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In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone

Nature Materials volume 13, pages 740–747 (2014)Cite this article

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Abstract

Ageing societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the hierarchical organization of bone. Here, we investigate the mechanical response under monotonic and cyclic compression of both single osteonal lamellae and macroscopic samples containing numerous osteons. Micropillar compression tests in a scanning electron microscope, microindentation and macroscopic compression tests were performed on dry ovine bone to identify the elastic modulus, yield stress, plastic deformation, damage accumulation and failure mechanisms. We found that isolated lamellae exhibit a plastic behaviour, with higher yield stress and ductility but no damage. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behaviour of bone at the microscale to a quasi-brittle response driven by the growth of cracks along interfaces or in the vicinity of pores at the macroscale.

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Figure 1: Observed failure modes of bone on the micro- and macroscale.
Figure 2: Experimental curves and post-yield behaviour of monotonic micropillar compression tests.
Figure 3: Model predictions, experimental curves and normalized apparent modulus evolution of cyclic compression tests on the micro- and macroscale.
Figure 4: Rheological model describing the mechanical response of bone under compression.
Figure 5: Dominant failure mechanism observed on the microscale.

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References

  1. Fratzl, P. & Weinkamer, R. Nature’s hierarchical materials. Prog. Mater. Sci. 52, 1263–1334 (2007).

    CAS  Google Scholar 

  2. Weiner, S., Traub, W. & Wagner, H. Lamellar bone: structure–function relations. J. Struct. Biol. 126, 241–255 (1999).

    Article  CAS  Google Scholar 

  3. Currey, J. D. Bones: Structure and Mechanics (Princeton Univ. Press, 2002).

    Google Scholar 

  4. Currey, J. D. The relationship between the stiffness and the mineral content of bone. J. Biomech. 2, 477–480 (1969).

    Article  CAS  Google Scholar 

  5. Lees, S., Tao, N-J. & Lindsay, S. Studies of compact hard tissues and collagen by means of Brillouin light scattering. Connect. Tissue Res. 24, 187–205 (1990).

    Article  CAS  Google Scholar 

  6. Giraud-Guille, M. M. Twisted plywood architecture of collagen fibrils in human compact bone osteons. Calcified Tissue Int. 42, 167–180 (1988).

    Article  CAS  Google Scholar 

  7. Weiner, S., Arad, T., Sabanay, I. & Traub, W. Rotated plywood structure of primary lamellar bone in the rat: Orientations of the collagen fibril arrays. Bone 20, 509–514 (1997).

    Article  CAS  Google Scholar 

  8. Martin, R. B. Porosity and specific surface of bone. Crit. Rev. Biomed. Eng. 10, 179–222 (1984).

    CAS  Google Scholar 

  9. Cowin, S. C. Bone Mechanics Handbook (CRC Press, 2001).

    Book  Google Scholar 

  10. Kutz, M. Standard Handbook of Biomedical Engineering and Design Ch. 8 (McGraw Hill, 2003).

    Google Scholar 

  11. Gruber, P. et al. Biomimetics-Materials, Structures and Processes Ch. 5 (Springer, 2011).

    Book  Google Scholar 

  12. Rho, J-Y, Kuhn-Spearing, L. & Zioupos, P. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 20, 92–102 (1998).

    Article  CAS  Google Scholar 

  13. O’Brien, F. J., Taylor, D. & Lee, T. C. An improved labelling technique for monitoring microcrack growth in compact bone. J. Biomech. 35, 523–526 (2002).

    Article  Google Scholar 

  14. Sun, X., Jeon, J. H., Blendell, J. & Akkus, O. Visualization of a phantom post-yield deformation process in cortical bone. J. Biomech. 43, 1989–1996 (2010).

    Article  CAS  Google Scholar 

  15. Zioupos, P., Hansen, U. & Currey, J. D. Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure. J. Biomech. 41, 2932–2939 (2008).

    Article  Google Scholar 

  16. Gupta, H. et al. Fibrillar level fracture in bone beyond the yield point. Int. J. Fracture 139, 425–436 (2006).

    Article  Google Scholar 

  17. Oliver, W. C. & Pharr, G. M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992).

    Article  CAS  Google Scholar 

  18. Lewis, G. & Nyman, J. S. The use of nanoindentation for characterizing the properties of mineralized hard tissues: state of the art review. J. Biomed. Mater. Res. B 87, 286–301 (2008).

    Article  CAS  Google Scholar 

  19. Zysset, P. K., Guo, X. E., Hoffler, C. E., Moore, K. E. & Goldstein, S. A. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J. Biomech. 32, 1005–1012 (1999).

    Article  CAS  Google Scholar 

  20. Lucchini, R. et al. Role of damage mechanics in nanoindentation of lamellar bone at multiple sizes: experiments and numerical modelling. J. Mech. Behav. Biomed. 4, 1852–1863 (2011).

