Evaluating Uncertainty in Residual Stress Measured Using the Deep‐Hole Drilling Technique

Abstract: The deep hole drilling (DHD) method measures the through‐thickness distribution of residual stress in a component. Sources of uncertainty in the application of the method are identified and three different methods for determining the magnitudes of uncertainty are presented. The analyses are applied to experimental measurements of stress in two calibration studies for ferritic steel and an aluminium alloy. Finally, the residual stresses measured in a repair welded steel pipe are examined to assess the level of uncertainty.     

Validated numerical analysis of residual stresses in Safety Relief Valve (SRV) nozzle mock-ups

In general, the tensile residual stresses typically associated with weldments, and the presence of corrosive environments, are a major concern due to the possibility of Stress Corrosion Cracking (SCC). In the case of the dissimilar metal welds typically used in the primary circuits of pressurised light water nuclear reactors the presence of tensile residual stress and corrosive environment leads to so-called Primary Water Stress Corrosion Cracking (PWSCC). It is thus of technological importance to know the residual stresses associated with the dissimilar metal welds in order to assess the susceptibility of components to PWSCC. The current paper presents finite element simulations of the full manufacturing process of dissimilar metal weld mock-ups with and without a full structural overlay weld. The present simulations are validated by comparison with deep hole drilling (DHD) and incremental deep hole drilling (iDHD) residual stress measurements. A dedicated welding heat source modelling tool was used in order to reduce the uncertainties in the thermal solution by calibrating ellipsoidal Gaussian volumetric heat sources using the detailed welding records. In the mechanical analysis a mixed isotropic–kinematic (Lemaitre-Chaboche) material hardening model was employed to produce the most representative material response to the cyclic thermo-mechanical loading imposed during welding.     

Application of Deep Hole Drilling to the Measurement and Analysis of Residual Stresses in Steel Shrink‐Fitted Assemblies

Abstract: Residual stress measurement of shrink‐fitted assemblies was achieved through finite element simulations and experiments using the deep hole drilling technique. Shrink‐fitted assemblies using stainless steel and cast iron were manufactured and residual stresses measured using a combination of deep hole and centre hole drilling. The results from the finite element simulations demonstrated that modifications to the deep hole drilling method were required to account for plastic relaxation during the measurement process. This was verified through the experimental measurements. The results from both the stainless steel and cast iron assemblies provided a clear demonstration that the final residual stress state was a consequence of the machining and assembly of the components.     

A Method of Measuring Through‐Thickness Internal Strains and Stresses in Graphite

Abstract: Currently, the structural integrity of the nuclear graphite reactor components is evaluated using irradiated material properties data obtained from test reactors. These data are applied to numerical or mathematical models to assess the integrity of the graphite components. On the other hand, there is a need to measure internal strains and stresses in reactor core graphite and to explore the potential for in‐situ measurement. The deep hole drilling (DHD) technique is a semi‐destructive method for measurement of the through thickness residual strains or stresses. Previously the technique has been applied successfully to metallic and composite materials. In this paper, the method for internal strain and stress measurement in polygranular graphite is examined particularly when a significant volume fraction of porosity is present. Finite element simulation shows that the method can be used to measure internal stresses generated by a thermal gradient. On the basis of this a series of experiments have been conducted using Pile Grade ‘A’ (PGA) and PG25 filter graphite; with the latter being a surrogate for service exposed material. Tests were conducted to illustrate that the bulk mechanical response was linear elastic for both graphites and elastic moduli were measured. The DHD method was then used to determine internal strain and stress profiles through the materials. The results were compared with the strain data obtained from strain gauges bonded to the samples. Overall, there was an excellent agreement between the measured through‐thickness internal strains and stresses and the surface strains and stresses determined from the applied loading.     

