Introduction

Fatigue failure is one of the most common forms of mechanical failure in industry. Most fatigue damage of mechanical parts occurs initially on the surface, and then, the fatigue crack propagates inside during cyclic load conditions (Ref 1). Mechanical surface treatments such as shot peening, hammering and cold rolling are widely used in the automotive, aerospace and spring manufacturing industries with the aim of introducing compressive residual stresses and changing the microstructure in surface layers, which can improve the service life of mechanical parts greatly. With the rapid development of nanoscience and technology, surface nanocrystallization (SNC) of metallic materials can be achieved by mechanical surface strengthening methods such as high-energy shot peening (HESP) and surface mechanical attrition treatment (SMAT) (Ref 2, 3).

Surface crack initiation can be prevented effectively due to the surface nanocrystalline layer and the fatigue crack propagation can be inhabited effectively due to the coarser grains in the interior (Ref 2, 4). The gradient nanostructure induced by severe plastic deformation via different ways can effectively improve the fatigue property of metallic component (Ref 5, 6). Heilmann et al. (Ref 7) found the grain refinement phenomenon appearing near the surface of copper via a sliding wear method to generate severe plastic deformation on a treated surface. Jang et al. (Ref 8) proposed a ball milling method to obtain nanostructure on the surface of iron. The experimental result showed that the surface hardness increased with grain refinement. Korznikov et al. (Ref 9) investigated the influence of severe plastic deformation on structure and phase composition of high carbon steel via upper immobile and lower rotatable Bridgman anvils. The nanocrystalline structure appeared on the treated surface and the surface hardness was 2.5 times higher than the initial state. Liu et al. (Ref 10) claimed the nanocrystalline structure appearing on the surface of 316 L stainless steel treated by ultrasonic shot peening and the grain size increasing gradually from 10 nm at the top surface layer to 100 nm at the depth of 30 μm. They also found the nanostructure surface layer on low-carbon steel via HESP in their following works (Ref 11). Wang et al. (Ref 12) studied the mechanical properties of nanocrystalline surface of 304 stainless steel obtained by sand blasting. Ivanisenko et al. (Ref 13) reported nanostructure appearing on the surface of UIC 86 V pearlitic steel by high pressure torsion and the surface grain size reaching up to 10 nm. In the work of Raja et al. (Ref 14), nanocrystalline was obtained on the surface of Ni-22Cr-13Mo-4W alloy via shot peening (SP) and low-temperature annealing, which could improve the corrosion resistance effectively under a thermal acid etching condition. Todaka et al. (Ref 15) studied the nanocrystallization of drill hole surface by high-speed drilling. The results showed the nanocrystalline layer formed on the inner surface of the hole, which had high hardness and high thermal stability. Wen et al. (Ref 16) investigated the surface microstructure of nickel-based alloys after SMAT treatment. The results showed that the saturation magnetization and coercivity of surface layer was significantly improved due to nanocrystalline grains on the surface. Wang et al. (Ref 17) analyzed the surface nanocrystalline of 1Cr18Ni9Ti stainless steel induced by HESP via x-ray diffraction (XRD) and transmission electron microscope (TEM) methods. The results showed that the great improvement of the corrosion resistance was achieved because of surface nanocrystalline. Bagherifard (Ref 18) investigated the bending fatigue of 39NiCrMo3 steel treated by HESP and the results showed the nanocrystalline surface was beneficial to the improvement of fatigue performan)ce. In all the existing mechanical surface treatments for obtaining nanocrystalline surface layer, HESP is one of the most promising choices for industry because of its own characteristics such as remarkable and efficient strengthening effect, relative simplicity of equipment, no limitation of treated component shape and applicability of different kinds of materials (Ref 19, 20). Therefore, HESP becomes one of the main choices to obtain nanocrystalline layer on metallic materials in recent years.

In addition to the experimental study on the SNC via the mechanical surface treatment, using numerical simulation, especially the finite element method (FEM) to investigate the SNC is becoming a hot topic because of rapid development of computing technology in recent years. Numerical simulation of SNC can not only reduce the cost of HESP experiment but also provide a mathematical way to investigate the fundamental mechanism of SNC via HESP. Some studies had shown that there was a critical value of the equivalent plastic strain (PEEQ) for nanocrystalline structure formation after severe plastic deformation (Ref 21, 22). Although the critical value was associated with the material’s own property, the minimum value of the PEEQ was about 7-8 (mm/mm) to generate nanocrystalline structure after the HESP treatment according to Umemoto et al. (Ref 21). In Valiev’s study (Ref 22), the nanostructure appeared in metals of severe straining with the value of PEEQ greater than 6-8 (mm/mm). The value of PEEQ can be regarded as a key evaluation parameter of nanostructure formation.

