Mixed-Mode Fracture of Human Cortical Bone

Fracture studies on the behavior of human cortical bone have provided much information on how the hierarchical microstructure of bone (see Fig. 1a) is able to resist the initiation and growth of incipient cracks at numerous length scales.  Of particular importance is how the nano/microstructure can affect the crack path, which in turn controls the specific fracture resistance.  The structure of bone is highly anisotropic with a preferred microstructural crack path aligned along the long axis of the bone in the form of the osteonal cement lines, the highly mineralized interfaces between the lamellae and the Haversian canals.  As fractures in the transverse (breaking) orientation (see Fig. 1b) are nominally aligned perpendicular to this weaker direction (i.e., parallel to the osteons), the  toughness of human cortical bone is far higher in the transverse, as compared to the longitudinal, orientation -- it is easier to split than to break.

However, to date most such studies on the fracture toughness of bone have been performed under tensile (mode I) loading, the underlying assumption being that the mode I toughness value is the lowest (as is the case for most materials).  However, such loading conditions are not typical of those experienced physiologically; moreover, due to the marked anisotropy of the bone-matrix structure, mode I loading is not necessarily worst-case.  

Accordingly, we are examining the fracture mechanics of human cortical bone under mixed-mode loads, specifically under mode I (tensile opening), mode II (in-plane shear) and mode III (anti-plane shear) loading conditions (see Fig.2).  We are investigating its fracture behavior in simulated physiological environments, both mechanistically and in terms of quantitative fracture toughness measurements. Results show that the fracture toughness of bone in the transverse orientation decreases with mode-mixity (see Fig. 3); specifically, the transverse toughness of bone is 25% or more higher in tension (mode I) than in shear (mode II), a trend that is exactly opposite for the longitudinal orientation [1].  We find that such complex behavior can be analyzed in terms of the competition between the directions of the maximum mechanical driving force and the minimum microstructural resistance. 

Figure 1. (a) Bone is a composite of collagen molecules (~1.5 nm in diameter) and hydroxyapatite crystals (HA). The HA is deposited between the heads and tails of the collagen molecules, which are in a staggered array; this structure is called a mineralized collagen fibril. The mineralized collagen fibrils form arrays called fibers and the fibers assemble into arrays called lamellae (~5-mm thick), which resemble sheets. The lamellae are concentrically arranged around a central vascular channel. This whole structure is called a secondary osteon (~250 mm in diameter) and is aligned parallel to the longitudinal axis of the bone. The lamellae in the secondary osteon are separated from the interstitial lamellae by a hypermineralized layer of material called a cement line (~5-mm thick).  (b) Due to the anisotropic nature of this structure, the toughness must be assessed in two different orientations. In the longitudinal orientation, the crack is parallel to the orientation of the osteons while in the transverse orientation, the crack is perpendicular to the orientation of the osteons.

Figure 2. In fracture mechanics, the stress intensity due to any loading scenario can be broken down into three modes of loading: (a) tensile opening -- mode I, (b) in-plane shear -- mode II, and (c) anti-plane shear -- mode III.

Figure 3. (a) For human cortical bone oriented in the transverse orientation, the toughness (measured in terms of the critical strain energy release rate) is higher in mode I (tension) than mode II (in-plane shear).  In this orientation, the preferred microstructural path (dark brown lines in schematic) is perpendicular to the orientation of the crack. When a mode II driving force is applied, the direction of the preferred mechanical path is at a 74° angle to the original plane of the crack (pink arrow in schematic); thus, the preferred direction of the microstructure and the driving force are commensurate and bone has a low toughness. For mode I, the direction of the driving force and the preferred microstructural path are at a 90° angle, which results in a high toughness. (b)  The opposite relation occurs in the longitudinal orientation, where the crack is oriented parallel to the preferred microstructural path. In this case, bone is tougher in shear than tension. This figure is supplemented with data from Norman et al. [2].

Current Researchers

E.A. Zimmermann

M.E. Launey

R.O. Ritchie

References

[1]    Zimmermann EA, Launey ME, Barth HD, Ritchie RO. Biomaterials. 2009;30(29):5877-84.

[2]    Norman TL, Nivargikar SV, Burr DB. J Biomech. 1996;29(8):1023-31.