Numerical Reconstruction of Residual Stress Fields from Limited Measurements

Abstract:

By finding stress states which are consistent both with any existing experimental measurements and with elasticity theory, residual stress fields can often be reconstructed from incomplete measurement data. We discuss such methods of residual stress reconstruction, their implementation using finite element analysis, and the measurement strategies which enable them. In general, reconstruction of residual stress fields must be formulated as an inverse problem, which can usually be solved using stress basis functions. However, prior knowledge of the form of the residual stress field and/or underlying eigenstrain distribution often allows the problem to be reduced such that inverse methods become unnecessary, greatly simplifying the analysis. Two examples of when residual stress field reconstruction can be simplified in this way are given.

• Periodical: Advanced Materials Research (Volume 996)
• Pages: 243-248
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.996.243
• Online since: August 2014
• Authors: Harry E. Coules*, David J. Smith, Karim H.A. Serasli
• Keywords: Eigenstrain, Finite Element Analysis (FEA), Stress Field Reconstruction

References

[1] G. S. Schajer and C. O. Ruud, Practical Residual Stress Measurement Methods, 1st ed., G. S. Schajer (Ed. ), Wiley, 2013, p.1–27.

DOI: 10.1002/9781118402832.ch1

[2] BSi 7910: Guide to methods for assessing the acceptability of flaws in metallic structures. BSi, (2005).

[3] R6: Assessment of the Inegrity of Structures Containing Defects, Revision 4, British Energy Generation Limited, R/H/R6, (2001).

[4] A. H. Mahmoudi, S. Hossain, C. E. Truman, D. J. Smith, and M. J. Pavier, A new procedure to measure near yield residual stresses using the deep hole drilling technique, Exp. Mech. 49 (2009) 595–604.

DOI: 10.1007/s11340-008-9164-y

[5] D. J. Smith, P. J. Bouchard, and D. George, Measurement and prediction of residual stresses in thick-section steel welds, J. Strain Anal. Eng. 35 (2000) 287–305.

DOI: 10.1243/0309324001514422

[6] T. -S. Jun and A. M. Korsunsky, Evaluation of residual stresses and strains using the eigenstrain reconstruction method, Int. J. Solids Struct. 47 (2010) 1678–1686.

DOI: 10.1016/j.ijsolstr.2010.03.002

[7] A. M. Korsunsky, Eigenstrain analysis of residual strains and stresses, J. Strain Anal. Eng. 44 (2009) 29–43.

[8] A. T. DeWald and M. R. Hill, Multi-axial contour method for mapping residual stresses in continuously processed bodies, Exp. Mech. 46 (2006) 473–490.

DOI: 10.1007/s11340-006-8446-5

[9] M. E. Kartal, C. D. M. Liljedahl, S. Gungor, L. Edwards, and M. E. Fitzpatrick, Determination of the profile of the complete residual stress tensor in a VPPA weld using the multi-axial contour method, Acta Mater. 56 (2008) 4417–4428.

DOI: 10.1016/j.actamat.2008.05.007

[10] A. M. Korsunsky, G. M. Regino, D. Latham, and J. Liu, D. Nowell, and M. Walsh, Eigenstrain analysis of synchrotron X-ray diffraction measurement of residual strains in machined nickel alloy plates, J. Strain Anal. Eng 41 (2006) 381–395.

DOI: 10.1243/03093247jsa135

[11] T. -S. Jun, A. M. Venter, and A. M. Korsunsky, Inverse eigenstrain analysis of the effect of non-uniform sample shape on the residual stress due to shot peening, Exp. Mech. 51 (2011) 165–174.

DOI: 10.1007/s11340-010-9346-2

[12] X. Song and A. M. Korsunsky, Fully two-dimensional discrete inverse eigenstrain analysis of residual stresses in a railway rail head, J. Appl. Mech. T. ASME 78 (2011) 031019.

DOI: 10.1115/1.4003364

[13] S. A. Faghidian, D. Goudar, G. H. Farrahi, and D. J. Smith, Measurement, analysis and reconstruction of residual stresses, J. Strain Anal. Eng. 47 (2012) 254–264.

DOI: 10.1177/0309324712441146

[14] G. H. Farrahi, S. A. Faghidian, and D. J. Smith, An inverse approach to determination of residual stresses induced by shot peening in round bars, Int. J. Mech. Sci. 51 (2009) 726–731.

DOI: 10.1016/j.ijmecsci.2009.08.004

[15] G. H. Farrahi, S. A. Faghidian, and D. J. Smith, An inverse method for reconstruction of the residual stress field in welded plates, J. Press. Vess. T. ASME 132 (2010) 612051.

DOI: 10.1115/1.4001268

[16] A. M. Korsunsky, G. M. Regino, and D. A. Nowell, Variational eigenstrain analysis of residual stresses in a welded plate, Int. J. Solids Struct. 44 (2007) 4574–4591.

DOI: 10.1016/j.ijsolstr.2006.11.037

[17] P. J. Bouchard, The NeT bead-on-plate benchmark for weld residual stress simulation, Int. J. Press. Vess. Pip. 86 (2009) 31–42.

DOI: 10.1016/j.ijpvp.2008.11.019

[18] H. E. Coules, D. J. Smith, K. Abburi Venkata, and C. E. Truman, A method for reconstruction of residual stress fields from measurements made in an incompatible region, Int. J. Solids Struct. 51 (2014) 1980-(1990).

DOI: 10.1016/j.ijsolstr.2014.02.008