Skip to main content
SpringerLink
Log in

Study of Local Mechanical Responses in an Epoxy–Carbon Fiber Laminate Composite Using Spherical Indentation Stress–Strain Protocols

  • Technical Article
  • Published:
Integrating Materials and Manufacturing Innovation Aims and scope Submit manuscript

Abstract

Successful deployment of the highly heterogeneous, laminated, polymer matrix composites (PMCs) in high-performance structural applications is currently hindered by the lack of reliable experimental protocols for evaluation of the local mechanical responses at the salient meso-length/structure scales present in these material systems. Our main interest in this paper lies in establishing and demonstrating protocols for high-throughput evaluation of the local mechanical responses in PMCs at a length scale larger than the fiber diameter but smaller than the individual laminate (i.e., ply) thickness. This goal was accomplished in this work through a successful extension of the spherical indentation stress–strain protocols demonstrated recently for metallic samples. Specifically, plies with fibers at 0°, 30°, 60°, and 90° to the indentation direction were tested, and the means and standard deviations of their indentation moduli and the indentation yield strengths were measured and reported in this paper. The measured values of the indentation moduli were validated with finite element (FE) simulations performed using estimated values of the effective single laminate stiffness parameters. Furthermore, the measured variation in the indentation moduli was shown to correlate extremely well with the corresponding FE predictions that accounted for the measured variation in the local fiber volume fractions in the primary indentation deformed zones in the sample. These comparisons provided strong support for the validity of the extended spherical indentation protocols developed in this work for PMC samples.

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

Similar content being viewed by others

References

  1. Cech V, Knob A, Hosein HA, Babik A, Lepcio P, Ondreas F et al (2014) Enhanced interfacial adhesion of glass fibers by tetravinylsilane plasma modification. Compos A Appl Sci 58:84–89

    Article  CAS  Google Scholar 

  2. Brosius D (2007) Boeing 787 update. Composites World. https://www.compositesworld.com/articles/boeing-787-update

  3. Soutis C (2005) Fibre reinforced composites in aircraft construction. Prog Aerosp Sci 41(2):143–151

    Article  Google Scholar 

  4. Sloan J (2014) Making of the BMW i3. Compos World

  5. Brown S (2013) Carbon fiber, light and strong, arrives where it’s most needed. The New York Times, p AU2

  6. Mouritz AP, Bannister MK, Falzon PJ, Leong KH (1999) Review of applications for advanced three-dimensional fibre textile composites. Compos A Appl Sci Manuf 30:1445–1461

    Article  Google Scholar 

  7. Kalidindi SR, Franco E (1997) Numerical evaluation of isostrain and weighted-average models for elastic moduli of three-dimensional composites. Compos Sci Technol 57(3):293–305

    Article  Google Scholar 

  8. Kalidindi SR, Abusafieh A (1996) Longitudinal and transverse moduli and strengths of low angle 3-D braided composites. J Compos Mater 30(8):885–905

    Article  CAS  Google Scholar 

  9. Engelstad SP, Action JE, Clay SB, Holzwarth RC, Robbins D, Dalgarno R (2014) Assessment of composite damage growth tools for aircraft structure part I. American Institute of Aeronautics and Astronautics, Inc.

  10. Engelstad SP, Clay S (2016) Assessment of composite damage growth tools for aircraft structure part II. In: 57th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference

  11. Reddy JR, Robbins DH (1994) Theories and computational models for composite laminates. Appl Mech 47:147–169

    Article  Google Scholar 

  12. Halpin JC, Kardos JL (1976) The Halpin–Tsai equations: a review. Polymer Eng Sci 16(5):344–352

    Article  CAS  Google Scholar 

  13. Griepentrog M, Kramer G, Cappella B (2013) Comparison of nanoindentation and AFM methods for the determination of mechanical properties of polymers. Polym Test 32(3):455–460

    Article  CAS  Google Scholar 

  14. Ronald K (1991) Theoretical analysis of the fiber pullout and pushout tests. J Am Ceram Soc 74(7):1585–1596

    Article  Google Scholar 

  15. ASTM D3039 / D3039M-17 (2017) Standard test method for tensile properties of polymer matrix composite materials. ASTM International, West Conshohocken, PA. https://www.astm.org/

  16. Hodzic A, Kalyanasundaram S, Kim JK, Lowe AE, Stachurski ZH (2001) Application of nano-indentation, nano-scratch and single fibre tests in investigation of interphases in composite materials. Micron 32(8):765–775

    Article  CAS  Google Scholar 

  17. Hodzic A, Kim JK, Stachurski ZH (2001) Nano-indentation and nano-scratch of polymer/glass interfaces. II: model of interphases in water aged composite materials. Polymer. 42(13):5701–5710