    Article  Google Scholar 

  21. Zhang, J., Michalenko, M. M., Kuhl, E. & Ovaert, T. C. Characterization of indentation response and stiffness reduction of bone using a continuum damage model. J. Mech. Behav. Biomed. 3, 189–202 (2010).

    Article  Google Scholar 

  22. Chen, X., Ogasawara, N., Zhao, M. & Chiba, N. On the uniqueness of measuring elastoplastic properties from indentation: the indistinguishable mystical materials. J. Mech. Phys. Solids 55, 1618–1660 (2007).

    Article  Google Scholar 

  23. Howie, P. R., Korte, S. & Clegg, W. J. Fracture modes in micropillar compression of brittle crystals. J. Mater. Res. 27, 141–151 (2012).

    Article  CAS  Google Scholar 

  24. Michler, J., Wasmer, K., Meier, S., Ostlund, F. & Leifer, K. Plastic deformation of gallium arsenide micropillars under uniaxial compression at room temperature. Appl. Phys. Lett. 90, 043123–043123-3 (2007).

    Article  CAS  Google Scholar 

  25. Bažant, Z. Scaling theory for quasibrittle structural failure. Proc. Natl Acad. Sci. USA 101, 13400–13407 (2004).

    Article  Google Scholar 

  26. Östlund, F. et al. Brittle-to-ductile transition in uniaxial compression of silicon pillars at room temperature. Adv. Funct. Mater. 19, 2439–2444 (2009).

    Article  CAS  Google Scholar 

  27. Östlund, F. et al. Ductile–brittle transition in micropillar compression of GaAs at room temperature. Phil. Mag. 91, 1190–1199 (2011).

    Article  CAS  Google Scholar 

  28. Griffith, A. A. The phenomena of flow and rupture in solids. Phil. Trans. R. Soc. A 221, 163–198 (1921).

    Article  Google Scholar 

  29. Hengsberger, S., Kulik, A. & Zysset, P. K. Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions. Bone 30, 178–184 (2002).

    Article  CAS  Google Scholar 

  30. Carnelli, D., Lucchini, R., Ponzoni, M., Contro, R. & Vena, P. Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response. J. Biomech. 44, 1852–1858 (2011).

    Article  Google Scholar 

  31. Reisinger, A. G., Pahr, D. H. & Zysset, P. K. Principal stiffness orientation and degree of anisotropy of human osteons based on nanoindentation in three distinct planes. J. Mech. Behav. Biomed. 4, 2113–2127 (2011).

    Article  Google Scholar 

  32. Franzoso, G. & Zysset, P. K. Elastic anisotropy of human cortical bone secondary osteons measured by nanoindentation. J. Biomech. Eng. 131, 117001 (2009).

    Article  Google Scholar 

  33. Chamay, A. Mechanical and morphological aspects of experimental overload and fatigue in bone. J. Biomech. 3, 263–270 (1970).

    Article  CAS  Google Scholar 

  34. Krajcinovic, D., Trafimow, J. & Sumarac, D. Simple constitutive model for a cortical bone. J. Biomech. 20, 779–784 (1987).

    Article  CAS  Google Scholar 

  35. Pearce, A. I., Richards, R. G., Milz, S., Schneider, E. & Pearce, S. G. Animal models for implant biomaterial research in bone: a review. Eur. Cells Mater. 13, 1–10 (2007).

    Article  CAS  Google Scholar 

  36. Ravaglioli, A. et al. Mineral evolution of bone. Biomaterials 17, 617–622 (1996).

    Article  CAS  Google Scholar 

  37. Reilly, D. T. & Burstein, A. H. The elastic and ultimate properties of compact bone tissue. J. Biomech. 8, 393–405 (1975).

    Article  CAS  Google Scholar 

  38. Zhang, H., Schuster, B. E., Wei, Q. & Ramesh, K. T. The design of accurate micro-compression experiments. Scr. Mater. 54, 181–186 (2006).

    Article  CAS  Google Scholar 

  39. Fantner, G. E. et al. Hierarchical interconnections in the nano-composite material bone: Fibrillar cross-links resist fracture on several length scales. Compos. Sci. Technol. 66, 1205–1211 (2006).

    Article  CAS  Google Scholar 

  40. Koester, K. J., Ager, J. W. & Ritchie, R. O. The true toughness of human cortical bone measured with realistically short cracks. Nature Mater. 7, 672–677 (2008).

    Article  CAS  Google Scholar 

  41. Peterlik, H., Roschger, P., Klaushofer, K. & Fratzl, P. From brittle to ductile fracture of bone. Nature Mater. 5, 52–55 (2006).

    Article  CAS  Google Scholar 

  42. Poundarik, A. A. et al. Dilatational band formation in bone. Proc. Natl Acad. Sci. USA 109, 19178–19183 (2012).

    Article  Google Scholar 

  43. Tai, K., Ulm, F-J. & Ortiz, C. Nanogranular origins of the strength of bone. Nano Lett. 6, 2520–2525 (2006).

    Article  CAS  Google Scholar 

  44. Mercer, C., He, M. Y., Wang, R. & Evans, A. G. Mechanisms governing the inelastic deformation of cortical bone and application to trabecular bone. Acta Biomater. 2, 59–68 (2006).

