2 Y. Zhang and D. Nelson Fig. 1.1 Schematic of a specimen cut from the central portion (diaphysis) of a bovine femur Fig. 1.2 Slitting geometry is unknown for larger specimens. Dissecting a bone into successively smaller pieces changed values of residual stresses measured by XRD [32]. Recent studies [22, 29] have also found that compressive residual stresses in small specimens, as measured via HAP crystals, dropped significantly with radiation dose. Doses are not reported in most of the XRD studies of bone and may or may not have influenced results. Residual stresses can also be measured in objects by releasing residual stresses, measuring resulting strains or deflections, and then using a computational model that relates the strains or deflections to the residual stresses. Stanwyck et al. [36] applied a strain gage in the longitudinal direction of a bovine metatarsal bone and sawed a 2 mm deep cut in the transverse direction of the bone, near the gage. A compressive strain of 180 © was reported. When the cut was deepened to 3 mm, the strain increased to 280 ©. The area surrounding the cut was irrigated with saline solution during the sawing. This experiment could be considered an early form of the slitting method for residual stress determination. Residual stresses were not computed from the measured strains, which is understandable since the methodology to do so was in its infancy when the experiment was conducted in the early 1980s. This paper will explore a version of the slitting method adapted to find residual stress vs. depth in bovine femurs, using a refined experimental approach and a finite element model. 1.2 Slitting Method As background, key features of the slitting method will be summarized. Suppose that a slit is introduced incrementally in depth into an object containing residual stresses normal to the slit and varying in an unknown manner with depth x, as depicted in Fig. 1.2. The slit releases residual stresses, causing the surface to develop strains © normal to the slit, which are typically measured with a strain gage near the slit location (and/or on the opposite side of the object if desired). Measured strain vs. depth data can be used with a computational model to determine the variation of with depth [37–39]. Assuming that residual stresses are constant in the z-direction, residual stresses can be related to strains by [40]: .ai/ DZ ai 0 G.x; ai/ .x/dx (1.1) where (ai) is the measured strain when a slit is at depthai. The functionG(x, ai) gives the strain response from a unit stress at depthx for a slit of depthai. Residual stresses vs. depth can approximated by .x/ DXn jD1 Aj Uj.x/ (1.2)
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