Skip to main content
SpringerLink
Log in

Accuracy Analysis on Counterweight-Balanced Column Bending Test

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

The counterweight-balanced column bending test (CWB-CBT) was developed by Fernandez and Murphey [1] to counter the gravity sag issue of column bending test and generate a better uniform bending stress state in characterizing thin composites’ bending behavior at large curvatures. When analyzing the test data the original processing method assumes that the specimen is under constant curvature deformation, but the sample is still subjected to small variable flexure moment and curvature due to concentrated compressive load.

Objective

Aims to evaluate the simplified processing method accuracy and provide comprehensive guidelines for CWB-CBT.

Methods

Euler’s elastica large deflection theory was applied to evaluate the curvature and moment error in the simplified solution. Laminate [0]4 and woven composites were selected to investigate the result accuracy by experimental validation and finite element model.

Results

Within the elastic range, the accuracy is independent of load and bending rigidity, but is related to the geometry. The simplified method tends to present higher stiffness results due to constant curvature assumption. A decreasing trend is exhibited for errors as the ratio of fixture arm span to coupon length increases. When the ratio reaches two, the curvature error is less than 5.7085%, and the bending moment error is under 3.2173‰. The error correction method is also provided.

Conclusions

The CWB-CBT can evaluate thin composites’ elastic bending behavior when considering the error correction. Attention should be paid to results reliability after material enters the nonlinear behavior stage.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Fernandez J, Murphey T (2018) A simple test method for large deformation bending of thin high strain composite flexures. 2018 AIAA Spacecraft Structures Conference. https://doi.org/10.2514/6.2018-0942

  2. Murphey T, Francis W, Davis B, Mejia-Ariza J, Santer M, Footdale J, Schmid K, Soykasap O, Guidanean K, Warren P (2015) High strain composites. 2nd AIAA Spacecraft Structures Conference, Kissimmee, Florida. https://doi.org/10.2514/6.2015-0942

  3. Gao J, Chen W, Yu B, Fan P, Zhao B, Hu J, Zhang D, Fang G, Peng F (2019) Effect of temperature on the mechanical behaviours of a single-ply weave-reinforced shape memory polymer composite. Compos Part B-Eng 159:336–345. https://doi.org/10.1016/j.compositesb.2018.09.029

    Article  Google Scholar 

  4. Liu Y, Du H, Liu L, Leng J (2014) Shape memory polymers and their composites in aerospace applications: a review. Smart Mater Struct 23:023001. https://doi.org/10.1088/0964-1726/23/2/023001

    Article  Google Scholar 

  5. Gao J, Chen W, Yu B, Fan P, Zhao B, Hu J, Zhang D, Fang G, Peng F (2019) A multi-scale method for predicting ABD stiffness matrix of single-ply weave-reinforced composite. Compos Struct 230:111478. https://doi.org/10.1016/j.compstruct.2019.111478

    Article  Google Scholar 

  6. Isshi T (1957) Bending tester for fibers, yarns and fabrics. Journal of the Textile Machinery Society of Japan 3(2):48–52. https://doi.org/10.4188/jte1955.3.2_48

    Article  Google Scholar 

  7. Popper P, Backer S (1968) Instrument for measuring bending-moment curvature relationships in textile materials. Text Res J 38(8):870–873. https://doi.org/10.1177/004051756803800811

    Article  Google Scholar 

  8. kawabata Manual for pure bending tester KES-FB-2, Kato Tekko Co., Ltd., Kyoto

  9. Brunet M, Morestin F, Godereaux S (2000) Nonlinear kinematic hardening identification for anisotropic sheet metals with bending-unbending tests. ASME J Eng Mater Technol 123(4):378–383. https://doi.org/10.1115/1.1394202

    Article  Google Scholar 

  10. Hoefnagels JPM, Ruybalid AP, Buizer CA (2015) A small-scale, contactless, pure bending device for in-situ testing. Exp Mech 55(8):1511–1524. https://doi.org/10.1007/s11340-015-0046-9

