Through-thickness Residual Stress Distributions Research Articles

Applying the Virtual Fields Method to Measure During Milling the Through-Thickness Residual Stress Distribution in Aluminum-Alloy Sheet Material

Residual stresses often cause distortion to occur when machining slender workpieces like those used in aeronautics. This distortion is undesirable and may even cause the workpiece to be scrapped. Identifying these residual stresses during machining is therefore crucial to limit their effect on the final geometry of the part. The aim of this work is to identify the through-thickness residual stress distribution by processing displacement/strain fields measured on the workpiece during machining. Digital Image Correlation is employed to measure, between successive milling passes, the displacement and strain fields on the lateral surface of the workpiece. These fields are then processed with the Virtual Fields Method to identify the through-thickness residual stress distribution. Compared to previous studies on this topic, no assumption is made concerning the real through-thickness displacement field. Simulations performed with synthetic data provided by a finite element model show the feasibility of this approach and quantifies its robustness when displacements are affected by measurement noise. Results obtained with this approach in a real case are then compared with their counterparts obtained with another identification technique, which assumes that the workpiece behaves as a beam. This study shows that it is possible to measure the through-thickness distribution of residual stress in slender workpieces during machining by using a classic subset-based DIC software and the Virtual Fields Method to process the displacement/strain maps. This opens the way for future developments aimed for instance at updating in live machining sequences in order to obtain machined parts immune from distortions caused by residual stresses.

Revealing the residual stress distribution in laser welded Eurofer97 steel by neutron diffraction and Bragg edge imaging

• Through-thickness residual stress distribution in three dimensions is evaluated. • High-resolution residual strain is mapped by neutron Bragg edge imaging. • Location-dependant reference lattice spacing is first applied on neutron imaging. • Correlation between microstructure, residual stress and micro-hardness is studied. Eurofer97 steel is a primary structural material for applications in fusion reactors. Laser welding is a promising technique to join Eurofer97 plasma-facing components and overcome remote handling and maintenance challenges. The interaction of the induced residual stress and the heterogeneous microstructure degrades the mechanical performance of such fusion components. The present study investigates the distribution of residual stress in as-welded and post-heat treated Eurofer97 joints. The mechanistic connections between microstructure, material properties, and residual stress are also studied. Neutron diffraction is used to study the through-thickness residual stress distribution in three directions, and neutron Bragg edge imaging (NBEI) is applied to study the residual strain in high spatial resolution. The microstructures and micro-hardness are characterised by electron backscatter diffraction and nanoindentation, respectively. The M-shaped residual stress distribution through the thickness of the as-welded weldment is observed by neutron diffraction line scans over a region of 1.41 × 10 mm 2 . These profiles are cross-validated over a larger area (∼56 × 40 mm 2 ) with the higher spatial resolution by NBEI. The micro-hardness value in the fusion zone of the as-welded sample almost doubles from 2.75 ± 0.09 GPa to 5.06 ± 0.29 GPa due to a combination of residual stress and cooling-induced martensite. Conventional post weld heat treatment (PWHT) is shown to release ∼ 90% of the residual stress but not fully restore the microstructure. By comparing its hardness with that of stress-free samples, it is found that the microstructure is the primary contribution to the hardening. This study provides insight into the prediction of structural integrity for critical structural components of fusion reactors.

Thermo-mechanical analysis of the repair welding residual stress of AISI 316L pipeline for ECA

