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Finite element analysis of the effect of the controlled parameters on plate forming induced by ultrasonic impact forming (UIF) process
Applied Surface Science 353 (2015) 382–390
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Finite element analysis of the effect of the controlled parameters on plate forming induced by ultrasonic impact forming (UIF) process Guo Chaobo, Hu Shengsun, Wang Dongpo, Wang Zhijiang ∗ Tianjin Key Laboratory of Advanced Joining Technology, School of Materials Science and Technology, Tianjin University, Tianjin, 300072, China
a r t i c l e
i n f o
Article history: Received 11 May 2015 Received in revised form 15 June 2015 Accepted 16 June 2015 Available online 24 June 2015 Keywords: Ultrasonic Impact Forming model Non-uniform residual stress Deformation
a b s t r a c t A three-step numerical model was used to simulate the Ultrasonic Impact Forming (UIF) process using non-uniform residual stress distributions within target plates. A nearly single curvature deformation was obtained by simulating the strip deformation process using different impact trajectories. The influence of the controlled parameters on the arc height and radius of curvature of the strips was investigated by analysing the non-uniform residual stress distributions. Increasing the pin velocity, and decreasing the device moving velocity and offset distance, resulted in an increase in strip deformation. The double curvature deformation was obtained by simulating a square plate. By comparing the forming results with the strip results, the deformation of the square plate was smaller in both the transverse and longitudinal directions. The relationships between the transverse and longitudinal deformations were analysed. Furthermore, the effects of both the residual stress distributions and plate stiffness on the deformations were investigated. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Ultrasonic Impact Forming is a dieless forming process, which may be used to form various components. The final shape of the component is achieved by bombarding its surface with a large number of impacts, which produce a thin layer of plastic deformations near the target surface. These plastic deformations induce a compressive residual stress layer, which produces a convex curvature in the specimen. In comparison with traditional shot peen forming [1], which is widely used to form airplane wing skins by inducing isotropic residual stress, the impact locations may be precisely controlled by adjusting the impact trajectory in the UIF process. This is helpful for the deformation of the thick plate, as well as to achieve a large-curvature deformation. Furthermore, the residual stress within the target component treated by the UIF displays anisotropic properties, which helps in obtaining different deformation curvatures in different directions. The main issue with the UIF process is predicting the shape of the target plate. Numerous controlled parameters such as the output frequency, device amplitude, pin size and impact trajectory have significant effects on the deformation of the plate. At present, the relationship between the controlled parameters and
∗ Corresponding author. Tel.: +86 22 27405889. E-mail address: [email protected] (Z. Wang). http://dx.doi.org/10.1016/j.apsusc.2015.06.094 0169-4332/© 2015 Elsevier B.V. All rights reserved.
the plate deformation is usually obtained using a trial and error process. However, with the advancement of information technology, it is now possible to use a finite element simulation to predict the deformation of a specimen in order to design the impact process, and to decrease the amount of experimental testing required. It is well known that the UIF process is a more developed version of the shot peen forming process. The UIF process, which resembles shot peen forming, may be divided into two phases. The first is the multiple impact process, using the UIF device, in which the plate is fixed into place using a holder. The second is the curvature forming process, which takes place after the holder has been removed. Thus far, neither of these two phases have been simulated in experimental studies. For the first phase, the model for the multiple-impact process in UIF may be established by referring to the models used for the shot peen process. Many finite element models for the shot peen process, such as 2D axisymmetric [2], 3D symmetric [3] and 3D impact models [4,5], have been established with different controlled parameters. With the development of the finite element method, more and more 3D models with multiple impacts are being simulated. 25-shot impacts on the target plate were simulated by Majzoobi et al. [6], 134-shots were considered by Bagherifard et al. [7], and a 121-shot model was developed by Klemenz et al. [8]. In the above models, all of the controlled parameters were related to the shots (including shot material and diameter) and to the process (including shot velocity and peen coverage). Analogous parameters
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require further consideration as far as the ultrasonic impact process is concerned. Two features of this process should also be taken into account. First, the pin size is large and the impact velocity is low for the ultrasonic impact process. Second, for ultrasonic impact processes, the impact locations may be predetermined by planning an impact trajectory, while those for shot peen processes are randomly distributed. For the second phase, due to the non-equilibrated stress and strain distributions within the target plate, a convex curvature of the specimen towards the impact direction is produced after removing the holder. At present, three methods have been developed to simulate curvature deformation using the shot peen process. This was done by directly or indirectly inputting nonequilibrated initial residual stress distributions into the numerical model. The first method inputs a set of non-equilibrated stresses, defined as the initial stress, into the numerical model [9]. However, the initial stress is always obtained by trial and error. The second method applies pressure to the model near the plate surface [10,11]. The third method introduces different temperatures across the thickness of the plate, through which a thermal load is induced by the different thermal expansion coefficients [12,13]. The values of the pressure and temperature applied in these models were obtained using a large number of experimental tests in order to determine the relationship between the residual stress and the pressure, or thermal load. For these three methods, one of the premises is that the stress distribution at each depth of the target plate is uniform. The UIF process is fundamentally against this premise, and therefore in order to simulate it, a method that inputs non-equilibrated stress distributions into the target plate was proposed. In this study, a three-step finite element model was developed to analyse the UIF process. The residual stress distributions, arc heights and the radii of curvature of the deformed plates were calculated. The regulations of the deformed radii of curvature with different controlled parameters were analysed. In particular, the difference between the plate deformations in the device moving and offset directions was examined. These result in a difference between the strip deformation and the square plate deformation.
383
Fig. 1. The UIF device.
2. Experimental procedure 2.1. Principles of the UIF device The UIF device used in the experiments is shown in Fig. 1. The ultrasonic wave generator delivers a sinusoidal electric field. The energy transducer transforms the electric energy into an ultrasonic vibration. Next, an ultrasonic horn amplifies it and then converts it into kinetic energy by impacting onto the pin. Through successive impacts on the specimen, which is fixed into place using a plate holder, the energy stored in the pin transfers into the material and generates a compressive residual stress field in the near-surface region, as shown in Fig. 2(a). After removal of the plate holder, and due to the changing of the boundary conditions, the nonequilibrated stress forces the plate to bend towards the impacted surface to form a concave curvature, as shown in Fig. 2(b).
Fig. 2. The residual stress distributions before (a) and after (b) remove the plate holder.
2.2. Experimental process The UIF process was performed using a TJU-HJ-III-style UIF device. The ultrasonic vibration frequency output was 20 kHz, and the amplitude range of the horn was between 0 and 30 m. The size of the pin is shown in Fig. 3. In this study, only normal impacts between the pin and the target specimen were considered. 2024 aluminium alloy was used as a target material, and its chemical composition is shown in Table 1.
Fig. 3. Size of the impacted pin.
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Table 1 Chemical compositions of 2024 aluminum alloy (wt%). Grade
Cu
Si
Fe
Mn
Mg
Zn
Cr
Ti
Al
2024
3.80–4.90
0.50
0.50
0.30–0.90
1.20–1.80
0.25
0.10
0.15
balance
transverse deformation and the longitudinal deformation were analysed through successive impacts onto the square plate. The dimensions of the square plate were 100 mm × 100 mm × 5 mm. For the impact process, the four corners were fixed into place and the total top surface was impacted successively. 3. Numerical model
Fig. 4. The impact trajectories of the UIF in strip forming. (a) Impact along the length direction of strip (IALD); (b) impact along the width direction of strip (IAWD).
