A perspective on residual stresses in welding

Introduction

Residual stress in welding occurs due to misfit between different parts, different phases, or different regions within the same part arising out of non-uniform thermal strain, and strains arising from solidification and solid-state phase transformations.1 During welding, the region around the weld pool is inevitably associated with tensile residual stresses in the direction of welding and the tensile stresses are balanced by compressive stresses further from the weld line.2 Welding induced tensile residual stress promotes brittle fracture, buckling deformation, and stress-corrosion cracking, and reduces the fatigue life of welded structures in service.2^– 5 Accurate quantitative estimation of residual stress in welded fabrications including repair welds is of significant interest.5^– 7 This special issue intends to assimilate recent activities towards estimation, measurement, and mitigation of welding induced residual stress.

The primary focus of research on welding induced residual stress has been to develop mathematical models to estimate and experimental techniques to measure and mitigate residual stress for various joint geometries and welding conditions. The efficacy of various stress-relieving techniques has remained another important area of research. The objective of this article is to provide a perspective of recent research activities on residual stress in welding.

The estimation of welding-induced residual stress based on analytical calculations of the temperature field has resulted in limited success.8^– 10 Computer based numerical models gained considerable attention because realistic boundary conditions, temperature dependent material properties and complex joint geometries could be considered. However, the numerical models faced three major challenges. First, an accurate estimation of the temperature field in a weld needs three-dimensional (3D) analysis considering both conduction and convection modes of heat transfer.11, 12 Such calculations are computationally intensive. Second, the natural evolution of thermo-mechanical strains as the weld pool solidifies and cools down to the room temperature depends on the transient temperature field and the mechanical constraints posed by the joint geometry, which are often too complex to consider.5^– 7, 13 Third, the constitutive models that can accurately describe the thermo-elastic-plastic stress–strain response of materials and consider the influence of solid-state phase transformation are rarely available for many engineering alloys.5^– 7

The numerical models to estimate welding induced residual stress started with the two-dimensional (2D) axisymmetric thermo-mechanical analysis by Hibbit and Marcal14 for gas metal arc (GMA) welding. Since then a large number of 2D models15^– 33 have been developed considering different welding processes and joint geometries. These models could consider evolution of temperature and resulting thermo-mechanical stress fields on a plane usually perpendicular to the welding direction assuming plane stress (zero out-of-plane stress), plane strain (zero out-of-plane strain) or axisymmetric condition. Thus, the 2D models could not compute longitudinal residual stress and its influence on the corresponding transverse and normal components in a realistic manner. In spite of those limitations, the 2D models set the roadmap towards quantitative evaluation of welding induced residual stress.

Karlsson and Josefson,34 and Tekriwal and Mazumdar35 started 3D analysis to compute welding induced residual stress and showed the need for simplifying assumptions to avoid increased computational demand required for 3D structures. For example, both the works34, 35 considered very coarse mesh and small solution domain compared to the actual size of the welded structure. Even with the recent improvement in the computational hardware, comprehensive 3D thermo-elasto-plastic analyses of large welded structures remain a major challenge. Significant efforts have been made to examine the utility of 2D (plane stress, plane strain or axisymmetric) analyses in predicting residual stress in several joining processes and joint geometries considering both single- and multi-pass welding.36^– 49 Remarkably, most of the modelling attempts15^– 49 used a conduction heat transfer analysis to predict the temperature field. Since convection is the main mechanism of heat transfer in the weld pool, the temperature and stress fields computed from heat conduction models are susceptible to large errors, particularly near the weld pool where temperature changes are significant.

Thermo-mechanical analysis was also attempted in Eulerian reference frame neglecting the edge effects to achieve twofold benefits.50^– 53 First, a reduced solution domain can be considered instead of the entire weld structure. Second, a fine mesh is required only near the weld seam to account for the steep temperature gradient and the resulting thermal strain gradient. Although this approach can increase computational efficiency, the application of appropriate boundary conditions and the calculation of the accumulated thermal strain remain as important challenges. Ueda et al. proposed a simplified procedure that computed local inelastic strain, referred to inherent strain, considering only the weld area and subsequently performed an elastic analysis of the entire structure considering the inherent strains as equivalent loads.54, 55 Although this approach was tested in single- and multi-pass welds,54, 55 the restraint effect due to the overall stiffness of a welded structure could not be considered appropriately in the local thermo-mechanical analysis.56^– 59 In recent years, efforts towards comprehensive 3D thermo-elasto-plastic analysis have been further facilitated by the increased availability of finite element method based commercial software.60, 61

