Study on residual stress and deformation of titanium alloy thin-walled parts by ultrasonic shot peening

Abstract

After ultrasonic shot peening (USP) treatment, the titanium alloy thin-walled parts will induce strengthening residual stress. Simultaneously, the parts will undergo bending deformation due to the residual stresses, which can affect subsequent assembly and usage. Therefore, it is necessary to effectively predict the deformation induced by USP. Aiming at prediction of residual stress and deformation of USP, the experiments of titanium alloy specimen were carried out in this paper. The surface residual stress and the variation law of residual stress along the depth were obtained by using the corrosion stress delamination method. The residual stress was characterized by constructing the functional relationship between residual stress and depth under different process parameters. Furthermore, by establishing a three-dimensional finite element model of workpiece, the deformation of the specimen was obtained. Also the relationship among amplitude, maximum deformation and shot diameter was analyzed. Comparative results between experiments and simulations indicate that the deformation trends are consistent. Furthermore, it was observed that the maximum deformations occur in the central region of the thin plate. The research is validated that the residual stress characterization model can predict the deformation of titanium alloys thin-walled parts due to the USP. Therefore, this model can achieve residual stress field reconstruction and deformation prediction analysis.

Keywords

titanium alloy ultrasonic shot peening residual stress deformation simulation

Introduction

Titanium alloys are widely used in aerospace applications owing to their advantageous properties, including high strength, low density, and excellent corrosion resistance.^1–3 Specifically, they are frequently employed in the machining and manufacturing of thin-walled components for aero-engines, such as blades, magazines, and housings.⁴ However, the drive toward thinner and lighter designs inevitably reduces the stiffness and strength of these components. Consequently, under complex loads within high-temperature and high-pressure environments, susceptibility to the initiation of fatigue cracks is increased. Propagation of these cracks can occur, ultimately leading to fatigue fracture. The reliability and safety of aerospace structural parts are critically compromised by this phenomenon.^5–7 Therefore, the implementation of surface modifications to extend component lifespan is considered of paramount importance. To enhance the performance and service life of titanium alloy thin-walled parts, surface strengthening techniques, such as shot peening,⁸ are commonly applied.

USP is considered deriving from mechanical shot peening but more advanced, with ultrasonic energy transfer being utilized.^9–12 Compared to mechanical shot peening, a multidirectional, discrete, low-speed impact mode is employed by USP. This approach is characterized by significant advantages, such as high energy utilization, pollution-free operation, and strong controllability over process parameters.^13–15 Consequently, USP is regarded as particularly effective for enhancing the surface properties of materials and is widely employed in the peening of thin-walled components. However, the size characteristics of thin-walled parts result in their being made susceptible to a certain degree residual stress and excessive differential deformation during the peening process. This can lead to dimensional instability or shape distortion, ultimately affect parts function and safety.^16,17 Now a significant amount of simulation and experimental research has been conducted on shot peening technology for thin-walled titanium alloy components. Chaise¹⁸ employed a semi-analytical method to compute the average plastic strain tensor in a half-space. The transfer of this plastic strain field to a finite element model was proposed in order to simulate the deformation induced by ultrasonic shot peening, with experimental validation conducted. Tian et al.¹⁹ used numerical simulation methods to analyze the shot peening deformation of the blade. Wang et al.²⁰ developed a prediction method of residual stress and deformation for complex structure using analytical model for residual stress distribution of shot peened workpiece, achieving effective prediction of deformation in thin-walled dish-shaped parts after strengthening. Zhang et al.²¹ predicted the shot peening deformation of compressor blades based on time-sequential loading residual stresses, providing a crucial reference value for studying residual stress deformation in blade machining. Fu et al.²² used numerical simulation methods to design and optimize a shot peening process for Ti-6Al-4V titanium alloy and experimentally verified the effectiveness of the designed process. Currently, an in-depth research of the residual stress and deformation mechanisms in titanium alloy thin-walled parts subjected to USP is still lacked, which leads to difficulties in predicting the residual stress and deformations that occur in thin-walled parts after strengthening. All of this restrict the engineering application of USP. Therefore, such studies should be aimed at mastering the distribution and evolution patterns of residual stress in titanium alloy strengthening and establishing reliable methods for predicting post-peening deformation. This work is considered essential to provide a theoretical foundation and experimental data supporting the improvement of titanium alloy material properties and its broader application.

Residual stress field of USP

The following studies are considered crucial for controlling deformation enhancement in USP: clarifying and predicting the distribution of residual stress, constructing an accurate deformation prediction model.

