Manufacturing Rev. 6, 3 (2019)© C. Ye et al., Published by EDP Sciences 2019https://doi.org/10.1051/mfreview/2019001

Available online at:https://mfr.edp-open.org

RESEARCH ARTICLE

Inspection of the residual stress on welds using laser ultrasonicsupported with finite element analysisChong Ye*, I. Charles Ume, Yuanlai Zhou, and Vishnu V.B. Reddy

The Georgia W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

* e-mail: c

This is an O

Received: 5 December 2018 / Accepted: 18 January 2019

Abstract.Ultrasonic evaluation for residual stress measurement has been an effective method owing to its easyimplementation, low cost and intrinsically being nondestructive. The velocity variations of acoustic waves inmaterials can be related to the stress state in the deformed medium by the acoustoelastic effects. In this study, alaser/EMAT ultrasonic method is proposed to evaluate the surface/subsurface longitudinal residual stressdistribution generated by gas metal arc welding (GMAW). The velocity variation DV/V of Rayleigh wave,which is a surface wave, will be experimentally measured. Q-Switched Nd:YAG laser is used to generate abroadband ultrasonic wave. An electromagnetic acoustic transducer (EMAT) is attached to the welding platefor Rayleigh wave pick up. As the ultrasound receiver, the EMAT is used to measure time of flight (ToF) of theRayleigh waves traveling along a specific path parallel to the direction of the welding seam. ToF measurementsare obtained by changing Rayleigh wave path to welding zone center distance from 0 to 45mm. A 3Dthermomechanical-coupled finite element model is then developed to validate the capability of the proposedtechnique for welding-induced residual stress evaluation. The distributions of the normalized velocity variationsfrom ToF experiments are compared with the distribution of the normalized longitudinal residual stresses fromfinite element analysis (FEA). It has been shown that there is a good correlation between these two distributions.The proposed technique provides a potential nondestructive avenue for surface/subsurface residual stressevaluation for welding parts.

Keywords: Nondestructive testing / residual stress / laser ultrasonics / electromagnetic acoustic transducer /finite element analysis

1 Introduction

Residual stress generated from various manufacturingprocesses would influence the mechanical reliability,fatigue life, and chemical corrosion resistance of engineer-ing structures [1–3]. Therefore, it is crucially important toprecisely characterize the residual stress generation for themanufacturing components. In a typical manufacturingprocess, the residual stress generation could be mainly dueto three reasons: the un-uniform plastic deformation, thetemperature gradient-induced nonuniform material ther-mal expansion, and the material volume change due tomaterial phase transformation [4]. For a typical weldingprocess, the sharp temperature change would directlyresult in the nonuniformmaterial volume change due to thelarge temperature gradient in the welding zone. Thus, thelocalized cooling and heating are the main sourcesintroducing the residual stresses in welding. Welding isintrinsically a material melting and solidification process.

hongtt.ye@gmail.com

pen Access article distributed under the terms of the Creative Comwhich permits unrestricted use, distribution, and reproduction

Therefore, the material phase transformation would alsooccur. Undesired residual stress in the welding structurewould be detrimental to the component fatigue life anddimensional accuracy. For example, large tensile residualstress on the welds would significantly reduce the structurefatigue life. Large magnitude of residual stress would resultin material plastic deformation, especially in the large-scalewelding structures with strict geometrical dimensionaltolerance. The in-depth understanding of residual stressgeneration in the welding structures could help to designand optimize the welding process parameters to ensuremanufacturing reliability.

Extensive efforts have been made to experimentallymeasure the residual stress for manufacturing component,which includes center-hole drilling [5], ring core method [6],X-ray diffraction (XRD) [7,8], and ultrasonic- [9,10] andmagnetic-based [11] techniques. Center-hole drilling meth-od has been a main stream technique to evaluate theresidual stress distribution in welding structures. However,a material removal procedure would be involved, whichcould damage the structure integrity. Therefore, it isdestructive and greatly limits its application for critical

mons Attribution License (http://creativecommons.org/licenses/by/4.0),in any medium, provided the original work is properly cited.