    Article  CAS  Google Scholar 

  18. Hodzic A, Stachurski ZH, Kim JK (2000) Nano-indentation of polymer–glass interfaces part I. Experimental and mechanical analysis. Polymer 41(18):6895–6905

    Article  CAS  Google Scholar 

  19. Jensen EM, Leonhardt DA, Fertig RS (2015) Effects of thickness and fiber volume fraction variations on strain field inhomogeneity. Compos A Appl Sci Manuf 69:178–185

    Article  CAS  Google Scholar 

  20. Ng Y-C (2016) Deriving composite lamina properties from laminate properties using classical lamination theory and failure criteria. J Compos Mater 39(14):1295–1306

    Article  CAS  Google Scholar 

  21. Flaggs DK, Kural MH (1982) Experimental determination of the in situ transverse lamina strength in graphite/epoxy laminates. J Compos Mater 16:103–116

    Article  CAS  Google Scholar 

  22. Huang ZM (2001) Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model. Compos A Appl Sci 32(2):143–172

    Article  CAS  Google Scholar 

  23. Desaeger M, Verpoest I (1993) On the use of the micro-indentation test technique to measure the interfacial shear strength of fibre-reinforced polymer composites. Compos Sci Technol 48(1):215–226

    Article  CAS  Google Scholar 

  24. Hardiman M, Vaughan TJ, McCarthy CT (2017) A review of key developments and pertinent issues in nanoindentation testing of fibre reinforced plastic microstructures. Compos Struct 180:782–798

    Article  Google Scholar 

  25. Gregory J, Spearing S (2005) Nanoindentation of neat and polymers in polymer-matrix composites. Compos Sci Technol 65(3–4):595–607

    Article  CAS  Google Scholar 

  26. Pharr GM, Oliver WC (2013) Measurement of thin film mechanical properties using nanoindentation. MRS Bull 17(7):28–33

    Article  Google Scholar 

  27. Oliver WC, Pharr GM (2011) Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J Mater Res 19(1):3–20

    Article  Google Scholar 

  28. Pathak S, Stojakovic D, Doherty R, Kalidindi SR (2009) Importance of surface preparation on the nano-indentation stress–strain curves measured in metals. J Mater Res 24(03):1142–1155

    Article  CAS  Google Scholar 

  29. Pathak S, Shaffer J, Kalidindi SR (2009) Determination of an effective zero-point and extraction of indentation stress–strain curves without the continuous stiffness measurement signal. Scr Mater 60(6):439–442

    Article  CAS  Google Scholar 

  30. Pathak S, Kalidindi SR (2015) Spherical nanoindentation stress–strain curves. Mater Sci Eng R 91:1–36

    Article  Google Scholar 

  31. Patel DK, Kalidindi SR (2017) Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals. Int J Plast 92:19–30

    Article  CAS  Google Scholar 

  32. Patel DK, Kalidindi SR (2016) Correlation of spherical nanoindentation stress–strain curves to simple compression stress–strain curves for elastic–plastic isotropic materials using finite element models. Acta Mater 112:295–302

    Article  CAS  Google Scholar 

  33. Donohue BR, Ambrus A, Kalidindi SR (2012) Critical evaluation of the indentation data analyses methods for the extraction of isotropic uniaxial mechanical properties using finite element models. Acta Mater 60:3943–3952

    Article  CAS  Google Scholar 

  34. Weaver JS, Khosravani A, Castillo A, Kalidindi SR (2016) High throughput exploration of process-property linkages in Al-6061 using instrumented spherical microindentation and microstructurally graded samples. Integr Mater Manuf Innov 5(1):10

    Article  Google Scholar 

  35. Weaver JS, Kalidindi SR (2016) Mechanical characterization of Ti–6Al–4V titanium alloy at multiple length scales using spherical indentation stress–strain measurements. Mater Des 111:463–472

    Article  CAS  Google Scholar 

  36. Pathak SS, Stojakovic D, Kalidindi SR (2009) Measurement of the local mechanical properties in polycrystalline samples using spherical nano-indentation and orientation imaging microscopy. Acta Mater 57:3020–3028

    Article  CAS  Google Scholar 

  37. Pathak S, Cambaz ZG, Kalidindi SR, Swadener JG, Gogotsi Y (2009) Viscoelasticity and high buckling stress of dense carbon nanotube brushes. Carbon 47(8):1969–1976

    Article  CAS  Google Scholar 

  38. Pathak S, Swadener JG, Kalidindi SR, Courtland H-W, Jepsen KJ, Goldman HM (2011) Measuring the dynamic mechanical response of hydrated mouse bone by nanoindentation. J Mech Behav Biomed Mater 4(1):34–43