In the HESP process, the resulting value of PEEQ in the surface region depends on many parameters such as shot velocity, shot diameter and surface coverage. However, in the previous researches of HESP, usually only one group of HESP parameters was chosen in their respective works (Ref 17,18,19, 21), and the quantitative relationship between PEEQ and grain size was not proposed (Ref 23). Therefore, in this paper, the relationship between the value of PEEQ and the degree of grain refinement was established according to the data from FE model and experimental analysis. Specifically, a random shot impact HESP model was built via the finite element (FE) software ABAQUS/Explicit firstly. In the next step, XRD analysis was carried out with the aim of obtaining the relationship between the value of PEEQ and the grain size. And then, the surface topography and the depth profiles of microhardness and full width at half maximum (FWHM) were obtained with the aim of assessing and verifying the surface integrity (SI) and nanostructure formation.

HESP Model Setup

FE-Geometry-Model Setup

As in our previous work (Ref 23), the HESP model was developed via the commercial FEM software ABAQUS/Explicit 6.10. Different parameters including shot velocity, shot diameter, surface coverage (number of shots) were set in a HESP model in order to study the influence of HESP parameters on surface grain refinement. According to the work of Bagherifard et al. (Ref 2), it is reasonable to choose the value of PEEQ as an evaluation criterion of the grain refinement after HESP treatment. Therefore, the value of PEEQ obtained from the HESP model was used to assess the grain refinement of peened surface in this work.

Figure 1 shows the schematic diagram of a HESP finite element model with 52 random shots. The model consisted of two parts including a target workpiece (square-shaped deformable plate) and rigid shots. The dimensions of the target workpiece were set the same as in our previous work (Ref 23). The dimensions of the target workpiece were 3 mm × 3 mm × 2 mm in the HESP model for different parameter cases. As the shots’ impact area was defined in the central area of the target workpiece, the maximum plastic deformation always appeared and nanocrystalline structure was very likely to appear in this region. The mesh was further refined in this region as in our previous work with dimensions of 1 mm × 1 mm × 2 mm in the central area of the target workpiece (Ref 23). The maximum values of PEEQ were extracted from this refined mesh region in different parameter cases. The influence of boundary conditions on the PEEQ value of this region could be ignored because the central region was far away from the around boundary constraint. Different mesh generation methods were carried out in the central region and marginal region of the target workpiece. Since the mesh density on the calculation accuracy of the value of PEEQ was studied in our previous work (Ref 23), 0.0 2mm was a proper size of regular hexahedron elements in the central area of the target workpiece, which was equal to 1/14 of the dimple diameter after the single shot peening (Ref 24, 25). The element size of the area out of the central region increased with the distance from the center point increasing. The mesh ratio was 0.025, as shown in Fig. 2. In ABAQUS, the element type was also chosen the same as in our previous work, eight-node brick with reduced integration and hourglass control (C3D8R) for the target workpiece and eight-node linear one-way infinite brick (CIN3D8) for the boundary of the target workpiece, to get good calculation accuracy (Ref 23, 26).

Fig. 1
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HESP model with 52 random shots impacting on the target workpiece

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Fig. 2
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Schematic diagram of the meshing method of the target workpiece in HESP model

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During the HESP process, numerous shots impacted the treated surface at random locations and in a random sequence. In order to describe the HESP process precisely, a random shot generation program was established via secondary development of ABAQUS by using Python script. Specifically, the reference point was assigned to the center of each shot and then shots were generated by the script program. These randomly distributed shots in 3D space were realized by using a random function to generate the random coordinates of each reference point. The random function is given in Eq 1 as follows:

$$\left\{ \begin{gathered} x = \, - 0.5 \, + \, 1.0 \, \times {\text{ random}}.{\text{random}}() \hfill \\ y = \, - 0.5 \, + \, 1.0 \, \times {\text{ random}}{\text{.random}}() \hfill \\ z = \, - 0.5 \, - \, \left( {N - 1} \right) \, \times \, 0.2 \, \times {\text{ random}}{\text{.random}}() \hfill \\ \end{gathered} \right.$$
(1)

where x, y, z were the coordinates of the reference point, N was the number of shots and random.random() was a random function that produced a random number between 0 and 1. The mass of shot, the moment of inertia of shot and the velocity of the shot were set to the reference point of each shot. All the parameters of the shot could be changed via the Python script. The meshing method and the element type of shots were chosen the same as in our previous work (Ref 23). The element size of the shots was 0.03 mm. The impact angle of all shots was 90° in all HESP models with different processing parameters. The contact between the shots and the target workpiece was defined via a kinematic contact pair, the same as in our previous work (Ref 23), with an isotropic Coulomb friction coefficient μ = 0.4 (Ref 27).

Material Model Setup

The material of the HESP workpiece for simulation and experiment was 42CrMo (AISI 4140). The heat treatments of 42CrMo in this work were the same as in our previous work (Ref 28). In order to describe the highly irregular elasto-plastic cyclic loading caused by the continuous impact of the shots and the work hardening under high strain rate during HESP, the Johnson–Cook model, which was suitable for describing the material response with high strain rate deformation, was chosen in the HESP model (Ref 29,30,31). The flow stress of material is also the same as in our previous work (Ref 28), and not given here to avoid redundancy.