2 C. Ye et al.: Manufacturing Rev. 6, 3 (2019)

components on field evaluation, even though it is relativelycost-effective. Ring core method can evaluate stress up to5–7mm into the specimen, deeper than a hole-drillingmethod. However, it causes more damage to the sample.XRD techniques are nondestructive but are only limited toresidual stress measurement on the surface. Additionally,appropriate polishing and sample preparation steps areneeded. The magnetic-based residual stress measurementcharacterizes the material residual stress by applying amagnetic field to the material. The resultant magneticpenetration will be evaluated to calculate the materialresidual stress states. Therefore, the magnetic-basedmethod limits itself for the ferromagnetic materialsapplication.

Different from the above-mentioned methods, theultrasonic-based residual stress measurement methodmeasures the travelling velocity of the ultrasonic wavesin the material to determine the material residuals stress.The ultrasonic wave has much larger penetration depththan the XRD method. The ultrasonic methods are basedon the material acoustoelastic effect, which means theresidual stress states could influence the wave velocity inthe material. There has been some reported research workshowing the potential to predict residual stress usinglongitudinal waves [12], longitudinal refracted (LCR)waves [13], and shear waves [14]. For the average stressmeasurement in the specimen thickness direction, the bulkwave method has been very effective. However, for most ofthe welding components or structures, the large magnitudeof tensile residual stress on the surface is the main rootcause for surface crack failures. Surface waves, whichpropagate along the surface of the medium, have thepotential to probe surface/subsurface stress, and are thusmore favorable in the research reported here. In this work,Rayleigh wave is selected for investigation because theradiation loss of Rayleigh waves is minimal. In addition toits low radiation loss, the Rayleigh wave penetration depthinto the specimen is only one wavelength, which makes it asuperior option for surface/subsurface measurement ofresidual stress.

Extensive research work has been devoted for thesurface wave propagation. The original surface wavepropagation theory in deformed solids with uniform stressstates was proposed by Hayes and Rivlin [10]. Iwashimizuextended this theory to consider propagation alongarbitrary direction, not necessarily coincident to aprincipal direction [15]. In a later study by Hirao [16],the theory was extended to nonuniform initial stressdistribution application. In the nonuniform stress states,the Rayleigh wave dispersion has been observed. Theacoustoelastic effect has been successfully applied for thestress evaluation in various isotropic engineering struc-tures. Similar research has also been carried out for thesurface wave propagation in anisotropic material [17,18]. Ina recent research conducted by Zhan et al. [19], the laserultrasonic combined with a laser Droppler vibrometer wasused to measure the welding-induced residual stress intitanium alloy.

There have been reported studies where the Rayleighwaves were used for surface residual stress evaluation withtraditional ultrasonic-based residual stress measurement

method [20,21]. Transmitters and receivers are required toemit and collect signals. However, high-quality interfacebetween the transducers and the specimen is important forthe accuracy of the measurement. Thus, liquid coolant isusually used in tradition to ultrasonic technique. There-fore, the development of noncontact ultrasonic technique isdesired. EMAT is superior to the transducer used intraditional ultrasonic method since it does not need directcontact with the surface of the specimen. In this study, alaser/EMAT ultrasonic technique (LEU) without directcontact with the measurement structure is introduced. TheEAMT collects the Rayleigh wave signals generated fromthe pulsed laser. Compared to the traditional ultrasonicmethods, the LEU does not involve direct contact with themeasurement structure, which makes it suitable for severeenvironment application, such as high temperature, fastmoving surface, and rough surface structures. The laser/EMAT has been a very promising technique for weldinginspection since early 1990s. In the work of Johnson andCarlson [22], the laser/EMAT was used to detect flaws inthe welding zone by analyzing the received wave signal. Inthe work of Oursler andWagner [23], the laser/EMAT wasused for the potential critical crack detection by analyzingshear waves. Different from what has been discussed in theprevious papers, the laser/EMAT for the surface/subsur-face residual stress emulation in the welding zone wasimplemented in this study. The laser/EMAT system forwelding inspection is not new. The residual stresscharacterization with laser ultrasonic has been done byprevious research. However, to the best knowledge of theauthors, the utilization of the laser/EMAT for welding-induced surface/subsurface residual stress evaluationbased on the Rayleigh wave, time of flight (ToF)measurement has never been done before. Compared tothe technique by Wang and Feng [24], using traditionalultrasonic detection system, EMAT is used in this study,which does not require any contact with the inspectedsample. In addition, this method does not require acomplicated wave signal processing, which could signifi-cantly improve the measurement reliability. Different fromthe research work of Dixon et al. [25] in using laser/EMATfor welding inspection without any quantitative measure-ment, we are using the laser/EMAT for the residual stressmeasurement, which imposes significantly more challengesfrom system setup, measurement accuracy, and dataanalyzing. Based on a previous study on welding residualstress calculation [26], a thermal/mechanical residualstress prediction model has been developed in this studyfor the residual stress prediction in the welding zone. Theprediction data show a good approximation to theexperimental measurement.