Through-thickness residual stress distribution is a fundamental input parameter for engineering critical assessment (ECA) according to BS 7910 Annex Q. In this paper, we investigated the through-thickness residual stress distribution at a weld toe/weld centerline. Firstly, we performed a simulation of the thermo-mechanical coupled-welding residual stress with/without repair welding of a thick wall pipeline. To further investigate the effects of component radius to wall thickness ratio(r/t) and heat input on the welding stress profile, we developed a welding pass size merging strategy on a mechanical basis. At least ten weld layers were utilized in finite element analysis(FEA) to improve efficiency, without affecting the through-thickness residual stress distribution. The influence of the r/t ratio on the through-thickness residual stress distribution was determined and described as membrane stress and bending stress. Hoop and axial bending stresses at a weld toe decreased gradually with the r/t ratio increased. In contrast, the hoop membrane stress at a weld toe gradually increased with the r/t ratio increased. Moreover, a similar trend was observed at weld centerlines. Analytical equations for predicting the through-thickness residual stress were established for both original welding and in-depth repair welding processes. It was shown that the residual stress distribution after the repair welding was more efficiently improved when a smaller repair depth was selected, i.e., the improvement was adversely related to the repair depth. The residual stress for the original and the repaired welds was expressed as a logarithmic function in terms of axial bending stress, hoop bending stress, and hoop membrane stress.

Effects of groove configuration and buttering layer on the through-thickness residual stress distribution in dissimilar welds

Dissimilar metal welds (DMW) of ferritic to austenitic stainless steel are broadly used in steam generators working in power generation industries. Frequent failure of DMWs from the heat-affected zone (HAZ) of the ferritic part necessitates structural integrity assessment of the DMWs in order to determine and extend the lifetime of these components. In this regard, typical DMWs of SA516–309L–304L and SA516–309L/308L–304L attributed to domestic reactors were fabricated under different welding conditions. The effects of conventional and narrow weld groove configurations, buttering layer, and varying buttering layer width on the through-thickness residual stress fields in the DMWs were investigated experimentally and with the help of numerical simulations. Results show that the narrow groove weld is beneficial in reducing the residual stresses in the weld zone. Incorporating an additional buttering layer in the narrow groove joint further reduced the residual stresses across the weld joint. A 6 mm thick buttering layer was found to be competent enough to minimize the residual stresses dispersed across the weld cross-section.

Evaluation of through-thickness residual stresses and microstructure in SA516 Gr. 70 steel welds

The critical working condition of nuclear power plant equipment necessitates meticulous determination of the welding process and parameters. In this work, some major influential factors of welding were investigated to observe their effects on the through-thickness residual stress distribution in multipass pressure vessel steel welds. In this regard, experiments were conducted to find the characteristics of residual stresses dispersed in SA516 Grade 70 steel welds of different groove geometries with distinct welding conditions. Three-dimensional finite element models of the weldments were developed considering a moving heat source with temperature-dependent material properties to simulate the welding thermal cycles and corresponding residual stress fields. Effects of weld groove geometry, number of weld passes, external constraints, and preheating on the through-thickness residual stress fields were studied. Additional attention was given to the evaluation of the heterogeneous microstructure and microhardness across the weld cross-section associated with their weld thermal history. Finally, the evolution of the through-thickness residual stresses attributed to subsequent weld passes was elaborated.

Significance of Finite Element Models and Solid-State Phase Transformation on the Evaluation of Weld Induced Residual Stresses

In the present study, different finite element (FE) models were prepared to investigate weld induced residual stresses in thick multi-pass butt welded joint of SA516 Gr. 70 plates. Both 3D and 2D full geometry models and their axisymmetric half models were taken into consideration. The competence of these FE models on the accuracy of predicting residual stress distribution across the weld cross-section was investigated by comparing it with the experimental results. Blind hole drilling technique and deep hole drilling technique were employed to evaluate the surface and through-thickness residual stress distributions, respectively. In addition, the change in volume and yield strength of weld material due to austenitic phase transformation was also incorporated in the material modeling to observe the effect of solid-state phase transformation (SSPT) on the evaluation of residual stresses. Computed residual stresses obtained from different FE models indicate that the 3D FE models procured the best accuracy compared with the experimental results. On the other hand, 2D models can save a significant amount of computational time with reasonable accuracy. Incorporation of SSPT in the 3D FE full model exhibited a better agreement of predicted results with the experimental measurements.

Numerical Prediction of Residual Stresses Distribution in Thin-Walled Press-Braked Stainless Steel Sections.