Calculation Method of Coverage

As the spatial distribution of the shots in this HESP model was random, the distribution of dimples on the surface of target workpiece, which was generated by the shots’ impact, was also random. The surface coverage was defined as the ratio of the area of deformed dimples to the entire treated surface area. In this work, the value of surface coverage was calculated according to the method proposed by Miao et al. (Ref 32) if surface coverage was less than 100%. According to their definition, the value of surface coverage was the ratio of the number of nodes, whose PEEQ value was larger than the PEEQ value of boundary node, to the total number of nodes in the entire treated surface area. In the condition of surface coverage larger than 100%, the calculated method for surface coverage was based on the work of Kirk et al. (Ref 33). According to the theoretical calculation and experimental verification in their work, the relationship between surface coverage (Cr) and the total number of shots (N) is given in Eq 2 and 3 as follows:

$$C_{r} = \left( {1 - e^{{ - A_{r} }} } \right) \times 100\%$$
(2)
$$A_{r} = \frac{{N \times \pi \left( {d_{i} /2} \right)^{2} }}{{\pi \left( {D/2} \right)^{2} }}$$
(3)

where Cr was surface coverage in simulation (represented by Cr in all the following figures), di was the dimple diameter after single shot impact, D was the diameter of treated area and Ar is the ratio of total dimple area to the treated area. Figure 3 shows the schematic diagram of surface coverage in the peened area. The value of D is 1 mm shown in Fig. 3. For practical purposes, 98% surface coverage was usually considered as 100% coverage based on SAE J2277 (Ref 34). According to Eq 2, Ar is 4 when Cr is about 98%. For instance, when the diameter of shot was 0.6 mm and the velocity of shots was 100 m/s, the dimple diameter after one shot impact could be obtained via the proposed HESP model with the value of 0.28 mm. And the number of shots (N) was 52 when the surface coverage was 100% according to Eq 3. In terms of other values of coverage, the number of shots in simulation can be obtained according to the corresponding ratio of required coverage to 100% surface coverage. Therefore, the number of shots for 200%, 300%, 400%, 800% and 1000% are 104, 156, 208, 416 and 520, respectively.

Fig. 3
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Schematic diagram of surface coverage in peened area

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The Extraction and Evaluation Method of PEEQ

Since severe plastic deformation led to nanocrystalline structure on the peened surface, the area where the large value of PEEQ appeared was chosen as the PEEQ extraction region. Figure 4 shows the top view of the PEEQ values on the peened surface and PEEQ extraction region. In order to compare the simulated and experimental data, the diameter of extraction region in simulation was the same as the diameter of the x-ray spot in XRD experiment. The script program for determining the diameter of extraction region in the HESP model was written by Python. As shown in Fig. 4, the diameter of extraction region was 0.2 mm, which was the same as the diameter of the x-ray spot in XRD experimental test (Bruker D8 advance x-ray equipment, Center for Materials Research and Analysis, Wuhan University of Technology). Specifically, the values of PEEQ of all nodes in the black circular region were extracted and averaged. The average value was regarded as the value of PEEQ of this layer. And the depth profiles of PEEQ were calculated and extracted from the HESP model via this proposed extraction method.

Fig. 4
figure 4

Top view of the PEEQ values on the peened surface and the PEEQ extraction region

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Experiment Setup

HESP Experiment

The material used in the HESP was 42CrMo with the quenched and tempered state as the same in our previous work (Ref 28). As mentioned in our previous study, HESP experiment was carried out using the XN-9065P pneumatic SP machine at a high-pressure level. The experimental peening surface coverage was achieved by visual inspection with the fluorescence measurement method (Ref 28). The different combinations of HESP parameters are given in Table 1. The material of shots used in the experiment was cast steel with hardness of 45-48 HRC. In the HESP process, the experimental shot velocity was calculated based on the peening pressure, the mass flow and the shot diameter via an empirical formula proposed by Klemenz (Ref 35).

Table 1 Different combinations of HESP parameters
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Microhardness Measurement

The microhardness measurements were taken on the surface and in depth of HESP treated workpiece by a HUAYIN HV-1000A hardness tester via a diamond indenter with a load of 5 N. In order to measure the microhardness in depth, the workpiece was cut via wire cut electrical discharge machining and then the lateral face of workpiece was polished. The microhardness depth profile was obtained by measuring on cross section successively along the depth direction. Three points were measured in each depth and then averaged in order to avoid accidental error.

Surface Topography and Microstructure Measurement

The surface topography and microstructure were measured by a KEYENCE VHX-5000 digital microscope. The surface topography treated by different HESP processes was obtained and the color in 3D surface topography could represent the surface quality and roughness. In terms of microstructure measurement, the chosen measurement areas were polished and etched via a mixed solution of saturated picric acid and sodium dodecyl benzene sulfonate.

