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Abstract

The ultrasonic impact treatment process is widely used to improve the fatigue life of the weldments by inducing compressive residual stresses at the sub-surface. The purpose of the article is to conduct the dynamic elastic–plastic finite element analysis of multiple impacts on 5A06 aluminum alloy with different controlled parameters. The numerical model was validated by pin drop test. The changes in penetration depth, maximum compressive residual stress, and surface residual stress were obtained by analyzing the residual stress field and equivalent plastic strain. The effect of impact times, impact velocities, pin shapes, and impact angles on the residual stress was investigated so that the ultrasonic impact treatment parameters could be controlled to obtain expected residual stress distributions.

Keywords

Multiple impacts residual stress penetration depth finite element analysis ultrasonic impact treatment

Introduction

Ultrasonic impact treatment (UIT) is a surface cold-working process which is widely used to produce surface nanocrystalline and improve the hardness and fatigue life of the metallic materials. The technology is a further development of the shot peening and hammer peening, which uses pins repeatedly impacting on the component by high-power energy. It was developed at the Northern Scientific and Technological Foundation in Severodvinsk, Russia, associated with Paton Welding Institute in Kiev, Ukraine,¹ for the shipbuilding industry.² Compared with other processes, such as traditional shot peening,³ ultrasonic shot peening,⁴ laser shot peening,⁵ and high pressure waterjet peening,⁶ the UIT device is more controllable and convenient, and it can induce lower surface roughness and deeper compressive residual stress layer. These characteristics promote the development of the UIT technology in the aerospace, automotive, and power industries. Especially in the welding industry, by impacting many times the weld bead and the base metals,^7,8 it will form a groove between the weld bead and the base material, in which the compressive residual stress and the refined grains^9,10 can be obtained to improve the fatigue life of the welded structures. The residual stress is usually measured by experiment at present. However, the high cost and poor efficiency make experimental method difficult to be applied widely. With the development of the finite element (FE) technology, it provides the possibility to predict material status without large physical tests.

Due to the complexity of the UIT process, the study of its simulation is rarely reported. Similar to the traditional shot peening process, the UIT process is also an impact process. The UIT model could be established by improving the traditional shot peening model. The shot peening process has already been simulated by many FE models, such as two-dimensional (2D) axisymmetric models,^11,12 three-dimensional (3D) symmetric models,^12–14 single/multiple impacts models,^12–16 and angled-impacts models.¹⁷ All these models were developed to fit the elastic–plastic deformation and the residual stress profile. Among the models above, 2D axisymmetric models have the longest history. Johnson¹⁸ initialized using a pseudo-dynamic approach to develop a dynamic impact model with a single shot, in which the inertial properties were considered. The relationships between the depth of plastic zone and the properties of the shot, such as radius, mass, and velocity, were obtained. With the development of computational capabilities, shot peening numerical models have been further improved. Edberg et al.¹⁹ were the first to use commercial FE program to analyze the shot peening process. Al-Hassani et al.²⁰ simulated the process of single and multiple shots impact and analyzed the situation of single shot impacting with an incident angle. Deslaef et al.²¹ and Rouhaud and Deslaef²² examined the effects of rigid/deformable shot on residual stress. Frija et al.²³ used an integrated damage law to obtain the residual stress, the plastic deformation profiles, and the surface damages. Dai et al.²⁴ developed a 3D FE model to discuss the final surface roughness, the processing time, the microstructure transformation, and changes in properties during the nanocrystallization and hardening process. Schwarzer et al.²⁵ used infinite elements to avoid strain wave reflections. Guagliano²⁶ discussed the relationships between the key parameters, such as shot velocity, shot size, and Almen intensity. Wang et al.²⁷ obtained the residual stress distribution by applying different temperature values to sample points through the thickness of the shell element.

