Abstract
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.
Similar content being viewed by others
References
AS Argon (1999) Rate processes in plastic deformation of crystalline and noncrystalline solids MA Meyers RW Armstrong HOK Kirchner (Eds) Mechanics and materials John Wiley New York 175–230
MF Ashby (1992) Materials selection in mechanical design Butterworth-Heinemann Oxford
MF Ashby LJ Gibson U Wegst R Olive (1957) ArticleTitleThe mechanical properties of natural materials. I. Material property charts Proc Roy Soc Lond A 450 132–140
K Beck B Brodsky (1998) ArticleTitleSupercoiled protein motifs: the collagen triple-helix and the alpha-helical coiled coil J Struct Biol 122 17–29 Occurrence Handle10.1006/jsbi.1998.3965
DB Burr C Milgrom D Fyhrie M Forwood M Nyska A Finestone S Hoshaw E Saiag A Simkin (1996) ArticleTitleIn vivo measurements of human tibial strains during vigorous activity Bone 18 405–410 Occurrence Handle10.1016/8756-3282(96)00028-2
RD Crowninshield MH Pope (1974) ArticleTitleThe Response of compact bone in tension at various strain rates Ann Biomed Eng 2 217–225 Occurrence Handle10.1007/BF02368492
JD Currey (2002) Bones: structure and mechanics Princeton University Press Princeton
GP Evans JC Behiri LC Vaughan W Bonfield (1992) ArticleTitleThe response of equine cortical bone to loading at strain rates experienced in vivo by the galopping horse Equine Vet J 24 125–128 Occurrence Handle10.1111/j.2042-3306.1992.tb02796.x
P Fratzl (2003) ArticleTitleCellulose and collagen: from fibres to tissues Curr Opin Colloid Sci 8 32–39 Occurrence Handle10.1016/S1359-0294(03)00011-6
P Fratzl N Fratzl-Zelman K Klaushofer (1993) ArticleTitleCollagen packing and mineralization Biophys J 64 260–266
P Fratzl HS Gupta EP Paschalis P Roschger (2004) ArticleTitleStructure and mechanical quality of the collagen-mineral nanocomposite in bone J Mater Chem 14 2115–2123 Occurrence Handle10.1039/b402005g
H Gao J Baohua IL Jaeger E Arzt P Fratzl (2003) ArticleTitleMaterials become insensitive to flaws at nanoscale: Lessons from nature P Nat Acad Sci 100 5597–5600 Occurrence Handle10.1073/pnas.0631609100 Occurrence Handle2003PNAS..100.5597G
JM Gere SPl Timoshenko (1984) Mechanics of materials EditionNumber2 PWS Engineering Boston
LJ Gibson MF Ashby (1988) Cellular solids EditionNumber2 Cambridge University Press Cambridge Occurrence Handle0723.73004
LJ Gibson MF Ashby GN Karam U Wegst HR Shercliff (1957) ArticleTitleThe mechanical properties of natural materials. II. Microstructures for mechanical efficiency Proc Roy Soc Lond A 450 141–162 Occurrence Handle1995RSPSA.450..141G
Gupta H, et al., this issue
Hillam (1996), Quote, by Currey (2002)
DJS Hulmes TJ Wess DJ Prockop P Fratzl (1995) ArticleTitleRadial packing, order and disorder in collagen fibrils Biophys J 68 1661–1670
I Jaeger P Fratzl (2007) ArticleTitleMineralized collagen fibrils—a mechanical model with a staggered arrangement of mineral particles Biophys J 79 1737–1746
HOK Kirchner (2001) Brittle fracture of snow E Bouchaud D Jeulin C Prioul S Roux (Eds) Physical aspects of fracture Kluwer Dordrecht 47–57
HOK Kirchner G Michot H Narita T Suzuki (2001) ArticleTitleSnow as a foam of ice: plasticity, fracture and the brittle- to-ductile transition Phil. Mag A 81 2161–2181 Occurrence Handle10.1080/01418610010029043 Occurrence Handle2001PMagA..81.2161K
H Koizumi HOK Kirchner T Suzuki (1993) ArticleTitleKink pair nucleation and critical shear stress Acta Metall et Materialia 41 3483–3493 Occurrence Handle10.1016/0956-7151(93)90228-K
S Krag T Olsen TT Andreassen (1997) ArticleTitleBiomechanical characteristics of the human anterior lens capsule in relation with age Investigations in Ophthalmological and Visual Sciences 38 357–363
