Mechanistic aspects of the fracture toughness of elk antler bone

Abstract

Bone is an adaptive material that is designed for different functional requirements; indeed, bones have a variety of properties depending on their role in the body. To understand the mechanical response of bone requires the elucidation of its structure–function relationships. Here, we examine the fracture toughness of compact bone of elk antler, which is an extremely fast-growing primary bone designed for a totally different function than human (secondary) bone. We find that antler in the transverse (breaking) orientation is one of the toughest biological materials known. Its resistance to fracture is achieved during crack growth (extrinsically) by a combination of gross crack deflection/twisting and crack bridging via uncracked “ligaments” in the crack wake, both mechanisms activated by microcracking primarily at lamellar boundaries. We present an assessment of the toughening mechanisms acting in antler as compared to human cortical bone, and identify an enhanced role of inelastic deformation in antler which further contributes to its (intrinsic) toughness.

Introduction

Biological materials are mostly complex systems in which large numbers of functionally diverse, and frequently multifunctional, sets of elements interact selectively and nonlinearly to produce coherent behavior. One of the most intriguing of these materials is bone, which is a highly hierarchical composite of assemblies of collagenous protein molecules, water, and mineral carbonated hydroxyapatite nanoparticles that form a tough, lightweight, adaptive and multi-functional material. Bone is often stereotyped as a protective and supportive framework for the body; though it performs these functions, it is a dynamic organ that is constantly remodeling and changing shape to adapt to the forces placed upon it. Like all natural materials, its mechanical properties are determined by its structure [1], [2], [3], which in turn is defined by its (primarily mechanical) function [4], [5]. The adaptation of compact bone to its mechanical environment includes both alteration of its shape and adaptation of its internal structure and hence properties. This dual optimization of form and structure is well known in engineering materials; however, in natural materials both are intimately related due to their common origin, the growth of the organ. Different bones grow at different rates, and the kind of primary bone laid down depends on this rate of accretion. Accordingly, different bones have different mechanical properties [4], [5] depending on the growth, structure and adaptation, all of which are interconnected to serve a specific function.

We focus here on the fracture resistance of non-structural¹ bone, namely the compact bone of elk antler. With the exception of reindeers, antlers are found only in males, and are grown in the spring and summer, used in the rut in the fall, and are shed in the winter. Unlike human bone, they provide neither structural support nor protection of organs. The functions of antlers are display and fighting, with no load-bearing role and low stiffness compared to skeletal bone; however, they are designed to undergo high impact loading and large bending moments without fracture.

There have been previous evaluations of the toughness of antler [4], [5], [6], [7], although many of these have been inaccurate due to problems of inappropriate measurement technique (e.g., measurements based on the area under a compression stress–strain curve). In particular, single-value linear-elastic fracture parameters based on crack initiation, such as K_Ic,² have been used but such measurements cannot capture, or even represent, the multiple length-scale toughening acting in cortical bone that leads to its characteristic resistance-curve (R-curve³) behavior [8], [9], [10], where the fracture resistance actually increases with crack extension. Antler bone is no exception. Vashishth et al. [11], [12] have reported rising R-curve (K_R, crack-extension resistance) behavior in antlers of red deer, and demonstrated that the superior toughness of antler bone is due to its enhanced ability to form microcracks during deformation and fracture. Although such stress-intensity-based R-curves do provide a means to characterize crack propagation, the underlying assumptions for such K_R calculations are based on linear-elastic fracture mechanics (LEFM), which cannot account for the energy associated with plastic deformation⁴ during bone fracture (an especially important phenomenon in antler). Specifically, for such LEFM measurements, the prevailing mode of deformation is assumed to be linear elasticity; accordingly, any region of “plasticity” that may form in the vicinity of the crack tip (i.e., the plastic zone) must be small enough to ignore. This places restrictions on how large a test specimen has to be for “valid” toughness measurements; specifically, that the in-plane specimen dimensions of crack size and uncracked ligament width must be at least an order of magnitude larger than the plastic-zone size (termed “small-scale yielding”); additionally, for geometry- and thickness-independent toughness values, the out-of-plane thickness dimension must be equally larger than the plastic zone (termed “plane strain” conditions). For example for antler bone, a LEFM K_Ic value of 10 MPa√m [6] would require test specimen dimensions (in terms of crack size, ligament depth and thickness) in excess of 50 mm for a valid linear-elastic K_Ic based on current ASTM validity criteria [13]. However, because the thickness of the cortical shell in antler bone is typically ∼5–10 mm, appropriate section sizes for LEFM K_Ic measurements are not feasible. This means that as the test samples used in previous studies in the most part were too small for any form of linear-elastic K measurement, the distribution of local stresses and displacements near a crack tip (i.e., near the fracture origin) would not be well represented by the K-fields [14] and the resulting K-based toughness values would be highly questionable. Consequently, for materials such as antler that display significant plastic deformation prior to fracture [15], LEFM is simply not an appropriate methodology to measure the fracture toughness.

For these reasons, a preferred, indeed essential, strategy to evaluate the fracture toughness of cortical antler bone is to use nonlinear elastic fracture mechanics. This approach can provide a more realistic description of the crack-tip stress and displacement fields and furthermore is able to additionally capture the contribution to the toughness from the energy consumed in “plastic” deformation prior to and during fracture [16], [17].

Accordingly, in this work we utilize J-integral⁵ measurements to determine the toughness of elk antler cortical bone using R-curves, in the presence of realistically sized small (<1 mm) cracks, to characterize the toughness associated with both crack initiation and growth.⁶ We confirm that antler bone is the toughest hard mineralized tissue reported to date, and provide a description of the toughening mechanisms underlying its exceptional resistance to fracture.