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TECHNICAL PAPERS

Computational Examination of the Effect of Material Inhomogeneity on the Necking of Stent Struts Under Tensile Loading

[+] Author and Article Information
J. P. McGarry1

Department of Mechanical and Biomedical Engineering and National Centre for Biomedical Engineering Science, National University of Ireland, Galway, Ireland and Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070pmcg@engineering.ucsb.edu

B. P. O’Donnell, P. E. McHugh, E. O’Cearbhaill

Department of Mechanical and Biomedical Engineering and National Centre for Biomedical Engineering Science, National University of Ireland, Galway, Ireland

R. M. McMeeking

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070

1

Corresponding author.

J. Appl. Mech 74(5), 978-989 (Jan 17, 2007) (12 pages) doi:10.1115/1.2722776 History: Received November 09, 2005; Revised January 17, 2007

This study presents a computational investigation of tensile behavior and, in particular, necking due to material inhomogeniety of cardiovascular stent struts under conditions of tensile loading. Polycrystalline strut microstructures are modelled using crystal plasticity theory. Two different idealized morphologies are considered for three-dimensional models, with cylindrical grains and with rhombic-dodecahedron grains. Results are compared to two-dimensional models with hexagonal grains. For all cases, it is found that necking initiates at a significantly higher strain than that at UTS (ultimate tensile stress). Two-dimensional models are shown to exhibit an unrealistically high dependence of necking strain on randomly generated grain orientations. Three-dimensional models with cylindrical grains yield a significantly higher necking strain than models with rhombic-dodecahedron grains. It is shown that necking is characterized by a dramatic increase in stress triaxiality at the center of the neck. Finally, the ratios of UTS to necking stress computed in this study are found to compare well to values predicted by existing bifurcation models.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 9

Contour plots of von Mises at a strain of 0.5 for (a) cylindrical crystal configuration and (b) rhombic-dodecahedron crystal configuration

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Figure 10

(a) Cross-sectional areas at ten evenly spaced sections throughout strut length, (b) 3D analysis with rhombic-dodecahedron grains (curves for sections 7–9 labeled), and (c) 2D analysis (curves for sections 7, 8 and the location of the neck (between 7 and 8) labeled). (d) Comparison of cross-sectional area at neck for 3D analyses using rhombic-dodecahedron and cylindrical grains.

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Figure 11

(a) Comparison of engineering stress (broken line), true stress computed from σ=s(1+e) (black line) and true stress computed from actual neck cross-sectional area (gray line) for 3D analysis using rhombic-dodecahedron grains. (b) Comparison of true stress-true strain curves for 3D analyses using rhombic-dodecahedron and cylindrical grains.

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Figure 12

(a) Cross-sectional area at the neck for the 2D analyses using three different sets of random crystal orientations and (b) sections of engineering stress-nominal strain curves, where hardening occurs post UTS shown in black, for the 2D analyses

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Figure 13

3D rhombic-dodecahedron grain model shown in Fig. 7. Location of element groups (a) remote from neck, (b) adjacent to neck, and (c) at neck.

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Figure 14

Plots of average (a) logarithmic strain ε11, (b) von Mises stress, (c) hydrostatic stress, and (d) triaxiality in region remote from necking (broken lines), in region adjacent to necking (black lines) and at neck (gray lines). (d) shows an additional curve for the average triaxiality of the elements on the outer edges of the necked region (black with triangles).

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Figure 15

Plots of section areas normalized by original section areas versus nominal strain for homogeneous struts with geometric imperfections: (a) 3D simulation for tapered strut, (b) 2D simulation for tapered strut, and (c) 2D simulation for notched strut. Unlabeled vertical line corresponds to nominal strain at which Eq. 6 is satisfied and vertical line labeled UTS corresponds to the nominal strain at UTS.

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Figure 1

SEM image of a 316L laser-cut strut, representative of that used in stents

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Figure 2

(a) 2D hexagonal grain finite element model with a typical hexagonal grain highlighted. 3D cylindrical grains finite element model: (b) break-out view with a typical grain highlighted and (c) full finite element mesh. The dimensions “width” and “thickness” discussed in the text are shown.

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Figure 3

3D close-packed rhombic-dodecahedron model: (a) one rhombic-dodecahedron grain, (b) arrangement of full rhombic-dodecahedron grains in the model (partial grains at surfaces and edges not shown), and (c) full finite element mesh. The dimensions “width” and “thickness” discussed in the text are shown.

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Figure 4

Plots of deformed meshes for two different sets of crystal orientations at a strain of 0.95

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Figure 5

Stress-strain curves for 2D models using a coarse mesh with first-order elements (broken gray curves), a fine mesh with second-order elements (solid black curves), and a fine mesh with first-order elements (solid gray curve): (a) full stress-strain curves and (b) stress-strain relationships at UTS

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Figure 6

Contour plots of von Mises stress at a strain of 0.5 for (a) a fine mesh with second-order elements and (b) a coarse mesh with first-order elements

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Figure 7

Deformed mesh at a strain of 0.95 for (a) the cylindrical grain configuration, (b)–(d) the rhombic-dodecahedron crystal configuration with three different sets of random crystal orientations

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Figure 8

Stress-strain curves for 3D models with the rhombic-dodecahedron crystal configuration (solid gray lines), cylindrical crystal configuration (solid black lines) and for 2D models with first-order elements (broken gray lines): (a) full stress-strain plot and (b) stress-strain relationships at UTS

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