X-ray Diffraction (XRD) Measurement

The XRD instrument was D8 Advance with a rated output power of 3 kW. The diffraction profiles of all specimens were measured by an x-ray diffractometer with Cu Kα radiation, with voltage 40 kV and current 30 mA. The angle of 2θ was in the range from 35 to 90°. The scanning mode was continuous scanning with a step size of 0.01° and a velocity of 2°/min. In order to investigate the gradient nanostructure in surface region after HESP treatment, the Voigt method was conducted to analyze the grain size in depth. According to the Voigt method, it was assumed that the Cauchy component of the XRD structural broadened profile was solely due to the crystallite size while the Gaussian component arose from microstrain (Ref 36, 37). The XRD structural broadened profile was obtained via separating the instrumental profile from the original measured line profile based on the work of Langford (Ref 38). Therefore, the value of grain size can be given in Eq 4 and 5 as follows:

$$G = \frac{K\gamma }{{\beta_{{{\text{ca}}}} \cos \theta }}$$
(4)
$$K = {{2\omega } \mathord{\left/ {\vphantom {{2\omega } \beta }} \right. \kern-\nulldelimiterspace} \beta }$$
(5)

where G is grain size, K is the shape factor, 2ω is the full width at half maximum (FWHM) of structural broadened profile, β is the integral width of structural broadened profile, subscript ca denotes the Cauchy components and γ is the wavelength of x-ray. The XRD measurements in depth were carried out by precise iterative electrolytic removal of thin surface layer. The depth profiles of FWHM and grain size can also be obtained via precise control of the thin surface layer removal.

Results and Discussion

Evaluation and Prediction of Nanostructure Formation

As given in Introduction, there are many different methods of severe plastic deformation to realize surface nanocrystallization, such as HESP, SMAT, high-energy ball milling and ultrasonic peening. Umemoto and Valiev et al. claimed the value of PEEQ can be regarded as a criterion to predict the nanostructure formation according to other researchers’ work and their own investigations (Ref 21, 22). Both of them proposed the minimum equivalent plastic deformation for nanostructure formation with the value of 6-8 (mm/mm), which provided a criterion for predicting nanostructure formation via FEM. Therefore, the value of PEEQ was regarded as an evaluation criterion of SNC in HESP treatment.

Figure 5(a) shows the XRD patterns of the HESP treated area in different depths with the shot velocity (V) of 100 m/s, the shot diameter (d) of 0.6 mm and the experimental surface coverage (C) of 1000%. Generally, there are three crystalline planes (110), (200) and (211) for the material 42CrMo (AISI 4140) with the quenched and tempered state in x-ray diffraction analysis. Compared with the planes of (200) and (211), the peak height of plane (110) is higher, the influence from the background error is relatively small, and the error of microstructure analysis is smaller. Figure 5(b) shows the normalized XRD patterns and the FWHM values of (110) crystal plane in different depths. The depth profiles of grain size can be calculated via the Voigt method shown in sect. 3.4 (Ref 38). Figure 6 shows the depth profiles of PEEQ obtained by the HESP model and grain size obtained by XRD analysis after HESP treatment with the shot velocity of 100 m/s, the shot diameter of 0.6 mm and the experimental surface coverage of 1000%. The red dot curve represents the grain size distribution in depth and the black square curve represents the PEEQ value distribution in depth. According to the work of Hassani-Gangaraj et al. (Ref 39), 300% surface coverage defined by Eq 2 and 3 in FEM was equivalent to the experimental surface coverage around 1000-1200%. Therefore, the simulated surface coverage (Cr) of 300% and the experimental surface coverage of 1000% can be comparable in this work.

Fig. 5
figure 5

(a) XRD patterns of the HESP treated area in different depths, (b) the normalized XRD patterns and the FWHM values of (110) crystal plane in different depths with shot velocity of 100 m/s, shot diameter of 0.6 mm and experimental surface coverage (C) of 1000%

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Fig. 6
figure 6

Depth profiles of the value of PEEQ and grain size after HESP treatment with shot velocity of 100 m/s, shot diameter of 0.6 mm and experimental surface coverage of 1000%

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Figure 6 shows that the value of PEEQ decreases and the grain size increases with depth increasing. The value of PEEQ drops close to 0 from 7.6 mm/mm when the depth increases to about 250 μm from 0 μm. And the grain size increases to about 340 nm from 27 nm and becomes stable from the depth of 250 μm to the depth of 384 μm. The grain size is smaller than 100 nm and the value of PEEQ is larger than 6 (mm/mm) in the depth range of 0-50 μm, which is in accordance with the results of Umemoto et al. (Ref 21) and Valiev et al. (Ref 22). According to the data shown in Fig. 6, it can be seen that there is a certain correspondence between the value of PEEQ and grain size in the depth direction and that the nanocrystalline structure appears when the PEEQ value is larger than 6 (mm/mm).