Stainless steels are increasingly used in construction today, especially in harsh environments, in which steel corrosion commonly occurs. Cold-formed stainless steel structures are currently increasing in popularity because of its efficiency in load-bearing capacity and its appealing architectural appearance. Cold-rolling and press-braking are the cold-working processes used in the forming of stainless steel sections. Press braking can produce large cross-sections from thin to thick-walled sections compared to cold-rolling. Cold-forming in press-braked sections significantly affect member behaviour and joints; therefore, they have attained great attention from many researchers to initiate investigations on those effects. This paper examines the behaviour of residual stress distribution of stainless steel press-braked sections by implementing three-dimensional finite element (3D-FE) technique. The study proposed a full finite element procedure to predict the residual stresses starting from coiling-uncoiling to press-braking. This work considered material anisotropy to examine its effect on the residual stress distribution. The technique adopted was compared with different finite element techniques in the literature. This study also provided a parametric study for three corner radius-to-thickness ratios looking at the through-thickness residual stress distribution of four stainless steels (i.e., ferritic, austenitic, duplex, lean duplex) in which have their own chemical composition. In conclusion, the comparison showed that the adopted technique provides a detailed prediction of residual stress distribution. The influence of geometrical aspects is more pronounced than the material properties. Neglecting the material anisotropy shows higher shifting in the neutral axis. The parametric study showed that all stainless steel types have the same stress through-thickness distribution. Moreover, R/t ratios’ effect is insignificant in all transverse residual stress distributions, but a slight change to R/t ratios can affect the longitudinal residual stress distribution.

Residual stresses in narrow-groove girth welds and applications for fitness-for-service assessment

Narrow gap welds have been increasingly used in pressure vessels and pipe components due to their unique advantages. A recent comprehensive investigation into residual stress distributions in narrow gap is presented in this paper, covering component wall thickness from 1” (25.4 mm) to 10” (254 mm), component radius to wall thickness ratio from 2 to 100, and linear welding heat input from low (300 J/mm) to high (18,000 J/mm). By means of a residual stress decomposition technique, two key parameters that govern through-thickness residual stress distributions in terms of their membrane and bending content have been identified. One is component radius to wall thickness ratio (r/t) and the other is a characteristic heat input density (Qˆ) having a unit of J/mm3. With these two parameters, a unified functional form for representing through-thickness residual stress profile in narrow gap welds is proposed for supporting defect assessment. Its adequacy for estimating residual stress distribution trends is further confirmed by comparing with thermomechanical finite element residual stress analyses for a number of selected narrow gap weld cases.

Use of Power Series Expansion for Residual Stress Determination by the Incremental Hole-Drilling Technique

The integral method of incremental hole-drilling is used extensively to determine the residual stress distribution in isotropic materials. When used with Tikhonov regularization, the method is robust and produces accurate results with minimal uncertainty. Alternatively, an optimal hole depth distribution can be found using the method of Zuccarello to improve the conditioning of the calibration matrices. If substantial measurement noise or a steep variation in stress exists, however, considerable uncertainty in, or distortion of, the calculated residual stress distribution can occur. Series expansion offers an alternative solution, but it has been reported to become unstable before meaningful accuracy can be achieved. Investigate the use of series expansion to determine a rapidly changing throughthickness residual stress distribution in an aluminium alloy 7075 plate subjected to laser shock peening treatment. Power series expansion of eigenstrains is used in finite element modelling to calculate the calibration coefficients. Monte Carlo simulation is used to determine robust uncertainties in the residual stress distributions. This allows the series order with the lowest RMS uncertainty in stress to be selected from those series orders that have converged. The best estimate of the residual stress distribution is thereby obtained. Series expansion is shown to be stable up to 8th order and convergence to a stress solution can be found before instability dominates. The method is insensitive to measurement errors due to the least-squares approach employed by the inverse solution. The use of series expansion reduces the RMS uncertainty in stress when compared to the regularized integral and Zuccarello methods.

