PSI - Issue 6

S.M. Bosiakov et al. / Procedia Structural Integrity 6 (2017) 27–33 Bosiakov et al./ Structural Integrity Procedia 00 (2017) 000–000

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granularity 240, 400, 600 and 1200, finishing with a fabric with polishing slurry with a pa rticle size of 3 μm and 1 μm). Nanoindentation process For experiments in this study, a NanoTest 600 testing machine (Loughborough University, UK) was used. Nanoindentation was carried out at a temperature of 23.3°C and relative humidity of air of 31.7%. For indentation, a spherical diamond tip with a radius of 25 μm and an indenting head for a small load of 0.1 -500 mN was employed. The sample was glued horizontally to a holder and attached to a front end of the system opposite to the indenter tip. Using the built-in microscope, the indenter was placed in the desired position. Tests were performed in the load control mode. The maximum load for each side was 222.3 mN, the maximum depth was approx. 2220 nm with a loading speed of 2 mN/s, and a time delay of 60 seconds. Five to seven cycles of loading-unloading were carried out. The indents into the sample were performed in central regions of its anterior (A), posterior (P), medial (M) and lateral (L) quadrants. 2.2. Finite-element modelling Computed tomography of the femur and bones of the lower leg was performed on a spiral X-ray tomograph Siemens Somatom Emotion 16, with the cutoff step of 2 mm. Finite-element modelling was performed using ScanIP (Simpleware Ltd., UK), CATIA V5 (Dassault Systémes, France) and ANSYS Workbench 14.0 (ANSYS Inc., USA). The load on the femur was applied along the biomechanical axis passing from the upper pole of the femoral head to the middle of the distance between the extreme lower sections of the condyles of the femur (Letter to the editor, 2002; Yoshioka et al., 1987). The region of application of the load was the third part of the upper segment of the head of the femur. The boundary conditions were defined in such a way that the femoral head (the acetabular contact area) and the lower sections of the condyles of the femur (the sites of contact with the condyles of the tibia) were rigidly embedded (Letter to the editor, 2002). In numerical simulations, a bone defect was located in the middle third of the femur in various quadrants of the cross section. The angular dimensions of the defects, irrespective of the quadrant, were 270°, while its linear dimensions were 50.2 mm. Variants of the location of the bone defect in the cross section of the femur are schematically presented in Figure 2. The femoral bone after surgical resection, corresponding to the variant 2 of the bone defect location (see Figure 2), is shown in Figure 3.

1 4 Fig. 2. Schematics of location of bone defect in different quadrants of cross section of femur: (1) anterior; (2) lateral; (3) posterior; (4) medial (the quadrant with the fragment of bone tissue left after surgical resection is highlighted in gray) The bone tissue was modelled as a homogeneous linear isotropic medium with the Poisson's ratio equal to 0.3 (Tanne and Sakuda, 1991). The bone’s elasticity modulus was set to be the same for the entire bone as a whole in accordance with the results of the nanoindentation test, depending on the location of the bone defect. The finite-element meshing of the femoral bone model was carried out automatically, except for the regions in the direct vicinity of the bone defect, using hexagonal and tetrahedral elements. The maximum size of the element for the femur was 5.0 mm (excluding the areas in the area of the bone defect). The finite-element meshing of the regions around the defect – stress concentrators – was performed using spheres of influence in ANSYS Tools; the maximum size of the element in these areas was 0.2 mm. An analysis of the net convergence for the model of the femur was carried out in (Bosiakov et al., 2016). 2 3