High accuracy and efficiency calculation model for predicting the reduction of residual stress on large pressure vessels by ultrasonic impact surface treatment

Ultrasonic impact treatment (UIT) is a new surface strengthening method to reduce the residual stresses on large pressure vessels induced by surface and repair welding. An accurate and high efficiency calculation model is the key to accurately predicting the full‐field residual stresses on large pressure vessels under the UIT process. In this article, a full‐coverage impacting model is proposed to simulate the impacting process of the UIT pin. The effects of UIT on the residual stresses on repair and surface welded pressure vessels were investigated by explicit dynamic simulation. Experiments were also performed to verify the prediction results. Results show that the proposed full coverage impacting model can greatly improve the simulation precision and the calculation efficiency. The predicted residual stresses after the UIT process using the proposed model are consistent with the measured results. A remarkable reduction in residual stress was achieved in the zone subjected to UIT. The tensile residual stresses on the surface of the treated area were reduced to compressive stresses. With the increase of the impact velocity and the coverage rate, the residual stresses on the surface and transition layers decreased and then tended to stabilize. The impact coverage rate should not exceed 200% to avoid damage and save time.


INTRODUCTION
Strip surface welding is an important process in the manufacture of large pressure vessels, such as, hydrogenators, and repair welding is required to restore the structure and extend the service life of surface welded pressure vessels with defects. 1 However, complex tensile residual stresses are inevitably generated after surface and repair welding, which have an adverse effect on the resistance to fatigue and stress corrosion cracking. 2Stress corrosion cracking (SCC), which is usually considered to be jointly caused by the corrosive environment, the specific materials, and tensile stress, is a prominent problem in petrochemical industry. 3Therefore, the effective control of the tensile residual stress induced by welding is of great significance in ensuring the structural integrity of surface-welding-manufactured and repair-welded pressure vessels.Currently, the common control methods for tensile residual stresses can be mainly divided into three groups: (1) post welding heat treatment (PWHT), (2) surface treatment, and (3) weld optimization design. 4As many researchers concluded, PWHT and weld optimization design can usually reduce the residual tensile stress but not to a compressive value.In contrast, surface treatment can reduce the residual tensile stress to compressive stress, thus preventing the SCC of pressure vessels.Ultrasonic impact treatment (UIT) is a common surface treatment method, which can reduce the stress concentration at the toe and has the merits of lightweight, low noise, high efficiency, low cost, flexible and convenient to use. 5 The principles of UIT is shown in Figure 1.UIT is based on conversion of harmonic oscillations of the ultrasonic transducer into impact pulses on the surface. 6Cheng et al. 7 measured the residual stresses induced by the UIT process using experimental measurement techniques and found that a compressive stress layer is generated.Chen et al. 8 investigated the effects of UIT on the residual stress in a repair welding joint by experimental and finite element (FE) methods.The longitudinal residual stresses basically were reduced to small tensile stresses from large tensile stresses, and the transverse residual stresses mainly decreased to compressive stresses from large tensile stresses after UIT.By introducing a strengthening layer with compressive residual stresses, UIT has been proven effective in improving the fatigue life of engineering structures.Vilhauer et al. 9 studied the fatigue lives of the A36 welded joint under UIT.They found that UIT can prolong the fatigue propagation lives by 5.7-6.7 times.Tang et al. 10 also found that UIT increases the fatigue lives of butt and T-joints by 2.5-30 and 5-35 times, respectively.
To accurately assess the fatigue life or stress corrosion performance improvement through UIT, the residual stress distribution before and after the UIT process should be accurately classified.Though a variety of methods have been proposed to measure the residual stresses, many of them have very small measuring areas. 11The full field distribution of residual stress is virtually impossible to obtain by measurements.Guo et al. 12,13 pointed that the application of the finite element method provides a great opportunity to clarify the distribution of full-field stress.Numerical simulation methods were recently utilized to predict the full field residual stress distribution induced by the UIT process. 13In the simulation of the UIT process, the impact process of the pin head can be simplified as the movement of the impact pin head under given control parameters.These parameters include the impact velocity, the contact force, and the pin displacement.Hence, the modeling methods of the UIT process can be classified into three methods: velocity-controlled simulation (VCS), force-controlled simulation (FCS), and displacement-controlled simulation (DCS). 14DCS is considered to be one of the most widely used modeling techniques for UIT simulation to estimate the compressive residual stress. 5,15owever, the current simulation method is mainly a single impacting pin model based on the DCS method in which the calculation accuracy and efficiency are poor, and it is unsuitable for wide area treatment of cladded pressure vessels.A full coverage ultrasonic impact model must be established to realize the highly efficient prediction of the reduction of the residual stress on large pressure vessels by UIT.In addition, the present research on the UIT process mainly focuses on the impact effect prediction on welded joints or stress-free specimens made of homogeneous materials.No experiments or numerical studies have been carried out on the control of the residual stress distribution on the repair cladded structure of large pressure vessels by UIT.The influence of the UIT process on the residual stress on repair cladded structure remains unclear.Consequently, no reliable theoretical guidance can be provided for the engineering application of the UIT process on cladded pressure vessels.