Evaluation of through-thickness residual stresses in conventional and narrow grooved stainless steel welds

Thick AISI 304L stainless steel plates were welded using the gas metal arc welding process, and through-thickness residual stresses were evaluated by finite element simulation and the deep hole drilling technique. 3D moving heat source-based thermo-mechanical models were implemented to evaluate through-thickness residual stresses. The effects of the weld groove geometries and external restraints on the pattern of through-thickness residual stresses were studied. The maximum magnitude of locked-in residual stresses was recorded beneath the top surface, at a depth of around 6 mm. In comparison to conventional weld groove, the narrow weld groove configuration exhibited a 20–40% reduction in peak residual stresses. A significant rise in residual stresses was observed in constrained welds. The effect of the yield strength of the filler material on the evaluation of the through-thickness residual stress distribution in the course of finite element modeling was illustrated. The evolution of through-thickness residual stresses was also assessed concerning each weld pass.

Theoretical prediction of residual stresses induced by cold spray with experimental validation

PurposeThe purpose of this paper is to develop a simple analytical model for predicting the through-thickness distribution of residual stresses in a cold spray (CS) deposit-substrate assembly.Design/methodology/approachLayer-by-layer build-up of residual stresses induced by both the peening dominant and thermal mismatch dominant CS processes, taking into account the force and moment equilibrium requirements. The proposed model has been validated with the neutron diffraction measurements, taken from the published literature for different combinations of deposit-substrate assemblies comprising Cu, Mg, Ti, Al and Al alloys.FindingsThrough a parametric study, the influence of geometrical variables (number of layers, substrate height and individual layer height) on the through-thickness residual stress distribution and magnitude are elucidated. Both the number of deposited layers and substrate height affect residual stress magnitude, whereas the individual layer height has little effect. A good agreement has been achieved between the experimentally measured stress distributions and predictions by the proposed model.Originality/valueThe proposed model provides a more thorough explanation of residual stress development mechanisms by the CS process along with mathematical representation. Comparing to existing analytical and finite element methods, it provides a quicker estimation of the residual stress distribution and magnitude. This paper provides comparisons and contrast of the two different residual stress mechanisms: the peening dominant and the thermal mismatch dominant. The proposed model allows parametric studies of geometric variables, and can potentially contribute to CS process optimisation aiming at residual stress control.

Residual stress distribution in Ni-based superalloy turbine discs during fabrication evaluated by neutron/X-ray diffraction measurement and thermomechanical simulation

Residual stress distribution induced by multistep fabrication processes is of great significance in reliable design of critical engineering components, such as powder metallurgy Ni-based superalloy turbine discs. By using neutron diffraction and 2D-detector X-ray diffraction, the through-thickness residual stress distribution was determined in fabricated turbine discs via isothermal forging, solution treatment and aging treatment. The experimental results demonstrated that residual stress exhibited typical thermal stress distribution while plastic deformation-induced surface stress was relieved surprisingly after solution treatment. After aging treatment, the reduction of matrix supersaturation after long-time diffusion contributed to increase of compressive radial stress in the rim of disc. By introducing temperature-dependent supplementary phase transformation latent heat into the thermo-mechanical model, overall residual stress distribution after solution treatment was simulated by the finite element method. Numerical simulated stress distribution is in agreement with the experimental results, with the deviation < 40 MPa.

Cold-bending of linepipe steel plate to pipe, detrimental or beneficial?

Systematic investigation was carried out to understand the effect of plate-to-pipe forming (U-bending) strain on the microstructure and mechanical properties of X80 linepipe steel and to establish a structure-property correlation. Finite element simulation predicted the von Mises stress state and through-thickness residual stress distribution. Transmission electron microscopy and electron back scattered diffraction studies detected the local strain gradients, which were verified by nanoindentation testing along with the estimation of through-thickness residual stress. Both yield strength and tensile strength increased after cold-bending operation due to dislocation generation. Also, post-uniform elongation increased, especially at inner diameter (ID) portion due to an overall more dislocation interaction. In the presence of compressive residual stress, ID sample revealed improved impact toughness than the as-received (AR) one at all tested temperatures in the range of −80 °C to room temperature. Low temperature (-80 °C) impact toughness increased by ~16% even at outer diameter (OD) of the pipe, despite the presence of a tensile residual stress state. This improvement in toughness is contributed by many factors, such as the increase in critical stress for yielding, the decrease in crystallographic unit size, less availability of potential sites for cleavage crack initiation, texture strengthening, and crack-divider type fissure formation.

