International Journal of Fracture

, Volume 139, Issue 3–4, pp 509–516 | Cite as

Ductility and brittleness of bone

  • Helmut Kirchner
Original Article


Human, bovine and equine bones show brittle to ductile transitions as a function of strain rate. The transition is not sharp, but occurs around a strain rate of 10−1 s−1. At lower rates, the strength increases proportional to the logarithm of the strain rate, at higher rates it decreases. Additionally, the work of fracture peaks around 10−1 s−1. Thermal activation analysis gives an activation volume of (1 nm)3, an activation enthalpy of 1 eV and an activation energy of about 0.5 eV. Plastic deformation occurs both within and between collagen fibrils. In the fibrils, the existence of screw dislocations parallel to the collagen molecules with a Burger’s vector of 1 nm length is postulated. Deformation occurs by thermally activated kink pair formation in these defects.


Bone Brittle to ductile transition Thermal activation Plasticity Activation volume Activation energy 


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  1. Argon, AS 1999Rate processes in plastic deformation of crystalline and noncrystalline solidsMeyers, MAArmstrong, RWKirchner, HOK eds. Mechanics and materialsJohn WileyNew York175230Google Scholar
  2. Ashby, MF 1992Materials selection in mechanical designButterworth-HeinemannOxfordGoogle Scholar
  3. Ashby, MF, Gibson, LJ, Wegst, U, Olive, R 1957The mechanical properties of natural materials. I. Material property chartsProc Roy Soc Lond A450132140Google Scholar
  4. Beck, K, Brodsky, B 1998Supercoiled protein motifs: the collagen triple-helix and the alpha-helical coiled coilJ Struct Biol1221729CrossRefGoogle Scholar
  5. Burr, DB, Milgrom, C, Fyhrie, D, Forwood, M, Nyska, M, Finestone, A, Hoshaw, S, Saiag, E, Simkin, A 1996In vivo measurements of human tibial strains during vigorous activityBone18405410CrossRefGoogle Scholar
  6. Crowninshield, RD, Pope, MH 1974The Response of compact bone in tension at various strain ratesAnn Biomed Eng2217225CrossRefGoogle Scholar
  7. Currey, JD 2002Bones: structure and mechanicsPrinceton University PressPrincetonGoogle Scholar
  8. Evans, GP, Behiri, JC, Vaughan, LC, Bonfield, W 1992The response of equine cortical bone to loading at strain rates experienced in vivo by the galopping horseEquine Vet J24125128CrossRefGoogle Scholar
  9. Fratzl, P 2003Cellulose and collagen: from fibres to tissuesCurr Opin Colloid Sci83239CrossRefGoogle Scholar
  10. Fratzl, P, Fratzl-Zelman, N, Klaushofer, K 1993Collagen packing and mineralizationBiophys J64260266Google Scholar
  11. Fratzl, P, Gupta, HS, Paschalis, EP, Roschger, P 2004Structure and mechanical quality of the collagen-mineral nanocomposite in boneJ Mater Chem1421152123CrossRefGoogle Scholar
  12. Gao, H, Baohua, J, Jaeger, IL, Arzt, E, Fratzl, P 2003Materials become insensitive to flaws at nanoscale: Lessons from natureP Nat Acad Sci10055975600CrossRefADSGoogle Scholar
  13. Gere, JM, Timoshenko, SPl 1984Mechanics of materials2PWS EngineeringBostonGoogle Scholar
  14. Gibson, LJ, Ashby, MF 1988Cellular solids2Cambridge University PressCambridgezbMATHGoogle Scholar
  15. Gibson, LJ, Ashby, MF, Karam, GN, Wegst, U, Shercliff, HR 1957The mechanical properties of natural materials. II. Microstructures for mechanical efficiencyProc Roy Soc Lond A450141162ADSGoogle Scholar
  16. Gupta H, et al., this issueGoogle Scholar
  17. Hillam (1996), Quote, by Currey (2002)Google Scholar
  18. Hulmes, DJS, Wess, TJ, Prockop, DJ, Fratzl, P 1995Radial packing, order and disorder in collagen fibrilsBiophys J6816611670Google Scholar
  19. Jaeger, I, Fratzl, P 2007Mineralized collagen fibrils—a mechanical model with a staggered arrangement of mineral particlesBiophys J7917371746Google Scholar
