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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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References

Kendall, D. P. , 2000, “ A Short History of High Pressure Technology From Bridgman to Division 3,” ASME J. Pressure Vessel Technol., 122(3), pp. 229–233. [CrossRef]
Stacey, A. , and Webster, G. A. , 1998, “ Determination of Residual Stress Distributions in Autofrettaged Tubing,” Int. J. Pressure Vessels Piping, 31(3), pp. 205–220. [CrossRef]
Lazzarin, P. , and Livieri, P. , 1997, “ Different Solutions for Stress and Strain Fields in Autofrettaged Thick-Walled Cylinders,” Int. J. Pressure Vessels Piping, 71(3), pp. 231–238. [CrossRef]
Gao, X. , 1992, “ An Exact Elasto-Plastic Solution for an Open-Ended Thick-Walled Cylinder of a Strain-Hardening Material,” Int. J. Pressure Vessels Piping, 52(1), pp. 129–144. [CrossRef]
Huang, X. , 2005, “ A General Autofrettage Model of a Thick-Walled Cylinder Based on Tensile-Compressive Stress-Strain Curve of a Material,” J. Strain Anal. Eng. Des., 40(6), pp. 599–608. [CrossRef]
Hosseinian, E. , Farrahi, G. H. , and Movahhedy, M. R. , 2009, “ An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition,” ASME J. Pressure Vessel Technol., 131(6), p. 061201. [CrossRef]
Parker, A. P. , 2001, “ Autofrettage of Open-End Tubes-Pressures, Stresses, Strains and Code Comparisons,” ASME J. Pressure Vessel Technol., 123(3), pp. 271–281. [CrossRef]
Gibson, M. C. , Hameed, A. , Parker, A. P. , and Hetherington, J. , 2006, “ A Comparison of Methods for Predicting Residual Stresses in Strain-Hardening, Autofrettage Thick Cylinders, Including the Bauschinger Effect,” ASME J. Pressure Vessel Technol., 128(2), pp. 217–222. [CrossRef]
Farrahi, G. H. , Hosseinian, E. , and Assempour, A. , 2008, “ General Variable Material Property Formulation for the Solution of Autofrettaged Thick-Walled Tubes With Constant Axial Strains,” ASME J. Pressure Vessel Technol., 130(4), p. 041209. [CrossRef]
Venter, A. M. , de Swardt, R. R. , and Kyriacou, S. , 2000, “ Comparative Measurements on Autofrettaged Cylinders With Large Bauschinger Reverse Yielding Zones,” J. Strain Anal. Eng. Des., 35(6), pp. 459–469. [CrossRef]
Perry, J. , and Aboudi, J. , 2003, “ Elasto-Plastic Stresses in Thick Walled Cylinders,” ASME J. Pressure Vessel Technol., 125(3), pp. 248–252. [CrossRef]
Krawitz, A. D. , 2011, “ Neutron Strain Measurement,” Mater. Sci. Technol., 27(3), pp. 589–603. [CrossRef]
Coules, H. E. , Smith, D. J. , Venkata, K. A. , and Truman, C. E. , 2014, “ A Method for Reconstruction of Residual Stress Fields From Measurements Made in an Incompatible Region,” Int. J. Solids Struct., 51(10), pp. 1980–1990. [CrossRef]
Korsunsky, A. M. , Regino, G. M. , and Nowell, D. , 2007, “ Variational Eigenstrain Analysis of Residual Stresses in a Welded Plate,” Int. J. Solids Struct., 44(13), pp. 4574–4591. [CrossRef]
Jun, T.-S. , and Korsunsky, A. M. , 2010, “ Evaluation of Residual Stresses and Strains Using the Eigenstrain Reconstruction Method,” Int. J. Solids Struct., 47(13), pp. 1678–1686. [CrossRef]
Faghidian, S. A. , 2014, “ A Smoothed Inverse Eigenstrain Method for Reconstruction of the Regularized Residual Fields,” Int. J. Solids Struct., 51(25–26), pp. 4427–4434. [CrossRef]
Faghidian, S. A. , 2015, “ Inverse Determination of the Regularized Residual Stress and Eigenstrain Fields Due to Surface Peening,” J. Strain Anal. Eng. Des., 50(2), pp. 84–91. [CrossRef]
Farrahi, G. H. , Faghidian, S. A. , and Smith, D. J. , 2010, “ An Inverse Method for Reconstruction of the Residual Stress Field in Welded Plates,” ASME J. Pressure Vessel Technol., 132(6), p. 061205. [CrossRef]
Faghidian, S. A. , 2015, “ A Note on the Inverse Reconstruction of Residual Fields in Surface Peened Plates,” Lat. Am. J. Solids Struct., 12(12), pp. 2351–2362. [CrossRef]
Korsunsky, A. M. , 2007, “ Residual Elastic Strains in Autofrettaged Tubes: Elastic–Ideally Plastic Model Analysis,” ASME J. Eng. Mater. Technol., 129(1), pp. 77–81. [CrossRef]
Korsunsky, A. M. , and Regino, G. M. , 2007, “ Residual Elastic Strains in Autofrettaged Tubes: Variational Analysis by the Eigenstrain Finite Element Method,” ASME J. Appl. Mech., 74(4), pp. 717–722. [CrossRef]
Farrahi, G. H. , Faghidian, S. A. , and Smith, D. J. , 2009, “ Reconstruction of Residual Stresses in Autofrettaged Thick-Walled Tubes From Limited Measurements,” Int. J. Pressure Vessels Piping, 86(11), pp. 777–784. [CrossRef]
Hoger, A. , 1986, “ On the Determination of Residual Stress in an Elastic Body,” J. Elasticity, 16(3), pp. 303–324. [CrossRef]
Mura, T. , 1987, Micromechanics of Defects in Solids, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Timoshenko, S. P. , and Goodier, J. N. , 1970, Theory of Elasticity, 3rd ed., McGraw-Hill, New York.
Hill, R. , 1950, The Mathematical Theory of Plasticity, Oxford University Press, New York.
Chakrabarty, J. , 1987, Theory of Plasticity, McGraw-Hill, New York.
Rees, D. W. A. , 1987, “ A Theory of Autofrettage With Applications to Creep and Fatigue,” Int. J. Pressure Vessels Piping, 30(1), pp. 57–76. [CrossRef]
Allaire, G. and Kaber, S. M. , 2008, Numerical Linear Algebra, Springer, New York.

Figures

Grahic Jump Location
Fig. 1

Schematic illustration of the geometry and the coordinate system

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 7

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

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