Welding simulation by finite element analysis (FEA) isattractive for the evaluation of the stress distribution inwelded structures. The first 2D thermomechanical modelfor the welding analysis was proposed by Hibbitt andMarcal [27]. With the development of computationalcapacity, 3D model has been conducted with commercialsoftware for the evaluation of transient temperature fieldand residual stress distribution [28]. In this paper, a 3Dthermomechanical-coupled model has been proposed usingANSYS for welding-induced residual stress evaluation. The

Fig. 1. Schematic diagram showing welding of two steel plates.

C. Ye et al.: Manufacturing Rev. 6, 3 (2019) 3

results show that the numerical predictions using FEAcorrelates well with experimental results.

2 Theory of ultrasonic measurement

The residual stress measurement method with ultrasonic isbased on the acoustoelastic effect. In the welds, thegenerated residual stress would change the Rayleigh wavetravelling velocity, which corresponds to different materialstress states. In this experiment, the sample is prepared bywelding two steel plates with GMAW technique, as shownin Figure 1. Rayleigh waves propagating only in the j1direction (the weld seam direction) are collected by atransducer. It is assumed that the Rayleigh waves couldfreely propagate on the welding plate surface. Forsimplification, a plane stress condition is assumed wherethe stress in the plate thickness direction j3 is zero. So, onlytwo stress components, s11 in the longitudinal direction j1and s22 in the transverse direction j2, are considered. Thisassumption is valid based on the free boundary conditionson the thickness direction of the welded steel plate. In thisstudy, only the principal stress components s11 and s22 areconsidered because the Rayleigh wave velocity change isassumed to be independent of the material shear stress.

The dependency of acoustic wave velocity on twoprincipal state cases has been derived by Tekriwal andMazumder [28]. The velocity variation of Rayleighwaves propagating along j1 direction on the free surface(j1� j2 plane) of an isotropic material could be related tothe biaxial stress state in the following equation:

DV R

V R¼ b1s11 þ b2s22; ð1Þ

where VR is the Rayleigh wave velocity, DVR is the changeof Rayleigh wave velocity between stress-free solid andstressed medium. b1 and b2 are acoustoelastic constants inthe longitudinal and transverse directions. This equationprovides the Rayleigh wave velocity variation in stressedsolids with two material-based constants. As also notedfrom this equation, the shear stress effect on the Rayleighwave propagation in thin welding plates is ignored.

According to a previous research work [26], the welding-induced residual stress s11 in the longitudinal direction ismuch larger than that of transverse direction stress s22.Additionally, thematerial coefficient b2 is smaller than b1 if

the propagation direction is along j1. Therefore, Rayleighwave velocity variation induced by the transverse directionstress component is negligible. In this case, the variations ofthe propagating velocity of Rayleigh waves shown inequation (1) can be simplified and expressed as follows:

DV R=VOR ¼ As11; ð2Þ

where DVR is the variation of Rayleigh wave velocityand DV R ¼ V O

R � V R:VOR is the Rayleigh wave velocity in

stress-free area. A is material-dependent acoustoelasticcoefficient, which could be determined by the materialsecond-order and third-order elastic constant coefficients.DV R=V

OR denotes the relative variation of the propagating

velocity of Rayleigh waves.From equation (2), it is easy to say that the increase in

wave velocity indicates tensile residual stress state anddecrease denotes compressive stress state. However, it ishard to measure Rayleigh wave velocity directly. Alterna-tively, we can measure the Rayleigh wave ToF when itpropagates to a specific distance. If we fix the distance to bed0, the relative variation of Rayleigh wave velocityDV R=V

OR corresponds to the relative variation of ToF

DtR=tOR. Therefore, the ToF variations can be related to

stress states as follows:

DtR=tOR ¼ As11; ð3Þ

where

DtR ¼ tR � tOR: ð4ÞtR° denotes ToF of Rayleigh waves traveling d0 in j1direction of stress-free steel plate and tR in welding zone.

