Research Papers: Design and Analysis

Analytical Approach for Inverse Reconstruction of Eigenstrains and Residual Stresses in Autofrettaged Spherical Pressure Vessels

[+] Author and Article Information
S. Ali Faghidian

Department of Mechanical and
Aerospace Engineering,
Science and Research Branch,
Islamic Azad University,
Tehran 19166, 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 29, 2015; final manuscript received January 12, 2017; published online April 21, 2017. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 139(4), 041202 (Apr 21, 2017) (7 pages) Paper No: PVT-15-1286; doi: 10.1115/1.4035980 History: Received December 29, 2015; Revised January 12, 2017

The stress function approach is revisited for the inverse determination of residual stresses and eigenstrains from limited pointwise data in spherically symmetric stress state. The robust least squares technique is utilized to minimize the deviation of the measurement data from the model predictions while a full range of continuum mechanics requirements are satisfied. The application of the newly proposed spherical stress function is effectively demonstrated for two cases of analytical and numerical solutions considering different material behavior models. Also, the eigenstrains are inversely determined satisfying the equation of strain compatibility and a closed form analytical solution is presented.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Kendall, D. P. , 2002, “ A Short History of High Pressure Technology From Bridgman to Division 3,” ASME J. Pressure Vessel Technol., 122(3), pp. 229–233. [CrossRef]
Webster, G. A. , and Ezeilo, A. N. , 2001, “ Residual Stress Distributions and Their Influence on Fatigue Lifetimes,” Int. J. Fatigue, 23(Supplement 1), pp. 375–383. [CrossRef]
Jahed, H. , Farshi, B. , and Hosseini, M. , 2006, “ Fatigue Life Prediction of Autofrettage Tubes Using Actual Material Behavior,” Int. J. Press. Vessels Piping, 83(10), pp. 749–755. [CrossRef]
Parker, A. P. , and Huang, X. , 2007, “ Autofrettage and Reautofrettage of a Spherical Pressure Vessel,” ASME J. Pressure Vessel Technol., 129(1), pp. 83–88. [CrossRef]
Adibi-Asl, R. , and Livieri, P. , 2007, “ Analytical Approach in Autofrettaged Spherical Pressure Vessels Considering the Bauschinger Effect,” ASME J. Pressure Vessel Technol., 129(3), pp. 411–419. [CrossRef]
Darijani, H. , Kargarnovin, M. H. , and Naghdabadi, R. , 2009, “ Design of Spherical Vessels Under Steady-State Thermal Loading Using Thermo-Elasto–Plastic Concept,” Int. J. Pressure Vessels Piping, 86(2–3), pp. 143–152. [CrossRef]
Perl, M. , and Perry, J. , 2010, “ The Beneficial Contribution of Realistic Autofrettage to the Load-Carrying Capacity of Thick-Walled Spherical Pressure Vessels,” ASME J. Pressure Vessel Technol., 132(1), p. 011204. [CrossRef]
Maleki, M. , Farrahi, G. H. , Haghpanah Jahromi, B. , and Hosseinian, E. , 2010, “ Residual Stress Analysis of Autofrettaged Thick-Walled Spherical Pressure Vessel,” Int. J. Pressure Vessels Piping, 87(7), pp. 396–401. [CrossRef]
Jahed, H. , and Dubey, R. N. , 1997, “ An Axisymmetric Method of Elastic–Plastic Analysis Capable of Predicting Residual Stress Field,” ASME J. Pressure Vessel Technol., 119(3), pp. 264–273. [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. , 2009, “ Eigenstrain Analysis of Residual Strains and Stresses,” J. Strain Anal. Eng. Des., 44(1), pp. 29–43. [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]
Faghidian, S. A. , 2017, “ Analytical Inverse Solution of Eigenstrains and Residual Fields in Autofrettaged Thick-Walled Tubes,” ASME J. Pressure Vessel Technol., 139(3), p. 031205. [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]
Hoger, A. , 1986, “ On the Determination of Residual Stress in an Elastic Body,” J. Elast., 16(3), pp. 303–324. [CrossRef]
Chakrabarty, J. , 1987, Theory of Plasticity, McGraw-Hill, New York.
Sokolnikoff, I. S. , 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.
Myint-U, T. , and Debnath, L. , 2007, Linear Partial Differential Equations for Scientists and Engineers, Birkhäuser, Berlin.
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. Press. Vessels Piping, 86(11), pp. 777–784. [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]
Mura, T. , 1987, Micromechanics of Defects in Solids, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Allaire, G. , and Kaber, S. M. , 2008, Numerical Linear Algebra, Springer, New York.
von Reuss, A. , 1930, “ Berücksichtigung der Elastischen Formänderung in der Plastizitätstheorie,” Z. Angew. Math. Mech., 10(3), pp. 266–274. [CrossRef]
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]
Parker, A. P. , Underwood, J. H. , and Kendall, D. P. , 1999, “ Bauschinger Effect Design Procedures for Autofrettaged Tubes Including Material Removal and Sachs' Method,” ASME J. Pressure Vessel Technol., 121(4), pp. 430–437. [CrossRef]
Troiano, E. , Parker, A. P. , and Underwood, J. H. , 2004, “ Mechanisms and Modeling Comparing HB7 and A723 High Strength Pressure Vessel Steels,” ASME J. Pressure Vessel Technol., 126(4), pp. 473–477. [CrossRef]
Taylor, M. , 2002, “ The Gibbs Phenomenon, the Pinsky Phenomenon, and Variants for Eigenfunction Expansions,” Commun. Partial Differ. Equations, 27(3–4), pp. 565–605. [CrossRef]
Jahed, H. , and Ghanbari, G. H. , 2002, “ Actual Unloading Behavior and Its Significance on Residual Stress in Machined Autofrettaged Tubes,” ASME J. Pressure Vessel Technol., 125(3), pp. 321–325. [CrossRef]


Grahic Jump Location
Fig. 1

Reconstructed residual stresses, selected measurements, and the results of the Reuss analytical solution [20] for 45% overstrain

Grahic Jump Location
Fig. 3

Reconstructed residual stresses, selected measurements, and the results of the VMP numerical solution [4] for HB7 steel

Grahic Jump Location
Fig. 4

Reconstructed eigenstrains distribution for the VMP results of HB7 steel

Grahic Jump Location
Fig. 2

Reconstructed eigenstrain distribution compared to the equivalent plastic strain profile



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In