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Research Papers: Design and Analysis

# Elastoplastic Analysis of a Miniature Circular Disk Bending Specimen

[+] Author and Article Information
Vishnu Verma, G. Behera, Kamal Sharma, R. K. Singh

Reactor Safety Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India

A. K. Ghosh

Reactor Safety Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, Indiaccss@magnum.barc.ernet.in

J. Pressure Vessel Technol 130(4), 041205 (Aug 21, 2008) (7 pages) doi:10.1115/1.2967812 History: Received July 26, 2006; Revised May 09, 2007; Published August 21, 2008

## Abstract

The miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and their properties (e.g., yield stress and strain hardening exponent) to determine mainly ductility loss in steel due to irradiation from the load-deflection behavior of the disk specimen. In the miniature disk bending machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with a spherical ball travels vertically. Analytical solutions for large amplitude plastic deformation become rather unwieldy. Hence, a finite element analysis has been carried out. The finite element model considers contact between the indentor and test specimen, friction between various pairs of surfaces, and elastic plastic behavior. This paper presents the load versus deflection results of a parametric study where the values of various parameters defining the material properties have been varied by $±10%$ around the base values. Some well-known analytical solutions to this problem have also been considered. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elastoplastic finite element solution at relatively small values of load. The finite element solution has been compared with one experimental result and values are in reasonably good agreement. With these results it will be possible to determine the material properties from the experimentally obtained values of load and deflection.

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## Figures

Figure 9

(a) Variation of load versus deflection with m, (b) variation of load versus deflection with A0, (c) variation of load versus deflection with E, and (d) variation of load versus deflection with σy

Figure 8

Localized plastic strain profiles in miniature disk at 425N with inelastic FE simulation

Figure 6

(a) Profile of deflection (millimeters) of miniature disk at 25N with inelastic properties and (b) profile of deflection (millimeter) of miniature disk at 425N with inelastic properties

Figure 5

Comparison of finite element simulations with analytical and experimental results: A1, analytical result, clamped, uniform distributed load, small deflection (Appendix); A2, analytical result, clamped, concentrated load, small deflection (Appendix); C1, FEM result; and B1, experimental result

Figure 4

Stress-strain curve for MDBT simulation

Figure 3

Finite element model of MDBT simulation

Figure 2

(a) Comparison of analytical solution for a concentrated load with experimental results: A1, analytical result simply supported, small deflection (Appendix); A2, analytical result, clamped, small deflection (Appendix); A3, analytical result, clamped, large deflection (Eq. 6); and B, experimental result. (b) Comparison of analytical solution with experimental results: A1, analytical result, clamped, uniform distributed load, small deflection (Appendix); A2, analytical result, clamped, concentrated load, small deflection (Appendix); and B1, experimental result.

Figure 1

Schematic drawing of the setup for miniature disk bending test

Figure 7

Localized plastic strain profile in miniature disk at 25N with inelastic FE simulation

## Errata

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