From equations (1) and (2), Rayleigh wave velocitychange is linearly dependent on the magnitude of theresidual stress state along the welder seam direction. Fromthe experimental measurement, the ToF for Rayleigh wavetraveling along distance d0 is directly measured by theEMAT. Acoustoelastic constant A links the velocityvariation and the longitudinal residual stress. It dependson material properties and could be calibrated usingINSTRON for uniaxial tensile test combined with theproposed laser ultrasonic technique. However, calibrationwas not carried out in this research work due toinstrumental limitations. As a result, the actual residualstress could not be obtained in the absence of acoustoelasticconstant. Alternatively, normalization is used during dataanalysis for the validation of the accuracy of the proposedlaser/EMAT technique.

A normalization procedure is implemented by dividingthe velocity measurement data with the maximum value.The welding-induced residual stress of the welder could beobtained from the resulting velocity variation distributionof the normalized Rayleigh waves.

3 Finite element analysis

A 114.3� 140� 12.5mm3 low carbon steel plate wasmodeled in ANSYS using the symmetric boundary

Fig. 2. The mechanical properties of low carbon steel as afunction of temperature.

Fig. 3. The thermal boundary in the FEA model.

Fig. 4. Mesh of FEA model.

4 C. Ye et al.: Manufacturing Rev. 6, 3 (2019)

conditions. The mechanical properties of the low carbonsteel as a function of temperature is listed in Figure 2 [29].Both the modulus and the yield strength would signifi-cantly decrease with the increasing temperature. Duringsimulation, thematerial is assumed to be elastic� perfectlyplastic. The material poison’s ratio is 0.29. The thermalexpansion coefficient dose not variate significantly with thetemperature, and it is selected to be 1.7� 10�6K�1. Thematerial density is 7.2� 103 kg/m. This model wasdeveloped with ANSYS in a two-step procedure. In thefirst step, heat flux of Gaussian distribution shown inequation (5) was applied as input to simulate the heatsource of welding process:

Q ¼ Qme�3ðx2þðy�V tÞ2Þ

R2 ; ð5ÞwhereX and Y represent the coordinates, and Y direction isparallel to the weld seam.V andR denote travel speed of the arc and effective weld arcradius, respectively.Qm is the maximum heat flux at the center and can beexpressed as follows:

Qm ¼ h∂UI

pR2; ð6Þ

where U and I are voltage and current during weldingprocess and h denotes welding thermal efficiency.

Convection was applied on all external boundaries andthe reference/ambient temperature was considered as20 °C. The applied boundary conditions are shown inFigure 3. The four-node linear element with thermal/mechanical coupling was selected for the analysis. Theimplicit algorithm was used to solve the problem.

In the next step, thermal results along with structuralboundary conditions were fed to solve the structuralproblem to get longitudinal residual stress distribution onthe surface of the welded plates.

Mesh convergence analysis was carried out, and anelement size of 1.25mm was found to give optimal solutionwith reasonable computational time. Mesh is shown inFigure 4. Both transient thermal and transient structuralanalysis were carried out in four time steps. During the firsttime step, which was the simulated welding process, 48substeps of 2 s per substep were considered. And thensubstep size was increased to 10 s gradually to reduce thecomputational time. Temperature distribution at t=5 sand t=1200 s are shown in Figures 5a and 5b. Since themaximum value of color bar in Figure 5a is around 1344 °C,the temperature of the welding center, which is beyond1344 °C, is not shown. Thermal solution data were saved atevery substep and then retrieved during the structuralloading. Temperature distribution at the end of 1200 s isuniform and very close to ambient temperature. Therefore,the stress at the end of 1200 s was regarded as the residualstress, which is shown in Figure 6.

After normalization, the distribution of simulatedresidual stress for all the corresponding test rows is shownin Figure 7. Each test row is a selected residual stresssampling line that is normal to the welding direction.