In the UIF process, several controlled parameters may influence the forming results. They are mainly related to the impact pin (size and velocity) and to the impact trajectories (device moving velocity and offset distance). For the UIF process, it is well known that the surface coverage is greater in the longitudinal direction than in the transverse direction. This different coverage will induce anisotropic deformations. In order to analyse the transverse and longitudinal deformations separately, a strip deformation was tested. The dimensions of the strip were 100 mm × 20 mm × 5 mm. For the impact process, the strip was fixed into place using a plate holder and the centre area of the strip was impacted. Two impact trajectories were simulated. These were the impact along the length direction of the strip (IALD) and the impact along the width direction of the strip (IAWD), as shown in Fig. 4. Because of the small deformation in the transverse direction of the strip, a nearly single curvature deformation was obtained after the ultrasonic impact treatment. This result may be used to analyse the effect of the controlled parameters on plate deformation in different directions. The relationships between the
The UIF simulation requires a large computation time due to the multiple impacts. A three-step numerical model, as shown in Fig. 5, was developed to simulate the multiple impact and forming processes. Due to the large number of impacts in the UIF process, it is quite costly and time-consuming to simulate all of these. The aim of the first step was to develop a submodel, which uses fewer impacts instead of the total number of impacts, to simulate the process and to obtain the distributions of the residual stress and strain within the target plate. Because of the distributions of the residual stress cannot be influenced by the other impacts with the distances larger than 2 mm [14]. In the submodel, the target plate was 8 mm × 8 mm × 5 mm and the impact zone was restricted to an area of 4 mm × 4 mm, as shown in Fig. 5(a). The impact trajectory is shown in Fig. 6. In the submodel, all sides of the plate face were surrounded by infinite elements, and the bottom surface was restrained and could not be displaced. The impact process using different controlled parameters, such as pin shape, impact amplitude, device- moving velocity and offset distance, was simulated for comparison with the experimental results. Considering the capacity of the UIF device, the impact frequency between the pin and the target plate was much lower than the output ultrasonic vibration frequency. The impact frequency was considered to be 100 Hz. Therefore, the distance between adjacent impact locations (d1 ), as shown in Fig. 6, may be calculated using the following equation: d1 =
vdev f
(1)
where vdev is the device moving velocity, and f is the impact frequency.
Fig. 5. The simulation loop of the UIF model. (a) The impact model. (b) The impact result. (c) The initial stress distribution within strip. (d) The initial stress distribution within squarre plate. (e) The strip forming result. (f) The square plate forming result.
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Fig. 7. The residual stress field in the Y direction within 1/4 submodel (the deformation is amplified five times).
Fig. 6. The impact locations of the pin in the impact model.
For the simulation, the initial velocity of the pin was assumed to be constant for each impact. The maximum initial shot velocity may be considered equivalent to the average velocity of the horn for the ultrasonic shot peen process [15]. The initial velocity (v) may be calculated as follows:
v = 2Afh
(2)
where A is the impact amplitude, and fh is the horn frequency. The horn frequency was 20 kHz in this case. The controlled parameters for the experiments and simulations are shown in Table 2. In the simulation process, the friction coefficient between the pin and the target plate was assumed to be 0.25. The Johnson–Cook equation (3), which takes into account both the work hardening and strain rate hardening of the plate, was used for the material model.
n
= A + B(ε)
1 + C ln
ε˙ ε˙ 0
1−
T − T m 0
Tm − T
(3)
Here, represents the stress to be evaluated, ε˙ 0 and T0 are the reference values of strain rate and temperature, ε˙ and T are the strain rate and temperature under consideration, and Tm is the melting temperature. The values of A, B, C, m, and n are 369 MPa, 684 MPa, 0.0083, 1.7 and 0.73, respectively, which were recommended values taken from literature [16]. In this study, the influence of the temperature variation was considered negligible. In order to analyse the simulation process of the numerical model, the three steps of the strip deformation along with the IAWD were simulated as an example. An impact velocity, v = 2 m/s, and indentation distance, d1 = 0.3 mm, and an offset distance, d2 = 1 mm, were used. The distribution of the residual stress for the simulation is shown in Fig. 7. Due to the different surface coverages in different directions, the residual stress distributions are not uniform at each depth of the target plate. In this submodel, the effect of the extra impacts which in the outside of the restricted zone (4 mm × 4 mm) on the residual stress and strain distributions where under the centre indentation of the target plate surface (centre-indentation zone) is weak. Therefore, the six independent stress and six independent strain components within the centre-indentation zone may be extended to the entire strip. The length and width of the centreindentation zone were determined using the distance between adjacent indentation centres. The dimensions of the zone were
Fig. 8. The cell of the forming model with width-impact.
0.3 mm × 1.0 mm × 5.0 mm (the X value range was −0.15 to 0.15, and the Y value range was −0.5 to 0.5). In order to increase the accuracy of the simulation results, the strip was meshed with different element sizes in the depth direction. These were determined using the gradient of the residual stress and strain distributions, as shown in Fig. 8. By using a MATLAB program, the stress and strain data for the centre-indentation zone of the submodel were extended to the entire plate, as shown in Fig. 9. Due to the non-equilibrated stress distributions within the plate, the forming process was simulated and a convex shape was finally produced, as shown in Fig. 10. Because of the high stiffness induced by the two non-impacted sides of the plate, a nearly single curvature outline was obtained for the shape of the plate. The UIF process with different controlled parameters may be simulated using the same method, as shown in Fig. 5(e) and (f).
Fig. 9. The initial stress field in the transverse direction within 1/4 forming model.
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Table 2 The controlled parameters of the experimental test and numerical simulating. Experimental parameters
Numerical parameters
Impact amplitude A (m) Moving velocity vdev (m/min) Offset distance d2 (mm)
Impact velocity v (m/s) Indentation distance d1 (mm) Offset distance d2 (mm)
8, 12, 16, 20, 24 1.2, 1.8, 2.4 0.5, 1, 1.5
1, 1.5, 2, 2.5, 3 0.2, 0.3, 0.4 0.5, 1, 1.5
Fig. 10. The deformation field of the forming model with width-impact.
Fig. 12. Comparison of numerical residual stress with experimental residual stress.
two indicates that the numerical deformations of the strip agree with the experimental results. As we know, the residual stress in the UIF process is nonuniform. The calculated average residual stress distributions along the plate depth were compared with an X-ray diffraction (XRD) test, as shown in Fig. 12. Their agreement further verifies the accuracy of the numerical model.
Fig. 11. The relationship between the prebending radius and the arc height.
4. Results and discussion 4.1. Numerical verification The numerical results of the UIF model above were verified through experiments. In these experimental tests, the vibration frequency, f, was 20 kHz and the amplitude, A, was 16 m. The strips were impacted using the UIF device, as shown in Fig. 3, in which the pin size was 4 mm × 30 mm and the offset distance between adjacent rows was 1 mm. The resultant arc heights for different controlled parameters were measured using the Almen gauge. The radii of curvature of forming were calculated using the arc height values, as well as the relationship between the arc height (Ahp ) and the radius of curvature (R) (shown in Fig. 11). This may be expressed using the following equation:
R2 = R − Ahp
2
+
l 2
(4)
2
Therefore, the radius of curvature may be formulated as follows: R=
4Ah2p + l2 8Ahp
≈
l2 8Ahp
(5)
where l is the length of the arc height measurement, which is equivalent to 31.75 mm. Table 3 presents the arc height from both the experimental test and the numerical simulation. The small difference between the
4.2. The strip deformation 4.2.1. The influence of pin size and velocity In the UIF process, the elastic and plastic energies in the target plate were transferred from the kinetic energy of the pin through impact. The kinetic energy of the pin was determined using the pin mass and pin velocity. Table 4 shows the arc heights of the strip for different pin velocities. As the pin velocity increases, the kinetic energy of the pin also increases, which causes an increase in the amount of energy transferred to the target plate. Therefore, an increase is seen in the deformations of the strip for impact along both the length and width directions. The radii of curvature calculated from the numerical arc heights using five different pin velocities (1.0 m/s, 1.5 m/s, 2.0 m/s, 2.5 m/s and 3.0 m/s) are shown in Fig. 13. As the pin velocity increases, the radius of curvature decreases nonlinearly. Due to the work hardening of the target plate, more energy must be provided in order to induce larger
Table 4 The experimental and numerical arc heights of the strip with different pin masses and pin velocities. velocity v (m/s)
Table 3 The experimental and numerical arc heights of the strip.
