© Y. Zhang et al., Published by EDP Sciences 2024

1 Introduction

2xxx aluminum alloy is a kind of precipitation hardening high strength aluminum alloy which is widely used in aerospace [1]. Among them, 2219 aluminum alloy is a typical material for rocket storage tanks, and thus it often serves in high temperature and high-pressure environment, which requires the material and its components to have high performance. However, the failure of the component often begins on the surface [2], so it is very important for the component to have good surface integrity. In addition, previous studies have shown that the enhancement of surface properties can improve the comprehensive performance of components [3]. Hence, it is necessary to carry out surface treatment on 2219 aluminum alloy.

Ultrasonic surface rolling process (USRP) is an integration of ultrasonic impact peening (UIP) and deep rolling (DR), which was proposed by Wang et al. in 2008 [4]. At present, scholars indicated that USRP technology can be applied successfully for many materials, such as steel [5], aluminum alloys [6], titanium alloys [7], magnesium alloys [8], high entropy alloys [9], even superalloys [10]. During USRP, the combined action of the static force and ultrasonic vibration on the target material surface imposed by rolling ball tip induces the surface severe plastic deformation (SPD) on the material surface, ultimately resulting in the formation of a gradient nanostructured (GNS) layer of about several hundred micrometers. USRP also can reduce surface roughness of the target material [11], which is attributed to the fact that the plastic flow produced in this process fills the peak of material surface into the trough, that is, peak clipping and valley filling. Moreover, the beneficial residual compressive stress is introduced into the surface of workpieces. John et al. [12] suggested that the repeated high-frequency ultrasonic impact integrated with the static force causes the large elastic and plastic deformation on the material. After removing the dynamic impact force and static force, the elastic deformation tends to recover, but it is limited by the plastic deformation of the surface layer and cannot be restored to the original state, thus forming a residual compressive stress on the surface. Decreasing the surface roughness can inhibit crack initiation [11], and introducing GNS layer and residual compressive stress can suppress crack propagation [13], which makes the material after USRP have superior surface mechanical properties. Accordingly, there has been a surge in research papers on USRP treatment nearly five years mainly including the following aspects—experimental research (microstructure evolution and nanocrystallization mechanism [14], surface integrity [15], tensile [16] and fatigue properties [17], corrosion resistance [18] and so on), analytical modeling and finite element simulation (residual stress [19], plastic strain [20], active forces [21] and even surface morphology and roughness [22]), force control strategy [23].

However, the mechanism of ultrasonic vibration in metal plastic forming is complex, which is more concerned by researchers. Since Blaha and Langenecker [24] found that the flow stress of single zinc crystals was reduced by ultrasonic vibration in 1955, ultrasonic vibration has been superimposed on many traditional processing technologies (such as turning, welding, rolling, extrusion, spinning, micro-forming and so on) as an assisted processing method, and then ultrasonic vibration assisted forming technology has emerged as the times require. Ultrasonic vibration has a special effect on the deformation of metal materials, and shows two common characteristics in different forming processes, namely, the reduction of material deformation resistance and the reduction of contact interface friction [25]. So far, the widely accepted mechanism of ultrasonic vibration on the deformation of metal materials is mainly surface effect and volume effect. The surface effect refers to the reduction of friction force between materials and tools [26], which is a kind of apparent reduction of average friction force in sliding caused by the reversal of friction vector in a cycle [27]. The volume effect refers to the reduction of flow stress of materials when ultrasonic vibration is applied on the tool, but the underlying mechanism of volume effect is still unclear and has been controversial for long years. The ultrasonic-induced stress reduction mainly includes elastic wave-induced stress superposition Δσ_s, and real stress reduction Δσ_r caused by variation of material properties, as shown in Figure 1 [28]. For stress superposition, it is the average stress reduction due to cyclic loading and unloading in ultrasonic frequency, which can be obtained by subtracting the average stress from oscillatory peak stress [29]. In addition, it is considered that no microstructural changes can be caused by stress superposition [30]. Nevertheless, for the real stress reduction, most scholars believed that it is the acoustic softening effect [31]. Regarding the mechanism of acoustic softening, it is currently widely recognized that ultrasonic vibration promotes the evolution of crystal defects such as dislocations and grain boundaries [32]. Hence, it is thought that acoustic softening can change the microstructure and properties of materials.

Furthermore, an important feature of ultrasonic vibration is that the ultrasonic tool can be periodically separated from the surface of the sample. Does this ultrasonic dynamic impact effect affect the plastic deformation of materials? Bai and Yang [33] indicated that thinner and softer materials are more susceptible to vibration during vibration-assisted micro-forming, and the thinner the thickness, the greater the plastic strain caused by vibration. And then, Hu et al. [30] found that the anti-barreling phenomenon in the ultrasonic assisted compression of pure aluminum, and proposed an ultrasonic dynamic impact effect which is different from acoustic softening effect. In another study [28] he showed that with low ultrasonic amplitude, stress reduction contains stress superposition and acoustic softening, which is because vibrated punch contacted with the specimen all the time during compression; However, with higher amplitude, forming stress is further reduced owing to the extra surface plastic deformation by the ultrasonic dynamic impact, after that, the dynamic impact is gradually replaced by the acoustic softening effect. In addition, he confirmed that whether the ultrasonic punch is able to detach from the surface of specimens is the key to the occurrence of ultrasonic dynamic impact effect. According to the above studies, we can conclude that the two critical factors affecting the ultrasonic dynamic impact effect are the thickness of the sample and whether the ultrasonic tool is separated from the sample. Based on the theory of Hu et al. [30], Liu Yang [34] established a criterion for the existence of ultrasonic dynamic impact effect, which is more in line with USRP, and showed that there is ultrasonic dynamic impact effect when the actual static force is less than the critical static force and the actual amplitude is greater than the critical amplitude.