4 Experiment

4.1 Sample description

For the FEA model validation, the same size low carbonsteel plates containing a single pass butt weld over theircenter produced by GMAW were prepared. The samplewas joined by a Miller Pulstar 450 GMAW machine. Theweld gun was controlled by a General Electric P50 processrobot. The welding voltage was 25V and the welding speed

Fig. 5. (a) Temperature distribution at 5 s (during the welding process. Units °C). (b) Temperature distribution at 1200 s (11min 48 safter the welding process stopped. Unit: °C).

Fig. 6. Welding-induced longitudinal stress (Unit: MPa).

Fig. 7. Distribution of longitudinal residual stress on welded sample from simulation.

C. Ye et al.: Manufacturing Rev. 6, 3 (2019) 5

6 C. Ye et al.: Manufacturing Rev. 6, 3 (2019)

was set as 0.375 in./s. The picture of the sample understudy and the designed coordinates are shown in Figure 8.The clamps were used to fix the plates at both ends duringthe welding process, as shown in Figure 9. After welding,the weld butt reinforcement needs to be removed to adaptto the EMAT probe flat surface. The micro-surfacegrinding process was used for the reinforcement of partremoval. The depth of cut in each grinding step was set to

Fig. 8. Welded sample.

Fig. 9. Welding setup (1 – sample, 2 – positioning system,3 – welding robot).

Fig. 11. Schematic diagram

be 15mm to avoid any residual stress introduced fromgrinding. Additionally, coolant was introduced in thegrinding process to reduce the temperature effect onexternal residual stress generation. The longitudinalresidual stress, which is the main residual stress developedfrom GMAW process, is along the weld seam as inx-direction.

4.2 Experimental setup

Figure 10 shows the laser measurement system setup,including a Nd:YAG pulsed laser, a customized EMAT, acontrol unit, a data acquisition system, and a two-dimensional position stage driven by step motors. Theschematic diagram of the measurement system is shown inFigure 11.

The pulsed Nd:YAG laser source (Continuum) wasused for laser generation. The laser was focused to thesurface of the sample through optic lenses. The incidentpoint on the sample surface has a diameter of around5mm. Rayleigh waves that were excited by the pulsedlaser propagated along all the directions on the surfaceof the testing sample. However, the EMAT (BWX

Fig. 10. Laser/EMAT stress measurement setup (1 – laser;2 – convex lens; 3 –EMAT; 4a� linear stage x; 4b� linear stage y).

of experimental system.

Fig. 12. Schematic diagram showing the ToF testing procedure.

C. Ye et al.: Manufacturing Rev. 6, 3 (2019) 7

Technologies, Inc.) only captured the Rayleigh wavestravelling along the welding seam direction. The EMAThas a reception bandwidth of (0.5MHz, 2.0MHz). Thereare four separate coils with 2mm pitch in-between. Thedata acquisition system consists of a high-speed four-channel Gage Compuscope 8349 PCI/AD card.

The two-dimensional translation stage consists of twolinear stages placed normal to each other, with one point tox-direction, and the other one along z-direction. Bothstages have a positional resolution of 25mm/step. Themicrocontroller was used to control the two-dimensionaltranslation stage movement. A MATLAB script was usedto power up the laser and control-positioning stagemovement. The laser system has a time resolution of1 ns to enable the accuracy of ToF measurements. Thewhole measurement system was automated and controlledby a MATLAB GUI on a PC.

The distance between the laser head and EMAT waskept constant at 11mm during the ToF measurement. Thewhole system was placed on a vibration table to avoidvibration-induced errors. The testing sample was clampedonto the linear stages. The wheels of the EMAT help tomake it roll on the surface of the sample when the samplemoves with the linear stages.

4.3 Time of flight measurements

ToFmeasurements have been widely used in acoustic wavemeasurement to determine the time required to travel acertain distance in a medium. The nondestructive testingfor defects or stress assessment employ a wide variety ofToF measurements [29,30]. In the measurements, wavestravel along a predetermined distance and the arriving timeof the signal of interest is recorded. Tomeasure the residualstress on the welding plate surface, the ToF of near surfaceRayleigh waves were measured. The reference time t0 wasobtained by measuring the ToF on a stress-free low carbonsteel sample. To get the residual stress distribution on thewelder, the ToF of Rayleigh waves were measured alongdifferent points normal to the weld seam direction.