Effect of interlayers and scanning strategies on through-thickness residual stress distributions in additive manufactured ferritic-austenitic steel structure

A total of five different types of specimens were additively manufactured by directed energy deposition (DED) process. The specimens have a functionally graded material (FGM) structure, which has been deposited with variation of chemical composition of ferritic and austenitic steel powders in each interlayer on a steel substrate. Residual stress distributions were experimentally measured through the thickness of the specimens by the contour method, neutron diffraction, and deep/incremental center hole drilling. Neutron diffraction provided three orthogonal stress components in each FGM part and the results were compared to the two-dimensional stress map obtained by the contour method and confirmed its criticalities from the highly spatial resolved depth profile by the hole drilling method. Significant variations from tension to compression (up to 950 MPa) in the sine-wave stress profile were alleviated to about 430 MPa when the FGM were deposited with orthogonal or island DED scanning strategies with interlayers. Gradual changes (16.3–12.1 × 10−6/°C) of the thermal expansion coefficient were measured among the inserted DED FGM parts and grain structure with defects along the interface was three dimensionally examined by neutron tomography.

Through-thickness distribution of residual stresses in Q345qD butt-welded steel plates

Welding residual stress measurements were performed on 16-, 40-, 60-, 80-, and 100-mm-thick, welded Q345qD steel plates. The through-thickness stresses are almost uniformly distributed in the thin specimen (16mm). In 40-mm-thick specimen, the stresses exhibit slight fluctuations as function of thickness. The through-thickness longitudinal and transverse stresses generally exhibit C-shaped distributions in thicker specimens (60, 80 and 100mm), while longitudinal stresses exhibit Σ-shaped distributions in these specimens at the weld centerline. High longitudinal stress (≥250MPa) regions occur predominantly at the surfaces and centers of the cross-sections, while high transverse stress regions occur predominantly in the surface layers. The longitudinal stress is almost always tensile at the mid-thickness regions of the welds, while the transverse stress is compressive. The longitudinal and transverse stresses distributions generally range from −250 to 550MPa. Commonly used empirical equations for residual stresses distribution were modified to expand their range of application based on the data obtained in present work.

A framework for estimating residual stress profile in seam welded pipe and vessel components Part II: Outside of weld region

Part I of this study has identified two key parameters (r/t ratio and characteristic heat input Qˆ) that dominate important through-thickness residual stress distribution characteristics, with which a residual stress profile estimation scheme has been developed for weld region, i.e., at weld centerline and weld toe. In Part II, we present an analytical model for achieving residual stress profile estimation for through-thickness sections away from the weld region in seam welded pipe and vessel components. A curved beam bending theory based model is analytically constructed through an assembly of two parts: One is weld fusion zone region and the other is the rest of the component section along circumferential direction. The final assembly of the two parts leads to a closed form solution to both axial (longitudinal) and hoop (transverse) residual stress components as a function of circumferential angular position away from weld toe. The effectiveness of the full-field residual stress estimation scheme is demonstrated by comparing with finite element modeling results over a broad range of weld geometries and welding conditions. The present development should provide a consistent and effective means for estimating through-thickness residual stress profile as a continuous function of pipe geometry and welding heat input.