In order to obtain the quantitative relationship between the value of PEEQ and the grain size, the function between the grain size and the value of PEEQ was established by a nonlinear equation fitting method based on the data shown in Fig. 6 and the data from the previous research results (Ref 40,41,42,43,44,45). Figure 7 shows the fitted curve of PEEQ values and grain sizes. It can be seen that most of the data are located on and around the fitted curve. The relatively small error represents that the fitting accuracy of the proposed nonlinear equation is high. And the fitting equation is given in Eq 6 as follows:

$$G = \, {{409.66 \, } \mathord{\left/ {\vphantom {{409.66 \, } {\left( {1 \, + \, \left( {\varepsilon^{pl} /3.15} \right)^{1.2} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 \, + \, \left( {\varepsilon^{pl} /3.15} \right)^{1.2} } \right)}} \, - \, 60.66$$
(6)

where G is the grain size in nm and εpl is the value of PEEQ in mm/mm. The grain size can be obtained according to Eq 6 if the value of PEEQ is given. Figure 8 shows the comparison of the grain size distributions in depth obtained by XRD analysis and by the proposed fitting equation in other two HESP parameter conditions. It can be seen that the depth profiles of grain size obtained by the proposed fitting equation are in good accordance with those obtained by XRD analysis, which verifies the validity of the proposed fitting equation to predict the grain size by the value of PEEQ. This prediction method is interesting because it not only provides a simple and effective way to predict grain size via FEM data but also proposes a methodology to build a relationship between experimental and numerical results.

Fig. 7
figure 7

Fitted curve of the values of PEEQ and grain sizes.

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Fig. 8
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Comparison of the grain size distributions in depth obtained by XRD analysis and by the proposed fitting equation in other two HESP parameter conditions: (a) shot velocity of 100 m/s, shot diameter of 1.0 mm and experimental surface coverage of 400%, (b) shot velocity of 80 m/s, shot diameter of 0.6 mm and experimental surface coverage of 1000%

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Based on the result shown in Fig. 8, it can be seen that the value of PEEQ obtained by the FE model can assess the grain refinement and predict the nanostructure formation on the surface of HESP treated component. Furthermore, the element size has a certain influence on the value of PEEQ in FE model. According to the work of Bagherifard et al. (Ref 24), the real value of PEEQ can only be obtained when the element size in FE model is zero. Li et al. (Ref 46) claimed the real value of PEEQ could be obtained by an extrapolation method when the element size approached 0. And the grain refinement can be estimated according to the real value of PEEQ. A linear relationship between the element size and the maximum PEEQ value was found by Bagherifard et al. (Ref 24). Therefore, the real value of PEEQ can be obtained by extrapolating the element size to 0 through at least two cases with different element sizes. Figure 9 shows the fitting linear relationship between the maximum PEEQ value (i.e., real value of PEEQ) and the element size with regard to (a) the influence of target element size (b) the influence of target and shot element sizes. It can be seen that the real value of PEEQ is 7.9 (mm/mm) when the element size of target is zero shown in Fig. 9(a) and that the real value of PEEQ is 8.85 (mm/mm) when both the element sizes of target and shot are zero shown in Fig. 9(b). Both of them are larger than the maximum PEEQ value of 7.6 (mm/mm) as shown in Fig. 6. Therefore, it is reasonable to confirm the nanocrystalline appearing on the peened surface of workpiece in this HESP parameter condition according to the evaluation method of nanostructure formation proposed by Umemoto and Valiev et al. (Ref 21, 22).

Fig. 9
figure 9

Fitting linear relationship between the maximum PEEQ value and the element size with regard to (a) the influence of target element size (b) the influence of target and shot element sizes

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Surface Topography Analysis

In the HESP process, the surface topography and SI mainly depend on the parameters of the HESP process for a certain material. Figure 10 shows the surface topography after HESP treatment with different HESP parameters. Figure 10(a1), (b1) and (c1) shows the 3D surface topography corresponding to the original surface topography in Fig. 10(a), (b) and (c), respectively.

Fig. 10
figure 10

Surface topography after HESP treatment with different HESP parameters. (a) and (a1) Surface coverage of 400%, 800% and 1000%, (b) and (b1) shot diameter of 0.3 mm, 0.8 mm and 1.0 mm, (c) and (c1) shot velocity of 60 m/s, 80 m/s and 100 m/s

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By comparing Fig. 10(a)(a1), (b)(b1) and (c)(c1), it can be seen that different HESP parameters lead to different surface topography. The color of 3D surface topography represents the surface roughness. The closer the color is to blue, the smaller the surface roughness is, and the closer the color is to red, the greater the surface roughness is. Meanwhile, the maximum value in each 3D surface topography can also reflect the surface roughness, similar to the maximum height of the surface profile defined as a roughness height parameter in the standard ASME B46.1-2009 about surface texture (surface roughness, waviness, and lay). In Fig. 10(a1), the maximum value in 3D surface topography increases when surface coverage increases, which represents the surface roughness increases with surface coverage increasing from 400% to 1000%. The increment of surface coverage means that more shots impact the surface of workpiece, which leads to large surface roughness of the whole peened surface.