Experimental arc height (mm) Numerical arc height (mm) Error (%)
IAWD
IALD
0.028 0.028359 −7.14
0.026 0.02531 −10.75
1 1.5 2 2.5 3
Experimental (mm)
Numerical (mm)
IAWD
IALD
IAWD
IALD
0.011 0.021 0.028 0.036 0.045
0.008 0.015 0.026 0.032 0.038
0.011393 0.020579 0.028359 0.037378 0.045476
0.007895 0.015926 0.02531 0.032675 0.037496
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Table 5 The experimental and numerical arc heights of the strip with different pin tips. Semi-axis b (mm)
1 2 3
Fig. 13. The numerical curvature radius of the strip with pin velocities.
plastic deformations. As the energy provided increases linearly, the radius of curvature decreases, as shown in Fig. 13. Table 4 and Fig. 13 also show that all of the deformations for IAWD are larger than those for IALD, which is due to the residual stress distributions within the strip before the plate holder is removed. To prove this, the residual stress distributions with a special controlled parameter (v = 2 m/s) were analysed as an example. The single curvature deformation was mainly determined using the compressive residual stress distributions in the length direction of the strip. Fig. 14 shows the residual stress distributions through the strip depth in the length direction of the strip. The residual stresses along three special lines were calculated. The first line was through the indentation centre, and the other two lines were 0.25 mm and 0.50 mm away from the first line in the offset direction. The compressive residual stress for IAWD is lower under the indentation centre and increases as the distance away from the first line increases. Then, the residual stresses along 6 × 10 = 60 uniformly distributed paths within the centre-indentation zone were extracted, and the average residual stresses were calculated, as shown in Fig. 14. This shows that the compressive residual stress for IAWD is lower near the plate’s top surface, but the integral residual stress is still high. The average residual stress for other controlled parameters may be calculated in the same manner. The high compressive
Fig. 14. The residual stress distributions along the plate depth in the length direction of the strip.
Experimental (mm)
Numerical (mm)
IAWD
IALD
IAWD
IALD
0.028 0.027 0.025
0.026 0.024 0.020
0.028359 0.026784 0.025543
0.02531 0.023281 0.021563
residual stress along the offset direction directly induces a large deformation of the strip when impacted along the width direction. The tip size of the pin is another important parameter to consider. It influences the amount of energy transferred into the target plate by controlling the contact area between the pin and the plate surface. The pin tip used in this study was semi-elliptical. The contact area may be controlled by changing the semi-axis length (b) of the pin tip, which is different from the traditional shot peen process. Table 5 presents the arc heights of the strip for three different values of b, and the numerical radii of curvature are shown in Fig. 15. They show that as b increases, the radius of curvature increases for both the IALD and IAWD scenarios. It is also important to note that the increases are nearly linear. As the value of b increases, the contact area between the pin tip and the plate surface gradually decreases. This causes the energy transferred into the plate to be concentrated towards the indentation centre. As shown in Fig. 14, this concentrated energy may increase the compressive residual stress near the plate’s top surface. However, as shown in Fig. 14, as the distance away from the line through the indentation centre increases, the influence of the impacts on the residual stress decreases, especially for the residual stress in the device moving direction. The concentrated energy further decreases the influence, which induces a decrease in the average penetration depth, as shown in Fig. 16. This directly induces a small deformation of the strip with a large value of b. However, the increase in compressive residual stress near the plate’s top surface may slow down the radius of curvature’s tendency to increase, especially for IALD. Due to the non-linearity of the stress-strain curve, the average residual stress changes very little as b values increase, and therefore, the plate deformation cannot be changed significantly by adjusting b.
Fig. 15. The numerical curvature radius regulations of the strip with different pin tips.
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Fig. 16. The residual stress distributions in the length direction with different pin tips. Table 6 The experimental and numerical arc heights of the strip with different device moving velocity and offset distance. d1 (mm)
0.2 0.3 0.4 0.3 0.3
d2 (mm)
1 1 1 0.5 1.5
Experimental (mm)
Numerical (mm)
IAWD
IALD
IAWD
IALD
0.035 0.028 0.027 0.040 0.020
0.025 0.026 0.023 0.033 0.021
0.03482 0.028359 0.026275 0.039136 0.021269
0.02563 0.02531 0.023645 0.032164 0.020948
4.2.2. The influence of device moving velocity and offset distance The plate surface coverage, which is determined by the indentation distributions after multiple impacts, is another factor that may significantly influence the residual stress distributions. In the UIF process, the impact locations may be determined using the impact trajectories and by including the device moving velocity and offset distance. Table 6 shows the arc heights of the strip for different device moving velocities and offset distances. The relationship between the device moving velocity (v) and the distance between the adjacent impact locations (d1 ) is shown in Table 2. The radii of curvature for different impact coverages are shown in Fig. 17. As both the distance (d1 ) and the offset distance (d2 ) decrease, the amount of energy transferred into the target plate increases due to the multiple impacts. This is beneficial for increasing the compressive residual stress at the subsurface. Then, the arc height of the strip increases and the deformation radius of curvature gradually decreases. Due to the residual stress distributions, the influence of the distance (d1 ) on the plate deformation is greater for IAWD, and the influence of the offset distance (d2 ) on the plate deformation is greater for IALD. As the distance (d1 ) decreases, the plastic deformation of the plate increases, which is beneficial for increasing the compressive residual stress at
the plate subsurface. The residual stress in the device moving direction beneath the indentation edge cannot increase effectively through the impacts. Therefore, the residual stress in the offset direction greatly increases, which induces a larger increase for IAWD, as shown in Fig. 18(a). However, due to the non-linearity of the stress-strain curve, the average residual stress cannot be effectively increased, which means that the influence of the device moving velocity on the plate deformation is small. When the offset distance (d2 ) decreases, the influence of the impacts on the residual stress beneath the indentation edge may be increased. Therefore, the average penetration depth increases significantly, as shown in Fig. 18(b). In particular, when the offset distance (d2 ) decreases from 1.5 mm to 1.0 mm, the residual stress in the device moving direction increases more than in the offset direction, which induces a greater increase in deformation for IALD. When the offset distance (d2 ) decreases from 1.0 mm to 0.5 mm, the uniformity of the residual stress along the offset direction increases. This increases the compressive residual stress and decreases the maximum compressive residual stress depth. Therefore, the plate deformation may be effectively controlled by adjusting the offset distance (d2 ). 4.3. The square plate deformation In order to analyse the relationship between the transverse and longitudinal deformations, a UIF process with multiple impacts on a square plate was simulated. In comparison with the numerical arc height of the strip, the deformations for square plates tend to decrease due to the stiffness of the plate. In the UIF process, the plate may be bent towards the impacted surface with a concave curvature. However, bending in one direction will increase the plate stiffness in the vertical direction, which could restrict the concave deformations in the other direction. Table 7 presents the main parameters of the average residual stress in the forming processes of square plates and strips. Comparing the numerical results, the surface compressive residual stress ( sur ), the maximum compressive residual stress ( max ), and the penetration depth (dpen ), are all smaller in the strip, which means that more residual stress is released after the plate is removed from the plate holder. Table 7 also shows that the difference in residual stress with the strip and square plate is small, and is difficult to measure using the experimental approach. However, by calculating the difference in residual stress, the difference between the deformation of the strip and that of a large- sized plate (such as aircraft wing skins) will be greater. Table 8 lists the arc heights and the radii of curvature of the square plate using different controlled parameters. It shows that all of the radii of curvature of the deformations of the square plate are smaller than those of the deformations of the strip. It also shows that all of the transverse deformations are larger than the longitudinal deformations, and that the changes in deformations using different controlled parameters are similar to those of the strips. For transverse deformations, as the initial impact velocity (v) increases, the difference between the strip and square plate decreases. This is because the average compressive residual stress in the transverse direction is larger than in the longitudinal
Table 7 The main parameters of the average residual stress within the square plate and strip. Parameters
sur (MPa) max (MPa) dpen (mm)
Strip
Square plate
Difference value
IAWD
IALD
Transverse
Longitudinal
Transverse
Longitudinal
135.161 265.144 0.646775
139.649 241.048 0.635521
135.181 265.165 0.646796
139.67 241.065 0.635544
−0.0204 −0.0208 −2.1E-05
−0.02112 −0.0172 −2.4E-05
sur —the surface compressive residual stress. max —the maximum compressive residual stress. dpen —the penetration depth.
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Fig. 17. The numerical curvature radius regulations of the strip with (a) different device moving velocity and (b) offset distance.