At present, previous studies have shown that compared with conventional surface rolling process (CSRP), USRP can make the material have a smoother surface, a deeper plastic deformation layer, and even a smaller grain size. For example, Cheng et al. [35] indicated that contrasted with conventional thread root rolling (CTRR), the thread specimens after ultrasonic thread root rolling (UTRR) have better surface finish (0.106 µm → 0.051 µm) and deeper microstructure-refined zone (12 µm → 20 µm). Bozdana and Gindy [36] reported that the residual compressive stress layer obtained by ultrasonic deep cold rolling (UDCR) at 380 N static force is deeper than that obtained by conventional deep cold rolling (CDCR) at 726 N static force, which means a deeper plastic deformation layer can be obtained with a smaller static force in the ultrasonic-assisted rolling process. Generally speaking, the decrease of surface roughness is attributed to the friction reduction between ultrasonic tool and specimens caused by the ultrasonic vibration-induced surface effect. For the increase of plastic deformation layer, some scholars thought that it is acoustic softening in the ultrasonic volume effect, such as Huang et al. [37] and Li et al. [25]. Liu Yang [34] indicated that there is ultrasonic dynamic impact effect in the process of copper strip treated by USRP, which leads to greater plastic strain of the material. Nevertheless, the thickness of copper strip in the above study is only few hundreds micron, thus it is not possible to judge whether ultrasonic vibration causes extra plastic deformation in thicker materials.

This study aims to enhance our understanding of the effect of ultrasonic vibration on the plastic deformation of materials during USRP, particularly the ultrasonic dynamic impact effect. To this purpose, the surface rolling finite element (FE) model of 2219 aluminum alloy with and without ultrasonic vibration was established, and the effect of ultrasonic vibration on plastic deformation was discussed based on FE simulation and experimental research. Moreover, their contribution of static force F_s and dynamic impact force F_d to plastic deformation of materials were clarified by comparing the plastic strain of 2219 aluminum alloy under different static force F_s and different dynamic impact force F_d. The findings of our work can provide new insight into the ultrasonic dynamic impact effect during USRP, and further clarify the role of ultrasonic vibration in USRP.

Fig. 1 Schematic diagram of stress reduction due to ultrasonic excitation.

2 Material and methods

2.1 Material and experimental procedures

The extruded 2219 aluminum alloy tube blank with the inner diameter of Φ200 mm and the thickness of 5 mm was used in this work. The main chemical composition of 2219 aluminum alloy was listed in Table 1.

The USRP tests were carried out on the CZ900/2CNC horizontal CNC spinning machine (Fig. 2a). Its schematic illustration was shown in Figure 2b. USRP executive system includes three parts − ultrasonic control cabinet, air compressor and ultrasonic tool assembly. The ultrasonic control cabinet consists of ultrasonic generator and cooling lubrication system to drive and cool the ultrasonic tool assembly. The air compressor drives the pneumatic slider of the ultrasonic tool assembly, resulting in providing the static force on the workpiece surface. The ultrasonic tool assembly consists of a transducer, a horn and a tool tip, where the tool tip is a freely revolving WC ball of 7 mm in radius. The transducer converts ultrasonic energy into high-frequency vibration, and then amplifies the amplitude through the horn to drive the tool tip to impact the workpiece surface with ultrasonic frequency.

Before USRP, the extruded 2219 aluminum alloy tube blank was manufactured into tube specimens with a thickness of 3 mm and a length of 150 mm, and then subjected to solution heat treatment (535 °C, 2 h). During USRP, the selection of ultrasonic frequency and amplitude is critically important. For ultrasonic frequency, Liu et al. [38] revealed that with the increase of frequency (20–30 kHz), the residual stress and equivalent plastic strain (PEEQ) both increase continuously. However, Zhao et al. [39] investigated the ultrasonic frequency effects on surface deformation in rotary ultrasonic roller burnishing Ti alloy, and pointed out that the residual compressive stress could reach the maximum value when the frequency up to 26 kHz, and above this threshold, the residual stress would decrease. Additionally, von Mises stress showed an increasing tendency with the increase of frequency, but the high von Mises stress was not conductive to the burnishing process. Thus, they indicated that the frequency with 26 kHz was the level off point. Based on the above studies, the excitation frequency (f) of ultrasonic generator was set to 27kHz in this work. For ultrasonic amplitude, many scholars indicated that residual stress and strain gradually increase with the increase of amplitude, such as Liu et al. [38] and Teimouri et al. [40], but the excessive amplitude can lead to too large deformation of materials, resulting in the decrease of surface quality and dimensional accuracy of the component. Therefore, the ultrasonic amplitude of 10 µm is selected. Other main parameters were shown in Table 2, such as static force (F_s), spindle speed, feed rate, processing pass and so on.