Figure 10(b1) shows that the surface roughness increases first and then decreases when the shot diameter increases from 0.3 to 1.0 mm. Compared with the surface roughness in d = 0.3 mm and d = 1.0 mm conditions, the surface roughness of d = 0.8 mm is the highest. We analyzed that this is mainly due to the combined influence of kinetic energy and diameter of shots on surface roughness. When the diameter of shots is 0.3 mm, the kinetic energy of shots is relatively small and the depth of dimple generated by a single shot is small. Therefore, the surface roughness is low and surface deformation is small. When the diameter of shots increases to 0.8 mm, the kinetic energy increment leads to surface roughness increasing. When the diameter of shot increases to 1.0 mm, both the depth of dimple and the radius of curvature of dimple increase. Increasing the depth of dimple leads to the increment of surface roughness but increasing the radius of curvature of dimple leads to the decrement of surface roughness. The combined effect of kinetic energy and diameter of shots on surface roughness causes the lower surface roughness in shots’ diameter of 1.0 mm condition than in shots’ diameter of 0.8 mm condition.

Figure 10(c1) shows the surface topography with the shot velocity of 60 m/s, 80 m/s and 100 m/s. It can be seen that the surface roughness increases with the shot velocity increasing. A high velocity of shot means high impact energy during the HESP process, which leads to large depth of dimple and high surface roughness. From the above analysis, it can be seen that the surface roughness is relevant to the HESP process parameters such as surface coverage, shot diameter and shot velocity. In the HESP process, on the one hand, the relatively high peening intensity is required to obtain nanocrystalline layer on peened surface. On the other hand, the relatively high peening intensity leads to the increment of surface roughness, stress concentration and microcrack on peened surface, which causes detrimental effect on SI and surface mechanical property. Therefore, how to balance the beneficial and detrimental effects of the relatively high peening intensity on surface mechanical property is very important for the HESP process.

In order to further evaluate SI after the HESP process, the peened surfaces treated by different HESP parameters were analyzed via KEYENCE VHX-5000 digital microscope with a magnification of 1000 times. Figure 11 shows the surface topography of peened surface with different HESP parameters (a) V = 100 m/s, d = 1.0 mm, C = 400%; (b) V = 80 m/s, d = 0.6 mm, C = 1000%; and (c) V = 100 m/s, d = 0.6 mm, C = 1000%. It can be seen that in all peened surfaces, both concave region and fold region appear because of shots impact. Even in the largest peening intensity condition shown in Fig. 11(c) (V = 100 m/s, d = 0.6 mm and C = 1000%), microcracks do not appear on a treated surface. There are two possible reasons for the ideal surface quality in this work. The first one is the good quality of the shots and efficient broken shot cleaning system, which make sure the shots are not easy to break and the broken shots can be cleaned out in time during the HESP process. The second reason is the precise control of the HESP parameters in our self-designed HESP equipment, which can generate the uniform impact on the surface and the microcracks caused by nonuniform impact are avoidable during HESP process.

Fig. 11
figure 11

Surface topography of peened surface with different HESP parameters (a) V = 100 m/s, d = 1.0 mm, C = 400%; (b) V = 80 m/s, d = 0.6 mm, C = 1000% and (c) V = 100 m/s, d = 0.6 mm, C = 1000%

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Microhardness Analysis

The hardness of the specimen without HESP treatment is measured to be 230 HV. After the HESP process, the microhardness near surface region increased due to work hardening and gradient nanostructure formation on peened surface. Figure 12 shows the depth profile of microhardness in different HESP parameter conditions: (a) surface coverage variation, (b) shot diameter variation and (c) shot velocity variation.

Fig. 12
figure 12

Hardness curve after HESP under different SP parameters: (a) surface coverage, (b) shot diameter, (c) shot velocity

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It can be seen that the microhardness in the surface layer increases in all HESP conditions and the microhardness decreases gradually from the surface to the core region. Large values of surface coverage, shot diameter and shot velocity lead to large microhardness in the surface region of peened workpiece. Compared with increasing shot diameter and shot velocity, the increment of surface coverage makes the surface microhardness increase more obviously. The surface microhardness reaches up to 690 HV in the HESP condition of V = 100 m/s, d = 0.6 mm, C = 1000% as shown in Fig. 12(a). However, compared with increasing surface coverage, increasing shot diameter and shot velocity makes the growth of HESP influence depth more pronounced as shown in Fig. 12(b) and (c). It is well known that most metals and alloys with nanostructure have super-high strength and hardness (Ref 5, 9). Furthermore, according to the experimental results of Valiev, Yin and Umemoto et al. (Ref 40, 41, 47), the surface microhardness of the workpiece with nanostructure was 7 GPa, 4.2 GPa and 6.8 GPa, respectively, which was much higher than that of the matrix material with ordinary grains. Figure 12(a) shows that surface hardness of the sample after HESP with V = 100 m/s, d = 0.6 mm, C = 1000% is about 690 HV, i.e., 6.8 GPa. According to the previous researches (Ref 47, 48), the yield strength of the workpiece can be calculated via the equation HV = 3σ (yield strength), and then, the grain size can be calculated by Hall–Petch formula. The large value of microhardness on peened surface represents that the nanostructure is very likely to appear in this region, which is also confirmed by the result of PEEQ and XRD diffraction analysis in Fig. 6.