    Article  Google Scholar 

  39. Abba MT (2015) Spherical nanoindentation protocols for extracting microscale mechanical properties in viscoelastic materials. Doctoral dissertation, Georgia Institute of Technology, Atlanta GA

  40. Kalidindi SR, Pathak S (2008) Determination of the effective zero-point and the extraction of spherical nanoindentation stress–strain curves. Acta Mater 56(14):3523–3532

    Article  CAS  Google Scholar 

  41. Hertz H (1896) Miscellaneous papers. MacMillan and Co., Ltd., New York

    Google Scholar 

  42. Vachhani SJ, Doherty RD, Kalidindi SR (2013) Effect of the continuous stiffness measurement on the mechanical properties extracted using spherical nanoindentation. Acta Mater 61(10):3744–3751

    Article  CAS  Google Scholar 

  43. Adams BL, Gao X, Kalidindi SR (2005) Finite approximations to the second-order properties closure in single phase polycrystals. Acta Mater 53(13):3563–3577

    Article  CAS  Google Scholar 

  44. Gong X, Mohan S, Mendoza M, Gray A, Collins P, Kalidindi S (2017) High throughput assays for additively manufactured Ti–Ni alloys based on compositional gradients and spherical indentation. Integr Mater Manuf Innov 6(3):218–228

    Article  Google Scholar 

  45. Iskakov A, Yabansu YC, Rajagopalan S, Kapustina A, Kalidindi SR (2018) Application of spherical indentation and the materials knowledge system framework to establishing microstructure-yield strength linkages from carbon steel scoops excised from high-temperature exposed components. Acta Mater 144:758–767

    Article  CAS  Google Scholar 

  46. Weaver JS, Priddy MW, McDowell DL, Kalidindi SR (2016) On capturing the grain-scale elastic and plastic anisotropy of alpha-Ti with spherical nanoindentation and electron back-scattered diffraction. Acta Mater 117:23–34

    Article  CAS  Google Scholar 

  47. Clay SB, Knoth PM (2016) Experimental results of fatigue testing for calibration and validation of composite progressive damage analysis methods. J Compos Mater 51:2083–2100

    Article  Google Scholar 

  48. Clay SB, Knoth PM (2016) Experimental results of quasi-static testing for calibration and validation of composite progressive damage analysis methods. J Compos Mater 51(10):1333–1353

    Article  CAS  Google Scholar 

  49. Wang HW, Zhou HW, Gui LL, Ji HW, Zhang XC (2014) Analysis of effect of fiber orientation on Young’s modulus for unidirectional fiber reinforced composites. Compos B Eng 56:733–739

    Article  CAS  Google Scholar 

  50. Patel DK, Al-Harbi HF, Kalidindi SR (2014) Extracting single-crystal elastic constants from polycrystalline samples using spherical nanoindentation and orientation measurements. Acta Mater 79:108–116

    Article  CAS  Google Scholar 

  51. Priddy MW (2016) Exploration of forward and inverse protocols for property optimization of Ti–6Al–4V. Doctoral dissertation, Georgia Institute of Technology, Atlanta, GA

  52. Bhattacharya AK, Nix WD (1988) Finite element simulation of indentation experiments. Int J Solids Struct 24(9):881–891

    Article  Google Scholar 

  53. Chamis CC (1989) Mechanics of composite-materials—past, present, and future. J Compos Technol Res 11(1):3–14

    Article  CAS  Google Scholar 

  54. Vlassak JJ, Nix WD (1994) Measuring the elastic properties of anisotropic materials by means of indentation experiments. J Mech Phys Solids 42(8):1223–1245

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the support of ForWarD to Materials Data Science and Informatics (FWD-MDSI), A Minority Leader-Research Collaboration Program (UTC/AFRL).

Author information

Authors and Affiliations

  1. GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Alicia Rossi, Andrew Castillo & Surya R. Kalidindi

  2. Air Force Research Laboratory, Dayton, OH, USA

    Craig Przybyla

Authors
  1. Alicia Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrew Castillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Craig Przybyla
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Surya R. Kalidindi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Surya R. Kalidindi.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rossi, A., Castillo, A., Przybyla, C. et al. Study of Local Mechanical Responses in an Epoxy–Carbon Fiber Laminate Composite Using Spherical Indentation Stress–Strain Protocols. Integr Mater Manuf Innov 8, 495–508 (2019). https://doi.org/10.1007/s40192-019-00163-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40192-019-00163-2

Keywords

Search

Navigation