Materials Processing
Numerical Analysis of Peen Forming for High-Strength Aluminum Alloy Plates
2021 Volume 62 Issue 6 Pages 846-855
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2021 Volume 62 Issue 6 Pages 846-855
Peen forming is a method of bending a metal plate by generating plastic strain near its surface when colliding with steel shots. In this study, the effect of coverage on the curvature after single-sided and double-sided peen forming of a high-strength aluminum alloy plate was investigated by experiments and finite element method (FEM) analysis. In the experiment, the curvature increased as the coverage increased in single-sided peen forming. In double-sided peen forming under the same peening conditions for both sides, the curvature is smaller than that after single-sided peening. FEM analysis was performed as follows. In step 1, multiple shot collisions were analyzed by the dynamic explicit FEM. In step 2, the plastic strain distributions analyzed in step 1 were input to the specimen to analyze the deformation by the static implicit FEM. FEM analysis results agreed with the experimental results in single-sided peen forming. In double-sided peen forming, the plastic strain distribution was calculated considering the residual stress distribution near the second surface after single-sided peen forming, and the analysis results agreed with the experimental results. A method of approximate calculation of the curvature was proposed, in which the plastic strain distribution was expressed as a function of coverage and initial stress. The curvature after single-sided and double-sided peen forming could be easily predicted by this method under various peening conditions.
This Paper was Originally Published in Japanese in J. JSTP 61 (2020) 115–123.
Peen forming is a method of bending a metal plate surface by applying a plastic strain near its surface via colliding it with a steel ball (shot). This method is mainly employed for forming the outer skins of aircraft wings and rocket tanks.1–4) The outer skin of a wing can have a complicated shape, such as spherical, saddle-shaped, and single-curved surface.
Peen forming is a dieless forming technique. Therefore, the conditions of shot peening in pneumatic shot peening, such as the shot material, shot diameter, air pressure, standoff distance, and projection angle, are varied to control the shape after peen forming. The coverage is also controlled. The coverage is the ratio (∑AI/Ao) of the total indentation area (AI) to the surface area (Ao) of the plate, and is set to 100% or more in conventional shot peening. Because peen forming does not require a 100% coverage, controlling the coverage is the easiest way to control the shape after peen forming. In saddle forming, a plate bent in the convex direction is rotated by 90° and bent in the concave direction. Because there exists a region that stretches to both sides of the plate, peening must be performed on both sides.
Many methods have been reported for predicting the shape after peen forming. Kopp et al. analyzed the relationship between the shot velocity and the residual stress in the case of a single shot using the dynamic explicit finite element method (FEM) to study the conditions for peen forming.4) Kopp et al. studied the double-sided peen forming of a plate and predicted the deformation using the dynamic explicit FEM under multiple-shot collision.5) Takahashi et al. determined the plastic strain generated when applying one shot to a plate, using the static implicit method, and the forming shape was analyzed by applying this strain to the surface of a shell element.6) Wang et al. analyzed the plastic strain distribution under a single-shot collision and determined the forming shape by inputting this strain to a shell element as a virtual thermal strain.7) Miao et al. calculated the bending moment and expansion force from the analysis results of the dynamic explicit FEM under multiple-shot collision and analyzed the forming shape by inputting them using the static implicit FEM.8) Gariépy et al. analyzed the generated stress using the dynamic explicit FEM under multiple-shot collision and analyzed the forming shape using the static implicit FEM with the stress as the input value.9) Furthermore, Gariépy et al. studied a model to analyze the forming shape of an actual wing considering the effects of pre-shot peening before peen forming and the effects of double-sided peen forming.9) Gariépy et al. conducted an analysis considering the number of collisions in the air flow during shot peening and the movement path of the nozzle and investigated their effects on the forming shape.10) Xiao et al. analyzed the bending moment and expansion force generated by a single-shot collision and four-shot collision using the dynamic FEM and static FEM and investigated the effect of initial tensile stress on stress peen forming.11) Xiao et al. analyzed the stress under single-shot and multiple-shot collisions by combining the dynamic FEM analysis and theoretical calculation. They proposed a method for calculating the stress generated during peening as a function of the coverage.12) Pierre et al. analyzed the forming shape by obtaining the eigenstrain from the experimental deformation and residual stress.13) Ohta analyzed the plastic strain distribution using dynamic explicit FEM during peen forming using a rectangular solid pin and analyzed the forming shape using the static implicit FEM with the plastic strain distribution as the input value.14)
As described above, many analysis methods for peen forming have been proposed. However, the analysis of double-sided peening for saddle-shaped forming has only been reported by Kopp et al.5) and Gariépy et al.9) They conducted peening on both sides simultaneously, not separately.