In these models, the common characteristic is that the shot size is small and the contact velocity is high, which is not suitable for the UIT technology. Besides these, other characteristics, such as the high contact frequency, the high surface coverage, and the multi pin shape, also indicate that the shot peen models cannot be used as the UIT model directly. The article aims at developing 3D FE models of the UIT process with different controlled parameters to predict the distributions of the residual stresses and the deformations by improving the shot peening models. An impact process will be first simulated to obtain the contact time between the pin and the target, which is used to estimate the time interval between the two consecutive impacts. The effect of impact times, impact velocities, and pin shapes on the residual stress profile will be discussed in detail. Also the multiple impacts on the target with different impact angles will be simulated and investigated.

FE modeling

The configuration of TJU-HJ-III style UIT device is shown in Figure 1. It consists of two parts: ultrasonic wave generator and UIT operator; the latter part includes energy transducer, ultrasonic horn, and peening pins. The center frequency of output ultrasonic vibration is 17 kHz and the amplitude range is 0–25 µm, while the impact frequency between the pins and the target is much lower than 17 kHz.

Figure 1.

Configuration of UIT device.

For simplifying the computation process, the following assumptions were set: the time intervals between the consecutive impacts are invariant and the process of one pin impacting many times on the target is assumed as multiple pins arranged in a preprogrammed array impacting the target.

Based on the shot peening models, the article developed 3D FE models to investigate the effect of key parameters on the residual stress using the commercial FE code Abaqus/Explict 6.10. The models for the process with one pin impacting the target one time (single-impact model) and multiple times (multi-impact model) were developed, as shown in Figure 2. Single-impact model is used to be validated by the experimental results. In the multi-impact model, 10 pins impacting the target at the same position are used to replace the process of one pin repeatedly impacting the target 10 times. Multi-impact model is employed to obtain relationships between the controlled parameters and the residual stress distributions.

Figure 2.

Finite element models for (a) single-impact and (b) multiple impacts.

The specimens are plates with geometry of 20 mm × 20 mm × 4 mm. The pin size is shown in Figure 3(a), where the diameter ϕ = 4 mm, the length L = 30 mm, the impact zone is semi-ellipsoid, and the semi-axis b = 1 mm. In the second model, the arrangement of the pins is shown in Figure 3(b). The interval between two consecutive impacts D is considered to be kept constant.

Figure 3.

Size and arrangement of the pins: (a) single-impact model and (b) multi-impact model.

In the UIT process, the pin endures much less deformation than the specimen, so the pin is defined as rigid body and the specimen is defined as elastic–plastic body. The pin is meshed with C3D4 elements. The specimen is meshed with reduced integration (C3D8R) elements, which is shown in Figure 4, the bottom of it is restrained against all displacements. The mesh near the contact region is refined for numerical accuracy and the mesh for the other region is coarse for saving computation time.

Figure 4.

The cell of the specimen (element: 105000; node: 111631).

The impact velocity of the pins is kept constant to simplify the simulation. Considering the capacity of the UIT machine, the initial velocity of the pin is 2 m/s. In the multi-impact model, the interval between two consecutive impacts is also kept constant, and the “distance” (namely, the height difference) between the two consecutive pins is obtained from the result of the single-impact model. The computation process will be explained in section “Result of single-impact model.” In the multi-impact model, the valid “pin number” (namely, impact times) which plays the most important function in the impact process is also determined.

In the impact process, the friction coefficient between the pin and the specimen is set to be 0.25. Due to the large deformation of elastic–plastic material, material model employed Johnson–Cook model, which can consider the strain rate on material hardening effectively, as expressed by

σ = [A + B {(ε)}^{n}] [1 + C \ln (\frac{\overset{\cdot}{ε}}{{\overset{\cdot}{ε}}_{0}})] [1 - {(\frac{T - T_{0}}{T_{m} - T})}^{m}]

(1)

where $σ$ is the stress to be evaluated; ${\overset{\cdot}{ε}}_{0}$ and $T_{0}$ are the reference values of strain rate and the temperature, respectively; $\overset{\cdot}{ε}$ and $T$ are the strain rate and the temperature under consideration, respectively; and $T_{m}$ is the melting temperature. $A$ , $B$ , $C$ , $m$ , and $n$ are the material constants to be determined. In this work, the effect of temperature is ignored as low temperature change. Therefore, only $A$ , $B$ , $C$ , $m$ , and $n$ are evaluated for the material.

