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Research Papers: Design and Analysis

Analytical Inverse Solution of Eigenstrains and Residual Fields in Autofrettaged Thick-Walled Tubes

[+] Author and Article Information
S. Ali Faghidian

Department of Mechanical
and Aerospace Engineering,
Science and Research Branch,
Islamic Azad University,
Tehran 1477893855, Iran
e-mail: Faghidian@gmail.com

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received December 24, 2015; final manuscript received August 23, 2016; published online November 24, 2016. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 139(3), 031205 (Nov 24, 2016) (8 pages) Paper No: PVT-15-1280; doi: 10.1115/1.4034675 History: Received December 24, 2015; Revised August 23, 2016

The smoothed inverse eigenstrain method is revisited for the reconstruction of residual fields and eigenstrains from limited strain measurements within axially symmetric tubes. The application of the present approach is successfully demonstrated for two cases of analytical solution and experimental measurements. The well-known advantage of the smoothed inverse eigenstrain approach is that it not only minimizes the deviation of measurements from the model predictions but also will result in an inverse solution satisfying all of the continuum mechanics requirements. As a result, less number of experimental measurements is required to reconstruct the complete residual fields. Consequently, the distribution of residual stresses is obtained without requiring the details of the hardening behavior of the material. Furthermore, the eigenstrain field is inversely determined satisfying the total strain compatibility equations, and a closed form analytical solution is presented for the distribution of eigenstrains.

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Figures

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Fig. 1

Schematic illustration of the geometry and the coordinate system

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Fig. 7

Reconstructed eigenstrain distribution by smoothed inverse eigenstrain analysis compared with the results of variational eigenstrain method [21]

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Fig. 3

Reconstructed residual stresses compared with the analytical solution [26] for 50% overstrain: (a) hoop residual stress and (b) radial residual stress

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Fig. 4

Reconstructed eigenstrain distribution compared with the plastic strain profile [28]

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Fig. 5

Neutron diffraction measurements [10] and reconstructed residual elastic strains by smoothed inverse eigenstrain analysis compared with the results of variational eigenstrain method [21]: (a) hoop RES and (b) radial RES

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Fig. 6

Reconstructed residual stresses by smoothed inverse eigenstrain analysis compared with the smoothed residual stresses based on neutron diffraction measurements [10]: (a) hoop residual stress and (b) radial residual stress

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Fig. 2

Reconstructed residual elastic strains based on analytical solution [26] for 50% overstrain: (a) hoop RES, selected measurements, and reconstructed profile and (b) radial RES and reconstructed profile

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