F I G U R E 1
The principles of UIT Therefore, this article aims to establish a full coverage impacting model to simulate the wide area treatment of UIT on repair cladded pressure vessels.The simulation was performed through explicit dynamic analysis.The residual stress distribution after the UIT process by the established model was also verified by experiment.The effects of the impact velocity and the coverage rate were also discussed, providing guidance for the UIT operation on site.

Preparation of cladded and repaired specimen on pressure vessels
Given the very small curvature radius of large pressure vessels, a plate surface cladded specimen was prepared to save in material resources and for operation simplicity, as shown in Figure 2A.In this study, the base metal is SA387Gr11CL2, and the cladding materials for the transition and surface layers are EQ309L and EQ316L, respectively.The base metal is 300 × 300 × 32 mm.Strip surface cladding was carried out by submerged arc welding with a wideband electrode.The band-electrode width is 60 mm.Before strip surface cladding, the floating rust, grease, and other impurities on the surface of base metal were removed.The preheating temperature was 100-150 • C. The welding voltage, current, and speed of the strip cladding were 140-160 A, 27 V, and 3 mm/s, respectively.After strip surface cladding, the specimen was subjected to PWHT in a heating furnace.The cladded specimen was held at 690 • C for 4 h.After PWHT, a groove was machined on the center of the cladding layer.The length and depth of the slot are approximately 180 and 7 mm, respectively.Then, repair welding was performed on the groove with eight passes, as shown in Figure 2B.The filling material for the 1st-2nd passes is 309 L and 316 L for 3rd-6th passes.

Treatment of ultrasonic impact
After repair welding, UIT was performed on the treated zone, as shown in Figure 3A.In the UIT process, the ultrasonic generator produces high-frequency ultrasonic waves, and the transducer converts the ultrasonic wave energy into high-frequency mechanical vibration.The transformed mechanical vibration drives the impact pin through the amplitude transformer to realize impact treatment on the surface of the treated specimen.The output current of the UIT device is 2.67 A, and the ultrasonic frequency is 40 kHz.The output amplitude of the amplitude transformer is approximately 30 μm.The moving speed of the UIT pin is 3 mm/s, and the total processing time is 10 min.The UIT pin is a flat impact needle.The needle material is W18Cr4V.The moving direction of the UIT pin is vertical to the repair length.The UIT process on-site is shown in Figure 3B.To fully cover the treated area, the impact pin in every position along the transverse and longitudinal directions are both 20 times in total.

