From brittle to ductile fracture of bone
HERWIG PETERLIK1,PAUL ROSCHGER2,KLAUS KLAUSHOFER2AND PETER FRATZL3*
1Institute of Materials Physics,University of Vienna,A-1090Vienna,Austria
2Ludwig-Boltzmann Institute of Osteology at the Hanusch Hospital WGKK and AUVA Trauma Centre Meidling,4th Medical Department,Hanusch Hospital,A-1140Vienna,Austria 3Max-Planck Institute of Colloids and Interfaces,D-14424Potsdam,Germany
*e-mail:fratzl@mpikg.mpg.de
Published online:11December2005;doi:10.1038/nmat1545
T oughness is crucial to the structural function of bone.
Usually,the toughness of a material is not just determined
by its composition,but by the ability of its microstructure
to dissipate deformation energy without propagation of the
crack1.Polymers are often able to dissipate energy by viscoplastic
?ow or the formation of non-connected microcracks2.In
ceramics,well-known toughening mechanisms are based on
crack ligament bridging and crack de?ection3.Interestingly,
all these phenomena were identi?ed in bone4–12,which is
a composite of a?brous polymer(collagen)and ceramic
nanoparticles(carbonated hydroxyapatite)13–16.Here,we use
controlled crack-extension experiments to explain the in?uence
of?bre orientation on steering the various toughening
mechanisms.We?nd that the fracture energy changes by two
orders of magnitude depending on the collagen orientation,and
the angle between collagen and crack propagation direction is
decisive in switching between di?erent toughening mechanisms.
Most biological materials with predominantly mechanical
function have a hierarchical structure consisting of several di?erent
hierarchical levels13.In this way,tough materials were designed
by nature,based on extremely di?erent base materials,for
example,polymers such as in wood17,polymer–ceramic particle
composites such as in bone14,structures consisting almost entirely
of mineral in many sea shells such as that of the conch Strombus gigas18,or even glass such as in some marine sponges19.Bone is a complex material based on collagen?brils reinforced with
nanosized mineral particles15.These nanosized mineral platelets
are able to sustain large tensile stress,whereas the protein layer
between them must sustain shear stress16.In mature cortical bone,
collagen?brils are assembled into a lamellar structure,which has
been described in analogy to plywood20,21.From a mechanical
viewpoint,bone contains defects ranging in size from micrometres
to millimetres,for example,cavities for blood vessels and for bone
cells(osteocytes),or the network of canaliculi.As a consequence,
bone tissue must be?aw-insensitive not only at the nanoscopic16
but also the microscopic level.A robust materials design requires
that when the local strain energy exceeds a certain critical level
it has to be e?ectively transferred into a large macroscopic
volume,as micrometre-sized channels or lacunae are acting as
stress concentrators.
Di?erent toughening mechanisms were previously identi?ed in
bone(Fig.1)and compared to similar phenomena in technical
Microcracking and crazing
(ceramics and polymers)
Viscoplastic flow (gels)
Crack bridging
(ceramic fibre composites)
Crack deflection
(composites)
Figure1The toughening mechanisms in bone.Different toughening mechanisms such as viscoplastic?ow4,5,microcracking6–8,crack bridging10–12and crack
de?ection9were identi?ed in bone.The shaded area visualizes the highly stressed region in the vicinity of the crack tip.
materials.As in polymers,the dissipation of energy to keep bone from fracture was attributed to viscoplastic?ow,with‘sacri?cial bonds’in collagen needing time to re-form after pulling4,5,which was correlated to the time needed for bone to recover its toughness, as measured by atomic force microscope indentation.Deformation energy has been shown to be dissipated by shearing of a thin‘glue’layer between mineral-reinforced collagen?brils22.The formation of microcracks in the vicinity of the main crack owing to stress concentrations ahead of the crack tip was visualized by laser scanning confocal microscopy in the frontal process zone6–8.Crack
R L
C
Load
W
Crack length a
Span
LVDT
Moving video-
microscope
B
Figure2The experimental setup of the controlled crack-extension experiment.Longitudinal(L),radial(R)and circumferential(C)denote the respective directions of crack propagation.Rectangular slabs were prepared from fragments of cortical bone from femoral and tibial diaphysis of a52-year-old woman,which were wet-machined in different directions to give?nal dimensions of approximately15×1.5×2mm3;they were then loaded under three-point bending.With a closed-loop control,a linear variable differential transducer(LVDT)ensured a constant displacement rate of3μm s?1corresponding to a peak strain rate of approximately200microstrain s?1.In several cycles the specimens were increasingly loaded to propagate the crack and then immediately unloaded.In distinction from other experimental methods,no arti?cial starting notch was used,but the crack was initiated by the load of the as-machined specimens.Furthermore,the crack was?lled with a wetting?uid containing the dyestuff rhodamine B after each cycle for a better visualization of the crack tip.