In order to evaluate stress states of a larger area,four inspection rows normal to the weld seam directionwith a pitch of 15mm were selected, as shown inFigure 12. The welding residual stress evaluationarea covers any location that is 45mm away from theweld seam. Along each inspection row, 15 equally spacedpoints between 0 and 45mm away from the welding seamwere chosen for the residual stress evaluation. Thewelding-induced residual stress distribution normal tothe welding seam could be obtained. In each measure-ment location, the ToF measurements were repeated 300times and the average was used to achieve better signal-to-noise ratio (SNR). A typical Rayleigh wave amplitudesignal by averaging 300 repeated measurements isshown in Figure 13. The Rayleigh wave has a bipolarpulse as shown in the figure, which corresponds to themaximum amplitude of the wave without radiation loss.The total time t that the Rayleigh wave travels throughis taken as the ToF. The B-spline curve interpolationmethod was implemented here to interpolate theRayleigh wave amplitude to achieve a time resolutionless than 1 ns.

The normalized distribution of relative velocityvariations on 15 locations with varying distance fromweld center is shown in Figure 14. The 3D distribution alsoshows the difference between each test row.

5 Results and discussion

From ToF measurements, longitudinal residual stresses offour test rows on the welded sample were obtained. On eachof the four measurement rows, the stress states weremeasured at 15 points with different distances away fromthe weld seam center. To get the true residual stress value,the acoustoelastic coefficient needs to be calibrated by theproposed technique together with Instron. In this study,the residual stress is normalized due to the lack ofacoustoelastic coefficient. The normalized residual stressdistribution as a function away from the welding seam was

Fig. 13. Rayleigh wave average signal by EMAT.

Fig. 14. Distribution of longitudinal residual stress on welded sample from ToF measurements.

8 C. Ye et al.: Manufacturing Rev. 6, 3 (2019)

also evaluated from FEA. The residual stress distributioncomparisons from the ToF measurement and FEAcalculations are plotted against each other, as shown inFigure 15.

From equation (1), the longitudinal residual stress afterwelding process is proportional to the relative variations ofthe phase velocity of Rayleigh waves propagating along theweld seam. Theoretically, the normalized longitudinalstress distribution should be the same as the normalizedvelocity variation profile. Figure 14 shows the comparisonbetween these two profiles, and there is a good correlationbetween them with an acceptable small deviation. Thereasons for these small deviations are as follows:

– The residual stress generation in welding could comefrom temperature gradient-induced material nonuniformvolume change and phase transformation-induced mate-rial volume change. As noted in this work, materialmelting and solidification during the welding process isnot considered in the simulation.

–

Rayleigh wave velocity depends on the stress state withinits propagation region, which is about one wavelengthdeep into the sample. Thus, the velocity variations ofRayleigh waves reflect the average stress state of its

propagation region. However, simulation evaluates onlysurface stress state.

Both the experimental and simulation results showthat the biggest tensile stress appears in the weld seam,which is in the melted zone. As the distance away fromthe weld seam, the large magnitude of tensile residualstress sharply decreases and changes to compressive oneat the edge of the heat-affected zone. The largemagnitude of the tensile stress in the center of meltingzone comes from the material volume shrinkage after thewelding during the cooling down process. At the hightemperature, the plate material was melted and thewelding groove was filled by liquid metal. During thecooling down, the weld center has the largest tempera-ture decrease, which results in the material shrinkagewhile the outer area temperature change is not signifi-cant. The fast and significant decrease of the tempera-ture in the weld center leads to the material shrinkage ofthe hot metal and a tensile stress develops.

As we expected, the difference of stress distributionbetween each test row is not obvious. This can be explainedby the temperature distribution during the weldingprocess, which only has large gradient in the direction

Fig. 15. Comparison of normalized relative velocity variationsfrom ToF experiments and normalized longitudinal residualstress from FEA simulation for (a) row#1 tests, (b) row#2 tests,(c) row #3 tests, and (d) row #4 tests.

C. Ye et al.: Manufacturing Rev. 6, 3 (2019) 9

normal to the weld seam. As a result, the magnitude ofwelding-induced residual stress is mainly dependent on thedistance to the weld seam center. That is to say, the stressstates of the inspection points are identical if the distances

of those inspection points to the weld seam center are thesame.

