for the VSCSs is presented, and the path could be used to produce the VSCSs by additive manufacturing (3D printing).
Similar content being viewed by others
References
Ghiasi, H., Pasini, D., Lessard, L.: Optimum stacking sequence design of composite materials Part I: Constant stiffness design. Compos. Struct. 90, 1–11 (2009)
Pedersen, P., Tobiesen, L., Jensen, S.H.: Shapes of orthotropic plates for minimum energy concentration. Mech. Struct. Mach. 20, 499–514 (1992)
Heller, M., Kaye, R., Rose, L.R.F.: A gradientless finite element procedure for shape optimization. J. Strain Anal. Eng. 34, 323–336 (1999)
Pedersen, P.: On optimal shapes in materials and structures. Struct. Multidiscip. Optim. 19, 169–182 (2000)
Gliesche, K., Hübner, T., Orawetz, H.: Application of the tailored fibre placement (TFP) process for a local reinforcement on an “open-hole” tension plate from carbon/epoxy laminates. Compos. Sci. Technol. 63, 81–88 (2003)
Zhu, Y., Qin, Y., Qi, S., Xu, H., Liu, D., Yan, C.: Variable angle tow reinforcement design for locally reinforcing an open-hole composite plate. Compos. Struct. 202, 162–169 (2018)
Katagiri, K., Honda, S., Minami, S., Tomizawa, Y., Kimu, D., Yamaguchi, S., Ehiro, T., Ozaki, T., Sonomura, H., Kawakita, S., Takemura, M., Yoshioka, Y., Sasaki, K.: CFRP manufacturing method by using electro-activated deposition and the effect of reinforcement with carbon fiber circumferentially around the hole. Compos. Struct. 207, 658–664 (2019)
Khan, S., Fayazbakhsh, K., Fawaz, Z., Nik, M.A.: Curvilinear variable stiffness 3D printing technology for improved open-hole tensile strength. Additive Manufacturing 24, 378–385 (2018)
Hyer, M.W., Charette, R.F.: Use of curvilinear fiber format in composite structure design. AIAA J. 29, 1011–1015 (1991)
Malakhov, A.V., Polilov, A.N.: Design of composite structures reinforced curvilinear fibres using FEM. Compos. Part A-Appl. S. 87, 23–28 (2016)
Zhang, H., Yang, D., Sheng, Y.: Performance-driven 3D printing of continuous curved carbon fibre reinforced polymer composites: A preliminary numerical study. Compos. Part B-Eng. 151, 256–264 (2018)
Mattheck, C.: Design in nature: learning from trees. Springer, Berlin (1998)
Zhu, Y., Liu, J., Liu, D., Xu, H., Yan, C., Huang, B., Hui, D.: Fiber path optimization based on a family of curves in composite laminate with a center hole. Compos. Part B-Eng. 111, 91–102 (2017)
Tosh, M.W., Kelly, D.W.: On the design, manufacture and testing of trajectorial fibre steering for carbon fibre composite laminates. Compos. Part A-Appl. S. 31, 1047–1060 (2000)
Gürdal, Z., Olmedo, R.: In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA J. 31, 751–758 (1993)
Lemaire, E., Zein, S., Bruyneel, M.: Optimization of composite structures with curved fiber trajectories. Compos. Struct. 131, 895–904 (2015)
Cho, H.K., Rowlands, R.E.: Optimizing fiber direction in perforated orthotropic media to reduce stress concentration. J. Compos. Mater. 43, 1177–1198 (2009)
Pedersen, P.: Examples of density, orientation, and shape-optimal 2D-design for stiffness and/or strength with orthotropic materials. Struct. Multidiscip. O. 26, 37–49 (2004)
Stodieck, O., Cooper, J.E., Weaver, P.M., Kealy, P.: Optimization of tow-steered composite wing laminates for aeroelastic tailoring. AIAA J. 53, 2203–2215 (2015)
Stodieck, O., Cooper, J.E., Weaver, P.M., Kealy, P.: Aeroelastic tailoring of a representative wing box using tow-steered composites. AIAA J. 55, 1425–1439 (2017)
Honda, S., Narita, Y.: Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers. Compos. Struct. 93, 902–910 (2011)
Tabakov, P.Y., Walker, M.: A technique for stiffness improvement by optimization of fiber steering in composite plates. Appl. Compos. Mater. 17, 453–461 (2010)
Bittrich, L., Spickenheuer, A., Almeida, J.H.S., Müller, S., Kroll, L., Heinrich, G.: Optimizing variable-axial fiber-reinforced composite laminates: the direct fiber path optimization concept. Math. Probl. Eng. Article ID 8260563, 11 (2019) pages
Huang, J., Haftka, R.T.: Optimization of fiber orientations near a hole for increased load-carrying capacity of composite laminates. Struct. Multidiscip. O. 30, 335–341 (2005)
Honda, S., Igarashi, T., Narita, Y.: Multi-objective optimization of curvilinear fiber shapes for laminated composite plates by using NSGA-II. Compos. Part B-Eng. 45, 1071–1078 (2013)
Hyer, M.W., Lee, H.H.: The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos. Struct. 18, 239–261 (1991)