In the present study, the effects of coverage on the curvature of a high-strength aluminum alloy (A7075-T6) specimen subjected to single-sided peening and double-sided peening were examined by conducting experiments and through FEM analysis, and the deformation mechanism of peen forming was clarified. Furthermore, an approximate calculation method for predicting the curvature after peen forming was investigated based on the deformation mechanism of peen forming.
The specimen used in this study was an aluminum alloy A7075-T6 (hardness value of 170 HV) with a plate thickness h of 5 mm, a width of 150 mm, and a length of 150 mm. The shots were made of steel and had a diameter of 4.76 mm and a hardness value of 772 HV. Because the larger shot diameter introduced the deeper plastic strain after peening, the maximum shot diameter projected by the equipment was selected. The shot peening machine was a direct-pressure machine, the nozzle was moved vertically to the specimen, and the entire surface of the specimen was peened. Three values of the coverage C were set: 10, 15, and 50%. Figure 1 shows the appearance of the specimen. The coverage was obtained through image processing after tracing the indentation.
Surface appearance of specimens.
As shown in Fig. 2, the experiment is conducted under two conditions: single-sided peening and double-sided peening. In double-sided peening, the first side was peened, and then, the second side was peened under the same conditions as those employed for the first side. Kopp et al.5) and Gariépy et al.9) investigated simultaneous double-side peening. However, in our study, the process was different because first, one surface was peened, and then, the other surface was peened.
Schematic illustration of peen forming (PF).
After peen forming, the deformed shape was measured using a laser shape-measuring machine. The measurement was performed on a total of eight lines in a range of approximately 70 mm in two directions: x and y.
As shown in Fig. 1, the size of the indentation varies. We measured 222 indentation diameters on the specimen with C = 10%. Figure 3 shows the indentation diameter distribution, which is between 0.4 and 1.4 mm. The highest indentation diameter ranges from 1.1 to 1.3 mm. We presumed that the small indentation diameter was the result of the shot bouncing in the device while colliding at a low velocity.
Measurement result of indentation diameters.
Figure 4 shows the shape measurement results of the specimen after single-sided peening when C = 10% and 50%. The peening indentations were on the surface of the specimen, and the surface had roughness. The deformation of the specimen with C = 50% was larger than that of the specimen with C = 10%. To obtain the radius of curvature, we fitted the equation of a circle that minimizes the sum of the squares of the error from the measurement result. The fitted circle is shown in the figure.
Measured profiles of specimens when C = 10% and 50% after single-sided peen forming.
Figure 5 shows the relationship between the coverage C and the curvature after peen forming. The figure shows the measurement results in the x- and y-directions. Gariépy et al. demonstrated that the rolling direction influences the shape after peen forming in a 2024-T3 alloy15); however, no clear anisotropy in the curvature was observed in this study. The curvature increased with the increase in the coverage in single-sided peen forming because of the increase in the plastic strain near the surface under shot peening. Similarly, the curvature increased with increasing coverage in double-sided peen forming. The forming shape was measured on the first surface, and the curvature formed after single-sided peening was reduced after double-sided peening. The plate did not completely return to its flat state. Because the same plastic strain distribution was formed on both sides in the double-sided peen forming under the same peening conditions, we assumed that the curvature would bend back to approximately 0; however, the experimental results showed otherwise. Therefore, we investigated the deformation mechanism of single-sided and double-sided peen forming using the FEM analysis.
Experimental relationship between coverage and curvature after single-sided and double-sided peen forming (PF).