Fig. 18. The residual stress distributions in the length direction with (a) different distances d1 and (b) offset distances (d2 ).
direction, which causes the transverse deformation to be larger than the longitudinal deformation. Therefore, the stiffness in the transverse direction is lower, which means that the effect of the stiffness on the transverse deformation is also lower. Thus, for transverse deformations, the compressive residual stress at the subsurface plays a more important role. For longitudinal deformations, as the impact velocity (v) increases, the difference between the strip and square plate decreases at first and then increases due to the stiffness and the compressive residual stress distributions within the target plate.
In the plate forming process, the plate deformation would be increased by an increase in the compressive residual stress at the subsurface, and decreased by an increase in the plate stiffness. When the impact velocity is low, because of the lower compressive residual stress at the subsurface, the effect of the plate stiffness on the deformation is great. As the impact velocity increases, the compressive residual stress increases significantly, which could decrease the effect of the stiffness on the deformation. Therefore, the difference between the square plate and strip decreases. When the impact velocity is high, because of the non-linearity of the
Table 8 The numerical arc heights and curvature radii of the square plate with different controlled parameters.
v
b
d1
d2
Arc height (mm)
(m/s)
(mm)
(mm)
(mm)
Transverse
Longitudinal
Transverse
Longitudinal
Transverse
Longitudinal
1 1.5 2 2.5 3 2 2 2 2 2 2
1 1 1 1 1 2 3 1 1 1 1
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.4 0.3 0.3
1 1 1 1 1 1 1 1 1 0.5 1.5
0.011303 0.020429 0.028166 0.037133 0.045212 0.026601 0.025366 0.034632 0.026078 0.038917 0.020472
0.007835 0.015816 0.025159 0.032477 0.04398 0.023139 0.021427 0.025445 0.023506 0.031954 0.020571
11148.17 6168.085 4473.756 3393.419 2787.044 4736.958 4968.762 3638.479 4831.958 3237.86 6155.13
16082.68 7967.11 5008.459 3879.909 2865.116 5445.69 5880.796 4952.164 5360.666 3943.413 6125.507
−0.796 −0.734 −0.685 −0.660 −0.584 −0.688 −0.722 −0.543 −0.755 −0.181 −3.893
−0.766 −0.695 −0.600 −0.610 −0.655 −0.614 −0.635 −0.727 −0.591 −0.257 −1.833
Curvature radius (mm)
Difference (%)
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stress-strain curve, the compressive residual stress cannot increase significantly. However, the increase in the compressive residual stress will produce more plate deformation, which will increase the effect of the plate stiffness. Thus, the difference increases. As the semi-axis length (b) increases, the decrease in the average compressive residual stress increases the effect of the stiffness on the plate deformation. This causes a direct increase in the difference between the square plates and strips. With increasing surface coverage, meaning with a decrease in the distance between the adjacent impact locations (d1 ) and the offset distance (d2 ), all of the differences between the strip and square plate decrease for the transverse deformation. For longitudinal deformations, because of the compressive residual stress distribution at the subsurface, as shown in Fig. 18, the effect of the plate stiffness on the deformation is smaller when changing the offset distance (d2 ). Therefore, as the offset distance (d2 ) decreases, the difference between the square plates and strips decreases. Furthermore, with a decrease in the distance (d1 ), the difference between the square plates and strips is also decreased. 5. Conclusion The ultrasonic impact forming process of multiple impacts on a 2024 aluminium alloy was simulated by developing a three-step numerical model. In the model, a plate with single and double curvatures was obtained by simulating the deformation in a strip and square plate. The effect of the controlled parameters on the strip and square plate was also examined. The following conclusions were established: (1) The average compressive residual stress at the subsurface is higher in the device offset direction, which induces a large plate deformation in this direction after the forming process. (2) The plate deformation is determined using the compressive residual stress at the subsurface and the stiffness of the plate after deformation. Furthermore, the deformations of the square plate are smaller than the deformations of the strip when using the same controlled parameters. (3) As the pin velocity increases, the plate deformation increases. The difference between the deformation of the strip and that of the square plate decreases in the transverse direction, and decreases first and then increases in the longitudinal direction. (4) As the semi-axis length increases, the compressive residual stress increases near the top surface of the plate. However, deformation decreases in both the transverse and longitudinal directions and the difference between the strip and square plate increases. (5) As the surface coverage increases, the plate deformation increases and the effect of the offset distance on the deformation is larger than the distance between the adjacent
impact locations. The difference between the strip and square plate increases with a surface coverage increase in the transverse direction. The difference decreases as the offset distance increases, and increases as the distance between the adjacent impact locations increases. The good agreement with the experimental results indicates the accuracy of the numerical model. The numerical results can be used to select the appropriate controlled parameters for the desired shapes. References [1] T.J. Burmeister, Peen forming of airfoil shapes for aircraft wing sections, in: Proceedings of the 2nd International Conference on Shot Peening, Chicago, Illinois, 1984, pp. 1–5. ´ A.J.L. Crook, D.R.J. Owen, A combined finite/discrete element [2] K. Han, D. Peric, simulation of shot peening processes Part I: studies on 2D interaction laws, Eng. Comput. 17 (2000) 593–619. [3] S.A. Meguid, G. Shagal, J.C. Stranart, Three-dimensional dynamic finite element analysis of shot-peening induced residual stresses, J. Daly. Finite. Elem. Anal. Des. 31 (1999) 179–191. [4] G.I. Mylonas, G. Labeas, Numerical modelling of shot peening process and corresponding products: Residual stress, surface roughness and cold work prediction, Surf. Coat. Technol. 205 (2011) 4480–4494. [5] T. Hong, J.Y. Ooi, B. Shaw, A numerical simulation to relate the shot peening parameters to the induced residual stresses, Eng. Fail. Anal. 15 (2008) 1097–1110. [6] G.H. Majzoobi, R. Azizi, N.A. Alavi, A three-dimensional simulation of shot peening process using multiple shot impacts, J. Mater. Sci. Technol. 164–165 (2005) 1226–1234. [7] S. Bagherifard, R. Ghelichi, M. Guagliano, A numerical model of severe shot peening (SSP) to predict the generation of a nanostructured surface layer of material, Surf. Coat. Technol. 204 (2010) 4081–4090. [8] M. Klemenz, V. Schulze, I. Rohr, D. Löhe, Application of the FEM for the prediction of the surface layer characteristics after shot peening, J. Mater. Process. Technol. 209 (2009) 4093–4102. [9] H.Y. Miao, S. Larose, C. Perron, M. Lévesque, Numerical simulation of the stress peen forming process and experimental validation, Adv. Eng. Softw. 42 (2011) 963–975. [10] D.L. Baughman, An overview of peen forming technology, in: Proceedings of the 2nd international conference on shot peening, Chicago, USA, 1984, pp. 28–33. [11] R. Kopp, H.W. Ball, Recent developments in shot peen forming, in: Proceedings of the 3rd international conference on shot peening, Garmisch Partenkirchen, Germany, 1987, pp. 297–308. [12] D.S. Gardiner, M. Platts, Towards peen forming process optimization, in: Proceedings of the 7th international conference on shot peening, Warsaw, Poland, 1999, pp. 235–243. [13] T. Wang, M. Platts, A. Levers, A process model for shot peen forming, J. Mater. Process. Technol. 172 (2006) 159–162. [14] C. Guo, Z. Wang, D. Wang, S. Hu, Numerical analysis of the residual stress in ultrasonic impact treatment process with single-impact and two-impact models, Appl. Surf. Sci. 347 (2015) 596–601. [15] T. Chaisea, J. Li, D. Néliasa, R. Kublerd, S. Taherib, G. Douchetc, V. Robine, P. Gillese, Modelling of multiple impacts for the prediction of distortions and residual stresses induced by ultrasonic shot peening (USP), J. Mater. Process. Technol. 212 (2012) 2080–2090. [16] G. Kay, Failure modeling of titanium 6Al–4V and aluminum 2024-T3 with the Johnson–Cook material model, in: Final Report-U.S. Department of Transportation: Federal Aviation Administration. FAA Report No. DOT/FAA/AR-03/57, 2003.