During USP, the workpiece surface is impacted by shots under high-frequency vibration. Upon impact, part of the shots’ kinetic energy is converted into the deformation energy of the workpiece, which induces elastic-plastic deformation of the workpiece. As the shots rebound, the elastically deformed region of the workpiece tends to recover its original shape, which causes the material interior to exert compressive force on the plastically deformed surface layer, resulting in that residual compressive stress is formed on the material surface, while tensile stress is exhibited in the interior. The residual stress distribution profile is illustrated in Figure 1,²³ and the Key characterization parameters for this profile include: Surface residual compressive stress (σ_srcs), Maximum residual compressive stress (σ_mrcs), Depth of the residual compressive stress layer (Z₀), Depth of the maximum residual compressive stress (Z_m).

Figure 1.

Schematic diagram of residual stress in USP.

To facilitate calculation of the USP stress field, an approximate function is proposed to characterize the average stress field of shot peening. As illustrated in Figure 1, the distribution of residual compressive stress along the plate thickness caused by shot peening can be approximated by a cosine function. Therefore, the residual compressive stress can be represented by a cosine function with respect to the through-thickness depth Z, as given by the following equation²⁴:

σ (z) = A \cos \frac{π (z - m_{i})}{2 (e_{i} - m_{i})}

Where: A is a control parameter; e_i is the depth of the compressive residual stress layer; m_i is the depth of the maximum compressive stress.

Experiments and analysis

Experimental device

An USP experimental apparatus was independently designed based on its working principle, as shown in Figures 2 and 3. It primarily consists of ultrasonic generator, ultrasonic vibrator (incorporating a transducer and a horn), vibration head, chamber, shots, and clamping device, etc. The key parameters of the apparatus include excitation frequency of 20 kHz, amplitude range of 0–80 μm, and the shots made of cast steel.

Figure 2.

USP test device.

Figure 3.

Schematic diagram of shot peening and installation of test piece.

To investigate the deformation induced by USP on titanium alloy materials, the titanium alloy blades were selected. Since deformation is prone to occur near the blade edges, where sampling was performed. As thin-walled parts generally refer to parts whose wall thickness-to-outline dimension ratio is less than 1:20,²⁵ and considering the plate thickness of 3 mm, the sampling area was determined to be 80 mm×60 mm. This area was then flattened to produce an 80 mm × 60 mm × 3 mm specimen. The sampling location are illustrated in Figure 4. The specimens were machined using wire-cutting technology, and Figure 5 shows the specimens.

Figure 4.

Sampling of titanium alloy thin plate.

Figure 5.

Processing specimen of titanium alloy thin plate.

To systematically investigate the influence of amplitude (the key variable in the USP process) on the deformation and residual stress distribution of titanium alloy materials, and to provide guidance for the selection of actual production process parameters, the following experimental studies were conducted. Based on existing research results and the parameters range of the apparatus itself,²⁶ six sets of test conditions (USP-1 to USP-6) were designed for USP treatment of titanium alloy specimens, employing amplitude values of 40 and 60 μm, and shot diameters of 1.4, 2, and 2.5 mm. The coverage rate for all cases is required to exceed 98%, and the fluorescence tracking method was employed to determine the coverage rate after USP strengthening. The fluorescent solution was uniformly applied to the surface of the test specimen. After shot peening for a specific duration, the residual condition of the fluorescent solution on the surface was examined. When no fluorescent residue remained on the surface, the coverage rate was determined to be 100%. Specific experimental parameters are shown in Table 1.

Table 1.

USP test parameters.

Exp. No.	Amplitude/μm	Shot diameter/mm
USP-1	40	1.4
USP-2	40	2.0
USP-3	40	2.5
USP-4	60	1.4
USP-5	60	2.0
USP-6	60	2.5

Internal residual stress test

Testing was performed employing a Proto-iXRD stress analyzer in conjunction with the electrochemical stripping method. The testing procedure is illustrated in Figure 6. As shown in the Figure 6, the corrosion crater was generated during the stress measurement of the titanium alloy thin plate. The analyzer operated at the voltage of 20 kV and the current of 0.4 mA, with the X-ray spot diameter of 2 mm and the diffraction angle of 140°. The corrosion depth of each layer is approximately 30 μm, determined by using a digital micrometer.

Figure 6.

Residual stress test diagram.