The FEM analysis of peen forming was performed in two steps. In step 1, the plastic strain generated by shot collision was analyzed using the dynamic explicit FEM of the model shown in Fig. 6. The analysis code was LS-Dyna (Ver. 800). In the analysis, multiple shots were collided with an evaluation area of 3 mm × 3 mm. The coverage was controlled by the number and position of the shots. The initial height (position in the z direction) of the shots was set at 0.5 mm intervals to avoid multiple shots being collided at the same time. The model shown in Fig. 6 is the case where the number of shots is 4 (C = 56%). The shots were set at 1.5 mm intervals in the x- and y-directions. The shots do not overlap, as shown in Fig. 6. To reduce the analysis time, the shots were arranged to overlap in this study. The shot was a steel ball with a diameter of 4.76 mm and an elastic body (Young’s modulus E = 210 GPa, and Poisson’s ratio ν = 0.3). The specimen had a thickness of 5 mm and was made of a high-strength aluminum alloy (A7075-T6). The specimen was an elastoplastic body with a bi-linear approximation (Young’s modulus E = 70 GPa, and Poisson’s ratio ν = 0.3), and its hardening rule was the mixed hardening rule. Figure 6 shows the stress–strain curve. The bottom of the specimen was completely fixed to suppress the vibration. The element was an eight-node hexahedral reduced integral element, and the size of the element was 0.03125 mm in the thickness direction and 0.0625 mm in the x- and y-directions near the surface. The contact friction was Coulomb friction, and the friction coefficient was 0.2, which is the typical value used under a no-lubricant condition.
FEM analytical model of step 1.
Because the shot velocity was not measured in the experiment, it was necessary to determine the input value. The indentation diameter was analyzed by varying the shot velocity when one shot was collided with the specimen. Figure 7 shows the relationship between the shot velocity and the indentation diameter. As shown, with the increase in the shot velocity, the indentation diameter increases. In the experiment shown in Fig. 3, the most frequent indentation diameter, ranging from 1.1 to 1.3 mm, coincides with a shot velocity of 20 m/s. The indentation diameter at this shot velocity was 1.26 mm. Assuming that the most frequent shot velocity dominated the deformation, the shot velocity was set to 20 m/s in this study.
Analytical results of relationship between shot velocity and indentation diameter.
In step 2, the deformation in a wide area (80 mm × 80 mm) with the bottom unconstrained was analyzed, as shown in Fig. 8. The plastic strain distribution in the thickness direction, obtained in step 1, was inputted as the eigenstrain, and an elastic analysis was conducted using the static implicit FEM. The analysis code was Marc (2015). Different linear expansion coefficients were inputted to the elements at the same depth from the surface to obtain the eigenstrain as the thermal strain, and the analysis was conducted under the condition of increase in specimen temperature to 100°C. The specimen deformed spherically because the coefficient of linear expansion was isotropic. The material properties were the same as that shown in Fig. 6. A 1/4 analytical model was created considering geometrical symmetry. For analyzing the double-sided peen forming, the element division in the thickness direction near the first and second surfaces coincided with the model of step 1.
FEM analytical model of step 2.
Figure 9 shows the plastic strain distribution on the surface of the evaluation region (3 mm × 3 mm) analyzed using the FEM in step 1. As typical examples, the cases where C = 14, 56, and 65% are presented. The tensile strains were mainly present in the element on the surface; however, small compressive strains were also observed. The strain was nonuniform in each element. The plastic strain occurred in a narrow region at C = 14% and in a wide region at C = 65%. Because the plastic strain distribution generated by shot collision was axisymmetric, the x-direction plastic strain (Figs. 9(a), (b), and (c)) and y-direction plastic strain (Figs. 9(d), (e) and (f)) exhibited approximately the same distribution, except for the fact that the directions were different.
Plastic strain distributions at surface. (a), (b), (c) Contour of x-direction strain. (d), (e), (f) Contour of y-direction strain.