The cross-sectional hardness of 2219 aluminum alloy sample was measured by LECO micro/macro automatic hardness testing system with a load of 25 gf for a dwell time of 10s. During microhardness test process, the indentation spacing along the depth direction was about 50 µm, and the measurement depth was approximately 2.8 mm. Location diagram of hardness measuring point was shown in Figure 3. The surface morphologies and roughness of 2219 aluminum alloy before and after USRP and CSRP were obtained by the Bruker Contour GT-K three-dimensional optical profilometer based on scanning white light interferometry. In addition, the scanning area was 1.9 mm × 2.5 mm.

Fig. 2 USRP experiment image of aluminum alloy: (a) experimental device; (b) the schematic illustration of ultrasonic executive system.

Fig. 3 Location diagram of hardness measuring point.

2.2 Finite element modeling of USRP

A two-dimensional finite element (FE) models of USRP on 2219 aluminum alloy was established using ABAQUS/Explicit in this study. By comparing and analyzing the simulation results of static force only and static force combined with dynamic impact force, the effect of ultrasonic vibration on plastic deformation in USRP is discussed. According to the simulation results under different static force and dynamic impact force, we try to find out the contribution of static force and dynamic impact force.

2.2.1 Geometrical model and meshing

Compared with 2219 aluminum alloy, the WC ball was almost not deformed during USRP, so it was regarded as an analytical rigid body when modeling. In order to facilitate meshing and save solution time, the arc section of 2219 aluminum alloy was simplified to a flat section. Thus, the geometrical dimensions of 2219 aluminum alloy was set to the thickness of 3 mm and the length of 18 mm. The surface-to-surface contact was set between the WC ball and 2219 aluminum alloy, and the friction coefficient (μ) was 0.15.

During USRP, the severe plastic deformation occurs mainly in the near surface (∼hundreds of microns) of materials, so the near surface needs to be meshed into particularly fine elements. For this reason, the multi-level transitional mesh method was used to mesh the target material in this paper. Since the minimum size and number of elements also have significant influence on the solution time, it is extremely important to determine the minimum size of elements. Bagherifard et al. [41] indicated that for the target workpiece, the computational results gained good convergence when the element size of impact zones was set as one twentieth of dimple diameter. Liu et al. [42] pointed out that when the element size was one-ten of dimple diameter, elements located in the center of contact appeared the hourglass mode after 2 repeated processing times during USRP, which was because the element size was not fine enough. Hence, they selected smaller element size (20 µm) and obtained stable simulation results. Based on the above researches, the minimum dimension of elements was determined to be 10 µm in our simulation work. Furthermore, the element type was set to four-node bilinear plane stress reduced integration (CPS4R) elements. The geometrical model and meshing in the process of USRP are shown in Figure 4.

Fig. 4 Two-dimensional FM model of USRP on 2219 aluminum alloy: (a) geometrical model; (b) meshing.

2.2.2 Material model

Johnson-Cook (J-C) constitutive model, considering the effect of flow stress and strain, strain rate, and temperature, is the most widely used constitutive model in impact dynamics. During USRP, 2219 aluminum alloy tube underwent high frequency dynamic impact, so the J-C constitutive model was selected as the material model. The J-C equation has been expressed in equation (1).

$$\sigma =\left(A+B{\epsilon }^n\right)\left(1+C\ln \frac{{\displaystyle \dot{\epsilon }}}{{\displaystyle \dot{{\epsilon }_0}}}\right)\left[1-{\left(\frac{T-T_{room}}{T_{melt}-T_{room}}\right)}^m\right]$$(1)

where A is the yield stress; B is the strain hardening coefficient; C is the strain rate constants; n denotes strain hardening index; m is thermal softening index; ${\displaystyle \dot{\epsilon }}$ and ${{\displaystyle \dot{\epsilon }}}_0$ represent the strain rate and reference strain rate (${{\displaystyle \dot{\epsilon }}}_0$ = 1), respectively. Mohsen et al. [43] pointed out the temperature rise is less than 40°C during USRP, thus the effect of temperature was ignored in the simulation, that is, the last term of J-C equation was not considered. The material properties of 2219 aluminum alloy and the material constants of J-C constitutive model are listed in Table 3.

2.2.3 Load and boundary conditions

As is well known, the target material is subjected to the combined action of static force and ultrasonic vibration displacement applied through the ball tip during USRP. However, for FE simulation by using ABAQUA software, it is incompatible to exert both force and displacement in the same direction, which indicates the amplitude of ultrasonic vibration cannot be expressed by displacement. Therefore, it is necessary to equivalent the amplitude to the dynamic force amplitude (F_d) or the static force to a certain displacement. In general, the expression of the dynamic impact force (F_n) between the tool tip and target material is as follows:

$$F_n=F_s+F_d\sin \left(2\pi ft\right).$$(2)

For the F_d, Liu et al. [45] and Wang Feng [46] measured it based on the piezoelectric sensor principle, and Tang et al. [47] calculated it based on the dynamic force calculation method proposed by Zhang et al. [48] and Teimouri et al. [20], as shown in Figure 5. From this figure, it can be seen that the F_d is linear with the F_s when the frequency and amplitude of ultrasonic vibration are constant. The relationship between the F_d and the F_s is fitted under the ultrasonic vibration conditions used in this work, which is expressed as formula (3).

$$F_d=0.163F_s+124.23.$$(3)

In addition, fixed constraints were set at the bottom and left side of 2219 aluminum alloy. In simulation process, the movement speed of the ultrasonic ball was equivalent to the linear speed of outer diameter of 2219 aluminum alloy tube during the experiment, which was about 330mm/s.

