Research Papers

Material Modeling for Autofrettage Stress Analysis Including the “Single Effective Material”

[+] Author and Article Information
Anthony P. Parker

Defence Academy of the United Kingdom,  University of Cranfield, Swindon, SN6 8LA, UKparker.ETR@tiscali.co.uk

Michael C. Gibson

Defence Academy of the United Kingdom,  University of Cranfield, Swindon, SN6 8LA, UKm.c.gibson@cranfield.ac.uk

Amer Hameed

Defence Academy of the United Kingdom,  University of Cranfield, Swindon, SN6 8LA, UKa.hameed@cranfield.ac.uk

Edward Troiano

 US Army WS & T Center, Benet Labs, Watervliet, NY 12189-4050edward.troiano@us.army.mil

J. Pressure Vessel Technol 134(4), 041004 (Jul 09, 2012) (7 pages) doi:10.1115/1.4006351 History: Received November 09, 2011; Revised December 03, 2011; Published July 09, 2012; Online July 09, 2012

Analytical and numerical stress analyses of the autofrettage process have made great strides in the last few years. The major challenge is no longer the stress analysis process but the incorporation of “real” material behavior, including Bauschinger effect. This means that material properties may vary at every radial location within the tube. In this paper, it is demonstrated that finite element analysis (FEA) may be accomplished using a “user programmable feature (UPF)” within a nonlinear FEA or, more simply using an elastic modulus and Poisson’s ratio adjustment procedure (EMPRAP) within a linear-effective FEA. The results of these two methods are shown to be in agreement with each other and with an independent numerical analysis. It is further demonstrated that the numerical solutions may be obtained using a single “fictitious” material. This is called a single effective material (SEMAT). While this requires a very small number of iterations for accurate convergence, it dramatically reduces the material-modeling challenges. Furthermore, SEMAT may be implemented into an analytical procedure thereby permitting highly accurate modeling of a real material whose unloading behavior varies with radius. Comparisons indicate that this is a robust, accurate procedure.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 8

Convergence behavior of single effective material (SEMAT); total equivalent strain–stress profiles (analytical procedure)

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Figure 9

Hoop residual stress calculated using analytical method compared to Hencky numerical solution for incompressible material

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Figure 1

Diagrammatic representation of pressure vessel steel behavior during uniaxial pull–push testing

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Figure 2

Overall tube geometry including initial yield radius (rc ) and reyield radius (rd )

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Figure 3

Maximum loading and unloading plastic strains during autofrettage, A723, 1130 MPa yield, ro /ri  = 2.5, 46.5% overstrain

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Figure 4

Loading and unloading profiles for five radial locations within the tube

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Figure 5

Hoop residual stress calculated using different numerical analysis methods

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Figure 6

Unloading profiles for five radial locations within the tube, single origin

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Figure 7

Convergence behavior of single effective material (SEMAT); equivalent nonlinear strain versus equivalent stress profiles (numerical procedure)



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