    Article  Google Scholar 

  11. Arnold G, Calloch S, Dureisseix D, Billardon R (2003) A pure bending machine to identify the mechanical behaviour of thin sheets. 6th. International ESAFORM Conference on Material Forming, Salerno, Italy, pp 1–4. https://hal.archives-ouvertes.fr/hal-00321284

  12. Yoshida F, Urabe M, Toropov VV (1998) Identification of material parameters in constitutive model for sheet metals from cyclic bending tests. Int J Mech Sci 40(2):237–249. https://doi.org/10.1016/S0020-7403(97)00052-0

    Article  Google Scholar 

  13. Boers SHA, Geers MGD, Kouznetsova VG (2010) Contactless and frictionless pure bending. Exp Mech 50(6):683–693. https://doi.org/10.1007/s11340-009-9257-2

    Article  Google Scholar 

  14. ASTM D790 (2016) Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials

  15. ASTM 6272 (2010) Standard Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending

  16. ASTM 7264 (2015) Standard Test Method for Flexural Properties of Polymer Matrix Composite Materials

  17. Perduijn AB, Hoogenboom SM (1995) The pure bending of sheet. J Mater Process Tech 51(1):274–295. https://doi.org/10.1016/0924-0136(94)01596-S

    Article  Google Scholar 

  18. Muñoz-Guijosa JM, Cruz VR, Caballero DF, Lantada AD, Otero JE (2012) Simple testing system for pure bending tests with large deflections. Expe Mech 52(7):679–692. https://doi.org/10.1007/s11340-011-9535-7

    Article  Google Scholar 

  19. Seffen KA, Pellegrino S (1999) Deployment dynamics of tape springs. Proc R Soc Lon A 455:1003–1048. https://doi.org/10.1098/rspa.1999.0347

    Article  MathSciNet  MATH  Google Scholar 

  20. Walker S, Aglietti G (2006) Experimental investigation of tape springs folded in three dimensions. AIAA J 44(1):151–159. https://doi.org/10.2514/1.15508

    Article  Google Scholar 

  21. Kwok K, Pellegrino S (2013) Folding, stowage, and deployment of viscoelastic tape springs. AIAA J 51(8):1908–1918. https://doi.org/10.2514/1.J052269

    Article  Google Scholar 

  22. Karakaya Ş, Soykasap Ö (2012) Homogenized tensile and bending properties of plain weave single-Ply E-glass/epoxy. Polym Composites 33(6):881–888. https://doi.org/10.1002/pc.22225

    Article  Google Scholar 

  23. Wisnom MR, Atkinson JW (1997) Constrained buckling tests show increasing compressive strain to failure with increasing strain gradient. Compos Part A-Appl S 28(11):959–964. https://doi.org/10.1016/S1359-835X(97)00067-5

    Article  Google Scholar 

  24. Guo SM, Sutton MA, Majumdar P, Reifsnider KM, Yu L, Gresil M (2013) Development and application of an experimental system for the study of thin composites undergoing large deformations in combined bending–compression loading. J Compos Mater 48(8):997–1023. https://doi.org/10.1177/0021998313481514

    Article  Google Scholar 

  25. Sanford G, Biskner A, Murphey T (2010) Large strain behavior of thin unidirectional composite flexures. 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 18th AIAA/ASME/AHS Adaptive Structures Conference, Orlando, Florida. https://doi.org/10.2514/6.2010-2698

  26. Duncan JL, Ding SC, Jiang WL (1999) Moment–curvature measurement in thin sheet—part I: equipment. Int J Mech Sci 41(3):249–260. https://doi.org/10.1016/S0020-7403(98)00031-9