Procedure to Perform a Validated Incremental Hole Drilling Measurement: Application to Shot Peening Residual Stresses

Abstract: The paper describes a test rig designed to check and assess the accuracy of the incremental hole drilling (IHD) method. An external load produces a controlled linearly through thickness variable uniaxial stress field (reference bending stress), known with good accuracy, that can be applied and removed at each hole increment. After the separation between the bending relaxed strain from the residual stress relaxed strain, it is possible to reproduce the bending stress distribution in order to have complete confidence of the residual stress measurement. The bending verification of the IHD method was already proposed by other investigators before, but residual stress measurements were then performed on independent configurations. The proposed testing procedure gives a ‘real time’ verification of the residual stress measurement. Any experimental malfunctioning due to the operator inexperience, or any error during the stress calculation from the relaxed strain would produce an evident difference between the expected reference bending stress and the IHD bending stress output. Moreover, the reference bending stress helped for understanding that the not perfect hole cylindrical shape causes an underestimate of the predicted stress near the surface. A zero depth offset correction was proposed. This correction was tested on the reference bending stress, and then applied to the residual stress prediction. Three shot peening residual stresses IHD measurements were successfully validated by means of the bending stress; moreover, they were in good agreement with independent X‐ray diffraction measures also proposed in the paper.     

On the correction of plasticity effect at the hole edge when using the centre hole method for measuring high welding residual stress

Significant error caused by plasticity at the hole edge may arise when measuring sufficiently high welding residual stress by means of the hole drilling method. According to elastoplastic theory, a critical parameter of plastic deformation round the centre hole is obtained. On the basis of this critical parameter, a simple method is proposed to correct the stresses for the plasticity effect. It is shown in the experiments with welded joints that the correction method may improve the accuracy of high residual stress measurement.     

Residual stress/strain evolution due to low‐cycle fatigue by removing local material volume and optical interferometric data

Three experimental methods, based on optical interferometric measurements of deformation response to local material removing, have been implemented for residual stresses determination. Two first techniques are employed to characterize initial residual stress values and their evolution near welded joints of aluminium plates under low‐cycle fatigue. The hole‐drilling method gives high‐accurate dependencies between residual stress components and number of cycles. The second approach comprises cracks modelling by narrow notches to describe residual stress distributions in more wide spatial range near the weld. The results demonstrate residual stress evolution is of complex character and cannot be uniquely qualified as a gradual relaxation. Besides, the secondary hole drilling method is developed and used as a fast and reliable tool to quantify the redistribution of residual strains near cold‐expanded holes due to low‐cycle fatigue. Dependencies of circumferential residual strains along the secondary hole edge versus number of cycles are constructed.     

Moiré Interferometry Assessement of Residual Stress Variation in Depth on a Shot Peened Surface

Abstract: The main goal of this work was the development of experimental techniques to measure in depth non‐uniform residual stresses, as alternative to the more conventional hole‐drilling method with strain gauges. The proposed experimental methodology is based on moiré interferometry. This high resolution field technique allows in‐plane displacement assessment without contact. Grating replication techniques were also developed to record high quality diffraction gratings onto the specimen’s surface. A laser interferometry setup was implemented to generate the master grating (virtual). The stress relaxation was promoted by blind hole‐drilling and the obtained fringe patterns were video recorded. Image processing techniques were applied to assess the in‐plane strain full‐field. A finite elements code (FEM), ANSYS^®, was used to simulate the stress relaxation process and to calculate the hole‐drilling calibration constants.     

A procedure for high residual stresses measurement using the ring‐core method

The ring‐core method is a mechanical technique used to determine the residual stresses on the surface of materials by milling a narrow circular groove around the point of interest and monitoring the strain variation. Original stress can be evaluated by using the relaxed strain through the linear elasticity theory. In case of a highly stressed field, the yielding of the material around the groove and its bottom causes an error related to the hypothesis of the basic theory of the method. In this paper, the plasticity effect of calculated residual stresses was considered. For this purpose, the ring‐core development and stress relaxation in a generally stressed body were simulated using a 3D parametric finite element model and the stress calculation errors were obtained by comparing calculation stress with the actual one. According to the results, the error value was affected by some parameters such as ring depth, stress magnitude and state, and material behaviour. In general, for residual stresses above 65% of the local yield strength, the plasticity‐induced errors were significant, as an error close to 35% was found. Based on the result, a correction procedure was proposed for the evaluation of the high level residual stresses in steel materials by the ring‐core method. By the method, true stresses can be obtained with considering the calculated stresses state, material properties, ring geometry, and estimated plasticity‐induced errors.     

