The fracture of bone due to indentation with a hard, sharp object is of significance in surgical procedures and certain trauma situations. In the study described below, the fracture of bovine bone under indentation was measured experimentally and predicted using the theory of critical distances (TCDs), a theory, which predicts failure due to cracking in the vicinity of stress concentrations. The estimated indentation fracture force was compared with the experimental results in three different cutting directions. Under indentation, the material experiences high levels of compression and shear, causing cracks to form and grow. The direction of crack growth was highly dependent on the bone’s microstructure: major cracks grew in the weakest possible structural direction. Using a single value of the critical distance , combined with a multiaxial failure criterion, it was possible to predict the experimental failure loads with less than 30% errors. Some differences are expected between the behavior of human bone and the bovine bone studied here, owing to its plexiform microstructure.
Issue Section:
Research Papers
Keywords:
biomechanics,
biomedical measurement,
bone,
compressibility,
cracks,
fracture,
indentation
1.
Carter
, D. R.
, and Hayes
, W. C.
, 1977, “Compact Bone Fatigue Damage. A Microscopic Examination
,” Clin. Orthop. Relat. Res.
0009-921X, 127
, pp. 265
–274
.2.
Barak
, M. M.
, Currey
, J. D.
, Weiner
, S.
, and Shahar
, R.
, 2009, “Are Tensile and Compressive Young’s Moduli of Compact Bone Different?
,” J. Mech. Behav. Biomed. Mater.
1751-6161, 2
(1
), pp. 51
–60
.3.
Vashishth
, D.
, Behiri
, J. C.
, and Bonfield
, W.
, 1997, “Crack Growth Resistance in Cortical Bone: Concept of Microcrack Toughening
,” J. Biomech.
0021-9290, 30
(8
), pp. 763
–769
.4.
Burr
, D. B.
, Turner
, C. H.
, Naick
, P.
, Forwood
, M. R.
, Ambrosius
, W.
, Sayeed Hasan
, M.
, and Pidaparti
, R.
, 1998, “Does Microdamage Accumulation Affect the Mechanical Properties of Bone?
,” J. Biomech.
0021-9290, 31
(4
), pp. 337
–345
.5.
George
, W. T.
, and Vashishth
, D.
, 2005, “Damage Mechanisms and Failure Modes of Cortical Bone Under Components of Physiological Loading
,” J. Orthop. Res.
0736-0266, 23
(5
), pp. 1047
–1053
.6.
Koester
, K. J.
, Ager
, J. W.
, and Ritchie
, R. O.
, 2008, “The True Toughness of Human Cortical Bone Measured With Realistically Short Cracks
,” Nature Mater.
1476-1122, 7
(8
), pp. 672
–677
.7.
Yan
, J.
, Mecholsky
, J. J. J.
, and Clifton
, K. B.
, 2007, “How Tough Is Bone? Application of Elastic-Plastic Fracture Mechanics to Bone
,” Bone
, 40
(2
), pp. 479
–484
.8.
Bonfield
, W.
, 1987, “Advances in the Fracture Mechanics of Cortical Bone
,” J. Biomech.
0021-9290, 20
(11–12
), pp. 1071
–1081
.9.
Taylor
, D.
, 2007, The Theory of Critical Distances
, Elsevier
, New York
.10.
Kasiri
, S.
, and Taylor
, D.
, 2008, “A Critical Distance Study of Stress Concentrations in Bone
,” J. Biomech.
0021-9290, 41
(3
), pp. 603
–609
.11.
Taylor
, D.
, and Kasiri
, S.
, 2008, “A Comparison of Critical Distance Methods for Fracture Prediction
,” Int. J. Mech. Sci.
0020-7403, 50
(6
), pp. 1075
–1081
.12.
Neuber
, H.
, 1985, Theory of Notch Stresses
, Springer
, New York
.13.
Neuber
, H.
, 1936, “Theorie der technischen Formzahl
,” Forsch. Ingenieurwes.
0015-7899, 7
, pp. 271
–274
.14.
Peterson
, R. E.
, 1959, Notch-Sensitivity Metal Fatigue
, McGraw-Hill
, New York
.15.
Whitney
, J. M.
, and Nuismer
, R. J.
, 1974, “Stress Fracture Criteria for Laminated Composites Containing Stress-Concentrations
,” J. Compos. Mater.
