Volume effects on yield strength of equine cortical bone

Volume effects are a fundamental determinant of structural failure. A material exhibits a volume effect if its failure properties are dependent on the specimen volume. Many brittle ceramics exhibit volume effects due to loading a structure in the presence of "critical" flaws. The number of flaws, their locations, and the effect of stress field within the stressed volume play a role in determining the structure's failure properties. Since real materials are imperfect, structures composed of large volumes of material have higher probabilities of containing a flaw than do small volumes. Consequently, large material volumes tend to fail at lower stresses compared to smaller volumes when tested under similar conditions. Volume effects documented in brittle ceramic and composite structures have been proposed to affect the mechanical properties of bone. We hypothesized that for cortical bone material, (1) small volumes have greater yield strengths than large volumes and (2) that compared to microstructural features, specimen volume was able to account for comparable amounts of variability in yield strength. In this investigation, waisted rectangular, equine third metacarpal diaphyseal specimens (n=24) with nominal cross sections of 3 x 4 mm and gage lengths of either 10.5, 21, or 42 mm, were tested monotonically in tension to determine the effect of specimen volume on their yield strength. Yield strength was greatest in the smallest volume group compared to the largest volume group. Within each group of specimens the logarithm of yield strength was positively correlated with the cumulative failure probability, indicating that the data follow the two-parameter Weibull distribution. Additionally, log yield strength was negatively correlated with log volume, supporting the hypothesis that small stressed volumes of cortical bone possess greater yield strength than similarly tested large stressed volumes.