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Finite element analysis of the effect of the controlled parameters on plate forming induced by ultrasonic impact forming (UIF) process Guo Chaobo, Hu Shengsun, Wang Dongpo, Wang Zhijiang ∗ Tianjin Key Laboratory of Advanced Joining Technology, School of Materials Science and Technology, Tianjin University, Tianjin, 300072, China
a r t i c l e
i n f o
Article history: Received 11 May 2015 Received in revised form 15 June 2015 Accepted 16 June 2015 Available online 24 June 2015 Keywords: Ultrasonic Impact Forming model Non-uniform residual stress Deformation
a b s t r a c t A three-step numerical model was used to simulate the Ultrasonic Impact Forming (UIF) process using non-uniform residual stress distributions within target plates. A nearly single curvature deformation was obtained by simulating the strip deformation process using different impact trajectories. The influence of the controlled parameters on the arc height and radius of curvature of the strips was investigated by analysing the non-uniform residual stress distributions. Increasing the pin velocity, and decreasing the device moving velocity and offset distance, resulted in an increase in strip deformation. The double curvature deformation was obtained by simulating a square plate. By comparing the forming results with the strip results, the deformation of the square plate was smaller in both the transverse and longitudinal directions. The relationships between the transverse and longitudinal deformations were analysed. Furthermore, the effects of both the residual stress distributions and plate stiffness on the deformations were investigated. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Ultrasonic Impact Forming is a dieless forming process, which may be used to form various components. The final shape of the component is achieved by bombarding its surface with a large number of impacts, which produce a thin layer of plastic deformations near the target surface. These plastic deformations induce a compressive residual stress layer, which produces a convex curvature in the specimen. In comparison with traditional shot peen forming [1], which is widely used to form airplane wing skins by inducing isotropic residual stress, the impact locations may be precisely controlled by adjusting the impact trajectory in the UIF process. This is helpful for the deformation of the thick plate, as well as to achieve a large-curvature deformation. Furthermore, the residual stress within the target component treated by the UIF displays anisotropic properties, which helps in obtaining different deformation curvatures in different directions. The main issue with the UIF process is predicting the shape of the target plate. Numerous controlled parameters such as the output frequency, device amplitude, pin size and impact trajectory have significant effects on the deformation of the plate. At present, the relationship between the controlled parameters and
∗ Corresponding author. Tel.: +86 22 27405889. E-mail address: [email protected] (Z. Wang). http://dx.doi.org/10.1016/j.apsusc.2015.06.094 0169-4332/© 2015 Elsevier B.V. All rights reserved.
the plate deformation is usually obtained using a trial and error process. However, with the advancement of information technology, it is now possible to use a finite element simulation to predict the deformation of a specimen in order to design the impact process, and to decrease the amount of experimental testing required. It is well known that the UIF process is a more developed version of the shot peen forming process. The UIF process, which resembles shot peen forming, may be divided into two phases. The first is the multiple impact process, using the UIF device, in which the plate is fixed into place using a holder. The second is the curvature forming process, which takes place after the holder has been removed. Thus far, neither of these two phases have been simulated in experimental studies. For the first phase, the model for the multiple-impact process in UIF may be established by referring to the models used for the shot peen process. Many finite element models for the shot peen process, such as 2D axisymmetric [2], 3D symmetric [3] and 3D impact models [4,5], have been established with different controlled parameters. With the development of the finite element method, more and more 3D models with multiple impacts are being simulated. 25-shot impacts on the target plate were simulated by Majzoobi et al. [6], 134-shots were considered by Bagherifard et al. [7], and a 121-shot model was developed by Klemenz et al. [8]. In the above models, all of the controlled parameters were related to the shots (including shot material and diameter) and to the process (including shot velocity and peen coverage). Analogous parameters
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require further consideration as far as the ultrasonic impact process is concerned. Two features of this process should also be taken into account. First, the pin size is large and the impact velocity is low for the ultrasonic impact process. Second, for ultrasonic impact processes, the impact locations may be predetermined by planning an impact trajectory, while those for shot peen processes are randomly distributed. For the second phase, due to the non-equilibrated stress and strain distributions within the target plate, a convex curvature of the specimen towards the impact direction is produced after removing the holder. At present, three methods have been developed to simulate curvature deformation using the shot peen process. This was done by directly or indirectly inputting nonequilibrated initial residual stress distributions into the numerical model. The first method inputs a set of non-equilibrated stresses, defined as the initial stress, into the numerical model [9]. However, the initial stress is always obtained by trial and error. The second method applies pressure to the model near the plate surface [10,11]. The third method introduces different temperatures across the thickness of the plate, through which a thermal load is induced by the different thermal expansion coefficients [12,13]. The values of the pressure and temperature applied in these models were obtained using a large number of experimental tests in order to determine the relationship between the residual stress and the pressure, or thermal load. For these three methods, one of the premises is that the stress distribution at each depth of the target plate is uniform. The UIF process is fundamentally against this premise, and therefore in order to simulate it, a method that inputs non-equilibrated stress distributions into the target plate was proposed. In this study, a three-step finite element model was developed to analyse the UIF process. The residual stress distributions, arc heights and the radii of curvature of the deformed plates were calculated. The regulations of the deformed radii of curvature with different controlled parameters were analysed. In particular, the difference between the plate deformations in the device moving and offset directions was examined. These result in a difference between the strip deformation and the square plate deformation.
383
Fig. 1. The UIF device.
2. Experimental procedure 2.1. Principles of the UIF device The UIF device used in the experiments is shown in Fig. 1. The ultrasonic wave generator delivers a sinusoidal electric field. The energy transducer transforms the electric energy into an ultrasonic vibration. Next, an ultrasonic horn amplifies it and then converts it into kinetic energy by impacting onto the pin. Through successive impacts on the specimen, which is fixed into place using a plate holder, the energy stored in the pin transfers into the material and generates a compressive residual stress field in the near-surface region, as shown in Fig. 2(a). After removal of the plate holder, and due to the changing of the boundary conditions, the nonequilibrated stress forces the plate to bend towards the impacted surface to form a concave curvature, as shown in Fig. 2(b).
Fig. 2. The residual stress distributions before (a) and after (b) remove the plate holder.
2.2. Experimental process The UIF process was performed using a TJU-HJ-III-style UIF device. The ultrasonic vibration frequency output was 20 kHz, and the amplitude range of the horn was between 0 and 30 m. The size of the pin is shown in Fig. 3. In this study, only normal impacts between the pin and the target specimen were considered. 2024 aluminium alloy was used as a target material, and its chemical composition is shown in Table 1.
Fig. 3. Size of the impacted pin.
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Table 1 Chemical compositions of 2024 aluminum alloy (wt%). Grade
Cu
Si
Fe
Mn
Mg
Zn
Cr
Ti
Al
2024
3.80–4.90
0.50
0.50
0.30–0.90
1.20–1.80
0.25
0.10
0.15
balance
transverse deformation and the longitudinal deformation were analysed through successive impacts onto the square plate. The dimensions of the square plate were 100 mm × 100 mm × 5 mm. For the impact process, the four corners were fixed into place and the total top surface was impacted successively. 3. Numerical model
Fig. 4. The impact trajectories of the UIF in strip forming. (a) Impact along the length direction of strip (IALD); (b) impact along the width direction of strip (IAWD).