Residual stress measurement in steel plates and welds using critically refracted longitudinal (LCR) waves

The application of acoustoelasticity using critically refracted longitudinal (L_CR) waves is described for measuring residual stress in welded steel plates. Residual stresses are self-equilibrating and may exist in a material that has been deformed in a nonhomogeneous manner. When unknown residual stress is present in a structure, the true stress may become significantly greater than the working stress. In a corrosive environment, highly stressed areas that have not been properly stress relieved are prone to stress corrosion cracking. Areas near welds are particularly susceptible to stress corrosion cracking.Two welded plates were investigated for the present work: one hot-rolled and the other cold-rolled. Residual stresses are usually greatest after welding. Further, longitudinal stress (i.e., stress parallel to the weld bead) is typically greater than the component transverse to the weld bead. Since the acoustoelastic behavior of the L_CR wave is largest when propagated parallel to a uniaxial stress, the L_CR wave traveling parallel to the weld bead was used to investigate the stress changes after stress relieving of the welded plates. Both 1 MHz and 2.25 MHz probe frequencies were used in this study. The stress changes in the welds and in the cold-rolled plate were clearly indicated by the L_CR data.Two verification methods were used: hole drilling (HD) and neutron diffraction (ND). The stress relief was verified by the hole-drilling technique. While the HD technique showed about the same stress magnitude as found by the L_CR results, the orientation was reversed. The stress orientation was probably caused by the grinding process used to flatten the weld bead. Texture was also investigated using a neutron diffraction (ND) technique on the (001)[110] texture. The through-the-thickness technique yields an average of the orientation distribution of the (110) planes. At locations in the parent metal and in the weld, the distribution was found to be very similar, indicating uniform texture throughout the weld and parent metal zones.     

A study on the induced drilling stresses in the centre hole method of residual stress measurement

This paper aims at the improvement of the accuracy of the centre hole method of residual stress measurement by reducing the error caused by the drilling itself. Based on the results of an intensive experimental investigation, a new approach is proposed for the determination of the induced drilling stresses caused by the mechanical drilling process. In this study, the electric discharge machining (EDM) technique was utilised to obtain a stress free sample from the bulk material. As compared to the annealing heat treatment method for obtaining a stress free sample, it was found that the EDM technique does not cause the changes of the structures and machining properties of the parent material. Thus, the induced drilling stresses in centre hole method can be evaluated more accurately by using a stress free sample obtained by EDM technique than by using an annealed one.     

Residual Stress Measurement in Steel Plates and Welds Using Critically Refracted Longitudinal (LCR) Waves

Abstract

The application of acoustoelasticity using critically refracted longitudinal (L_CR) waves is described for measuring residual stress in welded steel plates. Residual stresses are self-equilibrating and may exist in a material that has been deformed in a nonhomogeneous manner. When unknown residual stress is present in a structure, the true stress may become significantly greater than the working stress. In a corrosive environment, highly stressed areas that have not been properly stress relieved are prone to stress corrosion cracking. Areas near welds are particularly susceptible to stress corrosion cracking.

Two welded plates were investigated for the present work: one hot-rolled and the other cold-rolled. Residual stresses are usually greatest after welding. Further, longitudinal stress (i.e., stress parallel to the weld bead) is typically greater than the component transverse to the weld bead. Since the acoustoelastic behavior of the L_CR wave is largest when propagated parallel to a uniaxial stress, the L_CR wave traveling parallel to the weld bead was used to investigate the stress changes after stress relieving of the welded plates. Both 1 MHz and 2.25 MHz probe frequencies were used in this study. The stress changes in the welds and in the cold-rolled plate were clearly indicated by the L_CR data.

Two verification methods were used: hole drilling (HD) and neutron diffraction (ND). The stress relief was verified by the hole-drilling technique. While the HD technique showed about the same stress magnitude as found by the L_CR results, the orientation was reversed. The stress orientation was probably caused by the grinding process used to flatten the weld bead. Texture was also investigated using a neutron diffraction (ND) technique on the (001)[110] texture. The through-the-thickness technique yields an average of the orientation distribution of the (110) planes. At locations in the parent metal and in the weld, the distribution was found to be very similar, indicating uniform texture throughout the weld and parent metal zones.     