The residual stress generation in the welding zone is avery complicated process, which involves the thermal,mechanical and material phase transformation. A compre-hensive residual stress prediction for welding needs toinclude the uniform material deformation, temperaturegradient-induced nonuniformmaterial volume change, andmaterial phase transformation-induced volume change.The temperature gradient-induced nonuniform materialvolume change is the dominating factor contributing to theresidual stress generation in welding. So, in this study, onlythe temperature effect is considered in residual stressprediction. In terms of the experimental measurement, weare based on acoustoelastic effect. Assumptions are madeand we consider only the effect of longitudinal residualstress on wave velocity change and ignore the effect oftransverse residual stress. However, in cases wheretransverse residual stresses are large and cannot beignored, this assumption might introduce errors. Othermeasurement errors can also come from ToF measurementof Rayleigh waves, resulting in the error of Rayleigh wavevelocity.

The Rayleigh wave can only penetrate to around onewave length distance into the material. So, the proposedmethod is limited to the surface residual stress measure-ment. To measure the residual stress underneath thesurface, appropriate surface removal procedure needs to beimplemented, such as electrochemical polishing.

6 Conclusions

An ultrasonic-based laser/EMATmethod is developed inthis study for the welding-induced residual stressmeasurement with high accuracy. The method utilizesa high-precision EMAT to measure the ToF of theRayleigh waves traveling along the welding plate surfaceinduced by the laser pulse. The linear relationshipbetween the Rayleigh wave velocity variation along thewelding seam direction and the residual stress states hasbeen developed. The experimental measurement isconducted by measuring the normalized residual stressdistribution normal to the welding seam direction fromthe ToF measurements. A thermal–mechanical coupledFEA model was developed for the residual stressprediction during the metal welding process. A goodmatch is found between the experimental measurementand FEA model calculation. The laser/EMAT forresidual stress measurement could be used for machin-ing-induced residual stress measurement as well asmeasurement associated with residual stress develop-ment in metal additive manufacturing. Being also notedin this research, an EMAT with a flat surface would needto be attached to the sample in order to receive theacoustic signal. Therefore, the measurement sampleneeds to be well polished to have a surface that issufficiently flat. Regardless, the proposed FEA modeland intrinsically nondestructive and noncontact laser/EMAT method provide a useful means for residual stressevaluation for various engineering welding structures.

10 C. Ye et al.: Manufacturing Rev. 6, 3 (2019)

Author contribution statement

Conceptualization: Chong Ye; formal analysis: Chong Ye;investigation: Yuanlai Zhou; methodology: Chong Ye andYuanlai Zhou; resources: Charles Ume; supervision:Charles Ume; validation: Chong Ye and Vishnu V.B.Reddy; writing � original draft: Chong Ye; writing �review and editing: Charles Ume.

Funding

This research received no external funding.

Conflicts of interest

The authors declare no conflict of interest.

References

1. D. Radaj, Welding residual stress and distortion, HeatEffects of Welding, Springer, Berlin, 1992, pp. 129–246

2. Z. Pan et al., Turning induced residual stress prediction ofAISI 4130 considering dynamic recrystallization, Mach. Sci.Technol. 22 (2018) 507–521

3. D. Deng, FEM prediction of welding residual stress anddistortion in carbon steel considering phase transformationeffects, Mater. Des. 30 (2009) 359–366

4. Z. Pan, S.Y. Liang, H. Garmestani, Finite element simulationof residual stress in machining of Ti-6Al-4V with amicrostructural consideration, Proc. Inst. Mech. Eng. B: J.Eng. Manuf. 2018. DOI: doi.org/10.1177/0954405418769927

5. G. Schajer, Measurement of non-uniform residualstresses using the hole-drilling method. Part I: stresscalculation procedures, J. Eng. Mater. Technol. 110(1988) 338–343

6. A. Giri, M. Mahapatra, On the measurement of sub-surfaceresidual stresses in SS 304L welds by dry ring core technique,Measurement 106 (2017) 152–160

7. P.S. Prevey, X-ray diffraction residual stress techniques,Metals Handbook, American Society for Metals, Ohio, 1986,pp. 380–392