In the UIF process, several controlled parameters may influence the forming results. They are mainly related to the impact pin (size and velocity) and to the impact trajectories (device moving velocity and offset distance). For the UIF process, it is well known that the surface coverage is greater in the longitudinal direction than in the transverse direction. This different coverage will induce anisotropic deformations. In order to analyse the transverse and longitudinal deformations separately, a strip deformation was tested. The dimensions of the strip were 100 mm × 20 mm × 5 mm. For the impact process, the strip was fixed into place using a plate holder and the centre area of the strip was impacted. Two impact trajectories were simulated. These were the impact along the length direction of the strip (IALD) and the impact along the width direction of the strip (IAWD), as shown in Fig. 4. Because of the small deformation in the transverse direction of the strip, a nearly single curvature deformation was obtained after the ultrasonic impact treatment. This result may be used to analyse the effect of the controlled parameters on plate deformation in different directions. The relationships between the
The UIF simulation requires a large computation time due to the multiple impacts. A three-step numerical model, as shown in Fig. 5, was developed to simulate the multiple impact and forming processes. Due to the large number of impacts in the UIF process, it is quite costly and time-consuming to simulate all of these. The aim of the first step was to develop a submodel, which uses fewer impacts instead of the total number of impacts, to simulate the process and to obtain the distributions of the residual stress and strain within the target plate. Because of the distributions of the residual stress cannot be influenced by the other impacts with the distances larger than 2 mm [14]. In the submodel, the target plate was 8 mm × 8 mm × 5 mm and the impact zone was restricted to an area of 4 mm × 4 mm, as shown in Fig. 5(a). The impact trajectory is shown in Fig. 6. In the submodel, all sides of the plate face were surrounded by infinite elements, and the bottom surface was restrained and could not be displaced. The impact process using different controlled parameters, such as pin shape, impact amplitude, device- moving velocity and offset distance, was simulated for comparison with the experimental results. Considering the capacity of the UIF device, the impact frequency between the pin and the target plate was much lower than the output ultrasonic vibration frequency. The impact frequency was considered to be 100 Hz. Therefore, the distance between adjacent impact locations (d1 ), as shown in Fig. 6, may be calculated using the following equation: d1 =
vdev f
(1)
where vdev is the device moving velocity, and f is the impact frequency.
Fig. 5. The simulation loop of the UIF model. (a) The impact model. (b) The impact result. (c) The initial stress distribution within strip. (d) The initial stress distribution within squarre plate. (e) The strip forming result. (f) The square plate forming result.
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Fig. 7. The residual stress field in the Y direction within 1/4 submodel (the deformation is amplified five times).
Fig. 6. The impact locations of the pin in the impact model.
For the simulation, the initial velocity of the pin was assumed to be constant for each impact. The maximum initial shot velocity may be considered equivalent to the average velocity of the horn for the ultrasonic shot peen process [15]. The initial velocity (v) may be calculated as follows:
v = 2Afh
(2)
where A is the impact amplitude, and fh is the horn frequency. The horn frequency was 20 kHz in this case. The controlled parameters for the experiments and simulations are shown in Table 2. In the simulation process, the friction coefficient between the pin and the target plate was assumed to be 0.25. The Johnson–Cook equation (3), which takes into account both the work hardening and strain rate hardening of the plate, was used for the material model.
n
= A + B(ε)
1 + C ln
ε˙ ε˙ 0
1−
T − T m 0
Tm − T
(3)
Here, represents the stress to be evaluated, ε˙ 0 and T0 are the reference values of strain rate and temperature, ε˙ and T are the strain rate and temperature under consideration, and Tm is the melting temperature. The values of A, B, C, m, and n are 369 MPa, 684 MPa, 0.0083, 1.7 and 0.73, respectively, which were recommended values taken from literature [16]. In this study, the influence of the temperature variation was considered negligible. In order to analyse the simulation process of the numerical model, the three steps of the strip deformation along with the IAWD were simulated as an example. An impact velocity, v = 2 m/s, and indentation distance, d1 = 0.3 mm, and an offset distance, d2 = 1 mm, were used. The distribution of the residual stress for the simulation is shown in Fig. 7. Due to the different surface coverages in different directions, the residual stress distributions are not uniform at each depth of the target plate. In this submodel, the effect of the extra impacts which in the outside of the restricted zone (4 mm × 4 mm) on the residual stress and strain distributions where under the centre indentation of the target plate surface (centre-indentation zone) is weak. Therefore, the six independent stress and six independent strain components within the centre-indentation zone may be extended to the entire strip. The length and width of the centreindentation zone were determined using the distance between adjacent indentation centres. The dimensions of the zone were
Fig. 8. The cell of the forming model with width-impact.
0.3 mm × 1.0 mm × 5.0 mm (the X value range was −0.15 to 0.15, and the Y value range was −0.5 to 0.5). In order to increase the accuracy of the simulation results, the strip was meshed with different element sizes in the depth direction. These were determined using the gradient of the residual stress and strain distributions, as shown in Fig. 8. By using a MATLAB program, the stress and strain data for the centre-indentation zone of the submodel were extended to the entire plate, as shown in Fig. 9. Due to the non-equilibrated stress distributions within the plate, the forming process was simulated and a convex shape was finally produced, as shown in Fig. 10. Because of the high stiffness induced by the two non-impacted sides of the plate, a nearly single curvature outline was obtained for the shape of the plate. The UIF process with different controlled parameters may be simulated using the same method, as shown in Fig. 5(e) and (f).
Fig. 9. The initial stress field in the transverse direction within 1/4 forming model.
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Table 2 The controlled parameters of the experimental test and numerical simulating. Experimental parameters
Numerical parameters
Impact amplitude A (m) Moving velocity vdev (m/min) Offset distance d2 (mm)
Impact velocity v (m/s) Indentation distance d1 (mm) Offset distance d2 (mm)
8, 12, 16, 20, 24 1.2, 1.8, 2.4 0.5, 1, 1.5
1, 1.5, 2, 2.5, 3 0.2, 0.3, 0.4 0.5, 1, 1.5
Fig. 10. The deformation field of the forming model with width-impact.
Fig. 12. Comparison of numerical residual stress with experimental residual stress.
two indicates that the numerical deformations of the strip agree with the experimental results. As we know, the residual stress in the UIF process is nonuniform. The calculated average residual stress distributions along the plate depth were compared with an X-ray diffraction (XRD) test, as shown in Fig. 12. Their agreement further verifies the accuracy of the numerical model.
Fig. 11. The relationship between the prebending radius and the arc height.
4. Results and discussion 4.1. Numerical verification The numerical results of the UIF model above were verified through experiments. In these experimental tests, the vibration frequency, f, was 20 kHz and the amplitude, A, was 16 m. The strips were impacted using the UIF device, as shown in Fig. 3, in which the pin size was 4 mm × 30 mm and the offset distance between adjacent rows was 1 mm. The resultant arc heights for different controlled parameters were measured using the Almen gauge. The radii of curvature of forming were calculated using the arc height values, as well as the relationship between the arc height (Ahp ) and the radius of curvature (R) (shown in Fig. 11). This may be expressed using the following equation:
R2 = R − Ahp
2
+
l 2
(4)
2
Therefore, the radius of curvature may be formulated as follows: R=
4Ah2p + l2 8Ahp
≈
l2 8Ahp
(5)
where l is the length of the arc height measurement, which is equivalent to 31.75 mm. Table 3 presents the arc height from both the experimental test and the numerical simulation. The small difference between the
4.2. The strip deformation 4.2.1. The influence of pin size and velocity In the UIF process, the elastic and plastic energies in the target plate were transferred from the kinetic energy of the pin through impact. The kinetic energy of the pin was determined using the pin mass and pin velocity. Table 4 shows the arc heights of the strip for different pin velocities. As the pin velocity increases, the kinetic energy of the pin also increases, which causes an increase in the amount of energy transferred to the target plate. Therefore, an increase is seen in the deformations of the strip for impact along both the length and width directions. The radii of curvature calculated from the numerical arc heights using five different pin velocities (1.0 m/s, 1.5 m/s, 2.0 m/s, 2.5 m/s and 3.0 m/s) are shown in Fig. 13. As the pin velocity increases, the radius of curvature decreases nonlinearly. Due to the work hardening of the target plate, more energy must be provided in order to induce larger
Table 4 The experimental and numerical arc heights of the strip with different pin masses and pin velocities. velocity v (m/s)
Table 3 The experimental and numerical arc heights of the strip.