Development and comparison of residual stress measurement on welds by various methods

Abstract

Residual stress constitutes an integral part of the total stress acting on any component in service. It is imperative to determine residual stress to estimate the life of critical engineering components, especially those that are welded. The stresses caused by non-uniform temperature distribution due to welding and the effect of these multiaxial stresses upon service performance are discussed. A controlled thermal severity test (CTS) was performed on mild steel plates bolted together, with anchor welds deposited on opposite sides. After cooling, bithermal and trithermal test welds were deposited one after the other. Varying welding stresses were deliberately introduced by using different thicknesses of both plates to change the thermal severity numbers (TSN). The main experimental technique used here to determine the magnitude and nature of residual stress is based on X-ray diffraction (XRD). It was utilised to develop and standardise other techniques. The XRD method is based on the peak shiftin the diffraction profile due to the presence of stress using a sin² ψ method. The peak shift is determined by orienting the sample at different angles ± ψ to the incident X-ray beam. The semidestructive technique of hole drilling and use of a strain gauge was also employed to determine residual stress in CTS specimens. The magnitude, nature, and direction of principal stresses were determined by relieving stresses through incremental blind hole drilling and measuring strain values at each step. The surface displacements arising due to hole drilling can also be determined by laser holography. A sandwich holography technique was developed to avoid unwanted rigid body motions of samples due to hole drilling when relieving stresses. Stress values were obtained by measuring fringe displacement between two exposures of a sandwich hologram, due to hole drilling. Results on the change in residual stress values with TSN are discussed. The residual stress values determined by XRD and sandwich holography were found to be comparable, and stress values obtained by hole drilling/strain gauge measurement were higher than these values. The reasons are discussed.     

Application of Moiré Interferometry to Study Residual Deformation in Lap‐Welded Steel Plates

Abstract: Moiré interferometry combined with hole‐drilling is an effective method for measuring welding residual deformation. In this study, two lap‐welded rectangular steel plates with different overlap widths were manufactured, and cross‐gratings with a frequency of 1200 lines per mm were replicated on test areas of the welds. Sixteen through holes were drilled in the plates to release residual stress, while Moiré interferometry, integrated with a phase‐shifting technique, was used to determine the corresponding surface residual deformation. The distribution characteristics of the residual displacements around the drilled holes were investigated using the experimental data as basis. The relationship between the residual displacement located in the plates and the distance to the weld lines is also presented in this paper. Furthermore, the magnitude and direction of the residual strain both near the holes and within the plates were analysed. The experimental data and detailed analysis in this paper can serve as some reference for research on the residual strain of welds.     

Measurement of residual stresses in vvelded steel joints using hole drilling method

Abstract

An experimental investigation of the residual stresses in three types of welded structural steel joint is presented. A total of twelve specimens was tested. In this investigation, the blind hole-drilling method of ASTM E837 was used–adapted and improvedfor determination of residual stresses.To accountfor the effect of local plasticity due to stress concentration near the drilled hole, new calibration coefficients were obtained by carrying out a series of calibration tests. Then, the residual stresses in the welded joints were determined using the new coefficients. The improved hole drilling method presented in this paper was found to be much less time consuming than the conventional sectioning (saw cutting) method for residual stress measurement. The final results obtained in this study showed good agreement with the residual stresses obtained by previous researchers using the sectioning method.

MST/1486     

A new method of calibrating strain release coefficients in measuring welding stresses

The measured values of welding residual stresses often exceed material yield strength (σ_y) or tensile strength (σ_t), in measuring welding residual stresses in the welded joints of low carbon steel or stainless steel by drilling a blind hole. It is quite evident that measured values do not represent reality. Local plastic strain caused by residual stress concentrations round the blind hole has a main effect on the measuring error of welding residual stresses. This article presents a new method of calibrating strain coefficients A and B for eliminating influence of local plastic strain. In calibrating strain release coefficients A and B, calibrating stresses applied on the specimen were increased so that material round the blind hole produced local plastic deformation, ie coefficients A and B contained a component of the plastic strain. Numerial values of coefficients A and B were classified into four grades. Every grade coefficient contained a different quantity of the plastic strain for offseting the influence of the plastic strain round the blind hole. Test results have proved that by adopting these coefficients more satisfactory values for residual stresses can be obtained in practical engineering. The measuring average error in stainless steel (1Cr18Ni9Ti) reduces from 109% to 1.52%. The measuring average error in low carbon steel reduces from 54.69% to 3.21%.     