Fig. 5 The dynamic impact force measured by Liu et al. [45], Wang Feng [46] and calculated by Tang et al. [47].

3 Results

3.1 Model verification

In order to verify the accuracy and effectiveness of the model, the size of ultrasonic impact dimple was calculated based on the single point impact model and compared with the experimental results, as shown in Figure 6. Figure 6a provides the distribution of equivalent plastic strain (PEEQ) along Path1 of 2219 aluminum alloy after ultrasonic single point impact. It can be seen from this figure that the diameter of ultrasonic impact dimple is about 1.72 mm. The surface morphology of aluminum alloy after USRP2 and the surface profile along Path2 are showed in Figure 6b, we can find that the distance between the two peaks is close to 1.62 mm, which indicates that the dimple diameter measured in experiment is about 1.62 mm. The error between simulation results and experiment results is roughly 6%, which is within the acceptable range, indicating that the model established in this work has certain reliability.

Fig. 6 The size of ultrasonic impact dimple: (a) simulation results—the influence zone of plastic deformation of 2219 aluminum alloy after ultrasonic single point impact and PEEQ distribution along Path1; (b) experimental results—surface morphology of 2219 aluminum alloy after USRP2 and surface profile along Path2.

3.2 The comparison of simulation results with and without dynamic impact force

3.2.1 The effect of dynamic impact force F_d on the thickness reduction

Figure 7 provides the displacement variation of ultrasonic ball with the time when the dynamic impact force F_d is applied or not. According to equation (3) in Section 2.2.3, it can be calculated the dynamic impact force F_d under ultrasonic vibration conditions used in our work is approximately 190 N. One can find from Figure 7 that when only 400 N static force is applied, the downward displacement of ultrasonic ball is about 67.69 µm, and the ball does not produce periodic motion in the depth direction. After applying the dynamic impact force F_d, the displacement of the ball presents a sine function, the equilibrium position is near −68.17 µm, the amplitude is ∼0.3 µm. In particular, the value of dynamic impact force F_d used in simulation is based on the experiments (ultrasonic frequency of 27 kHz, ultrasonic amplitude of 10 µm, static force of 400 N), but the amplitude obtained by simulation is just 0.3 µm, which is far from the experiments, indicating that the actual amplitude during the experiment does not reach the set value of 10 µm. Therefore, the problem that there is a big gap between the actual amplitude and the set amplitude still needs to be further reconciled. Moreover, in comparison to without dynamic impact force F_d, the displacement is merely increased by 0.48 µm, the increasing amount is less than 1%, which indicates that the addition of ultrasonic vibration has no obvious effect on the thickness reduction of materials.

Fig. 7 The displacement variation of ultrasonic ball with the time: (a) comparison between applying static force Fs only and applying static force Fs + dynamic impact force Fd; (b) enlarged view of the selected region in figure (a).

3.2.2 The effect of dynamic impact force F_d on the plastic strain

The distribution of plastic strain and its components of 2219 aluminum alloy in depth and horizontal direction under the condition of 400 N static force F_s and 190N dynamic impact force F_d is provided in Figure 8. As shown green curves in Figures 8a and 8b, the PEEQ is gradient distribution in the depth direction, and the maximum value of PEEQ appears on the top surface of the material, nearly 0.2. when the depth is ∼1.251 mm, the value of PEEQ is 0, which illustrates that the thickness of plastic deformation layer is close to 1.251 mm. In addition, according to the distribution curves of plastic strain components (PE11-the principal strain of X direction, PE22-the principal strain of Y direction, PE33-the principal strain of Z direction, PE12-shear strain), it can be inferred that 2219 aluminum alloy is subjected to the compressive strain in Y direction (Radial direction of 2219 Al tube), the tensile strain in Z direction (Axial direction of 2219 Al tube), and the shear strain during USRP.

Figure 9 provides the distribution of PEEQ and PE12 along the horizontal direction with and without dynamic impact force F_d. Figures 9b and 9c are enlarged images of region 1 and region 2 in Figure 8a, respectively. From Figure 8b, we can find that the distribution curve (green dotted line) of PEEQ on the top surface of 2219 aluminum alloy along the horizontal direction is relatively straight without the dynamic impact force, and PEEQ value is about 0.1955. After the dynamic impact force is applied, the curve (green solid line) of PEEQ is fluctuant, and PEEQ mid value is about 0.197. By contrasting the PEEQ value, it can be found that the introduction of dynamic impact force makes the PEEQ increase slightly, but the increase is less than 1%. Under the condition of applying 400N static force+190N dynamic impact force, the PE12 mid value is approximately 0.1017, which is almost equal to the PE12 value under the condition of applying 400 N static force, as shown in Figure 9c. The undulant plastic strain (green and red solid line in Fig. 9) on the surface means that the distribution of plastic strain on the surface of materials is changed due to introducing the ultrasonic vibration.

