Elastic-Plastic Fracture Mechanics of Compact Bone

Bone is a composite composed mainly of organics, minerals and water. Most studies on the fracture toughness of bone have been conducted at room temperature. Considering that the body temperature of animals is higher than room temperature, and that bone has a high volumetric percentage of organics (generally, 35-50%), the effect of temperature on fracture toughness of bone should be studied. Single-edged V-shaped notched (SEVN) specimens were prepared to measure the fracture toughness of bovine femur and manatee rib in water at 0, 10, 23, 37 and 50°C. The fracture toughness of bovine femur and manatee rib were found to decrease from 7.0 to 4.3 MPa·m^1/2 and from 5.5 to 4.1 MPa·m^1/2, respectively, over a temperature range of 50°C. The decreases were attributed to inability of the organics to sustain greater stresses at higher temperatures.

We studied the effects of water and organics on fracture toughness of bone using water-free and organics-free SEVN specimens at 23°C. Water-free and organics-free specimens were obtained by placing fresh bone specimen in a furnace at different temperatures. Water and organics significantly affected the fracture toughness of bone. Fracture toughness of the water-free specimens was 44.7% (bovine femur) and 32.4% (manatee rib) less than that of fresh-bone specimens. Fracture toughness of the organicsfree specimens was 92.7% (bovine femur) and 91.5 % (manatee rib) less than that of fresh bone specimens.

Linear Elastic Fracture Mechanics (LEFM) is widely used to study bone. However, bone often has small to moderate scale yielding during testing. We used J integral, an elastic-plastic fracture-mechanics parameter, to study the fracture process of bone. The J integral of bovine femur increased from 6.3 KJ/mm² at 23°C to 6.7 KJ/mm² at 37°C.

Although the fracture toughness of bovine bone decreases as the temperature increases, the J integral results show a contrary trend. The energy spent in advancing the crack beyond the linear-elastic deformation was much greater than the energy spent in linearelastic deformation. This could be because bone has at least four toughening mechanisms and a high volumetric percentage of organics (approximately 42% for bovine femur). The J integral is shown to better describe the fracture process of bovine femur and manatee rib.

