Analysing the High Strain Rate Behaviour of Cortical Bone with the Image-Based Inertial Impact (IBII) Test

Traumatic bone fractures can occur under high strain rate loading. However, there is minimal high strain rate data available for cortical bone. Most existing data for the high strain rate properties of cortical bone has been obtained using the split-Hopkinson bar (SHB) under compressive loading. The SHB method requires that the test sample is in a state of quasi-static equilibrium which is difficult to achieve for quasi-brittle material (e.g. bone) loaded in tension. Recently, the Image-Based Inertial Impact (IBII) test was developed specifically for analysing the elastic stiffness and tensile failure stress of materials under high strain rate loading. Therefore, the overall aim of this study was to apply the IBII test to obtain new high strain rate data for the orthotropic stiffness components and tensile failure stress of cortical bone. Bovine cortical bone samples were tested parallel (longitudinal) and perpendicular (transverse) to the long axis of the bone. Using this test data it was possible to obtain high strain rate data for all four in-plane stiffness components as well as tensile failure stress. The results of this study provided an average longitudinal stiffness of 26 <i>GPa</i> at an effective strain rate of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1150</mml:mn> <mml:mspace></mml:mspace> <mml:msup><mml:mi>s</mml:mi> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> and transverse stiffness of 15.2 <i>GPa</i> at an effective strain rate of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1300</mml:mn> <mml:mspace></mml:mspace> <mml:msup><mml:mi>s</mml:mi> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Using paired quasi-static samples, this represents a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>22</mml:mn> <mml:mo>%</mml:mo></mml:mrow> </mml:math> rate sensitivity for the longitudinal samples and a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>5.5</mml:mn> <mml:mo>%</mml:mo></mml:mrow> </mml:math> rate sensitivity for the transverse samples. Slight misalignments of the projectile made it possible to obtain the shear modulus for some samples with an average shear modulus over all samples of 6.9 <i>GPa</i> with an effective strain rate of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1200</mml:mn> <mml:mspace></mml:mspace> <mml:msup><mml:mi>s</mml:mi> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The average tensile failure stress of the longitudinal samples was 146 <i>MPa</i> and 53.6 <i>MPa</i> in the transverse direction at a strain rate of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>5200</mml:mn> <mml:mspace></mml:mspace> <mml:msup><mml:mi>s</mml:mi> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> .