The distribution of PEEQ and PE12 along the depth direction with and without dynamic impact force is illustrated in Figure 10. From this figure, we can find that introducing 190 N dynamic impact force can slightly increase the thickness of plastic deformation layer of 2219 aluminum alloy (from 1.219 mm to 1.251 mm). In contrast to without dynamic impact force, the thickness of plastic deformation layer is lifted by ∼2.6%. Moreover, when the distance from the top surface is below ∼0.4 mm, the 2219 aluminum alloy is subjected to shear deformation. In the range of 0.4–1.25 mm, the material is mainly compressive strain in Y direction and tensile strain in Z direction. Although the dynamic impact force of 190N is superimposed on the static force, the distribution of plastic strain along the depth is almost coincident with that without dynamic impact force. This result shows that the occurrence of material's deformation during USRP is mainly caused by static force.

Fig. 8 The distribution of PEEQ and plastic strain components along the depth and horizontal direction after USRP: (a) depth direction; (b) horizontal direction.

Fig. 9 The distribution of PEEQ and PE12 along the horizontal direction under the condition of applying and not applying dynamic impact force Fd: (a) the horizontal direction; (b) enlarged view of region 1 in figure (a); (c) enlarged view of region 2 in figure (a).

Fig. 10 The distribution of PEEQ and PE12 along the depth direction under the condition of applying and not applying dynamic impact force Fd.

3.3 The effect of static force and dynamic impact force on plastic deformation

3.3.1 The simulation results under different static force

Under the different static force, the variation of ultrasonic ball displacement with the time is illustrated in Figure 11a. In comparison to 400 N static force, the displacement in Y direction of ultrasonic ball under 590 N static force is obviously improved (from 67.5 µm to131 µm), which is increased by about 94.07%. From the distribution of PEEQ along the depth direction (green curves in Fig. 11b), when the static force is enhanced from 400N to 590N, the thickness of plastic deformation layer is increased from ∼1.219 mm to ∼1.932 mm, an increase of about 58%. Furthermore, we can find from the green column plot in Figure 11b that the increment of PEEQ increases first and then decreases with increasing in the depth. Combined the red column plot with the green column plot, it can be seen that in the range of 150 µm from the top surface, the increase of PEEQ is caused by the joint increase of shear strain PE12, compressive strain in Y direction (PE22) and tensile strain in Z direction (PE33), and the increase of PE12 is dominant. However, with the further increase of depth, the increment of PE12 is gradually reduced, leading to that the increase of PEEQ is gradually dominated by the increase of PE22 and PE33. Figure 11c provides the comparison of PEEQ and plastic strain components (PE11, PE22, PE33, PE12) at different static force. When the static force is increased to 590 N from 400 N, the value of PE11 is almost unchanged and close to 0, which means that the material has almost no elongation in the X direction. The reason for this phenomenon is that the thinning amount of the material is relatively small during USRP or CSRP. Except for PE11, the other components have increased, such as PE22 increased by 37.05%, PE33 increased by 34.47% and PE12 increased by 40.61%, eventually leading to an increase in PEEQ. When the static force is enhanced from 400 N to 590 N, the PEEQ on the surface of 2219 aluminum alloy is of ascension by about 39.13%.

When the dynamic impact force of 190 N is superimposed, the extra plastic deformation of 2219 aluminum alloy is less than 1%, but when the static force of 190 N is added, the additional plastic deformation is close to 40%. Accordingly, we can conclude that the effect of the static force on plastic deformation of materials is far greater than that of the dynamic impact force.

Fig. 11 The effect of static force on the thickness reduction and the plastic strain of 2219 aluminum alloy: (a) the variation of ultrasonic ball displacement with the time; (b) the distribution of plastic strain along the depth direction; (c) the comparison of plastic strain at different static force.

3.3.2 The simulation results under different dynamic impact force

The displacement in Y direction of ultrasonic ball at different dynamic impact force is shown in Figure 12a. The thickness reduction of 2219 aluminum alloy is gradually increased with increasing in the dynamic impact force, and there is a quadratic nonlinear relationship between thickness reduction and dynamic impact force. The amplitude of ultrasonic ball is linearly added with the increase of the dynamic impact force, as shown in purple curve in Figure 12a. Theoretically, there is a certain relationship between the maximum dynamic impact force of ultrasonic vibration and the amplitude, which can be expressed as equation (4). Since the m and f in equation (4) are constant, the dynamic impact force is linearly related to the amplitude of ultrasonic vibration, which further reflects the accuracy of force loading model in our paper. However, this also reflects indirectly a problem, that is, the actual measured dynamic impact force is of greatly difference from the theoretical dynamic impact force.

$$F_{dmax}=m{A}_u{\omega }^2=m{A}_u{\left(2\pi f\right)}^2$$(4)

where m is the mass of ultrasonic ball; A_u is the amplitude of ultrasonic vibration; ω is circular frequency; f is the frequency of ultrasonic vibration.