Experimental arc height (mm) Numerical arc height (mm) Error (%)
IAWD
IALD
0.028 0.028359 −7.14
0.026 0.02531 −10.75
1 1.5 2 2.5 3
Experimental (mm)
Numerical (mm)
IAWD
IALD
IAWD
IALD
0.011 0.021 0.028 0.036 0.045
0.008 0.015 0.026 0.032 0.038
0.011393 0.020579 0.028359 0.037378 0.045476
0.007895 0.015926 0.02531 0.032675 0.037496
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Table 5 The experimental and numerical arc heights of the strip with different pin tips. Semi-axis b (mm)
1 2 3
Fig. 13. The numerical curvature radius of the strip with pin velocities.
plastic deformations. As the energy provided increases linearly, the radius of curvature decreases, as shown in Fig. 13. Table 4 and Fig. 13 also show that all of the deformations for IAWD are larger than those for IALD, which is due to the residual stress distributions within the strip before the plate holder is removed. To prove this, the residual stress distributions with a special controlled parameter (v = 2 m/s) were analysed as an example. The single curvature deformation was mainly determined using the compressive residual stress distributions in the length direction of the strip. Fig. 14 shows the residual stress distributions through the strip depth in the length direction of the strip. The residual stresses along three special lines were calculated. The first line was through the indentation centre, and the other two lines were 0.25 mm and 0.50 mm away from the first line in the offset direction. The compressive residual stress for IAWD is lower under the indentation centre and increases as the distance away from the first line increases. Then, the residual stresses along 6 × 10 = 60 uniformly distributed paths within the centre-indentation zone were extracted, and the average residual stresses were calculated, as shown in Fig. 14. This shows that the compressive residual stress for IAWD is lower near the plate’s top surface, but the integral residual stress is still high. The average residual stress for other controlled parameters may be calculated in the same manner. The high compressive
Fig. 14. The residual stress distributions along the plate depth in the length direction of the strip.
Experimental (mm)
Numerical (mm)
IAWD
IALD
IAWD
IALD
0.028 0.027 0.025
0.026 0.024 0.020
0.028359 0.026784 0.025543
0.02531 0.023281 0.021563
residual stress along the offset direction directly induces a large deformation of the strip when impacted along the width direction. The tip size of the pin is another important parameter to consider. It influences the amount of energy transferred into the target plate by controlling the contact area between the pin and the plate surface. The pin tip used in this study was semi-elliptical. The contact area may be controlled by changing the semi-axis length (b) of the pin tip, which is different from the traditional shot peen process. Table 5 presents the arc heights of the strip for three different values of b, and the numerical radii of curvature are shown in Fig. 15. They show that as b increases, the radius of curvature increases for both the IALD and IAWD scenarios. It is also important to note that the increases are nearly linear. As the value of b increases, the contact area between the pin tip and the plate surface gradually decreases. This causes the energy transferred into the plate to be concentrated towards the indentation centre. As shown in Fig. 14, this concentrated energy may increase the compressive residual stress near the plate’s top surface. However, as shown in Fig. 14, as the distance away from the line through the indentation centre increases, the influence of the impacts on the residual stress decreases, especially for the residual stress in the device moving direction. The concentrated energy further decreases the influence, which induces a decrease in the average penetration depth, as shown in Fig. 16. This directly induces a small deformation of the strip with a large value of b. However, the increase in compressive residual stress near the plate’s top surface may slow down the radius of curvature’s tendency to increase, especially for IALD. Due to the non-linearity of the stress-strain curve, the average residual stress changes very little as b values increase, and therefore, the plate deformation cannot be changed significantly by adjusting b.
Fig. 15. The numerical curvature radius regulations of the strip with different pin tips.
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Fig. 16. The residual stress distributions in the length direction with different pin tips. Table 6 The experimental and numerical arc heights of the strip with different device moving velocity and offset distance. d1 (mm)
0.2 0.3 0.4 0.3 0.3
d2 (mm)
1 1 1 0.5 1.5
Experimental (mm)
Numerical (mm)
IAWD
IALD
IAWD
IALD
0.035 0.028 0.027 0.040 0.020
0.025 0.026 0.023 0.033 0.021
0.03482 0.028359 0.026275 0.039136 0.021269
0.02563 0.02531 0.023645 0.032164 0.020948
4.2.2. The influence of device moving velocity and offset distance The plate surface coverage, which is determined by the indentation distributions after multiple impacts, is another factor that may significantly influence the residual stress distributions. In the UIF process, the impact locations may be determined using the impact trajectories and by including the device moving velocity and offset distance. Table 6 shows the arc heights of the strip for different device moving velocities and offset distances. The relationship between the device moving velocity (v) and the distance between the adjacent impact locations (d1 ) is shown in Table 2. The radii of curvature for different impact coverages are shown in Fig. 17. As both the distance (d1 ) and the offset distance (d2 ) decrease, the amount of energy transferred into the target plate increases due to the multiple impacts. This is beneficial for increasing the compressive residual stress at the subsurface. Then, the arc height of the strip increases and the deformation radius of curvature gradually decreases. Due to the residual stress distributions, the influence of the distance (d1 ) on the plate deformation is greater for IAWD, and the influence of the offset distance (d2 ) on the plate deformation is greater for IALD. As the distance (d1 ) decreases, the plastic deformation of the plate increases, which is beneficial for increasing the compressive residual stress at
the plate subsurface. The residual stress in the device moving direction beneath the indentation edge cannot increase effectively through the impacts. Therefore, the residual stress in the offset direction greatly increases, which induces a larger increase for IAWD, as shown in Fig. 18(a). However, due to the non-linearity of the stress-strain curve, the average residual stress cannot be effectively increased, which means that the influence of the device moving velocity on the plate deformation is small. When the offset distance (d2 ) decreases, the influence of the impacts on the residual stress beneath the indentation edge may be increased. Therefore, the average penetration depth increases significantly, as shown in Fig. 18(b). In particular, when the offset distance (d2 ) decreases from 1.5 mm to 1.0 mm, the residual stress in the device moving direction increases more than in the offset direction, which induces a greater increase in deformation for IALD. When the offset distance (d2 ) decreases from 1.0 mm to 0.5 mm, the uniformity of the residual stress along the offset direction increases. This increases the compressive residual stress and decreases the maximum compressive residual stress depth. Therefore, the plate deformation may be effectively controlled by adjusting the offset distance (d2 ). 4.3. The square plate deformation In order to analyse the relationship between the transverse and longitudinal deformations, a UIF process with multiple impacts on a square plate was simulated. In comparison with the numerical arc height of the strip, the deformations for square plates tend to decrease due to the stiffness of the plate. In the UIF process, the plate may be bent towards the impacted surface with a concave curvature. However, bending in one direction will increase the plate stiffness in the vertical direction, which could restrict the concave deformations in the other direction. Table 7 presents the main parameters of the average residual stress in the forming processes of square plates and strips. Comparing the numerical results, the surface compressive residual stress ( sur ), the maximum compressive residual stress ( max ), and the penetration depth (dpen ), are all smaller in the strip, which means that more residual stress is released after the plate is removed from the plate holder. Table 7 also shows that the difference in residual stress with the strip and square plate is small, and is difficult to measure using the experimental approach. However, by calculating the difference in residual stress, the difference between the deformation of the strip and that of a large- sized plate (such as aircraft wing skins) will be greater. Table 8 lists the arc heights and the radii of curvature of the square plate using different controlled parameters. It shows that all of the radii of curvature of the deformations of the square plate are smaller than those of the deformations of the strip. It also shows that all of the transverse deformations are larger than the longitudinal deformations, and that the changes in deformations using different controlled parameters are similar to those of the strips. For transverse deformations, as the initial impact velocity (v) increases, the difference between the strip and square plate decreases. This is because the average compressive residual stress in the transverse direction is larger than in the longitudinal
Table 7 The main parameters of the average residual stress within the square plate and strip. Parameters
sur (MPa) max (MPa) dpen (mm)
Strip
Square plate
Difference value
IAWD
IALD
Transverse
Longitudinal
Transverse
Longitudinal
135.161 265.144 0.646775
139.649 241.048 0.635521
135.181 265.165 0.646796
139.67 241.065 0.635544
−0.0204 −0.0208 −2.1E-05
−0.02112 −0.0172 −2.4E-05
sur —the surface compressive residual stress. max —the maximum compressive residual stress. dpen —the penetration depth.
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389
Fig. 17. The numerical curvature radius regulations of the strip with (a) different device moving velocity and (b) offset distance.
Fig. 18. The residual stress distributions in the length direction with (a) different distances d1 and (b) offset distances (d2 ).
direction, which causes the transverse deformation to be larger than the longitudinal deformation. Therefore, the stiffness in the transverse direction is lower, which means that the effect of the stiffness on the transverse deformation is also lower. Thus, for transverse deformations, the compressive residual stress at the subsurface plays a more important role. For longitudinal deformations, as the impact velocity (v) increases, the difference between the strip and square plate decreases at first and then increases due to the stiffness and the compressive residual stress distributions within the target plate.
In the plate forming process, the plate deformation would be increased by an increase in the compressive residual stress at the subsurface, and decreased by an increase in the plate stiffness. When the impact velocity is low, because of the lower compressive residual stress at the subsurface, the effect of the plate stiffness on the deformation is great. As the impact velocity increases, the compressive residual stress increases significantly, which could decrease the effect of the stiffness on the deformation. Therefore, the difference between the square plate and strip decreases. When the impact velocity is high, because of the non-linearity of the
Table 8 The numerical arc heights and curvature radii of the square plate with different controlled parameters.
v
b
d1
d2
Arc height (mm)
(m/s)
(mm)
(mm)
(mm)
Transverse
Longitudinal
Transverse
Longitudinal
Transverse
Longitudinal
1 1.5 2 2.5 3 2 2 2 2 2 2
1 1 1 1 1 2 3 1 1 1 1
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.4 0.3 0.3
1 1 1 1 1 1 1 1 1 0.5 1.5
0.011303 0.020429 0.028166 0.037133 0.045212 0.026601 0.025366 0.034632 0.026078 0.038917 0.020472
0.007835 0.015816 0.025159 0.032477 0.04398 0.023139 0.021427 0.025445 0.023506 0.031954 0.020571
11148.17 6168.085 4473.756 3393.419 2787.044 4736.958 4968.762 3638.479 4831.958 3237.86 6155.13
16082.68 7967.11 5008.459 3879.909 2865.116 5445.69 5880.796 4952.164 5360.666 3943.413 6125.507
−0.796 −0.734 −0.685 −0.660 −0.584 −0.688 −0.722 −0.543 −0.755 −0.181 −3.893
−0.766 −0.695 −0.600 −0.610 −0.655 −0.614 −0.635 −0.727 −0.591 −0.257 −1.833
Curvature radius (mm)
Difference (%)
390
C. Guo et al. / Applied Surface Science 353 (2015) 382–390
stress-strain curve, the compressive residual stress cannot increase significantly. However, the increase in the compressive residual stress will produce more plate deformation, which will increase the effect of the plate stiffness. Thus, the difference increases. As the semi-axis length (b) increases, the decrease in the average compressive residual stress increases the effect of the stiffness on the plate deformation. This causes a direct increase in the difference between the square plates and strips. With increasing surface coverage, meaning with a decrease in the distance between the adjacent impact locations (d1 ) and the offset distance (d2 ), all of the differences between the strip and square plate decrease for the transverse deformation. For longitudinal deformations, because of the compressive residual stress distribution at the subsurface, as shown in Fig. 18, the effect of the plate stiffness on the deformation is smaller when changing the offset distance (d2 ). Therefore, as the offset distance (d2 ) decreases, the difference between the square plates and strips decreases. Furthermore, with a decrease in the distance (d1 ), the difference between the square plates and strips is also decreased. 5. Conclusion The ultrasonic impact forming process of multiple impacts on a 2024 aluminium alloy was simulated by developing a three-step numerical model. In the model, a plate with single and double curvatures was obtained by simulating the deformation in a strip and square plate. The effect of the controlled parameters on the strip and square plate was also examined. The following conclusions were established: (1) The average compressive residual stress at the subsurface is higher in the device offset direction, which induces a large plate deformation in this direction after the forming process. (2) The plate deformation is determined using the compressive residual stress at the subsurface and the stiffness of the plate after deformation. Furthermore, the deformations of the square plate are smaller than the deformations of the strip when using the same controlled parameters. (3) As the pin velocity increases, the plate deformation increases. The difference between the deformation of the strip and that of the square plate decreases in the transverse direction, and decreases first and then increases in the longitudinal direction. (4) As the semi-axis length increases, the compressive residual stress increases near the top surface of the plate. However, deformation decreases in both the transverse and longitudinal directions and the difference between the strip and square plate increases. (5) As the surface coverage increases, the plate deformation increases and the effect of the offset distance on the deformation is larger than the distance between the adjacent
impact locations. The difference between the strip and square plate increases with a surface coverage increase in the transverse direction. The difference decreases as the offset distance increases, and increases as the distance between the adjacent impact locations increases. The good agreement with the experimental results indicates the accuracy of the numerical model. The numerical results can be used to select the appropriate controlled parameters for the desired shapes. References [1] T.J. Burmeister, Peen forming of airfoil shapes for aircraft wing sections, in: Proceedings of the 2nd International Conference on Shot Peening, Chicago, Illinois, 1984, pp. 1–5. ´ A.J.L. Crook, D.R.J. Owen, A combined finite/discrete element [2] K. Han, D. Peric, simulation of shot peening processes Part I: studies on 2D interaction laws, Eng. Comput. 17 (2000) 593–619. [3] S.A. Meguid, G. Shagal, J.C. Stranart, Three-dimensional dynamic finite element analysis of shot-peening induced residual stresses, J. Daly. Finite. Elem. Anal. Des. 31 (1999) 179–191. [4] G.I. Mylonas, G. Labeas, Numerical modelling of shot peening process and corresponding products: Residual stress, surface roughness and cold work prediction, Surf. Coat. Technol. 205 (2011) 4480–4494. [5] T. Hong, J.Y. Ooi, B. Shaw, A numerical simulation to relate the shot peening parameters to the induced residual stresses, Eng. Fail. Anal. 15 (2008) 1097–1110. [6] G.H. Majzoobi, R. Azizi, N.A. Alavi, A three-dimensional simulation of shot peening process using multiple shot impacts, J. Mater. Sci. Technol. 164–165 (2005) 1226–1234. [7] S. Bagherifard, R. Ghelichi, M. Guagliano, A numerical model of severe shot peening (SSP) to predict the generation of a nanostructured surface layer of material, Surf. Coat. Technol. 204 (2010) 4081–4090. [8] M. Klemenz, V. Schulze, I. Rohr, D. Löhe, Application of the FEM for the prediction of the surface layer characteristics after shot peening, J. Mater. Process. Technol. 209 (2009) 4093–4102. [9] H.Y. Miao, S. Larose, C. Perron, M. Lévesque, Numerical simulation of the stress peen forming process and experimental validation, Adv. Eng. Softw. 42 (2011) 963–975. [10] D.L. Baughman, An overview of peen forming technology, in: Proceedings of the 2nd international conference on shot peening, Chicago, USA, 1984, pp. 28–33. [11] R. Kopp, H.W. Ball, Recent developments in shot peen forming, in: Proceedings of the 3rd international conference on shot peening, Garmisch Partenkirchen, Germany, 1987, pp. 297–308. [12] D.S. Gardiner, M. Platts, Towards peen forming process optimization, in: Proceedings of the 7th international conference on shot peening, Warsaw, Poland, 1999, pp. 235–243. [13] T. Wang, M. Platts, A. Levers, A process model for shot peen forming, J. Mater. Process. Technol. 172 (2006) 159–162. [14] C. Guo, Z. Wang, D. Wang, S. Hu, Numerical analysis of the residual stress in ultrasonic impact treatment process with single-impact and two-impact models, Appl. Surf. Sci. 347 (2015) 596–601. [15] T. Chaisea, J. Li, D. Néliasa, R. Kublerd, S. Taherib, G. Douchetc, V. Robine, P. Gillese, Modelling of multiple impacts for the prediction of distortions and residual stresses induced by ultrasonic shot peening (USP), J. Mater. Process. Technol. 212 (2012) 2080–2090. [16] G. Kay, Failure modeling of titanium 6Al–4V and aluminum 2024-T3 with the Johnson–Cook material model, in: Final Report-U.S. Department of Transportation: Federal Aviation Administration. FAA Report No. DOT/FAA/AR-03/57, 2003.