  20. Kirchner, HOK 2001Brittle fracture of snowBouchaud, EJeulin, DPrioul, CRoux, S eds. Physical aspects of fractureKluwerDordrecht4757Google Scholar
  21. Kirchner, HOK, Michot, G, Narita, H, Suzuki, T 2001Snow as a foam of ice: plasticity, fracture and the brittle- to-ductile transitionPhil. Mag A8121612181CrossRefADSGoogle Scholar
  22. Koizumi, H, Kirchner, HOK, Suzuki, T 1993Kink pair nucleation and critical shear stressActa Metall et Materialia4134833493CrossRefGoogle Scholar
  23. Krag, S, Olsen, T, Andreassen, TT 1997Biomechanical characteristics of the human anterior lens capsule in relation with ageInvestigations in Ophthalmological and Visual Sciences38357363Google Scholar
  24. McElhaney, JH 1966Dynamic response of bone and muscle tissueJ Appl Phys2112311236Google Scholar
  25. Michot, G 1988Fundamentals of silicon fractureCrystal Properties and Preparation17-185598Google Scholar
  26. Misof, K, Landis, WJ, Klaushofer, K, Fratzl, P 1997aCollagen from the osteogenesis imperfect mouse model (oim) shows reduced resistance against tensile stressJ Clin Invest1004045CrossRefGoogle Scholar
  27. Misof, K, Rapp, G, Fratzl, P 1997bA new molecular model for collagen elasticity based on synchrotron X-ray evidenceBiophys J7213761381CrossRefGoogle Scholar
  28. Nabarro, FRN, deVilliers, HL 1995The Physics of CreepTaylor and FrancisLondonGoogle Scholar
  29. Orgel, JBRO, Miller, A, Irving, TC, Fischetti, RF, Hammersley, AP, Wess, T 2001The In Situ Supermolecular Structure of Type I CollagenStructure910611069CrossRefGoogle Scholar
  30. Pithioux, M, Subit, D, Chabrand, P 2004Comparison of compact bone failure under two different loading rates: experimental and modelling approachesMed Eng Phys2647653CrossRefGoogle Scholar
  31. Puxkandl, R, Zizak, I, Paris, O, Keckes, J, Tesch, W, Bernstorff, S, Purslow, P, Fratzl, P 2002Viscoelastic properties of collagen: synchrotron radiation investigations and structural modelPhilos T Roy Soc B357191197CrossRefGoogle Scholar
  32. Rho, JY, Kuhn-Sperling, I, Zioupos, P 1998Mechanical properties and the hierarchical structure of boneMed Eng Phys2092102CrossRefGoogle Scholar
  33. Rice, JR, Lapusta, N, Ranjith, K 2001Rate and state dependent friction and the stability of sliding between elastically deformable solidsJ Math Phys Solids4918651898zbMATHCrossRefADSGoogle Scholar
  34. Riedle, J, Gumbsch, P, Fischmeister, HF 1996Cleavage anisotropy in tungsten single crystalsPhys Rev Lett7635943596CrossRefADSGoogle Scholar
  35. Rimnac, CM, Petko, AA, Santner, TJ, Wright, TM 1993The effect of temperature, stress and microstructure on the creep of compact bovine boneJ Biomech26219228CrossRefGoogle Scholar
  36. Robertson, DM, Smith, DC 1978Compressive strength of mandibular bone as a function of microstructure and strain rateJ Biomech11455471CrossRefGoogle Scholar
  37. Schoeck, G 1965The activation energy of dislocation movementPhys Status Solidi8499507Google Scholar
  38. Seeger, A 1981The temperature and strain-rate dependeence of the flow stress of body-centered cubic metalsZ Metallkd72369380Google Scholar
  39. Seeger, A, Schiller, P 1966Kinks in dislocation lines and their effects on the internal friction in crystalsMason, WP eds. Physical acoustics IIIAAcademic PressNew York361495Google Scholar
  40. Wess, TJ, Hammersley, AP, Wess, L, Miller, A 1998A consensus model for molecular packing of Type I collagenJ Struct Biol12292100CrossRefGoogle Scholar
  41. Wright, TM, Hayes, WC 1976Tensile testing of bone over a wide range of strain rates: effects of strain rate, microstructure and densityMed Biol Eng14671679CrossRefGoogle Scholar
  42. P. Zioupos, 139:407–424Google Scholar
  43. Zioupos P, Hansen U, Currey JD (2005) Private communication by Prof. Zioupos, Cranfield UniversityGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Helmut KirchnerParisFrance

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