The red line in Figure 12b shows the relationship between dynamic impact force and maximum PEEQ, maximum PE12. It can be seen that the plastic strain (PEEQ, PE12) is nonlinearly related to the dynamic impact force, and when the dynamic impact force is lower than 1000 N, the variation of plastic strain is extremely small, particularly PE12. Moreover, the thickness of plastic deformation layer is also enhanced linearly with the increase of the dynamic impact force. In contrast of PEEQ value at 590 N static force, we can find that on the basis of 400 N static force, the dynamic impact force of nearly 3500 N is added to achieve the PEEQ value of 590 N static force; For PE12, it is necessary to superimpose a dynamic impact force nearly 5000 N. When the dynamic impact force of ∼4650 N is superimposed on the static force of 400 N, the thickness of plastic deformation layer can be consistent with the static force of 590 N. This further illustrates that in the process of USRP, the influence of static force on plastic deformation of 2219 aluminum alloy is greater than that of dynamic impact force.

Fig. 12 The effect of dynamic impact force on the thickness reduction and the plastic strain of 2219 aluminum alloy: (a) the displacement and the amplitude of ultrasonic ball in Y direction; (b) plastic strain and thickness of plastic deformation layer.

4 Discussion

4.1 The contribution of static force and dynamic impact force in USRP

According to the simulation results of 400 N static force + 190 N dynamic impact force (actual measured value) and 400 N static force + 5750 N dynamic impact force (theoretical calculated value), the contributions of static force and dynamic impact force to the plastic strain (such as PEEQ, PE12) and the thickness of plastic deformation layer of 2219 aluminum alloy were calculated respectively, as shown in Figure 13. When the dynamic impact force of 190 N is superimposed, for the plastic strain, the contribution of ultrasonic vibration is less than 1%; for the thickness of plastic deformation layer, the contribution of ultrasonic vibration is ∼2.6%. When the dynamic impact force of 5750 N is added, the contribution ratio of ultrasonic vibration to plastic strain can reach more than 35%, the contribution to the thickness of plastic deformation layer is nearly 43%. But in general, the contribution of static force to plastic deformation of 2219 aluminum alloy is larger than that of dynamic impact force. Therefore, the plastic deformation of materials is dominated by static force during USRP.

Due to the large difference between the actual measured value and the theoretical calculated value of dynamic impact force, the contribution of ultrasonic vibration to plastic deformation needs to be further evaluated. To this end, we tested and analyzed the hardness of the cross-section of 2219 aluminum alloy tube after USRP and CSRP, as shown in Figure 14. Figure 14a provides the hardness variation of 2219 aluminum alloy after USRP and CSRP with the depth. From Figure 14a, with increasing in the depth, the hardness difference between USRP and CSRP decreases gradually, which is due to the continuous attenuation of ultrasonic energy in depth direction. Moreover, observing the green curve in Figure 14a, we can see that when the depth exceeds 824 µm, the microhardness value is basically unchanged, maintaining at 113.47 HV, which indicates that the thickness of plastic deformation layer of 2219 aluminum alloy after USRP can reach 824 µm. According to the orange curve in Figure 14a, we can find that the thickness of plastic deformation layer after CSRP is ∼779 µm. The results shows that the influence range of ultrasonic vibration can arrive at ∼824 µm. In contrast to CSRP, the thickness of plastic deformation layer after USRP is increased by about 5.8%. By calculation, the contribution of ultrasonic vibration to the thickness of plastic deformation layer is ∼5.5% (Fig. 14b). Figure 14c provides the comparison of microhardness on the top surface of 2219 aluminum alloy after USRP and CSRP and the contribution of static force and dynamic impact force to the microhardness. After adding the ultrasonic vibration, the microhardness on the top surface is improved to 155HV from 136HV, which is increased by nearly 14%. For the microhardness, the contribution ratio of the ultrasonic vibration can reach 43.4%. The reason why the surface hardness of two methods has larger difference is the results of multi-pass accumulation.

Based on the above discussion, we can conclude that for the thickness of plastic deformation layer, the contribution of dynamic impact force and static force is about 5.5% and 94.5%, respectively. According to the relationship between the thickness of plastic deformation layer and dynamic impact force in Figure 12b, it can be seen that if the contribution ratio of dynamic impact force to the thickness of plastic deformation layer reaches 5.5%, the dynamic impact force should be about 420N. Therefore, the real value of dynamic impact force is closer to the measured value in the USRP process, which indicates that the amplitude of ultrasonic ball acting on the material surface does not reach the set value of 10 µm.

Fig. 13 The contribution of static force and dynamic impact force when the actual measured dynamic impact force and theoretical calculated dynamic impact force are superimposed on the 400N static force.

Fig. 14 Analysis of microhardness tests of 2219 aluminum alloy after USRP and CSRP: (a) the distribution of microhardness along the depth direction; (b) the contribution of ultrasonic vibration to the thickness of plastic deformation layer; (c) the contribution of ultrasonic vibration to the microhardness on the top surface.

4.2 Whether the ultrasonic ball is detached from the material in USRP?

Hu et al. [27] proposed a criterion for whether the ultrasonic tool head can detach from the workpiece periodically, which is whether the two times of ultrasonic amplitude exceeds the amount of elastic spring-back (σ_0.2H/E), that is, the critical amplitude can be calculated as follows:

$$A_{critical}=\frac{{\sigma }_{0.2}H}{2E}$$(5)

where σ_0.2 means the yield stress, H is the thickness of specimen, E is the Young's modulus of material. Figure 15 shows that the variation for the displacement of a node on the top surface of 2219 aluminum alloy with the time. It can be seen from this figure that the amount of elastic spring-back of 2219 aluminum alloy is about 6.5 µm. As a result, the critical amplitude can be calculated by equation (5), which is 3.25 µm. According to the formula (4), we can calculate the dynamic impact force is approximately 1869N when the ultrasonic amplitude is 3.25 µm. Nevertheless, based on the discussion in Section 4.1, the actual dynamic impact force imposed on 2219 aluminum alloy is ∼400 N during USRP. At this time, the amplitude of ultrasonic ball can arrive at 0.7 µm, which is far smaller than the critical amplitude. Hence, the ultrasonic ball is not detached form 2219 aluminum alloy tube in USRP process.