Setoodeh, S., Abdalla, M.M., IJsselmuiden, S.T., Gürdal, Z.: Design of variable-stiffness composite panels for maximum buckling load. Compos. Struct. 87, 109–117 (2009)
Madeo, A., Groh, R.M.J., Zucco, G., Weaver, P.M., Zagari, G., Zinno, R.: Post-buckling analysis of variable-angle tow composite plates using Koiter’s approach and the finite element method. Thin. Wall. Struct. 110, 1–13 (2017)
Wang, P., Huang, X., Wang, Z., Geng, X., Wang, Y.: Buckling and post-buckling behaviors of a variable stiffness composite laminated wing box structure. Appl. Compos. Mater. 25, 449–467 (2018)
Koricho, E.G., Khomenko, A., Fristedt, T., Haq, M.: Innovative tailored fiber placement technique for enhanced damage resistance in notched composite laminate. Compos. Struct. 120, 378–385 (2015)
Lopes, C.S., Gürdal, Z., Camanho, P.P.: Variable-stiffness composite panels: Buckling and first-ply failure improvements over straight-fibre laminates. Comput. Struct. 86, 897–907 (2008)
Marouene, A., Boukhili, R., Chen, J., Yousefpour, A.: Buckling behavior of variable-stiffness composite laminates manufactured by the tow-drop method. Compos. Struct. 139, 243–253 (2016)
Marouene, A., Boukhili, R., Chen, J., Yousefpour, A.: Effects of gaps and overlaps on the buckling behavior of an optimally designed variable-stiffness composite laminates – A numerical and experimental study. Compos. Struct. 140, 556–566 (2016)
Jasso, A.J.M., Goodsell, J.E., Ritchey, A.J., Pipes, R.B., Koslowski, M.: A parametric study of fiber volume fraction distribution on the failure initiation location in open hole off-axis tensile specimen. Compos. Sci. Technol. 71, 1819–1825 (2011)
HexTow, I.M.7 Carbon fiber product data sheet, Hexcel Composites (2018)
HexPly 8552 Epoxy matrix product data sheet, Hexcel Composites (2016)
HexPly 8552 Product Data, Hexcel Composites (2016)
Marlett, K.: Hexcel 8552 IM7 unidirectional prepreg 190 gsm & 35%RC qualification material property data report. National institute for aviation research, Wichita State University, CAM-RP-2009-015, Revision A (2011)
Almeida, J.B.D.: Analytical and experimental study on the evolution of residual stresses in composite materials. MSD Thesis, University of Porto, pp. 110 (2005)
Davila, C.G., Camanho, P.P., Rose, C.A.: Failure criteria for FRP laminates. J. Compos. Mater. 39, 323–345 (2005)
Puck, A., Schürmann, H.: Failure analysis of FRP laminates by means of physically based phenomenological models. Compos. Sci. Technol. 62, 1633–1662 (2002)
Malakhov, A.V., Polilov, A.N.: Construction of trajectories of the fibers which bypass a hole and their comparison with the structure of wood in the vicinity of a knot. J. Mach. Manuf. Reliab. 42, 306–311 (2013)
Jones, R.M.: Mechanics of composite materials. Taylor & Francis, Abingdon (1999)
Chang, F.-K., Chang, K.-Y.: A progressive damage model for laminated composites containing stress concentrations. J. Compos. Mater. 21, 834–855 (1987)
Tan, S.C.: A progressive failure model for composite laminates containing openings. J. Compos. Mater. 25, 556–577 (1991)
Tan, S.C., Perez, J.: Progressive failure of laminated composites with a hole under compressive loading. J. Reinf. Plast. Comp. 12, 1043–1057 (1993)
McCarthy, C.T., McCarthy, M.A., Lawlor, V.P.: Progressive damage analysis of multi-bolt composite joints with variable bolt–hole clearances. Compos. Part B-Eng. 36, 290–305 (2005)
Hallett, S.R., Green, B.G., Jiang, W.G., Wisnom, M.R.: An experimental and numerical investigation into the damage mechanisms in notched composites. Compos. Part A-Appl. S. 40, 613–624 (2009)
Hoos, K., Iarve, E.V., Braginsky, M., Zhou, E., Mollenhauer, D.H.: Static strength prediction in laminated composites by using discrete damage modeling. J. Compos. Mater. 51, 1473–1492 (2017)
Guo, Z., Zhu, H., Li, Y., Han, X., Wang, Z.: Simulating initial and progressive failure of open-hole composite laminates under tension. Appl. Compos. Mater. 23, 1209–1218 (2016)
Hashin, Z.: Failure criteria for unidirectional fiber composites. J. Appl. Mech. 47, 329–334 (1980)
Camanho, P.P., Matthews, F.L.: A progressive damage model for mechanically fastened joints in composite laminates. J. Compos. Mater. 33, 2248–2280 (1999)
Tserpes, K.I., Labeas, G., Papanikos, P., Kermanidis, Th: Strength prediction of bolted joints in graphite/epoxy composite laminates. Compos. Part B-Eng. 33, 521–529 (2002)