Microstructure Analysis

Figure 13 shows the microstructure of cross section after HESP treatment with parameters of V = 100 m/s, d = 0.6 mm and C = 1000% via KEYENCE VHX-5000. It can be seen that the fine grains are compressed and concentrated in the surface region with a clear boundary from the core region. The grain size increases from the surface to the core region and the depth of the compressed fine grain region is about 50 μm, which is the same as the depth where the grain size is smaller than 100 nm shown in Fig. 6. Saitoh et al. (Ref 49) claimed that in their work the repeated severe plastic deformation led to the formation of ultrafine grain structure on surface, i.e., so-called white etching layer. And this phenomenon is also observed in our work shown in Fig. 13. There is an obvious boundary between white etching layer and other severe plastic deformation region, even though nanocrystalline structure exists in both of these regions. Furthermore, the difference of microstructure between the near surface region and the core region can also be indicated by microhardness variation from the surface to the core region shown in Fig. 13. The grain refinement can also be explained by Jang et al. (Ref 8) for analyzing the phenomenon of grain refinement during ball milling. In the work of Jang et al. (Ref 8), a large number of dislocations were generated on the surface layer, and the low-angle grain boundaries were formed via the interaction between dislocations and dislocation rearrangement, i.e., grain refinement.

Fig. 13
figure 13

Microstructure of cross section after HESP process

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X-ray Diffraction Analysis

Figure 14 shows the depth profiles of FWHM from XRD measurement in different HESP parameter conditions. It is well known that the value of FWHM is one of the most important characterization parameters to describe the grain refinement phenomenon. In short, the refined grains lead to the value of FWHM increasing. The increment of peening intensity can be realized by increasing surface coverage, shot diameter and shot velocity and the degree of grain refinement depends on peening intensity of HESP process. Figure 14(a) shows the depth profile of FWHM in different surface coverage conditions (from 400 to 1000%) with constant shot velocity and shot diameter (V = 100 m/s and d = 0.6 mm). Compared with the value of FWHM in the core region (0.2°), the value of FWHM on top surface is about 0.330° and the increment rate is about 65% when the surface coverage is 1000%. Figure 14(b) shows the depth profile of FWHM in different shot diameter conditions (from 0.3 to 1.0 mm) with constant shot velocity and surface coverage (V = 100 m/s and C = 400%). The value of FWHM on top surface is about 0.274° and the increment rate is about 37% when the shot diameter is 1.0 mm. Figure 14(c) shows the depth profile of FWHM in different shot velocity conditions (from 60 to 100 m/s) with constant shot diameter and surface coverage (d = 0.6 mm and C = 1000%). The value of FWHM on top surface is about 0.320° and the increment rate is about 60% when the shot velocity is 100 m/s. By comparing with the depth profiles shown in Fig. 14(a), (b) and (c), it can be seen that the broadening effect of FWHM on surface layer is pronounced by increasing the surface coverage, shot diameter and shot velocity. For instance, when the values of surface coverage, shot diameter and shot velocity increase by 25% (i.e., from 800 to 1000%, from 0.8 to 1.0 mm and from 80 to 100 m/s), the values of FWHM increase by 14.5%, 14.6% and 14.2%, respectively. Compared with increasing surface coverage and shot velocity, increasing shot diameter can increase the HESP influence depth more obviously. For instance, the depth of the FWHM-affected layer reaches about 0.3 mm by increasing coverage to 1000% or increasing the shot velocity to 100 m/s, and meanwhile, the depth of the FWHM-affected layer reaches about 0.5 mm by increasing the shot diameter to 1.0 mm.

Fig. 14
figure 14

Depth profiles of FWHM from XRD measurement in different HESP parameter conditions: (a) only surface coverage variation, (b) only shot diameter variation, (c) only shot velocity variation

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The Value of PEEQ Analysis

From the previous analysis in sect. 4.5, it can be seen that the degree of influence of each parameter in HESP on surface grain refinement is different. Section 4.1 shows a certain relationship between the value of PEEQ and the grain refinement, which provides a practical way to study the influence of HESP parameters on grain refinement by the numerical simulation technology. Meanwhile, the numerical simulation technology can greatly save experimental costs and time of microstructure analysis. According to the analysis results shown in sect. 4.1, the grain refinement can be characterized by the value of PEEQ from the FE model. Figure 15 shows the influence of different HESP parameters, such as surface coverage, shot diameter and shot velocity on the depth profiles of PEEQ value.

