Studies of Fracture in Bone

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Abstract

A phenomenological study of the fracture processes in bovine cortical bone has been made. Three-point bending tests were performed at 37°C in physiological saline on V-notched specimens machined from compact bovine femoral diaphyses. The principal variables in these tests were microstructure and strain rate. The purpose of the study was severalfold: to determine the dependence of fracture behavior on these two variables, to delineate the method of crack initiation and mode(s) of propagation, to obtain quantitative information describing the onset of catastrophic fracture, to develop a model for predicting the fracture strength of bone based on the arrangement of the micro structure and to determine if information gained from these studies could be applied to the understanding of the fracture behavior of structurally different bone (in this case, osteoporotic).

The relationship between the fracture behavior of bone and micro structure is dependent upon regularity of structure, orientation of collagen fibrils, orientation of lamellae with respect to the stress axis and amount of ground substance. The strongest specimens are those consisting of extensive, regular, planar lamellae, of various orientations of regular lamellae, the strongest are those which are oriented parallel to the stress axis. Regular osteonal structures are next in strength. The weakest structures are those of irregular cross-section.

Though the ground substance is present in small amounts, it is of structural significance in acting as a weak interface, providing easy path for crack propagation and allowing osteonal or lamellar units to retain their integrity. Thus, the more irregular the subunits or the more curved the surface of the subunit, the greater the amount of ground substance with respect to the amount of ground substance between flat lamellar places and the weaker the specimen. In the case of differently oriented flat lamellar sheets, if lamellae are parallel to the stress axis, they take up most of the stress. If they are obliquely oriented, the interface must support a larger resolved component of the applied stress and the bone is correspondingly weaker,

The relationship between strength and strain rate was examined and it was found that while fracture strength is not a strong function of strain rate (about 20,000 psi throughout the range of testing), fracture mode is. This was seen by changes in the shape of the load-deflection curves with strain rate, by changes in work required to fracture the specimens (450 in-lb/in² at 0.000176 to 0.00176 min^-1 and 250 in-lb/in² at 0.0176 to 1.76 min^-1), and by examination of fracture profiles (optical microscopy) and surfaces (scanning electron microscopy). This latter study reveals a change from fibrous (ductile) tearing to a smooth (cleavage-like) fracture with increasing rates of loading. At intermediate rates, one finds a quasi-cleavage fracture surface with both ductile pull-out and flat, featureless areas.

There are two general methods of crack initiation: (1) pull out of osteons or lamellae. Such lamellar upheaval is generally accompanied by separation of adjacent lamellae; (2) plastic defor mation around internal flaws. Generally, this deformation occurs at the tips of small flaws such as lacunae and canaliculi creating cracks and extending them to a size sufficient for propagation.

The critical crack length was determined to be 0.01 in. From this, the fracture toughness, K_IC, was found to be 5930 ± 1800 psi in^0.5. It is independent of the existence of a precrack; thus, the major effort in fracturing bone is in crack propagation, not initiation. The plastic zone was estimated at 6.6 x 10^-4 in; physically, this means it extends from two to five lamellae. Crack propagation thus appears ens to be localized movement around individual lamellae.

The fracture strength of bone was able to be predicted using the maximum work theory and a microstructure simplified to one of alterating parallel plates of apatite-dispersed collagen and ground substance. The analysis permits a variety of loading conditions, which must be considered when an anisotropic material is stressed at various angles to its long axis.

Tests on osteoporotic bone showed that the same general principles governing the fracture behavior of normal bone could be applied successfully to the description of the behavior of structurally different bone.

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Cited By (19)

Year	Entry
1996	Egerer AK, Saha S, McMillan PJ, Rivera J. Morphology of the cement line in human bone and its relationship to bone strength. In: Proceedings of the 15th Southern Biomedical Engineering Conference. March 29-31, 1996; Dayton, OH.7-10.
1992	Evans GP, Behiri JC, Vaughan LC, Bonfield W. The response of equine cortical bone to loading at strain rates experienced in vivo by the galloping horse. Equine Vet J. March 1992;24(2):125-128.
1977	Wright TM, Hayes WC. Fracture mechanics parameters for compact bone: effects of density and specimen thickness. J Biomech. 1977;10(7):419-430.
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.
1978	Robertson DM, Smith DC. Compressive strength of mandibular bone as a function of microstructure and strain rate. J Biomech. 1978;11(10-12):455-471.
1979	Alto A, Pope MH. On the fracture toughness of equine metacarpi. J Biomech. 1979;12(6):415-421.
1982	Martin RB, Burr DB. A hypothetical mechanism for the stimulation of osteonal remodelling by fatigue damage. J Biomech. 1982;15(3):137-139.
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.
1985	Burr DB, Martin RB, Schaffler MB, Radin EL. Bone remodeling in response to in vivo fatigue microdamage. J Biomech. 1985;18(3):189-200.
1987	Bonfield W. Advances in the fracture mechanics of cortical bone. J Biomech. 1987;20(11-12):1071-1081.
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.
1989	Behiri JC, Bonfield W. Orientation dependence of the fracture mechanics of cortical bone. J Biomech. 1989;22(8-9):863-872.
1995	Norman TL, Vashishth D, Burr DB. Fracture toughness of human bone under tension. J Biomech. March 1995;28(3):309-320.
1998	Guo XE, Liang LC, Goldstein SA. Micromechanics of osteonal cortical bone fracture. J Biomech Eng. February 1998;120(1):112-117.
1980	Behiri JC, Bonfield W. Crack velocity dependence of longitudinal fracture in bone. J Mater Sci. June 1980;15(7):1841-1849.
2002	Egerer AK. The Relationship Between the Osteonal Cement Line and Bone Strength [PhD thesis]. Loma Linda University; June 2002.
1991	Pattin CAG. Cyclic Mechanical Property Degradation in Bone During Fatigue Loading [PhD thesis]. Stanford University; March 1991.
2002	Beardsley CL. Development of Quantitative Measures for Bone Comminution Severity [PhD thesis]. University of Iowa; May 2002.
1998	Yeni YN. Fracture Mechanics of Human Cortical Bone: The Relationship of Geometry, Microstructure and Composition With the Fracture of the Tibia, Femoral Shaft and the Femoral Neck [PhD thesis]. Morgantown, WV: West Virginia University; 1998.