Automatic Determination and Evaluation of Residual Stress Calibration Coefficients for Hole‐Drilling Strain Gauge Integral Method

Abstract: Residual stress calibration coefficients are used to calculate residual stresses from the measured strains relieved during hole‐drilling. The current residual stress measurement practice interpolates the published non‐dimensional coefficients for a given measurement condition. Errors are always introduced from the interpolation. In addition, the calibration coefficients vary with respect to factors such as sample geometry dimensions, radius, offset and incline of the drilled hole, and material properties as shown in our sensitivity studies and other researchers’ work. This paper presents a better solution that is to calculate the calibration coefficients for each specific measurement. A set of routines coded in Python language for Finite Element software ABAQUS is developed to address our sensitivity studies of these factors. With these automatic routines, a technician who is not familiar with Finite Element and programming can conveniently obtain the calibration coefficients for his measurement conditions and residual stresses automatically. Because coefficients are determined directly by Finite Element Analysis (FEA), dimensionless coefficients are not needed anymore; instead, a modified integral method is proposed and implemented. An experiment is conducted to demonstrate the practical procedures of measuring residual stresses using resistance strain rosette and calibration coefficients obtained with this set of routines. Bending stresses on a narrow and thin beam are measured using this set of routines and compared to the theoretical results and the stress obtained by interpolating non‐dimensional coefficients.     

Residual stress measurement in AlSi alloys

In this work, the relaxation of residual stresses inside a sample made of the aluminum alloy AlSi7Mg0.3 after tempering is described. The comparison of stress evaluation by X‐ray diffraction and incremental hole drilling method combined with electronic speckle pattern interferometry strain determination gives the opportunity to evaluate micro stresses together with first order macro stresses. Compressive stresses within the surface of a cold worked sample are relaxed by tempering. The X‐ray diffraction evaluation is supported by the analysis of a stress‐free sample through incremental hole drilling method.     

Error and Uncertainty Analysis of the Residual Stresses Computed by Using the Hole Drilling Method

Abstract: The hole‐drilling method is one of the most used techniques for the experimental analysis of the residual stresses in mechanical components. For both through‐thickness uniform and non‐uniform residual stress distributions, its application is standardised by the ASTM E837‐08. In accordance with the ASTM limitations, the analysis of uniform residual stresses, to which the present work deals with, leads in general to results with a maximum bias of about 10%. Unfortunately, in general the user does not have appropriate procedures to estimate the actual stress error; consequently, if one or more of the experimental influence parameters fall out of the corresponding standard limitations, the computed residual stresses have to be considered as qualitative results. In order to overcome such drawbacks as well as to permit in general the estimation of the stress uncertainty, in the present work the procedures for the correction of the effects of the main error sources and for the stress uncertainty estimation, are proposed. The practical application of such procedures is carried out by using a simple calculation code properly implemented in Matlab environment. Also, the use of this tool allows the user to highlight the relative error and the stress uncertainty contribution of each influence parameter.     

Through thickness residual stresses in large rolls and sleeves for metal working industry

Abstract

There is little experimental knowledge about the initial state of through thickness residual stresses in rolls and sleeves for the steel rolling industry. This is surprising bearing in mind the impact that residual stress has on the performance of the roll and sleeve materials in the highly aggressive loading environments of the metal working industry. Previous work has been confined to measurement of very near surface residual stresses and numerical predictions of residual stress distributions. In the present paper through thickness residual stress measurements were carried out using a deep hole drilling technique on a series of rolls and sleeves representative of those used in the rolling industry. Different features of the manufacturing processes used in their production are shown to influence the magnitude and distribution of the residual stresses. It is also shown that the measurements can be used, together with a finite element analysis, to determine the volumetric distribution of the residual stresses.