Each residual stress value must be tested at six points, and the average of these values is taken as the final result. Test results of the distribution of residual stress along the thickness of the titanium alloy specimen under USP-1-6 working conditions is shown in Figure 7. Among these, under amplitudes of 40 and 60 μm, as the shot diameter increases from 1.4 to 2.5 mm, both the surface residual compressive stress and maximum residual compressive stress demonstrate an increasing trend. Under amplitude of 40 μm, the surface residual compressive stress increases from 379 to 443.9 MPa, representing an increase of 17.1%. The maximum residual compressive stress increases from 456.8 to 534.1 MPa, representing an increase of 16.3%. Moreover, as the shot diameter increases, the depth of the compressive stress layer in the material’s surface region also increases to some extent. The same trend is observed under the amplitude of 60 μm, the surface residual compressive stress increases from 383.7 to 468.2 MPa, representing an increase of 22%, and the maximum residual compressive stress increases from 502.7 to 576.6 MPa, with an increase of 14.7%. When the shot diameter remains constant and only the amplitude parameter changes, the residual stress also varies with the increase of amplitude. For example, when the shot diameter is 2 mm, the surface residual compressive stress and maximum residual compressive stress at 40 μm amplitude are 391.6 and 532.6 MPa, respectively. Whereas at 60 μm amplitude, the surface residual compressive stress and maximum residual compressive stress are 424.7 and 570.9 MPa respectively, with increases of 8.5% and 7.2%. When both the amplitude and shot diameter increase simultaneously, the change in the corresponding values become more pronounced. When the shot diameter is 1.4 mm and the amplitude is 40 μm, the surface compressive stress and the maximum residual compressive stress are 379 and 456.8 MPa, respectively. Whereas at a shot diameter of 2.5 mm and amplitude of 60 μm, the surface compressive stress and maximum residual compressive stress are 468.2 and 576.6 MPa respectively, with corresponding increase of 23.5% and 26.2%. As could be seen from the above analysis results, with the increase of shot diameter and amplitude, both the surface residual compressive stress and the maximum residual compressive stress increase to varying degrees, which validate the accuracy of the FEM-DEM coupled model. The specific experimental results are presented in Table 2.

Figure 7.

Relationship between residual stress and depth.

Table 2.

USP test results.

Operating mode	Amplitude/μm	Shot diameter/mm	Surface residual compressive stress/MPa	Maximum residual compressive stress/MPa
USP-1	40	1.4	379.0	456.8
USP-2	40	2.0	391.6	532.6
USP-3	40	2.5	443.9	534.1
USP-4	60	1.4	383.7	502.7
USP-5	60	2.0	424.7	570.9
USP-6	60	2.5	468.2	576.6

Residual stress field characterization and reconstruction

Origin software was employed to perform customized nonlinear fitting on the residual stress test data of titanium alloy thin plates. As shown in Figure 8, the fitted curves passed nearly through all measured data points, accurately capturing experimental trends. Furthermore, the coefficients of determination (R²) for all fitting functions exceeded 0.92, confirming the model’s effectiveness in characterizing residual stress distributions. Given the discrete nature of measured stress data, the fitted stress function enabled initial predictions of internal residual stresses, facilitating assessment of residual stress field distributions.

Figure 8.

Residual stress fitting diagram. (a) USP-1. (b) USP-2. (c) USP-3. (d) USP-4. (e) USP-5. (f) USP-6.

Taking the workpiece depth Z as the independent variable, the residual stresses were represented by fitting curves to establish a function of the workpiece depth Z, thereby a residual stress evaluation function for the titanium alloy specimens under USP-1-6 conditions was constructed. The function expression was as follows.

The fitted residual stress function expression for specimen USP-1 is:

σ (z) = - 456.8 \times \cos \frac{25 π (z - 0.06)}{8} (0 \leq z \leq 0.23)

(1)

The fitted residual stress function expression for specimen USP-2 is:

σ (z) = - 532.6 \times \cos \frac{50 π (z - 0.08)}{17} (0 \leq z \leq 0.26)

(2)

The fitted residual stress function expression for specimen USP-3 is:

σ (z) = - 534.1 \times \cos \frac{25 π (z - 0.1)}{14} (0 \leq z \leq 0.39)

(3)

The fitted residual stress function expression for specimen USP-4 is:

σ (z) = - 502.7 \times \cos \frac{50 π (z - 0.09)}{19} (0 \leq z \leq 0.29)

(4)

The fitted residual stress function expression for specimen USP-5 is:

σ (z) = - 570.9 \times \cos \frac{5 π (z - 0.09)}{2} (0 \leq z \leq 0.3)

(5)

The fitted residual stress function expression for specimen USP-6 is:

σ (z) = - 576.6 \times \cos \frac{100 π (z - 0.085)}{43} (0 \leq z \leq 0.31)

(6)

Analysis of the residual stress fields in these specimens revealed relatively uniform stress distribution at the same depth, but significant variation along the depth. Assume that the stress distribution at the same depth is homogeneous, meaning that stress at all points at the same depth are equal, therefore, it is only necessary to add different stress along the depth. In order to accurately establish the initial residual stress field in the specimen, a SIGINI user subroutine was developed to directly call the residual stress evaluation function of the specimen for applying initial stress data. When the stress states were assigned to each node in the model in coordinate form, the initial stress field could be precisely reconstructed. The local three-dimensional residual stress distribution contour plots reconstructed for all specimens using the titanium alloy stress function are similar, and Figure 9 shows the results for the USP-1 specimen.