de?ection and crack blunting9at weak interfaces,toughening mechanisms well known from composites,were attributed to the interlamellar boundaries and the cement lines(at the secondary osteon boundaries).Crack bridging10–12in the wake zone,a mechanism well known in ceramics23,was proposed to play a dominant role in enhancing the fracture properties of bone.It was shown that uncracked ligaments span the crack wake and,thus, reduce the crack-tip driving force10–12.
These toughening mechanisms are strongly dependent on the orientation of the crack propagation:the fracture toughness of long bones is considerably lower if the crack propagates along the long axis of the bone rather than perpendicular to it.This strong anisotropy a?ects the fracture properties10,24–27as well as the elastic moduli26,28.The design of anisotropic structures,such as?bre composites,for example,is a widely used principle to improve the toughness in certain directions of a material at the expense of other(less critical)directions29.In long bones, anisotropy is a consequence of the preferential alignment of collagen?brils together with platelet-shaped mineral crystals aligned along their axis15,30.
In the current investigation,controlled crack extension in three-point bending experiments was used to determine the energy required to propagate a crack in di?erent directions.The results were then correlated to the main origin of anisotropy,the collagen angle.The method allowed the determination of the energy per area with a local resolution of20–500μm,depending on the amount of local crack extension(Fig.2).
The energy required to extend the crack by a certain amount of area was determined by the J-integral method(for a description of this method,see Supplementary Information). The energy was directly obtained from the area of the load–displacement curve up to the moment of crack extension, divided by the remaining ligament area that was able to sustain the respective load.For materials with strong viscoelastic behaviour such as bone,this approach is preferable to the crack-growth-resistance method,where the energy per loading cycle is divided by the amount of increase in the crack area. The crack-growth-resistance method tends to overestimate the energy per area,especially for small crack extension,as energy is consumed in loading–unloading cycles without contributing to
crack propagation3(see Supplementary Information).
The crack-extension energy per area was found to be strongly
dependent on the collagen angleγ,visualized by polarized light microscopy(Zeiss,Axiophot),with respect to the loading axis as
de?ned in Fig.3a.To extend the crack along the direction of
the collagen?brils with a misalignment between0and5?,only
375J m?2are required(with a lowest value of110J m?2for
the lowest misalignment angle of1.5?),whereas9,920J m?2are needed for a propagation perpendicular to the?brils(Fig.3a),
which is nearly an increase of two orders of magnitude!Only
a slight increase of the crack-extension energy was observed
with increasing collagen angle up to a level of about50?.At
this point a considerable jump in the crack-extension energy
per area is visible,followed again by an increase up to an
angle where the collagen?brils are oriented perpendicular to the
direction of crack extension.Accordingly,the crack path angle αchanges its appearance from straight to a zig-zag,Fig.3b.Its standard deviation,calculated from the distribution observed in
the scanning electron microscopy(Zeiss,DSM962)within the
respective ranges of constant collagen angles,shows low values(that
is,a straight and smooth crack path)for the case of collagen angles
lower than about50?and high values otherwise(that is,a de?ected,
zig-zag crack path).