8. A. Allen et al., Neutron diffraction methods for the study ofresidual stress fields, Adv. Phys. 34 (1985) 445–473

9. D. Crecraft, The measurement of applied and residualstresses in metals using ultrasonic waves, J. Sound Vib. 5(1967) 173–192

10. M. Hayes, R.S. Rivlin, Surface waves in deformed elasticmaterials, Arch. Rational Mech. Anal. 8 (1961) 358

11. I.C. Noyan, J.B. Cohen, Residual stress: measurement bydiffraction and interpretation, Springer, Berlin, 2013

12. A. Karabutov et al., Laser ultrasonic diagnostics of residualstress, Ultrasonics 48 (2008) 631–635

13. Y. Javadi, M. Akhlaghi, M.A. Najafabadi, Using finiteelement and ultrasonic method to evaluate welding longitu-dinal residual stress through the thickness in austeniticstainless steel plates, Mater. Des. 45 (2013) 628–642

14. R. King, C. Fortunko, Determination of in-plane residualstress states in plates using horizontally polarized shearwaves, J. Appl. Phys. 54 (1983) 3027–3035

15. Y. Iwashimizu, O. Kobori, The Rayleigh wave in a finitelydeformed isotropic elastic material, J. Acoust. Soc. Am. 64(1978) 910–916

16. M. Hirao, H. Fukuoka, K. Hori, Acoustoelastic effect ofRayleigh surface wave in isotropic material, J. Appl. Mech.48 (1981) 119–124

17. G.T. Mase, G. Johnson, An acoustoelastic theory for surfacewaves in anisotropic media, J. Appl. Mech. 54 (1987)127–135

18. J. Lothe, D. Barnett, On the existence of surface-wavesolutions for anisotropic elastic half-spaces with free surface,J. Appl. Phys. 47 (1976) 428–433

19. Y. Zhan et al., Residual stress in laser welding of TC4titanium alloy based on ultrasonic laser technology, Appl.Sci. 8 (2018) 1997

20. M. Duquennoy et al., Ultrasonic characterization of residualstresses in steel rods using a laser line source and piezoelectrictransducers, NDT & E Int. 34 (2001) 355–362

21. E. Tanala et al., Determination of near surface residualstresses on welded joints using ultrasonic methods, NDT & EInt. 28 (1995) 83–88

22. J.A. Johnson, N.M. Carlson, A laser/EMAT concurrent weldinspection system, Review of Progress in Quantitative Nonde-structive Evaluation, Springer, Berlin, 1991, pp. 2097–2104

23. D.A. Oursler, J.W. Wagner, Narrow-band hybridpulsed laser/EMAT system for non-contact ultrasonicinspection using angled shear waves, Review of Progress inQuantitative Nondestructive Evaluation, Springer, Berlin,1995, pp. 553–560

24. J. Wang, Q. Feng, Residual stress determination of railtread using a laser ultrasonic technique, Laser Phys. 25(2015) 056104

25. S. Dixon, C. Edwards, S.B. Palmer, A laser-EMAT system forultrasonic weld inspection, Ultrasonics 37 (1999) 273–281

26. C. Ye et al., Welding induced residual stress evaluation usinglaser-generated Rayleigh waves, AIP Conference Proceed-ings, AIP Publishing, College Park, MD, 2018

27. H.D. Hibbitt, P.V. Marcal, A numerical, thermo-mechanicalmodel for the welding and subsequent loading of a fabricatedstructure, Comput. Struct. 3 (1973) 1145–1174

28. P. Tekriwal, J. Mazumder, Finite element analysis of three-dimensional transient heat transfer in GMA welding,Welding J. 67 (1988) 150s–156s

29. J. Chen, B. Young, B. Uy, Behavior of high strengthstructural steel at elevated temperatures, J. Struct. Eng. 132(2006) 1948–1954

30. D. Stamenković, I. Vasović, Finite element analysis ofresidual stress in butt welding two similar plates, Sci. Tech.Rev. 59 (2009) 57–60

Cite this article as: Chong Ye, I. Charles Ume, Yuanlai Zhou, Inspection of the residual stress on welds using laser ultrasonicsupported with finite element analysis, Manufacturing Rev. 6, 3 (2019)