A framework for estimating residual stress profile in seam-welded pipe and vessel components part I: Weld region

A recent comprehensive investigation into residual stress distributions in pipe and vessel longitudinal seam welds is presented in this paper, covering component wall thickness from 1/4″ (6.35 mm) to 10″ (254 mm), component radius to wall thickness ratio from 2 to 20, and linear welding heat input from low (50 J/mm) to high (6000 J/mm). Through the use of a residual stress decomposition technique, two key parameters that govern through-thickness residual stress distributions in terms of their membrane and bending content have been identified. One is component radius to wall thickness ratio (r/t) and the other is a characteristic heat input density (Q^) having a unit of J/mm3. With these two parameters, a unified functional form for estimating through-thickness residual stress profile in seam welded components is proposed in this paper (Part I) for supporting fitness for service assessment for crack-like flaws in weld region. A curved beam bending theory based model is introduced in Part II as a means of analytically describing through-thickness residual stress profile as a function of circumferential position away from the weld region until residual stresses become zero. The effectiveness of this proposed framework for achieving residual stress profile estimation within weld region (Part I) for longitudinal seam welds in pressure vessel and piping components has been confirmed by finite element residual stress analysis results on a large number of component configurations and different welding conditions.

Numerical simulation of dissimilar metal welding and its verification for determination of residual stresses

This paper summarizes the results of the through-thickness residual stress distributions on dissimilar metal weld (DMW) mock-up. DMWs, as welded joints between ferritic steels and either austenitic stainless steels or nickel-based alloys, are commonly found in piping systems of NPPs as well as in other industrial plants. The welding of the mock-up is simulated by the 3D finite element model using temperature and phase dependent material properties. The commercial finite element code MSC.Marc is used to obtain the numerical results by implementing the Goldak’s double ellipsoidal shaped weld heat source and combined convection radiation boundary conditions. Residual stress measurements are performed on welded joints to validate the simulation results. The validated residual stress distributions can be used for the life time assessment and failure mode predictions of the welded joints.

An IIW residual stress profile estimation scheme for girth welds in pressure vessel and piping components

Over the years, one major objective of IIW Joint Working Group (JWG) on residual stresses and distortion prediction (RSDP) has been the development of consistent residual stress profiles for supporting fitness-for-service assessment of welded components. As a result of the JWG activities and further in-depth investigations, this paper presents a major development on a novel full-field residual stress estimation scheme that can be used for describing through-thickness residual stress profiles not only within a weld region, but also at any location away from a weld in pressure vessel and piping components. Within weld region, a systematic parametric finite element analysis is used to establish key parameters that govern through-thickness residual stress distribution characteristics by introducing membrane, bending, and self-equilibrating based decomposition technique. Away from weld region, a shell theory based method is developed for describing through-thickness residual stress distribution at any distance away from weld toe. This paper presents detailed results for single “V” joint preparation with pipe wall thickness varying from 6.25 to 250 mm and wall thickness to pipe radius ratio (r/t) varying from 2 to 100. The residual stress estimation method can be applied for double V and narrow groove joint preparations for girth welded components since all three joint preparations have been shown to follow a similar functional form to that seen in single V joint preparation.

Material Characterization and Numerical Simulation of a Dissimilar Metal Weld

A 3D thermal-mechanical-metallurgical finite element (FE) model has been developed to investigate the microstructure and the distribution of residual stress of a muck-up represents a dissimilar metal weld (DMW) joint of a VVER 440 reactor pressure vessel safety-end nozzle. In order to capture the correct microstructure evolution a number of material properties were required for present simulations. The first task of mechanical characterization was the determination, with accurate experimental devices and its numerical interpretation, of the mechanical properties in terms of stress-strain curve of all DMW constitutive materials: austenitic stainless steel, ferrite steel, heat affected ferrite steel zone and buttering layers properties. For characterization and validation purpose microstructure and hardness map were also evaluated. To get addition information for further investigation, fracture properties for base materials, heat affected ferrite steel zone and buttering layers were also measured. The welding was simulated by the 3D finite element model using temperature and phase dependent material properties. The commercial finite element code was used to obtain the numerical results by implementing the Goldak’s double ellipsoidal shaped weld heat source and combined convection radiation boundary conditions. The results of the simulation provide the size of the HAZ and the volume of the molten zone. The volume fraction of bainite and martensite can be quantified and serves as an additional response that can be used to validate this model with experiments and to predict phase volume fractions under new processing conditions. This paper also presents the results of the through-thickness residual stress distributions on the certain DMW. The results of FE analyses were compared with the experimental measurements in the ferritic steel section of the weld.