As shown in Fig. 9, the elements exhibit different plastic strains. Assuming that the average plastic strain affected the deformation, the average plastic strains of 2304 elements with the same depth from the surface within the evaluation region (3 mm × 3 mm) were evaluated. As shown in Fig. 9, the plastic strain distributions in the x- and y-directions are equivalent. Therefore, the plastic strain in the x-direction was evaluated. Figure 10 shows the plastic strain distribution in the thickness direction. The scale on the horizontal axis is expanded to 2 mm from the surface. The plastic strain was 0 in the region deeper than 2 mm. The average plastic strain increased with increasing coverage. Because the shot velocity was constant, and the indentations did not overlap with each other, as shown in Fig. 9, the depth of the plastic strain was constant at approximately 1.5 mm, which is equal to that introduced by one shot. The plastic strain distribution generated by one shot was the same, but the decrease in coverage reduced the average plastic strain because the region where the plastic strain was not introduced became large. At C = 65%, the increase in the plastic strain near the surface tended to increase owing to the overlap of the indentations.
Effect of coverage C on plastic strain distributions for single-sided peen forming.
Figure 11 shows the relationship between the coverage and the curvature after single-sided peen forming, which was analyzed using the FEM in step 2. The FEM analysis results are indicated by ■. The curvature was calculated by fitting the displacement of the node to the equation of a circle that minimizes the sum of the squared errors. The experimental results are also shown in the figure. Similar to the experimental results, the FEM analysis results demonstrated that the curvature increases with increasing coverage. As the coverage increased, the rate of increase in the curvature decreased and tended to saturate; however, the coverage did not saturate at 65%. Considering the significant variation in the experimental results, the FEM analysis results are in good agreement with the experimental results. The curvature was determined by the average plastic strain at the same depth from the surface. This technique of FEM analysis has been confirmed by the author to be consistent with the results of the experiment and analysis of peen forming using a pin14) and can be widely applied to peen forming.
Effect of coverage on curvature of specimen after single-sided peen forming.
As shown in Fig. 5, when peening is performed on both the surfaces under the same conditions, the convex-shaped deformation of the first surface remains. These results show that the plastic strain generated when peening the second surface was lower than that generated when peening the first surface. The cause may be the residual stress occurring near the second surface. Figure 12 shows the residual stress distribution in the thickness, which was analyzed using the FEM in step 2 after single-sided peen forming. As representative examples, the results obtained for C = 7, 28, and 56% are shown. The analytical model is the same as that shown in Fig. 7. Because the peening surface was deformed to be convex, a compressive residual stress was generated near the second surface owing to the bending moment. The compressive residual stress increased with increasing coverage, i.e., the curvature increased.
Effect of coverage C on residual stress distribution after single-sided peen forming.
Therefore, to analyze the effect of compressive residual stress, an FEM analysis of the shot collision (step 1) was performed by applying an initial compressive stress in the x- and y-directions in the analytical model shown in Fig. 6. Figure 13 shows the effect of initial compressive stress on the plastic strain distribution at C = 56%. In this analysis, Fig. 13 shows the average of the initial compressive stress from the surface to 1 mm because the initial residual stress varies slightly in each element. As the initial compressive stress increased, the plastic strain decreased, and the depth of plastic strain became shallow. The compressive hydrostatic pressure increased owing to the initial compressive stress, which made the tensile yield less likely to occur during a shot collision. Xiao et al. showed that the plastic strain increases owing to the initial tensile stress in stress peening;11) however, the opposite phenomenon was observed in the double-sided peen forming. The same effect was obtained at C = 7, 14, 28, 42, and 65%. Figure 14 shows the changes in the plastic strain at depths of 0.0156, 0.1688, and 1.0625 mm from the surface owing to the initial compressive stress. The plastic strain varies depending on the depth. Figure 14 shows the results of approximating the initial compressive stress dependence of the plastic strain using a cubic curve. By determining the initial compressive stress dependence for each coverage and for each depth from the surface, we determined the plastic strain distribution generated near the second surface after the single-sided peen forming shown in Fig. 12, and used it as the input value for the FEM analysis in step 2.
Effect of initial compressive stress on plastic strain distribution when C = 56%.
Effect of initial compressive stress on plastic strain at various depths when C = 56%.