Figure 9.

Residual stress reconstruction contour.

Numerical simulation and analysis of deformation in USP

To ensure consistency between simulation boundary conditions and experimental conditions, an 80 mm × 60 mm × 3 mm three-dimensional titanium alloy specimen model was established. Static analysis was employed to calculate stress redistribution and deformation in the thin plate. The material selected is TC4 titanium alloy, which has an elastic modulus of 110 GPa and a Poisson’s ratio of 0.3. Additionally, the model boundary conditions are set by referencing the original position selected for the specimen model, employing four-sided constraints with the bottom and top surfaces as free boundaries (detailed in Figure 10). The mesh partitioning for the titanium alloy thin plate is shown in Figure 11, in which a layered-mesh method was employed. To clearly illustrate the stress distribution, the minimum mesh edge length was set to 0.02 mm, the total number of elements was 325,600, and the total number of nodes was 336,027.

Figure 10.

Boundary condition setting.

Figure 11.

Thin plate grid division.

Figure 12 presents the deformation contour of the titanium alloy thin plate following USP. The contour reveals that the deformation distribution patterns of titanium alloy thin plates exhibited certain common characteristics. After stress release, the specimen exhibited overall bending and warping deformation, with the maximum deformation consistently located at the specimen center. As can be seen from Figure 12(a) and (d), when the shot diameter is 1.4 mm, the maximum deformations corresponding to amplitudes of 40 and 60 μm are 0.0143 and 0.019 mm respectively, with a deformation increase of 32.9%. As shown in Figure 12(b) and (e), the maximum deformations of 0.0191 and 0.0225 mm occurs at 40 and 60 μm amplitudes respectively for a 2 mm shot diameter, representing a 17.8% increase. Conversely, Figure 12(c) and (f) show that at a shot diameter of 2.5 mm, the maximum deformations corresponding to amplitudes of 40 and 60 μm are 0.02307 and 0.023085 mm, respectively, with no significant change. With the increase of shot diameter, the deformation gradually increases. As can be seen from Figure 12(a) to (c), when the amplitude is 40 μm, as the shot diameter increases from 1.4 to 2.5 mm, the maximum deformation changes from 0.0143 to 0.02307 mm, representing a deformation increase of 61.3%. As can be seen from Figure 12(d) to (f), under the amplitude of 60 μm, as the shot diameter increases from 1.4 to 2.5 mm, the maximum deformation changes from 0.01943 to 0.02308 mm, representing a deformation increase of only 18.8%. As both the amplitude and shot diameter increase simultaneously, the maximum deformation reaches 0.0143 mm under 40 μm amplitude and 1.4 mm shot diameter, whereas it is 0.02308 mm under 60 μm amplitude and 2.5 mm shot diameter, representing a significant deformation increase of 61.4% (Table 3). Analysis incorporating the process parameters indicates that titanium alloys thin-walled parts deformation progressively increased with both amplitude and shot diameter

Figure 12.

Deformation contour of titanium alloy thin plate. (a) USP-1. (b) USP-2. (c) USP-3. (d) USP-4. (e) USP-5. (f) USP-6.

Table 3.

Deformation results of USP test.

Operating mode	Amplitude/μm	Shot diameter/mm	Maximum deformation rises/mm
USP-1	40	1.4	0.0143
USP-2	40	2.0	0.0191
USP-3	40	2.5	0.0231
USP-4	60	1.4	0.0190
USP-5	60	2.0	0.0225
USP-6	60	2.5	0.0231

Test validation

The deformation of the titanium alloy thin plate was measured using a Daisy-10228 coordinate measuring machine (CMM), as shown in Figure 13. To quantify the deformation induced by USP, the deformation is defined as the difference (△Z)) between each point and its corresponding position on the original specimen. The schematic diagram illustrating this deformation is shown in Figure 14. Figure 15 shows the locations of the measurement points on the thin plate, and the specimen center was designated as point 3. Points were arranged in a rectangular grid along the X- and Y-axes at 10 mm intervals, resulting in a total of nine measurement points. The coordinates of these measurement points are detailed in Table 4.