Year	Entry
1998	Yeni YN, Brown CU, Norman TL. Influence of bone composition and apparent density on fracture toughness of the human femur and tibia. Bone. January 1998;22(1):79-84.
1998	Zioupos P. Recent developments in the study of failure of solid biomaterials and bone: “fracture” and “pre-fracture” toughness. Mater Sci Eng C Mater Biol Appl. September 1998;6(1):33-40.
2000	Yeni YN, Norman TL. Calculation of porosity and osteonal cement line effects on the effective fracture toughness of cortical bone in longitudinal crack growth. J Biomed Mater Res. September 5, 2000;51(3):504-509.
1984	Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.
1960	Dugdale DS. Yielding of steel sheets containing slits. J Mech Phys Solids. May 1960;8(2):100-104.
1959	Currey JD. Differences in the tensile strength of bone of different histological types. J Anat. January 1959;93(1):87-95.
1997	Yeni YN, Brown CU, Wang Z, Norman TL. The influence of bone morphology on fracture toughness of the human femur and tibia. Bone. November 1997;21(4):453-459.
2004	Wang X, Puram S. The toughness of cortical bone and its relationship with age. Ann Biomed Eng. January 2004;32(1):123-135.
2003	Malik CL, Stover SM, Martin RB, Gibeling JC. Equine cortical bone exhibits rising R-curve fracture mechanics. J Biomech. February 2003;36(2):191-198.
2000	Feng Z, Rho J, Han S, Ziv I. Orientation and loading condition dependence of fracture toughness in cortical bone. Mater Sci Eng C Mater Biol Appl. June 30, 2000;11(1):41-46.
2004	Nalla RK, Kruzic JJ, Kinney JH, Ritchie RO. Effect of aging on the toughness of human cortical bone: evaluation by R-curves. Bone. December 2004;35(6):1240-1246.
2003	Nalla RK, Kinney JH, Ritchie RO. Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater. 2003;2(3):164-168.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
2001	Lucksanasombool P, Higgs WAJ, Higgs RJED, Awain MV. Fracture toughness of bovine bone: influence of orientation and storage media. Biomaterials. December 2001;22(23):3127-3132.
1988	Burr DB, Schaffler MB, Frederickson RG. Composition of the cement line and its possible mechanical role as a local interface in human compact bone. J Biomech. 1988;21(11):939-945.
1998	Weiner S, Wagner HD. The material bone: structure-mechanical function relations. Ann Rev Mater Sci. August 1998;28:271-298.
2002	Wang X, Shen X, Li X, Agrawal CM. Age-related changes in the collagen network and toughness of bone [published correction appears in Bone. 2003;32(1):107]. Bone. 2002;31(1):1-7.
1999	Zioupos P, Currey JD, Hamer AJ. The role of collagen in the declining mechanical properties of aging human cortical bone. J Biomed Mater Res. May 1999;A45(2):108-116.
1977	Wright TM, Hayes WC. Fracture mechanics parameters for compact bone: effects of density and specimen thickness. J Biomech. 1977;10(7):419-430.
2002	Yamashita J, Li X, Furman BR, Rawls HR, Wang X, Agrawal CM. Collagen and bone viscoelasticity: a dynamic mechanical analysis. J Biomed Mater Res. 2002;63(1):31-36.
2002	Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.
1978	Robertson DM, Robertson D, Barrett CR. Fracture toughness, critical crack length and plastic zone size in bone. J Biomech. 1978;11(8-9):359-364.
1973	Evans FG. Mechanical Properties of Bone. Springfield, IL: Charles C. Thomas; 1973.
1975	Currey JD, Butler G. The mechanical properties of bone tissue in children. J Bone Joint Surg. September 1975;57A(6):810-814.
1975	Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.
1984	Behiri JC, Bonfield W. Fracture mechanics of bone: the effects of density, specimen thickness and crack velocity on longitudinal fracture. J Biomech. 1984;17(1):25-34.
1999	Bowman SM, Gibson LJ, Hayes WC, McMahon TA. Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone. J Biomech Eng. April 1999;121(2):253-258.
1976	Carter DR, Hayes WC. Fatigue life of compact bone, I: effects of stress amplitude, temperature and density. J Biomech. 1976;9(1):27-34.
1989	Behiri JC, Bonfield W. Orientation dependence of the fracture mechanics of cortical bone. J Biomech. 1989;22(8-9):863-872.
2001	Boskey AL. Bone mineralization. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:5-1–5-33.
1997	Vashishth D, Behiri JC, Bonfield W. Crack growth resistance in cortical bone: concept of microcrack toughening. J Biomech. August 1997;30(8):763-769.
1993	Rimnac CM, Petko AA, Santner TJ, Wright TM. The effect of temperature, stress and microstructure on the creep of compact bovine bone. J Biomech. March 1993;26(3):219-228.
1994	Ziv V, Weiner S. Bone crystal sizes: a comparison of transmission electron microscopic and x-ray diffraction line width broadening techniques. Connect Tissue Res. 1994;30(3):165-175.
1968	Bonfield W, Li CH. The temperature dependence of the deformation of bone. J Biomech. 1968;1(4):323-329.
1988	Giraud-Guille MM. Twisted plywood architecture of collagen fibrils in human compact bone osteons. Calcif Tiss Int. May 1988;42(3):167-180.
1990	Currey JD, Brear K. Hardness, Young's modulus and yield stress in mammalian mineralized tissues. J Mater Sci Mater Med. June 1990;1(1):14-20.
1996	Hamer AJ, Strachan JR, Black MM, Ibbotson CJ, Stockley I, Elson RA. Biomechanical properties of cortical allograft bone using a new method of bone strength measurement: a comparison of fresh, fresh-frozen and irradiated bone. J Bone Joint Surg. May 1996;78B(3):363-368.
1995	Norman TL, Vashishth D, Burr DB. Fracture toughness of human bone under tension. J Biomech. March 1995;28(3):309-320.
1990	Burr DB, Stafford T. Validity of the bulk-staining technique to separate artifactual from in vivo bone microdamage. Clin Orthop Relat Res. November 1990;260:305-308.
1992	Norman TL, Vashishth D, Burr DB. Effect of groove on bone fracture toughness. J Biomech. December 1992;25(12):1489-1492.
1995	Zioupos P, Currey JD, Mirza MS, Barton DC. Experimentally determined microcracking around a circular hole in a flat plate of bone: comparison with predicted stresses. Philos Trans R Soc Lond B Biol Sci. March 29, 1995;347(1322):383-396.
1989	Martin RB, Burr DB. Structure, Function, and Adaptation of Compact Bone. New York, NY: Raven Press; 1989.
2001	Jee WSS. Integrated bone tissue physiology: anatomy and physiology. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:1-1–1-68.
1993	Martin RB, Boardman DL. The effects of collagen fiber orientation, porosity, density, and mineralization on bovine cortical bone bending properties. J Biomech. September 1993;26(9):1047-1054.
1996	Burr DB, Milgrom C, Fyhrie D, Forwood M, Nyska M, Finestone A, Hoshaw S, Saiag E, Simkin A. In vivo measurement of human tibial strains during vigorous activity. Bone. May 1996;18(5):405-410.
1998	Zioupos P, Currey JD. Changes in the stiffness, strength, and toughness of human cortical bone with age. Bone. January 1998;22(1):57-66.
1987	Bonfield W. Advances in the fracture mechanics of cortical bone. J Biomech. 1987;20(11-12):1071-1081.
1975	Burstein AH, Zika JM, Heiple KG, Klein L. Contribution of collagen and mineral to the elastic-plastic properties of bone. J Bone Joint Surg. October 1975;57A(7):956-961.
2004	Vashishth D. Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements. J Biomech. June 2004;37(6):943-946.
1957	Robinson RA, Elliott SR. The water content of bone, I: the mass of water, inorganic crystals, organic matrin, and “CO₂ space” components in a unit volume of dog bone. J Bone Joint Surg. 1957;39A(1):167-188.
1996	Currey JD, Brear K, Zioupos P. The effects of ageing and changes in mineral content in degrading the toughness of human femora. J Biomech. February 1996;29(2):257-260.
1998	Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.
1954	Eastoe JE, Eastoe B. The organic constituents of mammalian compact bone. Biochem J. July 1954;57(3):453-459.
2001	Lucchinetti E. Composite models of bone properties. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:12-1–12-19.
1970	Currey JD. The mechanical properties of bone. Clin Orthop Relat Res. November–December 1970;73:210-231.