Fig. 15
figure 15

Influence of different SP parameters on the depth profiles of PEEQ value: (a) surface coverage, (b) shot diameter, (c) shot velocity

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By comparing the data shown in Fig. 15(a), (b) and (c), it can be seen that the value of PEEQ in surface region increases with the increment of the surface coverage, shot diameter and shot velocity, which indicates that increasing peening intensity of HESP can increase the plastic deformation in surface region and the degree of grain refinement. Compared with increasing shot diameter and shot velocity shown in Fig. 15(b) and (c), increasing surface coverage can not only increase the surface value of PEEQ, but also increase the influence depth of HESP greatly. When the surface coverage increases from 50 to 300%, the value of surface PEEQ increases from 1.16 to 7.6 (mm/mm), and the influence depth of HESP increases from 0.15 to 0.35 mm. It can be seen that compared with increasing shot velocity or shot diameter, increasing surface coverage is more effective to generate severe plastic deformation and SNC in the near surface region. For instance, according to the XRD (Fig. 6) and microstructure (Fig. 13) analyses, the depth of nanostructure layer is about 50 μm in the condition of V = 100 m/s, d = 0.6 mm and Cr = 300% (C = 1000%).

Figure 15(b) shows that the surface value of PEEQ increases with shot diameter increasing and the increment is less significant than that of increasing the surface coverage and shot velocity. However, the influence depth of HESP increases more significantly with shot diameter increasing than that of increasing the surface coverage and shot velocity, which is similar to the results of the microhardness and FWHM shown in Figs 12(b) and 14(b), respectively. When the shot diameter is small, the value of PEEQ in the near surface region decreases slightly in depth. When the shot diameter increases, the PEEQ value in the near surface region decreases sharply in depth. This can be explained by the calculation method of surface coverage shown in Eq 2 and 3. The small shot diameter leads to more shots impacting on the surface of the workpiece in the same surface coverage condition, which results in the relatively uniform plastic deformation layer in the near surface region. Therefore, the gradient of the PEEQ value in depth is relatively moderate with a small shot diameter.

Figure 15(c) shows that the surface value of PEEQ increases with the shot velocity increasing. It is very interesting to see that the maximum value of PEEQ appears on the top surface when shot velocity is larger than 80 m/s but appears in the subsurface when the shot velocity is smaller than 80 m/s. This phenomenon is due to that there are two competitive plastic deformation generating processes including the Hertz contact and the direct plastic elongation on surface during the HESP process. According to the Hertz contact analysis, the maximum value of plastic deformation appears in the subsurface region when the shot velocity is relatively low. With the increase of shot velocity, the direct plastic elongation on surface becomes a dominated factor and the value of plastic deformation shows its maximum directly at the surface (Ref 50). Furthermore, in terms of the influence depth of HESP, it can be seen that the influence depth is nearly the same when the shot velocity is smaller than 100 m/s. When the shot velocity is larger than 100 m/s, the influence depth increases obviously. This phenomenon indicates that it is necessary to increase the shot velocity to a certain value in the HESP process if both the surface PEEQ value and the HESP influence depth need to be improved.

In summary, increasing surface coverage, shot diameter and shot velocity are beneficial to grain refinement and nanostructure formation on peened surface after HESP treatment. Meanwhile, increasing values of these parameters in an inappropriate way also leads to detrimental effects on surface roughness and SI, which is harmful to overall mechanical properties of peened components. Therefore, it is very important to take into account the beneficial and harmful effects of HESP for choosing suitable HESP parameters. The relationship between HESP parameters and surface nanocrystallizaiton can be analyzed systematically by FEM. And FEM is a cost-effective way to optimize HESP parameters and a good supplement to experimental analysis to investigate the fundamental mechanisms of HESP.

Conclusion

In order to investigate the effects of HESP parameters on the grain refinement and SNC after HESP treatment, a 3D random shot impact HESP model was built via the finite element software ABAQUS/Explicit 6.10. The x-ray diffraction (XRD), the surface topography, microhardness and microstructure analysis were conducted with the aim of assessing and verifying the SI and nanostructure formation after HESP treatment. The following conclusions have been achieved:

  1. (1)

    Appropriate increment of surface coverage, shot diameter and shot velocity are beneficial to nanostructure formation on peened surface after HESP treatment. The values of PEEQ, microhardness and FWHM on surface increase with these parameters increasing. Compared with increasing shot diameter and shot velocity, increasing surface coverage leads to significant increment of these three values on surface. And compared with increasing shot velocity and surface coverage, increasing shot diameter leads to significant increment of influence depth of HESP.

  2. (2)

    Good quality of the shots, efficient broken shot cleaning system and precise control of process parameters are important to surface quality of HESP treated component. Through suitable process control of HESP, microcracks do not appear on a treated surface even when the surface coverage reaches up to 1000%.

  3. (3)

    Larger peening intensity is necessary to realize SNC in HESP treatment. The value of PEEQ on surface can reach 7-8 (mm/mm) and the depth of nanostructure layer is about 50 μm in the condition of shot velocity of 100 m/s, shot diameter of 0.6 mm and simulated surface coverage of 300% (experimental surface coverage of 1000%). The maximum value of PEEQ appearing on surface or subsurface depends on the two competitive plastic deformation generating processes including the Hertz contact and the direct plastic elongation on surface.

  4. (4)

    The quantitative relationship between the PEEQ values and grain sizes is established through comprehensive analysis of FEM and experimental data as follows: G = 409.66/(1 + (εpl/3.15)1.2) − 60.66.