    Article  MATH  Google Scholar 

  27. Zineb TB, Sedrakian A, Billoet JL (2003) An original pure bending device with large displacements and rotations for static and fatigue tests of composite structures. Compos Part B-Eng 34(5):447–458. https://doi.org/10.1016/S1359-8368(03)00017-9

    Article  Google Scholar 

  28. Weiss M, Wolfkamp H, Rolfe BF, Hodgson PD, Hemmerich E (2009) Measurement of bending properties in strip for roll forming. International Deep Drawing Research Group IDDRG 2009 International Conference, Golden, CO, USA, pp 521–532

  29. Murphey T, Peterson M, Grigoriev M (2013) Four point bending of thin unidirectional composite laminas. 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Boston, 1668. https://doi.org/10.2514/6.2013-1668

  30. Zehnder AT, Patel V, Rose TJ (2020) Micro-CT imaging of fibers in composite laminates under high strain bending. Exp Techniques 44:531–540. https://doi.org/10.1007/s40799-020-00374-9

    Article  Google Scholar 

  31. Rose TJ, Medina K, Francis W, Kwok K, Bergan A, Fernandez J (2019) Viscoelastic behavior of high strain composites. AIAA Scitech 2019 Forum. https://doi.org/10.2514/6.2019-2027

  32. Firth JA, Pankow MR (2019) Minimal unpowered strain-energy deployment mechanism for rollable spacecraft booms: ground test. J Spacecraft Rockets 57(2):346–353. https://doi.org/10.2514/1.A34565

    Article  Google Scholar 

  33. Sharma A, Perez R, Bearns N, Rose TJ, Jimenez F (2021) Some Considerations Involving Testing Guidelines for Large Curvature Bending of High Strain Composites using the Column Bending Test. AIAA Scitech 2021 Forum. https://doi.org/10.2514/6.2021-0196

  34. Sharma, A, Rose TJ, Seamone A, Murphey T, Jimenez F (2019) Analysis of the Column Bending Test for Large Curvature Bending of High Strain Composites. AIAA Scitech 2021 Forum. https://doi.org/10.2514/6.2019-1746

  35. Timoshenko SP, Gere JM (1972) Theory of Elastic Stability. Dover Publications

    Google Scholar 

  36. Ueda M, Saito W, Imahori R, Kanazawa D, Jeong T-K (2014) Longitudinal direct compression test of a single carbon fiber in a scanning electron microscope. Compos Part A-Appl S 67:96–101. https://doi.org/10.1016/j.compositesa.2014.08.021

    Article  Google Scholar 

  37. Murphey T, Sanford G, Grigoriev M (2011) Nonlinear elastic constitutive modeling of large strains in thin carbon fiber composite flexures. 16th International conference on composite structures, Porto, Portugal

Download references

Acknowledgements

The first author would like to thank Prof. W. Xu (School of Aeronautics and Astronautics, SJTU) for help in experiments. The Joint Research Centre of Aerospace Advanced Technology (USCAST2016-21), the National Postdoctoral Program for Innovative Talents of China (Grant. BX201600104) supported this work. The authors acknowledge to SJTU Instrumental Analysis Center for composite photomicrographs.

Author information

Authors and Affiliations

  1. Space Structures Research Center, Shanghai Jiao Tong University, Shanghai, 200240, China

    J. Gao, W. Chen, J. Hu & B. Zhao

  2. School of Naval Architecture, Shanghai Jiao Tong University, Ocean & Civil Engineering, Shanghai, 200240, China

    J. Chen & D. Zhang

  3. Shanghai Institute of Aerospace System Engineering, Shanghai, 201109, China

    G. Fang & F. Peng

Authors
  1. J. Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. D. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. G. Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. F. Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Chen.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, J., Chen, W., Chen, J. et al. Accuracy Analysis on Counterweight-Balanced Column Bending Test. Exp Mech 62, 137–150 (2022). https://doi.org/10.1007/s11340-021-00767-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00767-w

Keywords

Search

Navigation