Figure 15 shows the plastic strain distribution considering the effect of compressive residual stress generated near the second surface after single-sided peen forming. As shown in Fig. 12, the compressive stress occurs near the second surface before peening. The plastic strain generated near the second surface was lower than that generated near the first surface owing to the effect of compressive stress under the same coverage. When the coverage was higher, the compressive stress increased, whereas the plastic strain decreased significantly.
Effect of coverage C on plastic strain distributions for double-sided peen forming.
The plastic strain distribution, shown in Fig. 15, was inputted, and the curvature was obtained using the analysis in step 2. Figure 16 shows the relationship between the curvature and the coverage. The FEM analysis results are indicated by ■. The curvature obtained using the FEM analysis was smaller than that obtained using the experimental analysis at C = 50%, and the bending back was significant. In the double-sided peening, the tendency that the curvature after single-sided peening remains was consistent between the FEM analysis and experimental results when the second surface was peened under the same coverage.
Effect of coverage on curvature of specimen after double-sided peen forming.
The aforementioned results confirmed that the curvature after the double-sided peen forming was largely influenced by the compressive residual stress generated near the second surface after the single-sided peen forming.
From the FEM analysis results, it was clear that the curvature after single-sided peen forming was determined by the plastic strain distribution generated by shot collision, and the curvature after double-sided peen forming was significantly affected by the residual stress near the second surface after the single-sided peen forming. However, many FEM analyses must be performed to predict the curvature after the double-sided peen forming. Therefore, we investigated an approximate calculation method for the curvature using the plastic strain distribution in step 1 of the FEM analysis.
The plastic strain distributions, shown in Figs. 10 and 13, can be approximated using the polygonal line shown in Fig. 17. In the present study, because the shot diameter and shot velocity were constant, the depth at point B was 0.15625 mm, and the depth at point C was 0.46875 mm. The depth at point D varied under the influence of the initial compressive stress. Figure 18 shows the effects of the coverage and initial compressive stress on the plastic strain at points A, B, and C and on the depth at point D. The plastic strains at points A, B, and C were approximated using eq. (1) so that the plastic strains could be calculated in the case where no FEM analysis was performed.
| \begin{equation} \varepsilon^{*}{}_{(z)} = a(C+d)^{n}(\sigma_{c} + b)^{m} \end{equation} | (1) |
Approximation of plastic strain distribution when C = 56%.
Effect of coverage and initial compressive stress on approximate parameters of plastic strain distribution.
Here, C is the coverage, σc is the initial compressive stress, and a, b, d, n, and m are constants. The depth at point D was also approximated using eq. (1); however, n was set to 0 owing to the lack of the coverage effect.
Figure 18 shows the results approximated using eq. (1). It is possible to calculate the plastic strain distribution considering the coverage and the initial residual stress. Figure 17 shows the plastic strain distribution calculated using eq. (1) at C = 56%. The FEM analysis result are in good agreement with the calculated result.
When the surroundings are completely constrained, the stress $\sigma ^{*}{}_{(z)}$ generated in a small region wdz with a depth z from the surface owing to plastic strain $\varepsilon ^{*}{}_{(z)}$ can be calculated using eq. (2). Here, h and w are the thickness and the width of the specimen, respectively.
| \begin{equation} \sigma^{*}{}_{(z)} = -\frac{E}{(1-\nu^{2})}\varepsilon^{*}{}_{(z)}(1+\nu) \end{equation} | (2) |
The load balance is satisfied within the thickness by $\sigma ^{*}{}_{(z)}$; hence, stress σP(z) calculated using eq. (3) is generated.
| \begin{equation} \sigma_{P(z)} = \int_{0}^{h}\sigma^{*}{}_{(z)}wdz/wh \end{equation} | (3) |
A bending moment M is generated by $\sigma ^{*}{}_{(z)}$ and is calculated using eq. (4). Owing to M, the specimen deforms to the radius of curvature R calculated using eq. (5). Here, we consider the case where the specimen deforms into a spherical shape.
