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Research Papers: Design and Analysis

A Direct Method on the Evaluation of Ratchet Limit

[+] Author and Article Information
Haofeng Chen1

Department of Mechanical Engineering, University of Strathclyde, Glasgow G1 1XJ, UKhaofeng.chen@strath.ac.uk

Alan R. S. Ponter

Department of Engineering, University of Leicester, Leicester LE1 7RH, UK

1

Corresponding author.

J. Pressure Vessel Technol 132(4), 041202 (Jul 23, 2010) (8 pages) doi:10.1115/1.4001524 History: Received January 04, 2010; Revised March 18, 2010; Published July 23, 2010; Online July 23, 2010

This paper describes a new linear matching method (LMM) technique for the direct evaluation of the ratchet limit of a structure subjected to a general cyclic load condition, which can be decomposed into cyclic and constant components. The cyclic load history considered in this paper contains multiload extremes to include most complicated practical applications. The numerical procedure uses the LMM state-of-the-art numerical technique to obtain a stable cyclic state of component, followed by a LMM shakedown analysis, to calculate the maximum constant load, i.e., the ratchet limit, which indicates the load carrying capacity of the structure subjected to a cyclic load condition to withstand an additional constant load. This approach is particularly useful in conjunction with the evaluation of the stable cyclic response, which produces the cyclic stresses, residual stresses, and plastic strain ranges for the low cycle fatigue assessment. A benchmark example of a holed plate under the combined action of cyclic thermal load and constant mechanical load is presented to verify the applicability of the new ratchet limit method through a comparison with published results by a simplified method assuming a cyclic load with two extremes. To demonstrate the efficiency and effectiveness of the method for a complicated cyclic load condition with multiload extremes, a composite thick cylinder with a radial opening subjected to cyclic thermal loads and a constant internal pressure is analyzed using the proposed ratchet limit method. Further verification by the ABAQUS step-by-step inelastic analysis demonstrates that the proposed new method provides a general-purpose technique for the evaluation of the ratchet limit and has both the advantages of programming methods and the capacity to be implemented easily within a commercial finite element code Abaqus.

FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Stress , Pressure
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Figures

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Figure 1

Geometry of the holed plate subjected to varying thermal loads and its finite element mesh (D/L=0.2), the yield stress σY=360 MPa, and the elastic modulus E=208 GPa

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Figure 2

Cyclic load history with two distinct extremes to the elastic solution

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Figure 3

Comparisons of ratchet limit interaction curves for the holed plate subjected to various predefined changing thermal loads to withstand an additional constant mechanical load

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Figure 4

The maximum of the plastic strain range Δε¯maxP=23ΔεmaxPΔεmaxP occurring at locations A and B (Fig. 1) for the holed plate subjected to varying cyclic thermal loads Δθ/Δθ0

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Figure 5

Comparison of ratcheting mechanism of the holed plate subjected to various predefined changing thermal loads: (a) Δθ/Δθ0=0.5 (point A in Fig. 3) and (b) Δθ/Δθ0=3.0 (point B in Fig. 3)

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Figure 6

Convergence condition of iterative process for the ratchet analysis of the holed plate subjected to predefined changing thermal loads Δθ/Δθ0=5 to withstand an additional constant mechanical load

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Figure 7

Geometry model of the composite cylinder with a radial opening

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Figure 8

Finite element model of the composite cylinder with a radial opening

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Figure 9

Ratchet limit interaction curve for the composite cylinder with a radial opening subjected to cyclic thermal loads and a constant internal pressure

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Figure 10

Convergence conditions of iterative processes for the ratchet analysis of the composite cylinder with radial opening subjected to varying cyclic thermal loads Δθ/Δθ0 to withstand an additional internal pressure

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Figure 11

ABAQUS verification of the ratchet limit for different cyclic thermal loads using detailed step-by-step analysis

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Figure 12

Comparison of the ratcheting mechanisms by the proposed ratchet limit method and the ABAQUS step-by-step analysis method for the component subjected to a cyclic thermal load of Δθ/Δθ0=2 to withstand an additional internal pressure

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