Year

Entry

1998

Yeni YN, Brown CU, Norman TL. Influence of bone composition and apparent density on fracture toughness of the human femur and tibia. Bone. January 1998;22(1):79-84.

1998

Zioupos P. Recent developments in the study of failure of solid biomaterials and bone: “fracture” and “pre-fracture” toughness. Mater Sci Eng C Mater Biol Appl. September 1998;6(1):33-40.

2000

Yeni YN, Norman TL. Calculation of porosity and osteonal cement line effects on the effective fracture toughness of cortical bone in longitudinal crack growth. J Biomed Mater Res. September 5, 2000;51(3):504-509.

1984

Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.

1960

Dugdale DS. Yielding of steel sheets containing slits. J Mech Phys Solids. May 1960;8(2):100-104.

1959

Currey JD. Differences in the tensile strength of bone of different histological types. J Anat. January 1959;93(1):87-95.

1997

Yeni YN, Brown CU, Wang Z, Norman TL. The influence of bone morphology on fracture toughness of the human femur and tibia. Bone. November 1997;21(4):453-459.

2004

Wang X, Puram S. The toughness of cortical bone and its relationship with age. Ann Biomed Eng. January 2004;32(1):123-135.

2003

Malik CL, Stover SM, Martin RB, Gibeling JC. Equine cortical bone exhibits rising R-curve fracture mechanics. J Biomech. February 2003;36(2):191-198.

2000

Feng Z, Rho J, Han S, Ziv I. Orientation and loading condition dependence of fracture toughness in cortical bone. Mater Sci Eng C Mater Biol Appl. June 30, 2000;11(1):41-46.

2004

Nalla RK, Kruzic JJ, Kinney JH, Ritchie RO. Effect of aging on the toughness of human cortical bone: evaluation by R-curves. Bone. December 2004;35(6):1240-1246.

2003

Nalla RK, Kinney JH, Ritchie RO. Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater. 2003;2(3):164-168.

1998

Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.