| \begin{equation} M = \int_{0}^{h}\sigma^{*}{}_{(z)}(z - h/2)wdz \end{equation} | (4) |
| \begin{equation} R = \frac{Ewh^{3}(1 + \nu)}{12M(1 + \nu^{2})} \end{equation} | (5) |
The bending stress σM(z) calculated using eq. (6) occurs because of the balance of moments.
| \begin{equation} \sigma_{M(z)} = E(z - h/2)/R \end{equation} | (6) |
The residual stress σR(z) finally generated within the plate thickness is the sum of $\sigma ^{*}{}_{(z)}$, σP(z), and σM(z).
| \begin{equation} \sigma_{R(z)} = \sigma^{*}{}_{(z)} + \sigma_{P(z)} + \sigma_{M(z)} \end{equation} | (7) |
Figure 19 shows the calculation results of the stress distribution in the thickness direction after single-sided peen forming at C = 56%. The FEM analysis results are also shown. The FEM analysis results indicate a lower compressive stress near the first surface and a higher compressive stress near the second surface than the approximate calculation, and both the residual stress distributions are approximately the same.
Approximate calculated results of residual stress distribution when C = 56%.
The plastic strain distribution was determined using eq. (1), which is an approximation. The curvature calculated using eq. (5) is plotted in Fig. 11, as indicated by ○. The curvature obtained using the approximate calculation is slightly larger than that obtained from the FEM analysis. The approximate calculation results are almost consistent with the experimental results.
The curvature could be predicted by the approximate calculation, even for the coverage without the FEM analysis. However, the coverage was valid only in the range of 7–65%, in which the FEM analysis was performed in this study, and extrapolation was not possible.
This approximate calculation method can be applied to different thicknesses within a range that does not affect the plastic strain distribution under shot collision. Figure 20 shows the results of the calculation for h = 10 mm, including the experimental results. The experimental conditions were the same as those when h = 5 mm. The approximate calculation results are in agreement with the experimental results for h = 10 mm. Thus, for h ≥ 5 mm, the curvature can be predicted by the approximate calculation.
Effect of coverage on curvature of specimen after single-sided peen forming when h = 10 mm.
In double-sided peen forming, the compressive residual stress distribution near the second surface generated after single-sided peen forming was used as the input value. The plastic strains at points A, B, and C were determined using the approximation of eq. (1), and the plastic strain distribution near the second surface was calculated. The depth at point D was a position unaffected by the compressive residual stress, and was fixed at 1.47 mm. The curvature calculated using eq. (5) is plotted in Fig. 16, indicated by ○. The approximate calculation results are approximately consistent with the FEM analysis results. However, the approximate calculation results tend to be lower than that of the experimental results. This is attributed to the effect of changes in the shot peening conditions owing to the method of fixing the specimen during the experiment or changes in the shape after forming the first surface.
An approximate calculation of the curvature after double-sided peen forming was conducted by varying the coverage C1 of the first surface and the coverage C2 of the second surface. Figure 21 shows the approximate calculation results. When C1 = 42%, the remaining curvature after double-sided peen forming decreased as C2 increased, and C2 needed to be approximately 50% for perfect flatness. When C1 = 28%, C2 needed to be approximately 35% for perfect flatness. When C2 was greater than 35%, the second surface was deformed into a convex shape. The FEM analysis results are also shown in Fig. 21, which are approximately the same as the approximate calculation results.
Approximate calculated effect of coverage for second surface on curvature after double-sided peen forming with coverage for first surface C1 = 42% and 28%.
It is difficult to predict the shape after double-sided peen forming by conducting FEM analysis and experiments. The approximate calculation method can be used for easy prediction of the shape after double-sided peen forming and is an effective tool for predicting the forming conditions.
To examine the versatility of applying the approximate calculation, we conducted a study by varying the shot diameter and shot velocity. The shot diameter was 0.5 mm on average, which is the typical value used in shot peening, and the shot velocity was 40 m/s. The thickness h was 7 mm. Figure 22 shows the analytical model of step 1. The material properties of the specimen and the material properties of the shot were the same as those shown in Fig. 6. As shown in Fig. 22, 25 to 600 shots are randomly placed with a distance of 0.05 mm in the x- and y-directions within a range of 3.1 mm × 3.1 mm and collided at an initial velocity of 40 m/s. Figure 22(b) shows 100 shots, (c) 200 shots, (d) 300 shots, and (a) and (e) 600 shots. The initial height (position in the z-direction) of the shots was set at 0.04 mm intervals so that multiple shots do not collide at the same time. The indentation diameter under this condition was approximately 0.25 mm. The coverage was calculated by (the number of shots) × (indentation area) ÷ (3.1 × 3.1). The actual coverage was less than the calculated coverage because the indentations could overlap in the random arrangement.