The material for the specimen in the models is 5A06 aluminum alloy, and the chemical composition of the 5A06 aluminum alloy is given in Table 1. The material properties and the Johnson–Cook properties²⁸ are given in Table 2.

Table 1.

Chemical composition of 5A06 aluminum alloy (Wt %).

Grade	Si	Cu	Mg	Zn	Mn	Ti	Be	Fe	Al
5A06	≤0.4	≤0.1	5.8–6.8	≤0.2	0.5–0.8	0.02–0.1	0.0001–0.005	0.0–0.4	Balance

Table 2.

Material properties of 5A06 aluminum alloy.

Density (g/cm³)	Young’s modulus (GPa)	Poisson ratio	$A$ (MPa)	$B$ (MPa)	$C$	$m$	$n$
2.671	69	0.3	168.4	950.5	0.0165	1.0	0.71

Model validation

Due to the high impact frequency in the UIT process, the residual stress distribution by only one impact cannot be obtained by the experiment. Based on the Hertz contact theory, Miao et al.²⁹ indicated that the maximum plastic radius $a_{P}$ in the shot peening process can be described as

a_{P} = R {(\frac{8 ρ v^{2}}{9 σ_{s}})}^{\frac{1}{4}}

(2)

where $R$ is shot radius, $ρ$ is shot density, $v$ is impact velocity, and $σ_{s}$ is the yield stress of specimen. The similar relationships could also be obtained in the UIT process. The numerical model was validated indirectly by the indentation size obtained by the pin drop test. In this test, the impact velocity was 2 m/s and the height was 204 mm. The indentation profiles created on the surface is shown in Figure 5. The indentation diameter measured was 1.141 mm. The simulated indentation diameter for single-impact, as shown in Figure 6, was 1.136 mm. The closeness of the results indicates the accuracy of the numerical model.

Figure 5.

The indentations produced on the target.

Figure 6.

The indentation shapes in the surface zone.

Results and discussions

The effects of impact times, impact velocities, pin diameters, pin lengths, pin shapes, and impact angles on the residual stress distributions were investigated. Table 3 gives the simulations matrix. The residual stress with depth along the vertical axis through the center point of the impact zone is schematically shown in Figure 7, where $d_{p}$ is the penetration depth, $d_{b}$ is the maximum compressive residual stress depth, $σ_{max}^{res}$ is the maximum compressive residual stress, and $σ_{surf}^{res}$ is the surface residual stress. In the context, all residual stress distributions are plotted with the depth along the vertical axis through the center point of the specimen unless otherwise specified.

Table 3.

The controlled parameters of the models.

Parameters	Values
Impact times, N	1–10
Impact velocity, v (m/s)	1, 1.5, 2, 2.5, 3
Pin diameter, ϕ (mm)	3, 4, 5
Pin length, $L$ (mm)	20, 30
Semi-axis of pin tip, $b$ (mm)	1, 2, 3
Impact angle, $θ$ (°)	0, 15

Figure 7.

Important characteristics of typical compressive residual stress profile.

Influence of the impact times

Result of single-impact model

The contact time between the pin and the target was investigated in the single-impact model. The contact time is substituted by the deformation time of specimen. Figure 8 shows the deformation of the center point on the top surface. The jump of the curve shows the process of elastic deformation, elastic–plastic deformation, and the elastic rebound of the specimen. From Figure 8, the contact time is about 0.04 ms.

Figure 8.

Variation of deformation of midpoint of target top surface with time: v = 2 m/s, ϕ = 4 mm, b = 1 mm, and L = 30 mm.