In steel welds, the transformation strains due to solid-state phase transformation such as austenite to martensite or ferrite during cooling can strongly influence the residual stress.17,19,34 The kinetics of solid-state phase transformations under the conditions of welding has still remained a difficult area in weld modelling.11,12,62^– 67 Nevertheless, attempts to include the effect of solid-state phase transformation on volumetric strain and yield strength of weld material in modelling residual stresses are reported in recent studies.68^– 78 Taljat et al. 69 performed a 2D thermo-mechanical analysis using ABAQUS for GTA spot welding of HY-100 steel considering the volumetric strain due to austenite to martensite transformation. Further models58,70^– 72 showed that the consideration of volumetric strain due to austenite to martensite transformation could improve the estimated residual stresses markedly in welds of medium to high carbon steel, and stainless steel. Deng et al. 73,74 and Lee et al. 75,76 used Johnson–Mehl–Avrami–Kolmogorov and Koistinen–Marburger equations to track respectively austenite to bainite and austenite to martensite transformations, and considered their influence on the volumetric strain and yield strength in computing residual stress in high strength carbon steels welds. The influence of phase transformation on mechanical properties, in particular during load reversal, was also considered by Yamamoto et al. 77 in estimating residual stress in high strength steel and by Feng et al. 78 in aluminium alloys.

Direct measurements of residual stresses by destructive techniques such as slitting, hole-drilling and contour methods and non-destructive techniques based on laboratory and synchrotron X-ray and neutron diffraction have remained as important areas of research.79^– 91 All these techniques usually measure the residual strain over a sample gauge volume that approximately corresponds to the resolution of the measured values. The neutron diffraction, in particular, is capable of evaluating residual stress in three orthogonal directions deep inside a welded structure with a spatial resolution of 1 mm or smaller. In contrast, the synchrotron X-ray can measure residual stress in two dimensions while the high-energy shorter wavelength radiation allows a fast measurement sufficiently deep in the weld. The laboratory X-ray based measurements, however, has remained an effective tool to measure surface and sub-surface residual stress. The synchrotron X-ray and neutron diffraction methods are usually preferred as they are non-destructive and free from near surface defects that inhibit the use of other techniques, and also facilitate mapping of stresses over a large area. Comparison between the neutron and X-ray based diffraction techniques has shown that the former is capable of monitoring bulk residual strain while the later can be used to characterise small-scale residual strain variation such as the strains in crystallographic structure.79^– 87 Both synchrotron X-ray and neutron diffraction are also used to trace the in situ evolution of residual strain.86,88 Recently, a destructive technique such as the contour method involving monitoring of released strain during wire-electron discharge machining cutting of weld samples is also found effective in thick welded structure.89^– 91 One important outcome of these studies is the quantitative establishment of the nature and magnitude of residual stresses in friction stir welded joints in comparison to conventional fusion welded joints of aluminium as well as of steels.

Since welding induced residual stresses are common, various methodologies to alleviate and mitigate the stresses have been investigated. Mechanical92^– 95 and thermal96^– 102 tensioning of the weld joints either during or after welding are promising techniques to reduce residual stresses. Such tensioning techniques can be applied either globally to the entire component prior to or during welding or locally to the weld area during welding. For example, preheating of the entire component to be welded reduces the temperature gradient between the weld material and the surrounding parent material thereby reducing the net thermal strain and residual stress. Alternately, local hot or cold spots can be applied using an external source respectively in front of or immediately behind the welding heat source resulting in a reduction in the local temperature gradient, thermal strain and residual stress. In practice, thermal tensioning methods are more difficult to apply in actual welds due to complex joint geometries and the difficulties involved in applying appropriate external heat sources. Therefore, mechanical tensioning methods are popular for this purpose. There is also recent interest in engineering filler material composition in fusion welding of steels that can generate compressive strains due to solid-state phase transformation and hence, counter localised high tensile residual stress.103^– 107 Both experimental and theoretical calculations have indicated that an appropriately engineered filler material can counter local tensile residual stress by way of the strains associated with solid-state phase transformation in welds of complex steel materials effectively leading to a local equilibrium of stresses.

Papers in this special issue

This special issue comprises of 13 original research articles including five on modelling, six on experimental measurement, and two on design of filler material composition for mitigation of residual stress in welding. STWJ invited contributions from many authors based on publication records in the commonly available electronic databases. The papers that were received were peer reviewed in the usual manner. We thank all authors for their contributions and welcome commentaries and further contributions for the future issues of the journal.

Okano et al. 108 used an arc physics based model to estimate the surface heat source expression. A subsequent 3D sequentially coupled thermal and thermo-mechanical analysis is done to estimate residual stress in GTA welds of high strength structural steel for a wide range of welding conditions.

The paper by Michaleris and Lawrence109 shows the need for convective heat transfer based modelling of temperature fields in computing residual stress. The computed temperature field from a 3D conduction heat transfer model was fairly successful to compute residual stress in GMA welds but inadequate in laser-GMA hybrid welds because the formation of a keyhole and the resulting transport of heat in the weld pool could not be considered. Computed temperature fields considering convective transport of heat could predict residual stress more effectively in laser-GMA hybrid welds.

