Internal strains and stresses measured in cortical bone via high-energy X-ray diffraction

Abstract

High-energy synchrotron X-ray diffraction was used to study internal stresses in bone under in situ compressive loading. A transverse cross-section of a 12–14 year old beagle fibula was studied with 80.7 keV radiation, and the transmission geometry was used to quantify internal strains and corresponding stresses in the mineral phase, carbonated hydroxyapatite. The diffraction patterns agreed with tabulated patterns, and the distribution of diffracted intensity around 00.2/00.4 and 22.2 diffraction rings was consistent with the imperfect 00.1 fiber texture expected along the axis of a long bone. Residual compressive stress along the bone’s longitudinal axis was observed in the specimen prior to testing: for 22.2 this stress equaled −95 MPa and for 00.2/00.4 was between −160 and −240 MPa. Diffraction patterns were collected for applied compressive stresses up to −110 MPa, and, up to about −100 MPa, internal stresses rose proportionally with applied stress but at a higher rate, corresponding to stress concentration in the mineral of 2.8 times the stress applied. The widths of the 00.2 and 00.4 diffraction peaks indicated that crystallite size perpendicular to the 00.1 planes increased from t = 41 nm before stress was applied to t = 44 nm at −118 MPa applied stress and that rms strain ε rms rose from 2200 με before loading to 4600 με at the maximum applied stress. Small angle X-ray scattering of the unloaded sample, recorded after deformation was complete, showed a collagen D-period of 66.4 nm (along the bone axis).