2001

Lucksanasombool P, Higgs WAJ, Higgs RJED, Awain MV. Fracture toughness of bovine bone: influence of orientation and storage media. Biomaterials. December 2001;22(23):3127-3132.

1988

Burr DB, Schaffler MB, Frederickson RG. Composition of the cement line and its possible mechanical role as a local interface in human compact bone. J Biomech. 1988;21(11):939-945.

1998

Weiner S, Wagner HD. The material bone: structure-mechanical function relations. Ann Rev Mater Sci. August 1998;28:271-298.

2002

Wang X, Shen X, Li X, Agrawal CM. Age-related changes in the collagen network and toughness of bone [published correction appears in Bone. 2003;32(1):107]. Bone. 2002;31(1):1-7.

1999

Zioupos P, Currey JD, Hamer AJ. The role of collagen in the declining mechanical properties of aging human cortical bone. J Biomed Mater Res. May 1999;A45(2):108-116.

1977

Wright TM, Hayes WC. Fracture mechanics parameters for compact bone: effects of density and specimen thickness. J Biomech. 1977;10(7):419-430.

2002

Yamashita J, Li X, Furman BR, Rawls HR, Wang X, Agrawal CM. Collagen and bone viscoelasticity: a dynamic mechanical analysis. J Biomed Mater Res. 2002;63(1):31-36.

2002

Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.

1978

Robertson DM, Robertson D, Barrett CR. Fracture toughness, critical crack length and plastic zone size in bone. J Biomech. 1978;11(8-9):359-364.

1973

Evans FG. Mechanical Properties of Bone. Springfield, IL: Charles C. Thomas; 1973.

1975

Currey JD, Butler G. The mechanical properties of bone tissue in children. J Bone Joint Surg. September 1975;57A(6):810-814.

1975

Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.

1984

Behiri JC, Bonfield W. Fracture mechanics of bone: the effects of density, specimen thickness and crack velocity on longitudinal fracture. J Biomech. 1984;17(1):25-34.

1999

Bowman SM, Gibson LJ, Hayes WC, McMahon TA. Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone. J Biomech Eng. April 1999;121(2):253-258.

1976

Carter DR, Hayes WC. Fatigue life of compact bone, I: effects of stress amplitude, temperature and density. J Biomech. 1976;9(1):27-34.

1989

Behiri JC, Bonfield W. Orientation dependence of the fracture mechanics of cortical bone. J Biomech. 1989;22(8-9):863-872.

2001

Boskey AL. Bone mineralization. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:5-1–5-33.

1997

Vashishth D, Behiri JC, Bonfield W. Crack growth resistance in cortical bone: concept of microcrack toughening. J Biomech. August 1997;30(8):763-769.

1993

Rimnac CM, Petko AA, Santner TJ, Wright TM. The effect of temperature, stress and microstructure on the creep of compact bovine bone. J Biomech. March 1993;26(3):219-228.

1994

Ziv V, Weiner S. Bone crystal sizes: a comparison of transmission electron microscopic and x-ray diffraction line width broadening techniques. Connect Tissue Res. 1994;30(3):165-175.

1968

Bonfield W, Li CH. The temperature dependence of the deformation of bone. J Biomech. 1968;1(4):323-329.

1988

Giraud-Guille MM. Twisted plywood architecture of collagen fibrils in human compact bone osteons. Calcif Tiss Int. May 1988;42(3):167-180.

1990

Currey JD, Brear K. Hardness, Young's modulus and yield stress in mammalian mineralized tissues. J Mater Sci Mater Med. June 1990;1(1):14-20.

1996

Hamer AJ, Strachan JR, Black MM, Ibbotson CJ, Stockley I, Elson RA. Biomechanical properties of cortical allograft bone using a new method of bone strength measurement: a comparison of fresh, fresh-frozen and irradiated bone. J Bone Joint Surg. May 1996;78B(3):363-368.

1995

Norman TL, Vashishth D, Burr DB. Fracture toughness of human bone under tension. J Biomech. March 1995;28(3):309-320.

1990

Burr DB, Stafford T. Validity of the bulk-staining technique to separate artifactual from in vivo bone microdamage. Clin Orthop Relat Res. November 1990;260:305-308.