Zhao, Y.: Stress and strength of laminated composite containing a circular hole. LSU Historical Dissertations and Theses, 6880, Louisiana State University, pp. 144 (1998)
Scotchply type: 1002. https://www.grtgenesis.com/wp-content/uploads/2017/05/high-pressure-laminates-651328.pdf
Mittelman, A., Roman, I.: Tensile properties of real unidirectional Kevlar/epoxy composites. Composites 21, 63–69 (1990)
Karam, G.N.: Effect of fibre volume on tensile properties of real unidirectional fibre-reinforced composites. Composites 22, 84–88 (1991)
Rangaraj, S.S., Bhaduri, S.B.: A modified rule-of-mixtures for prediction of tensile strengths of unidirectional fibre-reinforced composite materials. J. Mater. Sci. 29, 2795–2800 (1994)
Lee, C., Hwang, W.: Modified rule of mixtures for prediction of tensile strength of unidirectional fiber-reinforced composites. J. Mater. Sci. Lett. 17, 1601–1603 (1998)
Chan, M., Piggott, M.R.: Transverse tests for fibre-polymer adhesion evaluation. Compos. Interface. 6, 543–556 (1999)
Sathishkumar, T.P., Navaneethakrishnan, P., Shankar, S., Rajasekar, R.: Mechanical properties and water absorption of snake grass longitudinal fiber reinforced isophthalic polyester composites. J. Reinf. Plast. Comp. 32, 1211–1223 (2013)
Collings, T.A.: Transverse compressive behaviour of unidirectional carbon fibre reinforced plastics. Composites 5, 108–116 (1974)
Bazhenov, S.L., Kozey, V.V.: Transversal compression fracture of unidirectional fibre-reinforced plastics. J. Mater. Sci. 26, 2677–2684 (1991)
Purslow, D.: The shear properties of unidirectional carbon fibre reinforced plastics and their experimental determination. ARC-CP-1381 (1977)
Tian, X., Liu, T., Yang, C., Wang, Q., Li, D.: Interface and performance of 3D printed continuous carbon fiber reinforced PLA composites. Compos. Part A-Appl. S. 88, 198–205 (2016)
Ning, F., Cong, W., Qiu, J., Wei, J., Wang, S.: Additive manufacturing of carbon fiber reinforced thermoplastic composites using fused deposition modeling. Compos. Part B-Eng. 80, 369–378 (2015)
Matsuzaki, R., Ueda, M., Namiki, M., Jeong, T.K., Asahara, H., Horiguchi, K., Nakamura, T., Todoroki, A., Hirano, Y.: Three-dimensional printing of continuous-fiber composites by in-nozzle impregnation. Sci. Rep. 6, 23058 (2016)
Wang, Q., Tian, X., Huang, L., Li, D., Malakhov, A.V., Polilov, A.N.: Programmable morphing composites with embedded continuous fibers by 4D printing. Mater. Design. 155, 404–413 (2018)
Wang, X., Jiang, M., Zhou, Z., Gou, J., Hui, D.: 3D printing of polymer matrix composites: A review and prospective. Compos. Part B-Eng. 110, 442–458 (2017)
Liu, T., Tian, X., Zhang, M., Abliz, D., Li, D., Ziegmann, G.: Interfacial performance and fracture patterns of 3D printed continuous carbon fiber with sizing reinforced PA6 composites. Compos. Part A-Appl. S. 114, 368–376 (2018)
Markforged company. https://markforged.com
Anisoprint company. http://anisoprint.com
Shaanxi Fibertech Technology Development Co., Ltd. http://www.fibertech3d.com
Dataset. https://drive.google.com/drive/folders/13yILKmBR5V7lqZRTEGhgpPHUUpe-S2bW
Justo, J., Távara, L., García-Guzmán, L., París, F.: Characterization of 3D printed long fibre reinforced composites. Compos. Struct. 185, 537–548 (2018)
Pyl, L., Kalteremidou, K.-A., Hemelrijck, D.V.: Exploration of the design freedom of 3D printed continuous fibre-reinforced polymers in open-hole tensile strength tests. Compos. Sci. Technol. 171, 135–151 (2019)
Hou, Z., Tian, X., Zheng, Z., Zhang, J., Zhe, L., Li, D., Malakhov, A.V., Polilov, A.N.: A constitutive model for 3D printed continuous fiber reinforced composite structures with variable fiber content. Compos. Part B-Eng. 189, 107893 (2020)
Acknowledgements
This work was carried out with financial support from Russian Foundation for Basic Research and National Natural Science Foundation of China under projects 18-08-00372, 18-58-53020 and 51575430, 51811530107, respectively. The authors of the paper would like to thank Proof-Reading-Service.com (www.proof-reading-service.com) for proofreading & editing of the paper in English.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Malakhov, A.V., Polilov, A.N., Zhang, J. et al. A Modeling Method of Continuous Fiber Paths for Additive Manufacturing (3D Printing) of Variable Stiffness Composite Structures. Appl Compos Mater 27, 185–208 (2020). https://doi.org/10.1007/s10443-020-09804-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10443-020-09804-8