FEM analytical model of step 1 with shot diameter of 0.5 mm.
Figure 23 shows the effect of the coverage on the plastic strain distribution within the thickness range. The introduced plastic strain is shallow, because the shot diameter is less than 4.76 mm. The plastic strain increased as the coverage increased, and the depth of the introduced plastic strain was unaffected by the coverage, which was similar to that when the shot diameter was 4.76 mm. The plastic strain near the surface increased with increasing coverage. In particular, the amount of increase was significant when the coverage was 100% or more. The increase in the plastic strain near the surface, owing to the increased coverage, can also be observed in Fig. 10, with a shot diameter of 4.76 mm. Because of the interference of the indentations, the amount of plastic strain increased more near the surface than that inside.
Effect of coverage C on plastic strain distributions for single-sided peen forming with shot diameter of 0.5 mm.
By approximating the same plastic strain distribution as in Fig. 17, we find that the depths at points B, C, and D are 0.046875, 0.109375, and 0.34375 mm, respectively. Figure 24 shows the results of approximating the plastic strains at points A, B, and C using eq. (1), considering the effect of coverage and not the effect of the initial stress. The plastic strains at points A, B, and C are approximately consistent with the results of the FEM analysis. In Fig. 23, the approximately calculated plastic strain distribution is indicated by polygonal lines. The distribution of the plastic strain at each coverage is largely similar to the results of the FEM analysis.
Effect of coverage on approximate parameters of plastic strain distribution with shot diameter of 0.5 mm.
Figure 25 shows the relationship between the curvature and the coverage calculated approximately when h = 7 mm. Owing to the shallow depth of the plastic strain introduced, the curvature was smaller than that when the shot diameter was 4.76 mm. The curvature increased rapidly when the coverage was 100% or less, and the increase rate decreased when the coverage was 100% or more. This behavior is consistent with the tendency of the saturation curve of the generally known peening intensity (arc height of an Almen strip). Figure 25 also shows the result of the FEM analysis in step 2, which is consistent with the results of the approximate calculation.
Effect of coverage on curvature of specimen after single-sided peen forming with shot diameter of 0.5 mm.
We verified the approximate calculation method by conducting experiments. The specimen material was A7075-T6. The shot diameter was 0.5 mm, on average, and the shot was made of steel with a hardness range of 420–540 HV. The coverage was 200%. Figure 26(a) shows an image taken using a high-speed camera (MEMRECAMACS-1 by nac Image Technology). The shots move from right to left, and the + marks in the figure indicate the trajectory of the measured shot. The shutter speed was 1/250,000 s, the frame speed was 50,000 fps, and the shooting range was approximately 150 mm. The shot velocity was calculated using the lateral movement of the shot every 0.1 ms. As shown in Fig. 26(b), the shot is accelerated by the high-speed air after being projected from the nozzle and then stabilizes at approximately 40 m/s near a standoff distance of 80 mm. This change in the shot velocity is consistent with the calculation results obtained by Ogawa et al.16) As shown in Fig. 25, the experimental results of the curvature and the results of the approximate calculation and FEM analysis are approximately the same.
Shot velocity distribution measurement results generated using high-speed camera.
As described above, we confirmed that the FEM analysis of the curvature and approximate calculation can be applied to peen forming with different shot diameters and shot velocities.
In this study, we examined the effect of coverage on the curvature of a high-strength aluminum alloy (A7075-T6) specimen after performing single-sided and double-sided peen forming. In the experiments, the shot diameter was 4.76 mm, the shot velocity was 20 m/s, and the coverage was 65% or less. The following are the conclusions drawn from the experimental results:
