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Research Papers: Design and Analysis

Ratchet Boundary Determination Using a Noncyclic Method

[+] Author and Article Information
R. Adibi-Asl1

 Atomic Energy of Canada Limited (AECL), Mississauga, ON L5K 1B2, Canadareza.adibiasl@amec.com

W. Reinhardt

 Atomic Energy of Canada Limited (AECL), Mississauga, ON L5K 1B2, Canada

1

Currently at AMEC NSS, 393 University Ave., Toronto, ON, Canada, M5G 1E6.

J. Pressure Vessel Technol 132(2), 021201 (Jan 14, 2010) (9 pages) doi:10.1115/1.4000506 History: Received January 07, 2009; Revised May 17, 2009; Published January 14, 2010; Online January 14, 2010

A simple and systematic procedure is proposed for shakedown analysis using a combination of linear and nonlinear finite element analysis (FEA). The method can identify the boundary between the shakedown and ratcheting domains directly and does not require a cyclic analysis (noncyclic). The proposed method performs an elastic-plastic FEA to determine the reduction in load carrying capacity due to the cyclic secondary loads. An elastic modulus adjustment procedure is then used to generate statically admissible stress distributions and kinematically admissible strain distributions under the applied primary loads. By modifying the local elastic moduli it is possible to obtain inelastic-like stress redistribution. The method is demonstrated with a “two-bar structure” model based on analytical routine. The analysis is then applied to some typical shakedown problems including the “classical Bree problem,” the “bimaterial cylinder,” and the “plate with a hole subjected to radial temperature gradient.”

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Application of noncyclic method to a beam subjected to cyclic linear variation in temperature through the thickness and sustained axial mechanical load

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Figure 3

Ratchet boundary of the two-bar model: (a) case I (L2=2L1;  A2=A1), (b) case II (L2=L1;  A2=4A1)

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Figure 4

Classical Bree problem: (a) schematic geometry and loading and (b) typical finite element mesh

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Figure 5

Ratchet boundary of the classical Bree problem (beam with steady primary axial and cyclic thermal loadings)

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Figure 6

Axisymmetric bimaterial problem: (a) schematic geometry and loading and (b) typical finite element mesh

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Figure 7

Ratchet boundary of the axisymmetric bimaterial problem: L=0.254 m (10 in.)

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Figure 8

Variation in normalized radial displacement to thickness during the cyclic elastic-plastic analysis: L=0.254 m (10 in.) and ΔT=840°C

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Figure 9

Ratchet boundary of the axisymmetric bimaterial problem for different lengths of fused rings

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Figure 10

Plate with a hole: (a) schematic geometry and loading and (b) typical finite element mesh

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Figure 11

Ratchet boundary for plate with a hole

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Figure 12

Variation in limit load multiplier for Δσth/σt0=1.6792 (where (P/σy)Upper bound=0.3773 and (P/σy)Lower bound=0.3729)

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