JH McElhaney (1966) ArticleTitleDynamic response of bone and muscle tissue J Appl Phys 21 1231–1236
G Michot (1988) ArticleTitleFundamentals of silicon fracture Crystal Properties and Preparation 17-18 55–98
K Misof WJ Landis K Klaushofer P Fratzl (1997a) ArticleTitleCollagen from the osteogenesis imperfect mouse model (oim) shows reduced resistance against tensile stress J Clin Invest 100 40–45 Occurrence Handle10.1172/JCI119519
K Misof G Rapp P Fratzl (1997b) ArticleTitleA new molecular model for collagen elasticity based on synchrotron X-ray evidence Biophys J 72 1376–1381 Occurrence Handle10.1016/S0006-3495(97)78783-6
FRN Nabarro HL deVilliers (1995) The Physics of Creep Taylor and Francis London
JBRO Orgel A Miller TC Irving RF Fischetti AP Hammersley T Wess (2001) ArticleTitleThe In Situ Supermolecular Structure of Type I Collagen Structure 9 1061–1069 Occurrence Handle10.1016/S0969-2126(01)00669-4
M Pithioux D Subit P Chabrand (2004) ArticleTitleComparison of compact bone failure under two different loading rates: experimental and modelling approaches Med Eng Phys 26 47–653 Occurrence Handle10.1016/j.medengphy.2004.05.002
R Puxkandl I Zizak O Paris J Keckes W Tesch S Bernstorff P Purslow P Fratzl (2002) ArticleTitleViscoelastic properties of collagen: synchrotron radiation investigations and structural model Philos T Roy Soc B 357 191–197 Occurrence Handle10.1098/rstb.2001.1033
JY Rho I Kuhn-Sperling P Zioupos (1998) ArticleTitleMechanical properties and the hierarchical structure of bone Med Eng Phys 20 92–102 Occurrence Handle10.1016/S1350-4533(98)00007-1
JR Rice N Lapusta K Ranjith (2001) ArticleTitleRate and state dependent friction and the stability of sliding between elastically deformable solids J Math Phys Solids 49 1865–1898 Occurrence Handle1093.74512 Occurrence Handle10.1016/S0022-5096(01)00042-4 Occurrence Handle2001JMPSo..49.1865R
J Riedle P Gumbsch HF Fischmeister (1996) ArticleTitleCleavage anisotropy in tungsten single crystals Phys Rev Lett 76 3594–3596 Occurrence Handle10.1103/PhysRevLett.76.3594 Occurrence Handle1996PhRvL..76.3594R
CM Rimnac AA Petko TJ Santner TM Wright (1993) ArticleTitleThe effect of temperature, stress and microstructure on the creep of compact bovine bone J Biomech 26 219–228 Occurrence Handle10.1016/0021-9290(93)90360-Q
DM Robertson DC Smith (1978) ArticleTitleCompressive strength of mandibular bone as a function of microstructure and strain rate J Biomech 11 455–471 Occurrence Handle10.1016/0021-9290(78)90057-X
G Schoeck (1965) ArticleTitleThe activation energy of dislocation movement Phys Status Solidi 8 499–507
A Seeger (1981) ArticleTitleThe temperature and strain-rate dependeence of the flow stress of body-centered cubic metals Z Metallkd 72 369–380
A Seeger P Schiller (1966) Kinks in dislocation lines and their effects on the internal friction in crystals WP Mason (Eds) Physical acoustics IIIA Academic Press New York 361–495
TJ Wess AP Hammersley L Wess A Miller (1998) ArticleTitleA consensus model for molecular packing of Type I collagen J Struct Biol 122 92–100 Occurrence Handle10.1006/jsbi.1998.3991
TM Wright WC Hayes (1976) ArticleTitleTensile testing of bone over a wide range of strain rates: effects of strain rate, microstructure and density Med Biol Eng 14 671–679 Occurrence Handle10.1007/BF02477046
P. Zioupos, 139:407–424
Zioupos P, Hansen U, Currey JD (2005) Private communication by Prof. Zioupos, Cranfield University
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kirchner, H. Ductility and brittleness of bone. Int J Fract 139, 509–516 (2006). https://doi.org/10.1007/s10704-006-0050-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10704-006-0050-2