0021-9983, 8
, pp. 253
–265
.16.
Taylor
, D.
, 2007, “Multiaxial Loading: Fracture and Fatigue Under Complex Stress States
,” The Theory of Critical Distances
, Elsevier
, Oxford
.17.
Araujo
, J. A.
, Susmel
, L.
, Taylor
, D.
, Ferro
, J. C. T.
, and Mamiya
, E. N.
, 2007, “On the Use of the Theory of Critical Distances and the Modified Wohler Curve Method to Estimate Fretting Fatigue Strength of Cylindrical Contacts
,” Int. J. Fatigue
0142-1123, 29
(1
), pp. 95
–107
.18.
Susmel
, L.
, and Taylor
, D.
, 2008, “The Theory of Critical Distances to Predict Static Strength of Notched Brittle Components Subjected to Mixed-Mode Loading
,” Eng. Fract. Mech.
0013-7944, 75
(3–4
), pp. 534
–550
.19.
Ramamurthy
, T.
, 2001, “Shear Strength Response of Some Geological Materials in Triaxial Compression
,” Int. J. Rock Mech. Min. Sci.
1365-1609, 38
(5
), pp. 683
–697
.20.
Palchik
, V.
, 2006, “Application of Mohr-Coulomb Failure Theory to Very Porous Sandy Shales
,” Int. J. Rock Mech. Min. Sci.
1365-1609, 43
(7
), pp. 1153
–1162
.21.
Sweeney
, A.
, Byers
, R.
, and Kroon
, R.
, 1965, “Mechanical Characteristics of Bone and its Constituents
,” ASME Human Factors Conference, 65-WA (HUF-7)
, American Society of Mechanical Engineers
, New York
, pp. 1
–17
.22.
Ibuki
, S.
, 1964, “Study on the Shearing Strength of Human and Animal Compact Bones
,” Journal of Kyoto Prefectural University of Medicine
, 73
, pp. 495
–512
.23.
Johnson
, W. M.
, and Rapoff
, A. J.
, 2007, “Microindentation in Bone: Hardness Variation With Five Independent Variables
,” J. Mater. Sci.: Mater. Med.
0957-4530, 18
, pp. 591
–597
.24.
Burstein
, A. H.
, Currey
, J. D.
, Frankel
, V. H.
, and Reilly
, D. T.
, 1972, “The Ultimate Properties of Bone Tissue: The Effects of Yielding
,” J. Biomech.
0021-9290, 5
(1
), pp. 35
–42
, IN1–IN2, 43–44.25.
Reilly
, D. T.
, and Burstein
, A. H.
, 1974, “The Mechanical Properties of Cortical Bone
,” J. Bone Jt. Surg., Am. Vol.
0021-9355, 56
(5
), pp. 1001
–1022
.26.
Lawn
, B. R.
, 1975, Fracture of Brittle Solids
, Press Syndicate of the University of Cambridge
, Cambridge, England
.27.
Lawn
, B. R.
, and Wilshaw
, R.
, 1975, “Review Indentation Fracture: Principles and Applications
,” J. Mater. Sci.
0022-2461, 10
, pp. 1049
–1081
.28.
Puttick
, K. E.
, 1978, “The Mechanics of Indentation Fracture in Poly(Methyl Methacrylate)
,” J. Phys. D
0022-3727, 11
(4
), pp. 595
–604
.29.
Behiri
, J. C.
, and Bonfield
, W.
, 1989, “Orientation Dependence of the Fracture Mechanics of Cortical Bone
,” J. Biomech.
0021-9290, 22
(8–9
), pp. 863
–872
.30.
Zioupos
, P.
, Gresle
, M.
, and Winwood
, K.
, 2008, “Fatigue Strength of Human Cortical Bone: Age, Physical, and Material Heterogeneity Effects
,” J. Biomed. Mater. Res. A
, 86A
(3
), pp. 627
–636
.31.
O’Brien
, F. J.
, Taylor
, D.
, and Lee
, T. C.
, 2005, “The Effect of Bone Microstructure on the Initiation and Growth of Microcracks
,” J. Orthop. Res.
0736-0266, 23
(2
), pp. 475
–480
.32.
Nalla
, R. K.
, Kruzic
, J. J.
, and Ritchie
, R. O.
, 2004, “On the Origin of the Toughness of Mineralized Tissue: Microcracking or Crack Bridging?
,” Bone
, 34
(5
), pp. 790
–798
.33.
Ritchie
, R. O.
, Kinney
, J. H.
, Kruzic
, J. J.
, and Nalla
, R. K.
, 2005, “A Fracture Mechanics and Mechanistic Approach to the Failure of Cortical Bone
,” Fatigue Fract. Eng. Mater. Struct.
8756-758X, 28
(4
), pp. 345
–371
.34.
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.
0021-9304, 33
(1
), pp. 13
–21
.35.
King
, M. J.
, 1999, “Knife and Impact Cutting of Lamb Bone
,” Meat Sci.
0309-1740, 52
(1
), pp. 29
–38
.36.
Wiggins
, K. L.
, and Malkin
, S.
, 1976, “Drilling of Bone
,” J. Biomech.
0021-9290, 9
(9
), pp. 553
–559
.37.
Taylor
, D.
, 2008, “Microstructural Parameters in the Theory of Critical Distances
,” Mater. Sci. Forum
0255-5476, 567–568
, pp. 23
–28
.38.
Nalla
, R. K.
, Kinney
, J. H.
, and Ritchie
, R. O.
, 2003, “Mechanistic Fracture Criteria for the Failure of Human Cortical Bone
,” Nature Mater.
1476-1122, 2
(3
), pp. 164
–168
.39.
Krause
, W. R.
, 1987, “Orthogonal Bone Cutting: Saw Design and Operating Characteristics
,” ASME J. Biomech. Eng.
0148-0731, 109
(3
), pp. 263
–271
.40.
Giraud
, J. Y.
, Villemin
, S.
, Darmana
, R.
, Cahuzac
, J. P.
, Autefage
, A.
, and Morucci
, J. P.
, 1991, “Bone Cutting
,” Clin. Phys. Physiol. Meas.
0143-0815, 12
(1
), pp. 1
–19
.41.
Plaskos
, C.
, Hodgson
, A.
, and Cinquin
, P.
, 2003, “Modelling and Optimization of Bone-Cutting Forces in Orthopaedic Surgery
,” Medical Image Computing and Computer-Assisted Intervention— Miccai 2003
, Springer
, Berlin, Heidelberg
.42.
Parsamian
, G. P.
, and Norman
, T. L.
, 2001, “Diffuse Damage Accumulation in the Fracture Process Zone of Human Cortical Bone Specimens and Its Influence on Fracture Toughness
,” J. Mater. Sci.: Mater. Med.
0957-4530, 12
(9
), pp. 779
–783
.43.
Vashishth
, D.
, Tanner
, K. E.
, and Bonfield
, W.
, 2003, “Experimental Validation of a Microcracking-Based Toughening Mechanism for Cortical Bone
,” J. Biomech.
0021-9290, 36
(1
), pp. 121
–124
.44.
Vashishth
, D.
, Koontz
, J.
, Qiu
, S. J.
, Lundin-Cannon
, D.
, Yeni
, Y. N.
, Schaffler
, M. B.
, and Fyhrie
, D. P.
, 2000, “In Vivo Diffuse Damage in Human Vertebral Trabecular Bone
,” Bone
, 26
(2
), pp. 147
–152
.45.
Schaffler
, M. B.
, Pitchford
, W. C.
, Choi
, K.
, and Riddle
, J. M.
, 1994, “Examination of Compact Bone Microdamage Using Back-Scattered Electron Microscopy
,” Bone
, 15
(5
), pp. 483
–488
.46.
Kasiri
, S.
, Reilly
, G.
, and Taylor
, D.
, 2007, “Simulation of Bone Indentation
,” Biomedicine and Health
, Wessex Institute of Technology
, UK
, Vol. 12
.47.
Reilly
, D. T.
, and Burstein
, A. H.
, 1975, “The Elastic and Ultimate Properties of Compact Bone Tissue
,” J. Biomech.
0021-9290, 8
(6
), pp. 393
–405
.48.
Susmel
, L.
, and Taylor
, D.
, 2008, “On the Use of the Theory of Critical Distances to Predict Static Failures in Ductile Metallic Materials Containing Different Geometrical Features
,” Eng. Fract. Mech.
0013-7944, 75
(15
), pp. 4410
–4421
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