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Technical Briefs

# Residual Stress Around the Cortical Surface in Bovine Femoral Diaphysis

[+] Author and Article Information
Satoshi Yamada

Division of Human Mechanical Systems and Design, Graduate School of Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo 060-8628, Japan

Shigeru Tadano1

Division of Human Mechanical Systems and Design, Graduate School of Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo 060-8628, Japantadano@eng.hokudai.ac.jp

1

Corresponding author.

J Biomech Eng 132(4), 044503 (Mar 17, 2010) (4 pages) doi:10.1115/1.4001163 History: Received November 01, 2009; Revised January 12, 2010; Posted February 02, 2010; Published March 17, 2010; Online March 17, 2010

## Abstract

Residual stress in living tissue plays an important role in mechanical strength. We have reported that residual stress exists in the bone tissue of a rabbit’s tibiofibula. The purpose of this study is to measure the residual stress around the outer cortical region of bovine femoral diaphysis and to discuss the distribution of the stress. This work proposed the $sin2 ψ$ method of X-ray diffraction to the measurement of residual stresses in bone tissue. In this method, residual stress can be estimated from the variation in the interplanar spacings orientated to a number of directions without the lattice strain in the stress direction. Four-point bending tests of strip specimens taken from bovine femoral diaphysis were carried out during X-ray irradiation in advance. In the proximal, middle, and distal sections of bovine femoral diaphyses, the residual stresses at the cortical surface were measured using characteristic $Mo-Kα$ X-rays. The bending tests of strip specimens with X-ray irradiation showed that the method could reliably estimate residual stresses in the bone tissue. The residual stress of the bone axial direction was larger than that of the circumferential direction. The stresses in the middle part of five diaphyses along the bone axial direction were tensile. The maximum stress was 162 MPa at the lateral position and the minimum was 78 MPa at the posterior position. The residual stress in the bone axial direction varies around the circumferential region. In addition, the bone axial distributions of residual stresses were different in the proximal, middle, and distal sections of the individual femur. Furthermore, it was confirmed that residual stress in the bone tissue was released by the cutting out of the specimen. The residual stresses in bone tissue could be measured by this method. The results show that residual stress in the bone axial direction at the cortical surface in bovine femoral diaphysis is tensile and varies around the circumferential region.

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## Figures

Figure 1

Displacement of the interplanar spacing d of HAp crystals at a nonstrained state and under tensile loading. The variation in d with orientation ψ normal to the lattice planes of the HAp crystals is shown in polar coordinates, and the lengths and directions of the vectors in the diagram show the interplanar spacing and plane-normal direction, respectively. At a nonstrained state, the interplanar spacing is d0. Under tensile loading horizontal to the surface regions of the specimen, the lattice plane deforms and the interplanar spacing of the lattice planes oriented to the loading direction is the largest and that oriented normal to the surface the smallest.

Figure 2

Coordinate systems on the specimen surface and the X-ray planes for the measurements in the (a) bone axial and (b) circumferential directions of the sections of the diaphyses

Figure 3

Bovine femoral diaphysis with three sections used in the measurements indicated. The proximal and distal sections were used to compare the residual stresses in one femur.

Figure 4

Measurement positions on the circumference of the diaphysis specimens. A denotes anterior, AL denotes lateral anterior, L denotes lateral, LP denotes lateral posterior, P denotes posterior, PM denotes medial posterior, M denotes medial, and MA denotes medial anterior.

Figure 5

Residual stresses in the middle section of a diaphysis (average of five measurements) of the bone axial direction (the dark-gray bar) and the circumferential direction (the white bar). In addition, to confirm the existence of residual stress in the bone axial direction of the surface region, the same specimen was cut 2 mm above, in the upward direction from where the stress measurements were made. The light-gray bar shows the residual stress of the bone axial direction after the second cutting.

Figure 6

Mean values of the residual stresses in the bone axial directions for the middle diaphysis sections of the five specimens

Figure 7

Residual stresses in the bone axial directions of the three sections of one femur: proximal section, middle section, and distal section of the diaphysis

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