Measurement of residual stress
The surface residual stresses along path P2 (shown in Figure 3) after the UIT process were measured by the impact indentation strain gage method.In this approach, the operation is simple and the maximum measurement error is ±20 MPa, which can meet the measurement accuracy.Furthermore, serious structure destruction can be avoided.The method uses a spring impactor to push the spherical head to produce a certain depth of indentation on the measured point.There is a strain increment produced by the superposition of the impact indentation and original residual stress.The strain increment values can be recorded by strain gauge, and then the residual strain can be calculated through the prior calibrated relationship between strain increment and elastic strain.According to the relationship between the strain increment and the stresses, the residual stresses determined by this approach are calculated using Equations ( 1) and ( 2) 16 : where  eT and  eL are the respective transverse and longitudinal elastic strain increments, while  T and  L are the transverse and longitudinal residual stresses, respectively.The measurement principle diagram and setup are shown in Figure 4.The measurement procedure is conducted strictly according to Chinses National Standard. 17ix points were measured.Points 2-5 are located in the weld, while Points 1 and 6 are located in the base metal.

F I G U R E 4
The residual stresses measurement principle (A) and setup (B)

Finite element model
According to the actual geometric size of the repair-cladded specimen, a finite element model was built using the ABAQUS software.To improve the calculation efficiency, the element in the repair and impact zones is dense and becomes coarse away from these zones.The element sensitivity was investigated.Finally, 122,738 elements and 132,619 nodes were meshed.Figure 5 shows the finite element mesh of the specimen and the UIT pin.The repaired specimen and the impact pin are recognized as solid and rigid bodies, respectively.The element type of the repaired specimen for the temperature field and stress field analysis are DC3D8 and C3D8R, respectively.The element numbers are the same for the thermal and stress analyses.

Simulation of welding residual stress
Currently, the finite element modeling has become a mature method to simulate welding residual stresses. 18Rong et al. [19][20][21] made many great investigations on the simulation of welding deformation and residual stress.The welding simulation involves welding temperature analysis, which is followed by stress analysis, using the temperature obtained from the thermal analysis.The repair welding process is simulated by a moving double-ellipsoidal model, 22 which is described in Equations ( 3) and ( 4): where q f and q r are the power density distributions in the front and rear quadrants, respectively. is the weld arc efficiency, U is the weld voltage, and I is the weld current.f f and f r are the fractions of total heat in the front and rear quadrants, respectively, f f + f r = 2. a f , a r , b, and c are the parameters that describe the dimensions of the molten pool, representing the front length, the rear length, the width, and the depth, respectively.x, y, and z are the local coordinates of the double ellipsoid model aligned with the welded plate.
During strip surface welding, the width of the band electrodes is more than 60 mm, so the welding pool is flat and wide.The traditional double ellipsoid model cannot meet the shallow depth and wide width requirements of molten pool.The new heat source model proposed in Reference [23] was employed to simulate strip surface welding.The heat source model of the strip surface welding that considers the magnetic pinch effect can be described as follows: where  f and  r are the heat flow influence coefficients by the transversal redistribution of the welding heat flux and flow of molten pool, respectively.The exact values of  f and  r cannot be obtained by measurement or computation and were determined through trial-and-error method in the analysis.The residual stress field is calculated from the temperature field analysis results, and the total strain rate consists of three components as shown in Equation ( 7): where d e , d p , and d th are the elastic, plastic, and thermal strain increments, respectively.The elastic strain is modeled through the isotropic Hooke's law.The plastic strain is obtained by the coefficient of thermal expansion.The thermal strain is calculated by the rate-independent plastic model with the Von Mises yield surface and isotropic hardening model.
During the mechanical analysis of strip surface welding, the movements and rotations of the specimen in the transverse, longitudinal, and normal directions were restrained.After the stress analysis of the strip surface welding, the PWHT process was simulated according to the actual PWHT technology, and the creep behaviors at holding were considered to follow the Norton law. 24The temperature dependent thermal conductivity, density, and specific heat were considered in the temperature simulation, while the temperature dependent thermal expansion coefficient, Young's modulus, Poisson's ratio and yield strength were considered in the stress simulation.The temperature dependent material properties were shown in Figure 6. 23