Since the impact frequency between the pin and the target is about 100 Hz, the time interval between two pins is about 10 ms. Taking 2 m/s as the pin velocity, the “distance” between the consecutive pins is 20 mm. However, as the computation time interval is larger than the contact time and the process before the contact is no need to simulate, the distance between every two pins was designed to D = 0.2 mm for the following models.

Result of multi-impact model

Due to the high coverage feature of UIT, a new model was established to simulate the multiple impact process. The model is shown in Figure 2(b). The residual stress profiles for different impact times are shown in Figure 9. $d_{p}$ and $d_{b}$ increased with the impact numbers but $σ_{max}^{res}$ increased with the first three impacts and then decreased slightly. With the increase in the impact times, $d_{p}$ increased from 1.15 to 1.72 mm, $d_{b}$ increased from 0.33 to 0.59 mm, and $σ_{max}^{res}$ increased from 197 to 215 MPa at the third impact and then decreased to 207 MPa for the further impacts. $d_{p}$ , $d_{b}$ , and $σ_{max}^{res}$ did not change linearly with the impact times. The first four impacts took up 80% of the total increase in $d_{b}$ and 70% in $d_{p}$ .

Figure 9.

Effect of impact times upon residual stress distribution along the specimen center line: v = 2 m/s, ϕ = 4 mm, b = 1 mm, and L = 30 mm.

In the impact process, the kinetic energy of pin is converted to elastic and plastic energy in the target. As is known, increasing impact times also increases plastic energy in the target, hence the maximum residual stress increases. But the stress–strain curve is non-linear. The deeper the plastic zone is produced, the more the energy should be provided. With the increase in the plastic zone, it needs to cost more energy to produce further deformation. After the third impacts, the impacted surface has been fully work-hardened. Further impacts cannot increase the maximum compress residual stress but the energy could be transmitted to the deeper zone of the specimen, which leads to the increase in the penetration depth. Meanwhile, the force of the center part of the plastic zone, induced by the surrounding zone, could be reduced by the increase in the plastic zone, so the maximum compress residual stress declines after the third impact. According to the Figure 9, first four impacts almost took up most of the increase for $σ_{max}^{res}$ , $d_{p}$ , and $d_{b}$ . Thus, in order to minimize the calculating time, four pins are chosen for the further analysis.

Due to the expanding of the top surface, $σ_{surf}^{res}$ is produced at the center of the indentation, which is different from the shot peening result. The distributions of the surface residual stress along the X direction are shown in Figure 10. It can also be seen from Figures 9 and 10 that it decreases gradually with the increase in impact times. Kobayashi et al.,³⁰ who dropped the Φ50 mm steel ball onto the 100 mm × 50 mm plate specimen from a height of 2 m, indicated that the tensile residual stress is produced at the center of the indentation; when the other ball is dropped at almost the same point of the first ball, the tensile residual stress is partially produced at the overlapped point. However, the article did not present why the tensile residual stress is produced. To study the phenomenon, the equivalent plastic strain (PEEQ) contour in the Y–Z plane through the specimen center is presented in Figure 11. The maximum plastic strain is produced near the edge of the indentation. The tensile residual stress at the center zone of the top surface is induced by the high strain gradient produced by the different plastic strain. Namely, the phenomenon is induced by the plastic deformation of the surface region. And with the increase in the impacts, the decrease of the strain gradient at the center zone of the indentation induces the decrease of the $σ_{surf}^{res}$ .

Figure 10.

The distributions of the surface residual stress: v = 2 m/s, ϕ = 4 mm, b = 1 mm, and L = 30 mm.

Figure 11.

Equivalent plastic strain (PEEQ) contour for (a) single-impact model and (b) 10-impact model (cutting in the Y-Z plane). The center of the impact zone is marked with the arrow indicated.