In addition, to further verify the contact between the ultrasonic ball and the material, we also analyzed the contact stress between ultrasonic ball and the material under different amplitude in an ultrasonic period, as shown in Figure 16. From this figure, it can be seen that when the ultrasonic amplitude exceeds 4 µm, there is a section of time when the contact stress is 0 MPa in one ultrasonic period, which indicates that ultrasonic ball detaches from the material surface. This amplitude also is close to the critical amplitude. However, the actual amplitude during USRP is far less than 4 µm based on the discussion in Section 4.1. This result is consistent with that of the force boundary condition.

Fig. 15 The variation for the displacement of a node with the time.

Fig. 16 In an ultrasonic period and at different ultrasonic amplitudes, the contact between the ultrasonic ball and the material: (a) 2 µm; (b) 4 µm; (c) 6 µm; (d) 8 µm; (e) 10 µm.

4.3 The role of ultrasonic vibration on plastic deformation in USRP

Generally speaking, ultrasonic vibration can reduce the surface roughness of materials, which is attributed to the reduction of friction induced by surface effect. In this study, the consistent phenomenon is discovered, as shown in Figure 17. Before CSRP and USRP, 2219 aluminum alloy was turned to remove the surface oxide layer produced by solid solution treatment, resulting in the ploughing scratches with a period of 0.22 mm on the surface (Fig. 17a). Moreover, Ra of turned surface is 2.565 µm (Fig. 18). Figure 17b shows the surface morphology of 2219 aluminum alloy after CSRP, and combined this figure with Figure 18, we can find that the surface roughness Ra after CSRP is reduced, but obvious turning marks can still be seen on the surface. In contrast to the initial surface, the roughness after CSRP decreases by 77.04%, and is about 0.589 µm. After USRP, the ploughing morphology on the surface disappears obviously, but ultrasonic rolling traces still exist on the surface, as shown in Figure 17c. At this time, the surface roughness is about 0.558 µm. Compared to the turned surface, the Ra after USRP is reduced by 78.25%, but in comparison to the surface after CSRP, the Ra value is dropped by 5.26% only. This result indicates that the contribution of ultrasonic vibration to the reduced amount of surface roughness Ra is extremely small, and it is ∼1.5%. Combined with the discussion of Section 4.1, during USRP, the influence of ultrasonic vibration on the material is far lower than that of static force.

Since the introduction of ultrasonic vibration will reduce the friction between ultrasonic tool tip and workpiece, thereby dropping the surface roughness, can the reduction of friction lead to extra plastic deformation on the near surface? Figure 19a provides the distribution of PEEQ along horizontal direction under different friction coefficient. It can be seen from this figure that the mid value of PEEQ rises slightly with the decrease of the friction coefficient. At the same time, when the friction coefficient is 0.1, the fluctuation of PEEQ value is largest, as shown in Figure 19b. The above results indicate that the decrease of friction coefficient is expected to produce slightly larger plastic deformation on the near surface, but it is not the smaller the friction coefficient, the greater the plastic deformation. Therefore, in USRP process, the surface effect of ultrasonic vibration slightly contributes to the plastic deformation on the near surface, but does not increase the thickness of plastic deformation layer. To sum up, the surface effect is existent in the process of USRP based on the simulation and experiment results, but its influence is minimal for plastic strain.

Fig. 17 Surface morphologies at different processing method: (a) initial surface; (b) the surface after CSRP10; (c) the surface after USRP10.

Fig. 18 Surface roughness at different processing method.

Fig. 19 The influence of friction coefficient on the PEEQ: (a) the distribution of PEEQ along the horizontal direction under different friction coefficient; (b) under different friction coefficient, the PEEQmean and the fluctuation of PEEQ.

5 Conclusions

In this study, the effect of ultrasonic vibration on plastic deformation of 2219 aluminum alloy tube was explored by comparing the FE simulations with and without dynamic impact force. The thickness reduction and the distribution of plastic strain at different values of static force and dynamic impact force were investigated to analyze their effect on plastic deformation. In addition, combined with experiment, the role of ultrasonic vibration was discussed. The main conclusions are summarized as follows:

• During USRP, the actual ultrasonic dynamic impact force is far lower than the value of theoretical calculation. Moreover, the actual ultrasonic amplitude acted on the material is less than the critical amplitude required to detach from the surface of the material, which means the ultrasonic ball is always in contact with 2219 aluminum alloy tube.

• From the FE simulation, in contrast to without dynamic impact force, the increment of plastic strain with dynamic impact force is less than 1%, and the thickness of plastic deformation layer is lifted by ∼2.6%. According to the hardness experiments, the thickness of plastic deformation layer is increased by about 5.8%. Therefore, ultrasonic vibration plays an infinitesimal role in plastic deformation. In addition, the reasons for the difference between the simulation and experiment results may be the effect of temperature and friction.