Simulation of UIT process
The simulation of the UIT process involves the contact and separation between the impact pin and the specimen surface during the impact and springback process.Reasonable contact conditions will directly affect the calculation efficiency and accuracy.In this study, the contact surface of the impact pin was set as the master surface, and the treated surface of the specimen was set as the slave surface.The penalty function friction model was adopted between the impact pin and the specimen surface, and the friction coefficient was set to 0.15.The master-slave surface was set as the hard contact.Explicit dynamic analysis was used for calculation, and the mass scaling technique was used to make full use of the computing resources and reduce the solving time.
In general, the computational speed of an explicit dynamic model depends on the minimum stability time increment, which is closely related to the grid size and the material properties.The mass magnification of the model can effectively increase the increment of the stabilization time.However, excessive mass release aggravates the negative effect of inertia, resulting in inaccurate results.In this study, the target incremental step of the stability time was set as 1 × 10 −7 s to avoid excessive inertia effect and accelerate the calculation.According to the moving path of the impact pin shown in Figure 2, the moving distance along the transverse and longitudinal directions are 1.9 and 10 mm, respectively.To ensure that the size of the impact zone is the same as the actual size, the moving times of impact pin are the same with the experiment.The movement of the impact pin is driven by the proposed full coverage impacting model, which is described in detail in the following section.

FULL COVERAGE IMPACTING MODEL OF UIT PIN
During UIT, the impact pin moves back and forth between the contact and treated surfaces under the periodic drive of the amplitude transformer.The maximum energy (E o ) output by the lug lever is given by the following equation 25 : where Ω is the cross-section area of the amplitude transformer, u 0 is the vibration amplitude of the amplitude transformer, E is the elastic modulus of the amplitude transformer, and L is the average distance between the treated and contact surfaces.
Ignoring the loss of energy transfer between the amplitude transformer and the impact pin, the energy output of the amplitude transformer is completely converted into the kinetic energy of the impact pin: where v n1 is the speed of the first impact.When the impact pin hits the treated surface at high speed, the kinetic energy of the impact pin will be converted into the deformation energy of the specimen.The deformation energy of the specimen consists of two parts: the elastic and plastic deformation energies.
where  s is the yield strength, and V is the volume of the plastic zone.
As the contact progressed, the velocity of the impact pin gradually decreased, the plastic dissipation increased, and the final impact load dropped to zero.Subsequently, the elastic deformation of the specimen was released and then converted into the springback kinetic energy of the impact pin.The springback kinetic energy is described as follows: where v r1 is the springback velocity.
After the impact pin rebounds, it will come in contact with the amplitude transformer again and obtain the impact energy from the amplitude transformer again.At this time, the kinetic energy of the impact pin (E kr2 ) is The impact pin velocity is where f is the output frequency of the ultrasonic wave, and A is the maximum displacement amplitude at the output end of the amplitude transformer.Here, v im = 7.5 m/s.A complete UIT process should contain many single shocks at one position, and the process is accompanied by the transverse and longitudinal movements of the impact pin.To reflect this process, the impact process was discretized, and the full coverage impact model was redeveloped using a Python subroutine in this study.
Figure 7 shows the diagram of the full coverage impacting model for the UIT process.For the first impact, the initial stress state is the repair welded state.In the subsequent impact treatment, the material state is updated.The updated content is the stress, strain, and deformation at the end of the previous impact.The impact pin movement was simulated by explicit dynamic analysis.To further control the inertia effect caused by mass amplification and ensure the accuracy of calculation, the explicit dynamic calculation results were imported into the general static (Abaqus Standard) for stabilization treatment the impact reached a certain number of times.The result of the standard analysis was then also used as a predefined field for the subsequent dynamic explicit analysis computation until the end of the impact processing.
Figure 8 shows the stress evolution of the stress-free state specimen under the single impact treatment.At the initial stage, the impact pin moves toward the surface of the specimen at high speed.At t = 3.4 × 10 −4 s, the impact pin touched the treated surface, and then energy transfer occurred.The kinetic energy of the impact pin was gradually converted into the internal energy and a small amount of the kinetic energy of the specimen.At t = 3.5 × 10 −4 s, the deceleration of the impact pin was completed.At this point, the kinetic energy of the impact pin was completely transformed.Then, the elastic strain energy of the specimen was released and used for the impact pin to produce rebound.When t = 4.0 × 10 −4 s, the impact pin separated from the treated surface and continued to move toward the amplitude transformer.The maximum value of the von Mises stress during the UIT process was 197.5 MPa on the impacted surface.After the specimens rebounded from the deformation, the stress stabilized rapidly with a maximum value of 188.6 MPa.

Residual stresses distribution
Figure 10 shows the transverse and longitudinal residual stress distribution before and after UIT.Before UIT, high longitudinal tensile stress was formed in the repair weld and near the heat affected zone, and the transverse and longitudinal residual stress distribution between the tensile and compressive phases was formed in the matrix.After UIT, the residual stress distribution in the repair welding area has been significantly improved, and the transverse and longitudinal tensile stress on the surface has been effectively eliminated, and a certain amount of residual compressive stress has been generated at local locations.
To quantitatively analyze the influence of UIT on the residual stress of the surfacing layer repair welded joint, the residual stresses along paths P1-P4 were analyzed in detail.The paths are shown in Figure 11.

F I G U R E 11 Schematic of analysis paths
Figure 12 shows the comparison of the transverse and longitudinal residual stress distributions along P1 before and after UIT.Obviously, the influence of UIT on the residual stress distribution gradually weakened with the increase of the distance from the treated surface along the thickness direction.The impact pin was directly applied on the surfacing layer, and the plastic deformation of the surfacing layer is the largest, so the change of the residual stress on the surfacing layer is the most significant.The difference in the material properties of the surface layer, the transition layer, and the base metal resulted in the uncoordinated response of each part to the impact load during the UIT process.After the UIT process, the degree of discontinuity of the transverse and longitudinal residual stresses at the interface between the surface and transition layers and the matrix increased.The transverse stress in the base metal near the interface increased, and the longitudinal stress decreased obviously.The stresses in the inner part of the base metal did not change.Both transverse and longitudinal stresses decreased slightly.UIT can stimulate the stress wave of ultrasonic frequency.When the sum of dynamic stress and residual stress is greater than the yield strength of the material, the peak of residual stress produces local yield, and the elastic strain develops into plastic deformation, so that the residual stresses in surfacing layer and transition layer are decreased.Due the self-equilibrating effect of residual stress, the residual stresses in interior were corresponding increased.
Figure 13 shows the comparison of the transverse and longitudinal residual stresses on the surfacing layer before and after the UIT process.The transverse residual stress in the impact zone of the surface layer reached the lowest of −82.7 MPa, with a decrease of 140%, while the maximum longitudinal residual compressive stress was −155.4MPa, with a decrease of 143%.In the untreated region, the stress was slightly released in the local area near the impacted region, while the residual stress in the other tensile stress regions was reduced a little.The variation of the transverse and longitudinal residual stresses on the untreated surface layer was inconsistent.The transverse residual stress decreased while the longitudinal residual stress increased in the untreated zone after the UIT process.
Figure 14 shows the comparison of the transverse and longitudinal residual stresses in the interface of the transition layer and the base metal before and after the UIT process.The changes in the transverse and longitudinal residual stresses of the transition layer are consistent with those of the surface layer.The main difference lies in that the compressive residual stress was not formed at the repair welding seam of the transition layer, probably because the maximum kinetic energy carried by the impact pin was not enough to eliminate or even transform the transverse and longitudinal residual stresses of the transition layer into compressive stresses.Moreover, the metal in the transition layer under the impact zone was restrained by the surface layer and the base metal, preventing excessive compressive deformation.After the UIT process, the transverse and longitudinal residual stresses in the weld decreased by 20% and 35%, respectively.The transverse and longitudinal residual stress distributions of the transition layer is more uniform than the surface residual stress after the UIT process.
Figure 15 shows the comparison of transverse and longitudinal residual stresses at the bottom of the base material before and after the UIT process.The tensile transverse and longitudinal stresses at the bottom decreased slightly.The maximum transverse tensile stress decreased from 443.2 to 378.6 MPa, and the maximum longitudinal tensile stress decreased from 282.0 to 257.0 MPa, with a decrease of 15% and 9%, respectively.The depth of the reduction effect of the UIT process on residual stress has a certain range.

Effects of moving velocity of impact pin
The kinetic energy of the impact pin impinged to the specimen surface directly determines the value of energy conversion between the impact pin and the specimen, so the moving velocity (v im ) of the impact pin is the key factor affecting the treatment effect.By changing the initial velocity of the impact pin in the finite element model, the full coverage UIT models with impact velocities of 6.0, 7.5, 9.0, and 12.0 m/s were established, and the influence of the impact velocity on the residual stress distribution of repair welding on the surface layer was analyzed, as shown in Figure 16.The impact velocity has a significant influence on the transverse and longitudinal residual stress distributions within the cladded structure.When the impact velocity was 12 m/s, the longitudinal residual stress of the substrate near the interface decreased from 539 to 415 MPa, with a decrease of 22.9%.When the impact velocity was 6 m/s, the stress decreased to 499 MPa, with a decrease of only 7.4%.

Effects of coverage rate of UIT
The different moving speeds and the number of repeated processing times will produce different impact strengths to the surface of the treated specimen, resulting in different reduction effects on residual stress.In general, the coverage rate is used to represent the difference in impact strength caused by the moving speed and number of repeated treatments.The coverage rate () is defined as where t a is the actual treatment time, and t r is the time required to complete a qualified full coverage impact treatment.
To study the influence of coverage rate on the residual stress distribution on the basis of the existing model with an initial residual stress state, calculation analysis was carried at coverage rates of 100%, 200%, 300%, and 500%, without changing the other settings.Figure 17 compares the distributions of residual stress along thickness path P1 under different coverage rates.The reduction effect of the residual stress on the surface layer was enhanced with the increase of the coverage rate, but the variation amplitude of the stress decreased gradually.When the coverage increased from 300% to 500%, the transverse and longitudinal residual stresses tended to stabilize.The maximum transverse and longitudinal residual compressive stress on the surface layer increased with the increase.When the coverage rate was 100%, the maximum transverse and longitudinal compressive stresses in the surfacing layer were 75.3 MPa and 103.4 MPa, respectively.When the coverage rate increased to 500%, the stresses were 123.9 and 120.9 MPa, respectively, with corresponding increases of 64.5% and 16.9%, respectively.The coverage rate has a significant influence on the transverse and longitudinal residual tensile stresses on the transition layer and the heat affected zone of the base metal, while it has little effect on the other parts of the base metal.As the coverage rate increased from 100% to 200%, the longitudinal stresses in the transition layer and the heat affected zone of the base metal decreased by approximately 100 MPa.The transverse and longitudinal stresses in the part below the heat affected zone of the base metal were nearly unaffected by the coverage rate.However, as the coverage rate increased from 200% to 500%, the longitudinal stresses showed little changes.Moreover, excessive UIT can cause surface defects or damage. 14,26,27Thus, the impact coverage should not exceed 200% to avoid surface damage.

Discussion
The above analysis indicates that the UIT process has a great influence on the residual stresses of the surface layer.The tensile stresses on the surfacing layer can be reduced to compressive stresses by the UIT process.The reduction value of the residual stresses decreased with the increase of the distance from the surface.The discontinuous stress distribution in the interface between different materials cannot be improved by the UIT process.Furthermore, the tensile residual stresses below the surfacing layer cannot be reduced to compressive stresses by increasing the impacting velocity and the coverage rate.Therefore, blindly increasing the UIT parameters blindly for the residual stress control of strip cladded pressure vessels is unreasonable.The approach is only necessary to ensure that the UIT process can reduce the residual tensile stress on surfacing layer to compressive stress.Strip cladding and repair are often required in the inner wall of large pressure vessels.The tensile residual stresses are a key factor in inducing the SCC of the welded joint under a corrosive environment.The compressive stresses on the weld surface is beneficial to preventing SCC.In our previous study, 15 we concluded that the tensile stresses on the repair weld of cladded structures cannot be reduced by PWHT.The UIT process is a proper method of reducing residual stresses in the repair weld of a cladded structure.The proposed high-accuracy and -efficiency calculation model is beneficial to the rapid prediction of the reduction of residual stresses for large inner surface welded pressure vessels by UIT.

CONCLUSION
This article presents a study on the effects of UIT on the residual stresses on large repair/cladded pressure vessels.Explicit dynamic analysis was performed to simulate the UIT process on the basis of the proposed impacting model.The residual stresses on the repair cladded structure before and after UIT were measured by the indentation gauge method and then used to verify the simulation results.The effects of the impacting velocity and the coverage rate were also discussed.The following conclusions can be drawn based on the obtained results: 1.A full coverage impacting model is proposed to simulate the impacting process of the UIT pin.A good simulation precision and the calculation efficiency were achieved by the proposed impacting model.The predicted residual stresses after the UIT process by explicit dynamic simulation are consistent with the measurement results.2. The UIT process can effectively eliminate the residual tensile stress on the treated surface.The UIT process produces a plastic deformation layer on the surface with a certain thickness, thus inducing residual compressive stress on the surface layer.The transverse and longitudinal residual stresses in the transition layer were reduced by ∼20% and ∼35%, respectively, and the transverse and longitudinal residual stresses at the bottom were reduced by 15% and 9%, respectively.The influence of the UIT process on the residual stress decreased with the increase of the distance from the treated area.3.Both the transverse and longitudinal residual compressive stresses of the surfacing layer increased with the impacting velocity but had no obvious effect on the untreated area.The transverse and longitudinal residual stresses of the transition layer decreased, and the reduced value of the residual stress also increased.The effect of impact velocity on the residual stress below the heat affected zone of base metal is not obvious.4. The influence of the coverage rate on the residual stress of the repair welding is weaker than that of the impact velocity.
The transverse and longitudinal residual stress peaks of the surface and transition layers increased and tended to stabilize rapidly with the increases of the coverage rate.As the coverage rate reached 200%, the residual stress did not change significantly.Therefore, the impact coverage should not exceed 200% to avoid surface damage.

F I G U R E 2
Strip cladded specimen (A) and repaired welded specimen (B) of pressure vessels F I G U R E 3 Treated zone of UIT (A) and UIT process on-site (B)

F I G U R E 6
Temperature dependent material properties of base metal (A), transition layer (B), and surface layer (C)

F I G U R E 7 5 VERIFICATIONFigure 9 9
Figure 9 compares the transverse and longitudinal stresses after the UIT process by finite element simulation and measurement.The finite element results are consistent with the experimental results, and the maximum relative errors of the simulated and measured transverse and longitudinal residual stresses are 8.5% and 9.4%, respectively, indicating that the proposed full coverage impacting model of the UIT pin has high prediction accuracy and reliability.The influence of UIT on the residual stress distribution of welded joints has a large locality, and the improvement of the transverse and longitudinal residual stresses by impact treatment is limited to the treated area.

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I G U R E 10 Contour distribution of (A, C) transverse (B, D) longitudinal residua stress before (A, B) and after (D, D) UIT

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Comparison of (A) transverse and (B) longitudinal residual stress distribution along P1 before and after UIT F I G U R E 13 Comparison of (A) transverse and (B) longitudinal residual stress distribution along P2 before and after UIT (A) (B) F I G U R E 14 Comparison of (A) transverse and (B) longitudinal residual stress distribution along P3 before and after UIT

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Comparison of (A) transverse and (B) longitudinal residual stress distribution along P4 before and after UIT Comparison of (A) transverse and (B) longitudinal residual stress distribution along P1 under different impact velocity

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I G U R E 17 Comparison of (A) transverse and (B) longitudinal residual stress distribution along P1 under different coverage