Influence of the initial velocity

In the actual UIT experiment, the impact velocity of the pin could be set by adjusting the device amplitude. In the multi-impact UIT model, different initial impact velocities (1, 1.5, 2, 2.5, and 3 m/s) are employed to analyze the residual stress distributions, and the residual stress profiles are shown in Figure 12. Due to the increased kinetic energy of the pin, $d_{p}$ , $d_{b}$ , and $σ_{max}^{res}$ increased with the pin speeds, but $σ_{max}^{res}$ , $d_{b}$ , and $d_{p}$ did not increase linearly due to the non-linearity of the stress–strain curve. Increasing speed from 1 to 1.5 m/s gave 11 MPa increase in $σ_{max}^{res}$ (from 185 to 196 MPa), 0.12 mm increase in $d_{b}$ (from 0.33 to 0.45 mm), and 0.35 mm increase in $d_{p}$ (from 0.95 to 1.30 mm), while increasing speed from 2 to 3 m/s gave 9 MPa increase in $σ_{max}^{res}$ (from 196 to 205 MPa), 0.07 mm increase in $d_{b}$ (from 0.45 to 0.52 mm), and 0.24 mm increase in $d_{p}$ (from 1.30 to 1.54 mm).

Figure 12.

Effect of initial velocity upon residual stress distribution along the center line after four impacts: ϕ = 4 mm, b = 1 mm, and L = 30 mm.

Influence of the pin size

Influence of the pin diameters

In the multi-impact UIT model, three different diameters are chosen; the initial velocity of the pins and the boundary conditions of the specimen are the same as the previous model. The diameters of the pins are 3, 4, and 5 mm, and the curvature of the impact surfaces is invariant.The residual stress against the pin diameters is plotted in Figure 13. It shows that $d_{p}$ , $d_{b}$ , and, $σ_{max}^{res}$ increase with the pin diameter. With the increase in the pin diameter from 3 to 5 mm, $σ_{max}^{res}$ increased by only 13 MPa, and $d_{p}$ and $d_{b}$ increased by 0.52 and 0.23 mm, respectively. Increase in pin diameter will increase the mass, and then it will increase the energy of the impact pin. Furthermore, it will produce deeper plastic zone, higher compressive residual stress, and deeper penetration. Using the pins with different diameters, $σ_{max}^{res}$ did not change significantly but larger pin diameter left bigger indentation which could increase the roughness of the impacted surface. Therefore, it is important to choose a reasonable pin diameter.

Figure 13.

Effect of pin diameter upon residual stress distribution along the center line after four impacts: v = 2 m/s, b = 1 mm, and L = 30 mm.

Influence of the pin length

The residual stress distributions with two different pin lengths (20 and 30 mm) are shown in Figure 14. With the increase in the pin length from 20 to 30 mm, $σ_{max}^{res}$ increased by only 1 MPa, $d_{p}$ increased by 0.22 mm, and $d_{b}$ increased by 0.07 mm. The increase in the pin mass, which also increases the energy input, induces the increase in residual stress, but the increase in residual stress is insignificant.

Figure 14.

Effect of pin length upon residual stress distribution along the center line after four impacts: v = 2 m/s, ϕ = 4 mm, and b = 1 mm.

Influence of the pin tip

In the UIT process, many kinds of pin tips could be chosen, so the effect of the pin tips upon the residual stress is considered. Figure 15 shows the effect of pins (which have the same mass) with three different tip shapes, namely, three semi-axis bs (1, 2, and 3 mm) upon the residual stress. The increase in the semi-axis resulted in an increase in $σ_{max}^{res}$ and a decrease in $d_{p}$ and $d_{b}$ . Figure 16 shows the indentation shapes in the surface zone with different bs. When the semi-axis was large, in which case the elastic and plastic energy is more concentrated in the specimen, indentation shapes were narrow and deep. When the semi-axis was small, the indentation shape was wide and shallow, which induced a low $σ_{max}^{res}$ , a large $d_{p}$ , and a large $d_{b}$ .