• Compared to CSRP, the turning marks on the initial surface are obviously eliminated after superimposing ultrasonic vibration, and the roughness also is decreased by ∼5.26%. This result shows that the role of ultrasonic vibration is mainly concentrated on the material's surface.

• When the static force rises by 47.5%, from 400N to 590N, the thickness of plastic deformation layer, PEEQ, and plastic strain components are all increased obviously, more than 35%. However, simulation results indicate that to achieve the same degree of plastic strain as 590N static force, the dynamic impact force needs to be improved by about 17 times; to achieve the same thickness of deformation layer, the dynamic impact force needs to be lifted by nearly 25 times. Thus, the influence of static force on plastic deformation is much higher than that of dynamic impact force.

• According to the results of experiment and simulation, the contribution ratio of ultrasonic vibration to the thickness of plastic deformation layer is about 5.5%, while the contribution of static force can reach nearly 95%. This indicates that static force dominates the plastic deformation.

Acknowledgments

The authors would like to gratefully acknowledge the support of National Natural Science Foundation of China (Grant number: 52130507; Grant number: 52122509).

Funding

This work was financially supported by the National Natural Science Foundation for Key Program of China (Grant number: 52130507) and the National Natural Science Foundation for Outstanding Young Scholars of China (Grant number: 52122509).

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

The datasets supporting the conclusions of this article are included within the article.

Author contribution statement

YuanQi Zhang: Experiment, Analysis and Writing—original draft preparation; Mei Zhan: Supervision, Resources and Writing—review and editing; Xiaoguang Fan: Conceptualization, Methodology, Resources and Writing—review and editing; All authors read and approved the final manuscript.

References

All Tables

All Figures

	Fig. 1 Schematic diagram of stress reduction due to ultrasonic excitation.
In the text

	Fig. 2 USRP experiment image of aluminum alloy: (a) experimental device; (b) the schematic illustration of ultrasonic executive system.
In the text

	Fig. 3 Location diagram of hardness measuring point.
In the text

	Fig. 4 Two-dimensional FM model of USRP on 2219 aluminum alloy: (a) geometrical model; (b) meshing.
In the text

	Fig. 5 The dynamic impact force measured by Liu et al. [45], Wang Feng [46] and calculated by Tang et al. [47].
In the text

	Fig. 6 The size of ultrasonic impact dimple: (a) simulation results—the influence zone of plastic deformation of 2219 aluminum alloy after ultrasonic single point impact and PEEQ distribution along Path1; (b) experimental results—surface morphology of 2219 aluminum alloy after USRP2 and surface profile along Path2.
In the text

	Fig. 7 The displacement variation of ultrasonic ball with the time: (a) comparison between applying static force Fs only and applying static force Fs + dynamic impact force Fd; (b) enlarged view of the selected region in figure (a).
In the text

	Fig. 8 The distribution of PEEQ and plastic strain components along the depth and horizontal direction after USRP: (a) depth direction; (b) horizontal direction.
In the text

	Fig. 9 The distribution of PEEQ and PE12 along the horizontal direction under the condition of applying and not applying dynamic impact force Fd: (a) the horizontal direction; (b) enlarged view of region 1 in figure (a); (c) enlarged view of region 2 in figure (a).
In the text

	Fig. 10 The distribution of PEEQ and PE12 along the depth direction under the condition of applying and not applying dynamic impact force Fd.
In the text

	Fig. 11 The effect of static force on the thickness reduction and the plastic strain of 2219 aluminum alloy: (a) the variation of ultrasonic ball displacement with the time; (b) the distribution of plastic strain along the depth direction; (c) the comparison of plastic strain at different static force.
In the text

	Fig. 12 The effect of dynamic impact force on the thickness reduction and the plastic strain of 2219 aluminum alloy: (a) the displacement and the amplitude of ultrasonic ball in Y direction; (b) plastic strain and thickness of plastic deformation layer.
In the text

	Fig. 13 The contribution of static force and dynamic impact force when the actual measured dynamic impact force and theoretical calculated dynamic impact force are superimposed on the 400N static force.
In the text

	Fig. 14 Analysis of microhardness tests of 2219 aluminum alloy after USRP and CSRP: (a) the distribution of microhardness along the depth direction; (b) the contribution of ultrasonic vibration to the thickness of plastic deformation layer; (c) the contribution of ultrasonic vibration to the microhardness on the top surface.
In the text

	Fig. 15 The variation for the displacement of a node with the time.
In the text

	Fig. 16 In an ultrasonic period and at different ultrasonic amplitudes, the contact between the ultrasonic ball and the material: (a) 2 µm; (b) 4 µm; (c) 6 µm; (d) 8 µm; (e) 10 µm.
In the text

	Fig. 17 Surface morphologies at different processing method: (a) initial surface; (b) the surface after CSRP10; (c) the surface after USRP10.
In the text

	Fig. 18 Surface roughness at different processing method.
In the text

	Fig. 19 The influence of friction coefficient on the PEEQ: (a) the distribution of PEEQ along the horizontal direction under different friction coefficient; (b) under different friction coefficient, the PEEQmean and the fluctuation of PEEQ.
In the text