    Article  CAS  Google Scholar 

  45. Gupta, H. et al. Intrafibrillar plasticity through mineral/collagen sliding is the dominant mechanism for the extreme toughness of antler bone. J. Mech. Behav. Biomed. 28, 366–382 (2013).

    Article  CAS  Google Scholar 

  46. Hayes, W. C. & Carter, D. R. Postyield behavior of subchondral trabecular bone. J. Biomed. Mater. Res. 10, 537–544 (1976).

    Article  CAS  Google Scholar 

  47. Schaffler, M. B., Choi, K. & Milgrom, C. Aging and matrix microdamage accumulation in human compact bone. Bone 17, 521–525 (1995).

    Article  CAS  Google Scholar 

  48. Carter, D. R. & Hayes, W. C. Compact bone fatigue damage: A microscopic examination. Clin. Orthop. Relat. R. 127, 265–274 (1977).

    Google Scholar 

  49. Martin, R. B. & Burr, D. B. Structure, Function, and Adaptation of Compact Bone (Raven Press, 1989).

    Google Scholar 

  50. Currey, J. D. Stress concentrations in bone. Q. J. Microsc. Sci. 103, 111–133 (1962).

    Google Scholar 

  51. Zysset, P. K. A Constitutive Law for Trabecular Bone PhD thesis, Ecole Polytechnique Federale de Lausanne (1994)

  52. Fischer-Cripps, A. C. Nanoindentation (Springer, 2002).

    Book  Google Scholar 

  53. Nyman, J. S. et al. The influence of water removal on the strength and toughness of cortical bone. J. Biomech. 39, 931–938 (2006).

    Article  Google Scholar 

  54. Wolfram, U., Wilke, H-J. & Zysset, P. K. Rehydration of vertebral trabecular bone: Influences on its anisotropy, its stiffness and the indentation work with a view to age, gender and vertebral level. Bone 46, 348–354 (2010).

    Article  Google Scholar 

  55. Ziegler, J. F. & Biersack, J. P. The Stopping and Range of Ions in Matter (Springer, 1985).

    Book  Google Scholar 

  56. Nalla, R. et al. Ultrastructural examination of dentin using focused ion-beam cross-sectioning and transmission electron microscopy. Micron 36, 672–680 (2005).

    Article  CAS  Google Scholar 

  57. Rabe, R. et al. Observation of fracture and plastic deformation during indentation and scratching inside the scanning electron microscope. Thin Solid Films 469, 206–213 (2004).

    Article  CAS  Google Scholar 

  58. Ashby, M. & Jones, D. Engineering Materials (Pergamon, 1980).

    Google Scholar 

  59. R Development Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2008).

    Google Scholar 

  60. Shapiro, S. S. & Wilk, M. B. An analysis of variance test for normality (complete samples). Biometrika 52, 591–611 (1965).

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank M. Mirzaali for help with the specimen preparation, I. Utke for the discussions about ion–matter interactions and SRIM, C. Schwiedrzik for valuable comments on the manuscript, and D. Frey and G. Buerki for technical assistance with the in situ indenter and FIB milling.

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Author notes

  1. Johann Michler and Philippe Zysset: These authors share senior authorship for this work.

Authors and Affiliations

  1. Institute for Surgical Technology and Biomechanics, University of Bern, Stauffacherstr. 78 CH-3014 Bern, Switzerland,

    Jakob Schwiedrzik, Alexander Bürki, Uwe Wolfram & Philippe Zysset

  2. EMPA, Swiss Federal Laboratories for Material Science and Technology, Laboratory of Mechanics of Materials and Nanostructures, Feuerwerkerstr. 39, CH-3602 Thun, Switzerland

    Rejin Raghavan, Victor LeNader & Johann Michler

  3. Present address: Max-Planck-Institut für Eisenforschung, Structure and Nano/Micromechanics of Materials, Max-Planck.Str. 1, D-40237 Düsseldorf, Germany.,

    Rejin Raghavan

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Contributions

The initial planning of the study was done by J.S., R.R., J.M. and P.Z. The FIB was operated by R.R. Micropillar compressions and SEM imaging were performed by J.S. and R.R., Raman measurements and interpretation were performed by V.L. Monte Carlo simulations and microindentations were performed by J.S. Macroscopic tests were performed by J.S., U.W. and A.B. Data analysis was performed by J.S. and R.R. with the assistance of U.W., and interpreted in cooperation with J.M. and P.Z. Modelling was performed by J.S. and P.Z. The manuscript was written by J.S. with contributions from all the authors.

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Correspondence to Jakob Schwiedrzik.

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Schwiedrzik, J., Raghavan, R., Bürki, A. et al. In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone. Nature Mater 13, 740–747 (2014). https://doi.org/10.1038/nmat3959

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