Figure 15.

Effect of pin shape upon residual stress distribution along the center line after four impacts: v = 2 m/s, ϕ = 4 mm, and L = 30 mm.

Figure 16.

The indentation shapes in the surface zone with different bs after four impacts: v = 2 m/s, ϕ = 4 mm, and L = 30 mm.

Influence of the impact angle

In the actual UIT process, the pin is not always normal to the specimen surface. Under special conditions, an angle is specified between the pin and the target, as shown in Figure 17. In the multi-impact UIT model, the impact process with pins impacting the target at different incident angles ( $θ$ ) is simulated. In order to obtain the same pin tip curvature at the impact zone, the tip is designed as hemisphere. Figure 18 shows the profile of indentation shapes in the surface zone for 15° incident angle (inclined impact) as compared to that for 0° incident angle (normal impact). The indentation was not symmetric about the center line of the specimen, the right pile-up was 6.11 µm, the left one was 3.21 µm, and the indentation depth was 13.26 µm which was smaller than that for the normal impact. The residual stress distribution was also not symmetric about the center line, as shown in Figure 19(a), and the offset of $σ_{max}^{res}$ is about 0.35 mm. Compared with the normal impact process, as shown in Figure 19(b), the effect of the inclined impact on $d_{p}$ and $d_{b}$ was insignificant, while the effect on the $σ_{surf}^{res}$ is large. From Figure 19(a), $σ_{surf}^{res}$ at the contact zone was compressive residual stress. In the inclined impact process, due to the less constraint, more plastic deformation could be produced at the specimen surface with same energy input, as shown in Figure 20(a). Thus, low strain gradient was produced by the large equivalent plastic strain (PEEQ) at the contact zone of the top surface, and the stress state is changed to compressive stress due to which the surface properties could be improved by adjusting impact angles.

Figure 17.

The schematic diagram of inclined impact process.

Figure 18.

The indentation shapes in the surface zone with different impact angles: v = 2 m/s, ϕ = 4 mm, and L = 30 mm.

Figure 19.

The residual stress contour after (a) 15° oblique impacts and (b) 0° normal impacts (cutting in the X–Z plane). The center of the impact zone is marked with the arrow indicated. v = 2 m/s; ϕ = 4 mm; L = 30 mm.

Figure 20.

Equivalent plastic strain (PEEQ) contour after (a) 15° oblique impacts and (b) 0° normal impacts (cutting in the X–Z plane). The center of the impact zone is marked with the arrow indicated. v = 2 m/s, ϕ = 4 mm, and L = 30 mm.

Conclusion

The 3D explicit models for UIT process with single-impact or multiple-impacts on 5A06 aluminum alloy were developed using ABAQUS/Explicit, which were validated by pin drop test. The simulation results of UIT process showed,

Increase in impact times induces the increase in the depth and magnitude of the compressive residual stress and the decrease in the surface tensile residual stress. The maximum compress residual stress reaches its maximum after the third impact and further increase in impact times offers less effect on it.

Increase in initial velocity, pin diameter, pin length, and pin semi-axis significant increases the penetration depth, the maximum residual stress depth, and the maximum compressive residual stress but the trends are non-linear.

The effect of the inclined impact on the depth and magnitude of the maximum compressive residual stress was insignificant but it can change the surface residual stress from tensile residual stress (normal impact) to compressive residual stress (inclined impact).

Footnotes

Appendix 1 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant No. 51275343).

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Finite element analysis of residual stress evolution with multiple impacts on one point in ultrasonic impact treatment process

Abstract

Keywords

Introduction

FE modeling

Model validation

Results and discussions

Influence of the impact times

Result of single-impact model

Result of multi-impact model

Influence of the initial velocity

Influence of the pin size

Influence of the pin diameters

Influence of the pin length

Influence of the pin tip

Influence of the impact angle

Conclusion

Footnotes

Appendix 1

Declaration of conflicting interests

Funding

References