1992

Norman TL, Vashishth D, Burr DB. Effect of groove on bone fracture toughness. J Biomech. December 1992;25(12):1489-1492.

1995

Zioupos P, Currey JD, Mirza MS, Barton DC. Experimentally determined microcracking around a circular hole in a flat plate of bone: comparison with predicted stresses. Philos Trans R Soc Lond B Biol Sci. March 29, 1995;347(1322):383-396.

1989

Martin RB, Burr DB. Structure, Function, and Adaptation of Compact Bone. New York, NY: Raven Press; 1989.

2001

Jee WSS. Integrated bone tissue physiology: anatomy and physiology. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:1-1–1-68.

1993

Martin RB, Boardman DL. The effects of collagen fiber orientation, porosity, density, and mineralization on bovine cortical bone bending properties. J Biomech. September 1993;26(9):1047-1054.

1996

Burr DB, Milgrom C, Fyhrie D, Forwood M, Nyska M, Finestone A, Hoshaw S, Saiag E, Simkin A. In vivo measurement of human tibial strains during vigorous activity. Bone. May 1996;18(5):405-410.

1998

Zioupos P, Currey JD. Changes in the stiffness, strength, and toughness of human cortical bone with age. Bone. January 1998;22(1):57-66.

1987

Bonfield W. Advances in the fracture mechanics of cortical bone. J Biomech. 1987;20(11-12):1071-1081.

1975

Burstein AH, Zika JM, Heiple KG, Klein L. Contribution of collagen and mineral to the elastic-plastic properties of bone. J Bone Joint Surg. October 1975;57A(7):956-961.

2004

Vashishth D. Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements. J Biomech. June 2004;37(6):943-946.

1957

Robinson RA, Elliott SR. The water content of bone, I: the mass of water, inorganic crystals, organic matrin, and “CO₂ space” components in a unit volume of dog bone. J Bone Joint Surg. 1957;39A(1):167-188.

1996

Currey JD, Brear K, Zioupos P. The effects of ageing and changes in mineral content in degrading the toughness of human femora. J Biomech. February 1996;29(2):257-260.

1998

Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.

1954

Eastoe JE, Eastoe B. The organic constituents of mammalian compact bone. Biochem J. July 1954;57(3):453-459.

2001

Lucchinetti E. Composite models of bone properties. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:12-1–12-19.

1970

Currey JD. The mechanical properties of bone. Clin Orthop Relat Res. November–December 1970;73:210-231.

Year	Entry
2014	Marinozzi F, Bini F, Quintino A, Corcione M, Marinozzi A. Experimental study of diffusion coefficients of water through the collagen: apatite porosity in human trabecular bone tissue. BioMed Res Int. 2014;2014:796519.
2007	Yan J, Mecholsky JJ Jr, Clifton KB. How tough is bone? application of elastic–plastic fracture mechanics to bone. Bone. February 2007;40(2):479-484.
2019	Shitole P, Gupta A, Ghosh R. Fracture mechanism and fracture toughness at the interface between cortical and cancellous bone. J Biomech Eng. November 2019;141(11):114502.
2007	Olszta MJ, Cheng X, Jee SS, Kumar R, Kim Y-Y, Kaufman MJ, Douglas EP, Gower LB. Bone structure and formation: a new perspective. Mater Sci Eng R Rep. November 28, 2007;58(3-5):77-116.

Year

Entry

2014

Marinozzi F, Bini F, Quintino A, Corcione M, Marinozzi A. Experimental study of diffusion coefficients of water through the collagen: apatite porosity in human trabecular bone tissue. BioMed Res Int. 2014;2014:796519.

2007

Yan J, Mecholsky JJ Jr, Clifton KB. How tough is bone? application of elastic–plastic fracture mechanics to bone. Bone. February 2007;40(2):479-484.

2019

Shitole P, Gupta A, Ghosh R. Fracture mechanism and fracture toughness at the interface between cortical and cancellous bone. J Biomech Eng. November 2019;141(11):114502.

2007

Olszta MJ, Cheng X, Jee SS, Kumar R, Kim Y-Y, Kaufman MJ, Douglas EP, Gower LB. Bone structure and formation: a new perspective. Mater Sci Eng R Rep. November 28, 2007;58(3-5):77-116.