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Research Papers

Residual Stresses in Titanium Spinal Rods: Effects of Two Contouring Methods and Material Plastic Properties

[+] Author and Article Information
Francesca Berti, Agnese Piovesan, Tomaso Villa, Giancarlo Pennati

Laboratory of Biological Structure Mechanics,
Department of Chemistry,
Materials and Chemical Engineering
“Giulio Natta,”
Politecnico di Milano,
Piazza Leonardo da Vinci 32,
Milan 20133, Italy

Luigi La Barbera

Laboratory of Biological Structure Mechanics,
Department of Chemistry,
Materials and Chemical Engineering
“Giulio Natta,”
Politecnico di Milano,
Piazza Leonardo da Vinci 32,
Milan 20133, Italy
e-mail: luigi.labarbera@polimi.it

Dario Allegretti, Claudia Ottardi

Laboratory of Biological Structure Mechanics,
Department of Chemistry,
Materials and Chemical Engineering
“Giulio Natta,”
Politecnico di Milano,
Piazza Leonardo da Vinci 32,
Milan 20133, Italy

1Corresponding author.

Manuscript received January 10, 2018; final manuscript received May 24, 2018; published online August 20, 2018. Assoc. Editor: Giuseppe Vairo.

J Biomech Eng 140(11), 111001 (Aug 20, 2018) (8 pages) Paper No: BIO-18-1020; doi: 10.1115/1.4040451 History: Received January 10, 2018; Revised May 24, 2018

Posterior spinal fixation based on long spinal rods is the clinical gold standard for the treatment of severe deformities. Rods need to be contoured prior to implantation to fit the natural curvature of the spine. The contouring processes is known to introduce residual stresses and strains which affect the static and fatigue mechanical response of the implant, as determined through time- and cost-consuming experimental tests. Finite element (FE) models promise to provide an immediate understanding on residual stresses and strains within a contoured spinal rods and a further insight on their complex distribution. This study aims at investigating two rod contouring strategies, French bender (FB) contouring (clinical gold standard), and uniform contouring, through validated FE models. A careful characterization of the elastoplastic material response of commercial implants is led. Compared to uniform contouring, FB induces highly localized plasticizations in compression under the contouring pin with extensive lateral sections undergoing tensile residual stresses. The sensitivity analysis highlighted that the assumed postyielding properties significantly affect the numerical predictions; therefore, an accurate material characterization is recommended.

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Figures

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Fig. 1

Experimental setup (top) and FE models (bottom) of uniform contouring (a) and FB contouring (b). In (a) the supporting pin is depicted as fixed while the loading pin trajectory is displayed by an arrow, as well as the fixed central and moving roller in (b). The FE models are built based on the symmetries of the experimental setup.

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Fig. 2

Experimental tensile loading–unloading stress–strain curve obtained on a dog-bone specimen (a). Experimental average stress–strain curve obtained by tensile test; standard deviation is also reported on yield and ultimate points (b): (a) loading–unloading tensile tests and (b) experimental average.

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Fig. 3

Schematic drawing of the procedure adopted to assess the local curvature radius on a contoured rod (the same procedure applies in case of uniform contouring). The contoured region of interest comprised by lines s (coinciding with the Y symmetry of the rod) and r is identified. Three points are selected on the rod cross section to define r, namely A, C, and B, lying, respectively, on the concave, convex, and on the midline of the rod. D is the middle point of the rod cross section, where s line passes. ϕ is the resulting intersection angle between r and s. The assessed curvature radius was defined as: R = 0.5*z/sin(ϕ/2), with ϕ = arctan(m). Points coincided, respectively, with specific nodal elements and with pixels, respectively, for numerically and experimentally bent rods. A sensitivity analysis proved that a slight variation in the identification of these points may lead to a difference in curvature radius estimation lower than 10%.

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Fig. 6

Residual stress (σ*) trends after release along the circumferential (top) and radial (bottom) directions for the uniform bending (a) and FB (b) models. The graphs were obtained on a transversal section both in the gage length (AA) and under the loading pin (BB): these sections collapse for the FB contouring model: (a) uniform contouring and (b) FB.

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Fig. 5

Residual stress (σ*) fields color maps at peak bending (top) and after release (middle), predicted during uniform (a) and FB (b) contouring on the transversal yz and the frontal yx planes. A qualitative comparison with an experimentally contoured rod is also provided (bottom).

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Fig. 4

Comparison between the numerical prediction and the experimental force–deflection curve obtained in a four-point bending. The standard deviation is also reported on yield and maximum displacement points.

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