Feulvarch et al. 110 computed residual stress in multi-pass pipe welds between ferritic and austenitic steels considering the effect of solid-state phase transformation and temperature on material properties. A full 3D analysis is shown to be requisite to predict residual stress in multi-pass circular welds and 2D axisymmetric analysis is justified for a few initial weld passes only.

To alleviate huge computational demand when computing residual stress in large structure with many weld joints, Biswas et al. 111 has performed 3D thermal–mechanical analysis in and around the weld areas and subsequently, an elastic stress analysis of the entire structure by imposing the local plastic strains as boundary conditions. A significant reduction in the computational demand with very little loss in accuracy in prediction is reported.

Yaghi et al. 112 modelled residual stresses during welding of P91 steel pipes and stress-relieving during post weld heat treatment (PWHT) considering Norton's creep law during PWHT. The Norton creep constants were obtained from experiments. The computed results showed a significant reduction in the residual hoop and axial stresses after PWHT, which was also verified experimentally.

Assuncao et al. 113 measured residual stresses by neutron diffraction in conduction and keyhole mode laser welds. The peak longitudinal tensile residual stresses were found to be similar in both types of welds while the former contained a larger stress affected region. Suder et al. 114 showed that the hybrid laser-GTA welds can lead to nearly 50% higher tensile longitudinal stress in comparison to a laser weld for a constant weld penetration. This is significant since the hybrid laser-GTA is often considered as a recourse to laser welding to avoid the stringent requirement of joint fit-up in the latter case. Thirumala et al. 115 used neutron diffraction to map 2D residual stresses in girth welds of large diameter, thick walled X-65 carbon steel pipelines used in the oil and gas industry. Residual stresses were measured in a carbon steel weld with fully ferritic weld metal and in an Inconel 625 dissimilar weld with fully austenitic weld metal. Both types of the welds showed a similar nature and magnitude of axial and hoop residual stresses.

To estimate the residual strain, the diffraction methods require a value for the stress-free lattice spacing, which depends on the microstructure and is difficult to assign reliably in dissimilar metal welds. Zhang et al. 116 proposed a recourse to estimate the stress-free lattice spacing as a function of the measured lattice spacing in three orthogonal directions in the actual weld considering plane stress conditions. The proposed methodology was tested in multi-pass GMA welds of 304L stainless steel plates with nickel alloy 82 filler material. The measured through-thickness residual stresses were in fair agreement with similar results measured using the deep-hole drilling technique.

Hashimoto117 proposed an improved X-ray based measurement technique using a 2D detector combined with multi-axial rocking for Ni-based alloy welds. In such a case, the final weld microstructure is devoid of solid-state phase transformations. The X-ray based measurement is difficult due to the preferred orientation of the unidirectional solidification and grain growth in the heat-affected zone. The 2D detector combined with multi-axial rocking is shown to be able to capture the location of the maximum tensile residual stress fairly accurately. The influence of the softening behaviour of the material on the evolution and final residual stress distribution in friction stir welds of AA6061 and of AZ31B alloys are outlined in the paper by Woo and Choo.118 The authors used neutron diffraction to measure welding induced residual stress and standard procedures to simultaneously evaluate the yield strength and hardness at several locations in and around the weld region.

The last two papers in this special issue examine the role of filler material composition in balancing tensile residual stress. Reddy and Ramana119 reported the influence of filler wire composition on residual stress in similar and dissimilar welds of maraging steel and medium alloy medium carbon steel. In similar welds of maraging steel and medium carbon steel, the measured residual stresses were compressive and tensile, respectively. In the dissimilar welds, the residual stress in fusion zone was compressive in maraging steel and tensile in medium carbon steels. In another interesting work, Moat et al. 120 showed that an engineered martensitic filler metal with low-transformation-temperature could counter the tensile residual stress in typical ferritic and austenitic welds by exploiting the strains associated with solid-state phase transformation.

Concluding remarks

The literature on residual stress in welding including the papers in this special issue of STWJ shows the recent advancements made in the field and indicates the opportunities and challenges that lie ahead. Improved access to neutron and synchrotron X-ray diffraction has certainly facilitated the use of diffraction based methods for the measurement of residual stress. It is expected that the use of these high energy beams for real-time studies of phase transformations and the evolution of strains during actual welding process will provide new insights not easily attainable by other techniques. Such studies, when appropriately planned, will also be able to provide realistic constitutive relations during solid-state phase transformation. Reliable constitutive equations are needed for important engineering alloys that take into account the influence of solid-state phase transformations on the mechanical behaviour of alloys. An important research need in the area of residual stress calculations is to use realistic 3D transient temperature fields based on convective heat transfer in a computationally efficient manner. Finally, finding appropriate ways to alleviate distortion and residual stress in welding has remained an important priority. Designing appropriate filler materials that can counter local tensile residual stress through the strains associated with solid-state phase transformation will certainly remain an important area of research. With the continuing improvements in the software and hardware, realistic determination of the nature and strength of the external heat sources that can mitigate welding induced distortion and residual stress is likely to be within the reach of the welding research community.