Determination of the profile of the complete residual stress tensor in a VPPA weld using the multi-axial contour method M.E. Kartal 1 , C.D.M. Liljedahl, S. Gungor, L. Edwards 2 , M.E. Fitzpatrick * Materials Engineering, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK Received 7 December 2007; received in revised form 28 April 2008; accepted 1 May 2008 Available online 13 June 2008 Abstract The multi-axial contour method is a recent development of the contour method of stress measurement. It permits measurement of the 3D residual stress distribution in a body, based on the assumption that the residual stresses are due to an inelastic misfit strain (eigen- strain) that does not change when a sample containing residual stresses is sectioned. The eigenstrain is derived from measured displace- ments due to residual stress relaxation when the specimen is sectioned. By carrying out multiple cuts, the full residual stress tensor in a continuously processed body can be determined, where the specimen has an initial length-to-width aspect ratio of 2:1. In the present study, first a finite element simulation of the technique was carried out to verify the method numerically. The method was then used to determine the residual stresses in a VPPA-welded sample, and the results were validated by neutron diffraction measurements. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Residual stresses; Neutron diffraction; Welding 1. Introduction Residual stresses are those stresses that can exist within a material in the absence of any externally applied loads or self load. They can be introduced into the material by vir- tually any manufacturing processes that cause thermal or compositional gradients or that involve plastic deforma- tion. Thus, they can be produced by forming, joining, machining, heat treatment, abrasion and many other rela- tively simple processes. The importance of residual stresses in the structural integrity of materials and components is due to the fact that they can have the same effects on a material as stresses generated by applied loads. They can add to an externally applied load to cause yield, for exam- ple, even though the external load on its own may not be high enough to do so. As they can cause premature failure if they are not accounted for, it is imperative that their magnitude and distribution within materials are known in safety-critical structures. Although numerical methods are now commonly employed to model residual stress generation, experimental measurements are often required to validate the predic- tions. This is especially true when the material in question has gone through a complicated fabrication process, such as welding. The measurement methods can be classified into two categories. Destructive techniques are based on the principle that the strain measured in a material as a result of sectioning, or removing, part of the material is directly related to the residual stresses in the material before the cut is made. Examples include hole drilling, layer removal, compliance and contour methods. Non-destruc- tive methods rely on the measurement of a change in a cer- tain physical property of the material, such as lattice spacings or magnetic properties, owing to the residual stresses. Diffraction methods, which use X-rays or neu- trons, are currently among the most popular measurement techniques, though they do have some limitations [1]. For 1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.05.007 * Corresponding author. Tel.: +44 1908 653100; fax: +44 1908 653858. E-mail address: m.e.fitzpatrick@open.ac.uk (M.E. Fitzpatrick). 1 Present address: Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK. 2 Present address: Institute of Materials Engineering, ANSTO, PMB1, Menai, NSW 2234, Australia. www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 56 (2008) 4417–4428