Figure 13.

Schematic diagram of deformation test for titanium alloy thin plate.

Figure 14.

Schematic diagram of thin plate deformation definition. (a) Schematic diagram of length test. (b) Schematic diagram of width test.

Figure 15.

Distribution of deformation detection points for titanium alloy thin plate.

Table 4.

Coordinates of deformation measurement points for titanium alloy plates.

Measurement points	1	2	3	4	5
Coordinate (X, Y) /mm	(−20,0)	(−10,0)	(0,0)	(10,0)	(20,0)
Measurement points	6	7	8	9
Coordinate (X, Y)/mm	(0,20)	(0,10)	(0,−10)	(0,−20)

Based on the experimental deformation test point locations, the deformation for Points 1–9 from the simulation models (USP-1–USP-6) were extracted and compared with the experimentally measured deformation. Figure 16 presents a comparison of the deformation between experiment and simulation. As shown in Figure 16, the deformation trends predicted by the simulation agree well with the experimental measurements, and the maximum deformation occurs at the center region of the specimen. Comparative analysis shows that under USP-1 working condition, the average X-direction deformation error between simulation and experimental test is 9.4%, while the average Y-direction deformation error is 10.5%. Under USP-2 working condition, the average X-direction deformation error between simulation and experimental test is 9%, while the average Y-direction deformation error is 11.2%. Under USP-3 working condition, the average X-direction deformation error between simulation and experimental test is 9.1%, while the average Y-direction deformation error is 10.6%. Under USP-4 working condition, the average X-direction deformation error between simulation and experimental test is 8.8%, while the average Y-direction deformation error is 9.5%. Under USP-5 working condition, the average X-direction deformation error between simulation and experimental test is 10.4%, while the average Y-direction deformation error is 11.6%. Under USP-6 working condition, the average X-direction deformation error between simulation and experimental test is 11.3%, while the average Y-direction deformation error is 12.1%. Based on the comparative analysis above, the following conclusion can be drawn: the experimentally measured deformation is typically larger than the simulated deformation, with a maximum error of 12.1%. The reason for the errors may be attributed the simulation model’s failure to account for the preexisting minor deformation of the specimen before shot peening, secondly, it may be due to the simplification of the residual stress field. The residual stress field of the specimen after USP contains six independent stress components, but in practice only the stresses in the X, Y direction were applied. Although there are numerical differences between the deformation obtained from numerical simulation and actual measurements, they share the same variation trend. Based on the comparison between experimental results from titanium alloy specimen tests and simulation outcomes, the deviation between simulation and measurement results is less than 12.5% (Table 5). Therefore, simulation results can be used to accurately predict actual deformation and applied to deformation prediction in practical engineering projects as well as to guide process optimization implementation.

Figure 16.

Comparison of thin plate deformation test and simulation results. (a) USP-1. (b) USP-2. (c) USP-3. (d) USP-4. (e) USP-5. (f) USP-6.

Table 5.

Error in the USP test results.

Operating mode	X-direction error	Y-direction error
USP-1	9.4%	10.5%
USP-2	9.0%	11.2%
USP-3	9.1%	10.6%
USP-4	8.8%	9.5%
USP-5	10.4%	11.6%
USP-6	11.3%	12.1%

Conclusions

This study conducted experimental research and simulation prediction on the residual stress characterization, reconstruction, and deformation in titanium alloys after USP strengthening. The following conclusions were drawn:

(1) Based on the similarity in residual stress distribution patterns within specimen after USP treatment, a mathematical function can be employed to describe the distribution characteristics of residual stresses. Consequently, a residual stress characterization function for USP has been established.

(2) Thin plate specimens of titanium alloy were prepared and subjected to USP under various process parameters. Residual stress distribution data along the depth were obtained by using the electrochemical stripping method. Based on experimental data, nonlinear fitting was employed to derive residual stress characterization function expressions under different process conditions.

(3) A three-dimensional model of the titanium alloy thin plate was established. The reconstruction of residual stress fields and deformation simulation for USP were completed. The deformation of thin plate was measured using a CMM, and the measure data were compared with simulation data, showing a maximum error of no more than 12.1%. Finally, the effectiveness and consistency between simulation and experimental results of residual stress characterization, reconstruction, and deformation prediction were validated.

Footnotes

Handling Editor: Jianjian Wang

ORCID iDs

Dou Yan-Tao

Zhang Hong-Wei

Zhang Jiu-Ju

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

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

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