A miniaturized version of the double cantilever beam (DCB) test is used to determine the fracture energy in human cortical bone under pure mode I loading. An equivalent crack length based data-reduction scheme is used with remarkable advantages relative to classical methods. Digital image correlation (DIC) technique is employed to determine crack opening displacement at the crack tip being correlated with the evolution of fracture energy. A method is presented to obtain the cohesive law (trapezoidal bilinear softening) mimicking the mechanical behavior observed in bone. Cohesive zone modeling (CZM) (finite-element method) was performed to validate the procedure showing excellent agreement.

References

References
1.
Ritchie
,
R. O.
,
Nalla
,
R. K.
,
Kruzic
,
J. J.
,
Ager
,
J. W.
,
Balooch
,
G.
, and
Kinney
,
J. H.
,
2006
, “
Fracture and Ageing in Bone: Toughness and Structural Characterization
,”
Strain
,
42
(
4
), pp.
225
232
.
2.
Norman
,
T. L.
,
Vashishth
,
D.
, and
Burr
,
D. B.
,
1991
, “
Mode I Fracture Toughness of Human Bone
,”
Adv. Bioeng., BED
,
20
, pp.
361
364
.
3.
Norman
,
T. L.
,
Vashishth
,
D.
, and
Burr
,
D. B.
,
1995
, “
Fracture Toughness of Human Bone Under Tension
,”
J. Biomech.
,
28
(
3
), pp.
309
320
.
4.
Norman
,
T. L.
,
Nivargikar
,
S. V.
, and
Burr
,
D. B.
,
1996
, “
Resistance to Crack Growth in Human Cortical Bone is Greater in Shear Than in Tension
,”
J. Biomech.
,
29
(
8
), pp.
1023
1031
.
5.
Yeni
,
Y. N.
,
Brown
,
C. U.
, and
Norman
,
T. L.
,
1998
, “
Influence of Bone Composition and Apparent Density on Fracture Toughness of the Human Femur and Tibia
,”
Bone
,
22
(
1
), pp.
79
84
.
6.
Brown
,
C. U.
,
Yeni
,
Y. N.
, and
Norman
,
T. L.
,
2000
, “
Fracture Toughness is Dependent on Bone Location: A Study of the Femoral Neck, Femoral Shaft, and the Tibial Shaft
,”
J. Biomed. Mater. Res. A
,
49
(
3
), pp.
380
389
.
7.
Ural
,
A.
, and
Mischinski
,
S.
,
2013
, “
Multiscale Modeling of Bone Fracture Using Cohesive Finite Elements
,”
Eng. Fract. Mech.
,
103
, pp.
141
152
.
8.
Vashishth
,
D.
,
Behiri
,
J. C.
, and
Bonfield
,
W.
,
1997
, “
Crack Growth Resistance in Cortical Bone: Concept of Microcrack Toughening
,”
J. Biomech.
,
30
(
8
), pp.
763
769
.
9.
Nalla
,
R.
,
Kinney
,
J.
, and
Ritchie
,
R.
,
2003
, “
Mechanistic Fracture Criteria for the Failure of Human Cortical Bone
,”
Nat. Mater.
,
2
(
3
), pp.
164
168
.
10.
Nalla
,
R. K.
,
Kruzic
,
J. J.
,
Kinney
,
J. H.
, and
Ritchie
,
R. O.
,
2005
, “
Mechanistic Aspects of Fracture and R-Curve Behaviour in Human Cortical Bone
,”
Biomaterials
,
26
(
2
), pp.
217
231
.
11.
Koester
,
K. J.
,
Ager
,
J. W.
, and
Ritchie
,
R. O.
,
2008
, “
How Tough is Human Bone? In Situ Measurements on Realistically Short Cracks
,”
Nat. Mater.
,
7
(
8
), pp.
672
677
.
12.
Irwin
,
G. R.
,
1960
,
Structural Mechanics
,
Pergamon Press
,
London, UK
.
13.
Krafft
,
J. M.
,
Sullivan
,
A. M.
, and
Boyle
,
R. W.
,
1961
, “
Effect of Dimensions on Fast Fracture Instability of Notched Sheets
,”
Proc. Crack Propag. Symp.
,
1
, pp.
8
28
.
14.
Vashishth
,
D.
,
Behiri
,
J. C.
,
Tanner
,
K. E.
, and
Bordield
,
W.
,
1996
, “
Toughening Mechanisms in Cortical Bone
,”
42nd Ann. Meeting ORS
, Atlanta, GA, pp.
19
22
.
15.
Vashishth
,
D.
,
Behiri
,
J. C.
, and
Bonfield
,
W.
,
1997
, “
Crack Growth Resistance in Cortical Bone: Concept of Microcrack Toughening
,”
J. Biomech.
,
30
(
8
), pp.
763
769
.
16.
Zioupos
,
P.
,
1998
, “
Recent Developments in the Study of Failure of Solid Biomaterials and Bone: ‘Fracture’ and ‘Pre-Fracture’ Toughness
,”
Mater. Sci. Eng. C
,
6
(
1
), pp.
33
40
.
17.
Yang
,
Q. D.
,
Cox
,
N. B.
,
Nalla
,
K. R.
, and
Ritchie
,
R. O.
,
2006
, “
Fracture Length Scales in Human Cortical Bone: The Necessity of Nonlinear Fracture Models
,”
Biomaterials
,
27
(
9
), pp.
2095
2113
.
18.
Yan
,
J.
,
Clifton
,
K. B.
,
Mecholsky
,
J. J.
, Jr.
, and
Reep
,
R. L.
,
2006
, “
Fracture Toughness of Manatee Rib and Bovine Femur Using a Chevron-Notched Beam Test
,”
J. Biomech.
,
39
(
6
), pp.
1066
1074
.
19.
Wang
,
X.
, and
Agrawal
,
C. M.
,
1996
, “
Fracture Toughness of Bone Using a Compact Sandwich Specimen: Effects of Sampling Sites and Crack Orientations
,”
J. Biomed. Mater. Res.
,
33
(
1
), pp.
13
21
.
20.
Phelps
,
J. B.
,
Hubbard
,
G. B.
,
Wang
,
X.
, and
Agrawal
,
C. M.
,
2000
, “
Microstructural Heterogeneity and the Fracture Toughness of Bone
,”
J. Biomed. Mater. Res.
,
51
(
4
), pp.
735
741
.
21.
Zimmermann
,
E. A.
,
Gludovatz
,
B.
,
Schaible
,
E.
,
Busse
,
B.
, and
Ritchie
,
R. O.
,
2014
, “
Fracture Resistance of Human Cortical Bone Across Multiple Length-Scales at Physiological Strain Rates
,”
Biomaterials
,
35
(
21
), pp.
5472
5481
.
22.
Morais
,
J. J. L.
,
de Moura
,
M. F. S. F.
,
Pereira
,
F. A. M.
,
Xavier
,
J.
,
Dourado
,
N.
,
Dias
,
M. I. R.
, and
Azevedo
,
J. M. T.
,
2010
, “
The Double Cantilever Beam Test Applied to Mode I Fracture Characterization of Cortical Bone Tissue
,”
J. Mech. Behav. Biomed. Mater.
,
3
(
6
), pp.
446
453
.
23.
de Moura
,
M. F. S. F.
,
Dourado
,
N.
, and
Morais
,
J.
,
2010
, “
Crack Equivalent Based Method Applied to Wood Fracture Characterization Using the Single Edge Notched-Three Point Bending Test
,”
Eng. Fract. Mech.
,
77
(
3
), pp.
510
520
.
24.
Xavier
,
J.
,
Oliveira
,
J.
,
Monteiro
,
P.
,
Morais
,
J. J. L.
, and
de Moura
,
M. F. S. F.
,
2014
, “
Direct Evaluation of Cohesive Law in Mode I of Pinus Pinaster by Digital Image Correlation
,”
Exp. Mech.
54
(
5
), pp.
829
840
.
25.
GOM mbH
,
2007
, aramis dic 2D/3D Commercial Software 2007, aramis 6.0.2.
26.
Xavier
,
J.
,
de Jesus
,
A. M. P.
,
Morais
,
J. J. L.
, and
Pinto
,
J. M. T.
,
2012
, “
Stereovision Measurements on Evaluating the Modulus of Elasticity of Wood by Compression Tests Parallel to the Grain
,”
Constr. Build. Mater.
,
26
(
1
), pp.
207
215
.
27.
Sousa
,
A. M. R.
,
Xavier
,
J.
,
Vaz
,
M.
,
Morais
,
J. J. L.
, and
Filipe
,
V. M. J.
,
2011
, “
Cross-Correlation and Differential Technique Combination to Determine Displacement Fields
,”
Strain
,
47
(
Suppl. 2
) pp.
87
98
.
28.
Sousa
,
A. M. R.
,
Xavier
,
J.
,
Morais
,
J. J. L.
,
Filipe
,
V. M. J.
, and
Vaz
,
M.
,
2011
, “
Processing Discontinuous Displacement Fields by a Spatio-Temporal Derivative Technique
,”
Opt. Laser Eng.
,
49
(
12
), pp.
1402
1412
.
29.
Kaute
,
D. A. W.
,
Shercliff
,
H. R.
, and
Ashby
,
M. F.
,
1993
, “
Delamination, Fibre Bridging and Toughness of Ceramic Matrix Composites
,”
Acta Metall. Mater.
,
41
(
7
), pp.
1959
1970
.
30.
Koester
,
K. J.
,
Barth
,
H. D.
, and
Ritchie
,
R. O.
,
2011
, “
Effect of Aging on the Transverse Toughness of Human Cortical Bone: Evaluation by R-Curves
,”
J. Mech. Behav. Biomed.
,
4
(
7
), pp.
1504
1513
.
31.
Koester
,
K. J.
,
Ager
,
J. W.
, and
Ritchie
,
R. O.
,
2008
, “
The True Toughness of Human Cortical Bone Measured With Realistically Short Cracks
,”
Nat. Mater.
,
7
(
8
), pp.
672
677
.
32.
Wagermaier
,
W.
,
Gupta
,
H. S.
,
Gourrier
,
A.
,
Paris
,
O.
,
Roschger
,
P.
,
Burghammer
,
M.
,
Reikel
,
C.
, and
Fratzl
,
P.
,
2007
, “
Scanning Texture Analysis of Lamellar Bone Using Microbeam Synchrotron X-Ray Radiation
,”
J. Appl. Crystallogr.
,
40
(
1
), pp.
115
120
.
33.
ISO 15024
:
2001
,
2002
,
Fibre-Reinforced Plastic Composites—Determination of Mode I Interlaminar Fracture Toughness, GIc, for Unidirectionally Reinforced Materials
, BSI, Switzerland.
34.
Park
,
K.
, and
Paulino
,
G. H.
,
2011
, “
Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces
,”
ASME Appl. Mech. Rev.
,
64
(6), p. 060802.
35.
Rice
,
J. R.
,
1968
, “
A Path Independent Method Integral and the Approximate Analysis of Strain Correlation by Notches and Cracks
,”
ASME J. Appl. Mech.
,
35
(
2
), pp.
379
386
.
36.
Lancaster
,
P.
, and
Salkauskas
,
K.
,
1986
,
Curve and Surface Fitting: An Introduction
,
Academic Press
,
New York
.
37.
Wirtz
,
D. C.
,
Schiffers
,
N.
,
Pandorf
,
T.
,
Radermacher
,
K.
,
Weichert
,
D.
, and
Forst
,
R.
,
2000
, “
Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of the Proximal Femur
,”
J. Biomech.
,
33
(
10
), pp.
1325
1330
.
You do not currently have access to this content.