The sudden increase in the crack-extension energy per area
and the appearance of the cracks(Fig.3)cannot be related to
just one of the various toughening mechanisms proposed for
bone tissue.The sudden increase in the numerical values of the
energies suggests a transition from a brittle to a quasiductile
fracture mode.Figure4shows evidence for this transition for
the two extreme cases,the orientation of collagen?brils being
perfectly aligned with the mean crack path(Fig.4a)and the
orientation being perfectly perpendicular to the mean crack path
(Fig.4b).When the main crack propagates along the?brils and
the lamellae,the crack path is straight and the crack?anks appear
smooth,which is typical for brittle fracture.When the main
crack crosses the collagen?brils,the structure appears heavily
distorted and torn perpendicular to the main crack propagation
direction,which is characteristic for a quasiductile fracture(further
Loading direction
α
γ14,00012,00010,0008,0006,0004,000
2,000
080
60
40
20
20
4060
80
C r a c k e x t e n s i o n e n e r g y (J m –2)
(°)
γ (°)Crack path
Orientation of collagen fibrils 9,920 J m –2
375 J m –2
a
b
γ
αFigure 3Crack extension as a function of the collagen angle γ.a ,The energy
required for crack extension and b ,the standard deviation of the crack path angle α.The total number of values is 76for a ,showing the mean and the standard error,and 169for b .A signi?cant jump for both parameters is observed at approximately 50?.The standard deviation was calculated from the distribution of the crack path angles (obtained from digitized scanning electron microscopy images with a resolution of about 1μm),which were overlaid with the digitized images from polarization light microscopy,on which the ranges of constant collagen angles were identi?ed (which are typically in the range of about 10μm,but signi?cantly larger,up to 100μm,for specimens cut out in the longitudinal direction).Thus,a distribution of crack-path angles was obtained within each interval of approximately constant collagen angle,from which mean values and a standard deviation could be calculated.
images are shown in the Supplementary Information).Figure 4c summarizes the evolution of the fracture process with respect to the collagen orientation.For a perfectly aligned structure,the crack is able to follow precisely the collagen ?brils at low crack-extension energy (about 100J m ?2).In the case of a small misorientation,misaligned ?brils act as crack bridges,reducing the actual driving force available at the crack tip and leading to an increase of the crack-extension energy per area with increasing misalignment angle (see Fig.3a).At a misalignment angle of about 50?,a transition from brittle to quasiductile fracture takes place and several di ?erent toughening mechanisms emerge.The sequence of di ?erent collagen ?bril orientations in the lamellae 20,21constitutes regions of di ?erent sti ?ness and induces the development of a process zone with low and strongly strained regions.Microcracks emanate in the higher strained parts,whereas the less-strained regions are still able to sustain a load and bridge the destroyed parts of the contact zone,being accompanied by crack de?ection (Fig.4b).
The lamellar morphology of cortical bone seems a perfect design for a tough material.A variety of toughening mechanisms are active and there is a transition from a brittle to a quasiductile fracture mode when the angle between the collagen and the mean
a
c
b
10 μm 10 μm
Figure 4Scanning electron micrographs of the crack path.a ,Longitudinal crack extension,where the crack ?anks appear straight and smooth.b ,Circumferential crack extension,where the crack ?anks appear de?ected and heavily distorted.Radial crack extension gives a similar picture.c ,A scheme showing the orientation of the ?brils and the lamellae to explain the transition from brittle to quasiductile behaviour.Fibrils parallel to the crack,a crack bridge and a schematic of the plywood model 20are shown from the left-hand to the right-hand side.
crack increases beyond 50?.From a fracture-resistance point of view,the variation of ?bril angles across the bone tissue according to the plywood model 20,21therefore gives several advantages over perfect alignment:it increases the crack-extension energy per area,transports energy into a higher volume and,consequently,leads to a more ductile fracture behaviour of bone tissue.
Received 13July 2005;accepted 24October 2005;published 11December 2005.References
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This study was supported by the AUV A(Austrian Insurance for Occupational Risk),by the WGKK (Social Health Insurance Vienna)and the FWF(Austrian Science Funds,project P16880-B13).We acknowledge A.Nader from the Institute for Pathology at the Hanusch Krankenhaus in Vienna for supplying the bone tissue.
Correspondence and requests for materials should be addressed to P.F.
Supplementary Information accompanies this paper on https://www.doczj.com/doc/7510886822.html,/naturematerials. Competing?nancial interests
The authors declare that they have no competing?nancial interests.
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