Research Article

Finite Element Modeling of Ultrasonic Surface Nanocrystallization Process

Farhadi F 1,2 , Behbahani S 3 , Karimzadeh F 2 , Loeian MS *,4 , Masoud Loeian 1
1Metal Processing Institute, Worcester Polytechnic Institute, Worcester, MA, USA
2Department of Material Science and Engineering, Isfahan University of Technology, Isfahan, Iran
3Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
4Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA

*Corresponding author:

Loeian MS, Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA, Email:


Surface treatment, Nanocrystallization, Ultrasonic, Severe plastic deformation, Finite element simulation, Residual stress, Surface roughness

Ultrasonic Surface Nanocrystallization (USN) is a new technology that uses severe plastic deformation to create a nanocrystalline layer at the surface of an object. In this paper, a finite element model has been developed in order to predict the residual stress, surface roughness, and the thickness of the generated nano layer at the surface. The effect of the most important process parameters including tool velocity, static force, and vibration amplitude on the results has been investigated. The obtained results show that increasing the amplitude results in increasing the residual stress and the thickness of nano structure layer on the surface, while the best surface roughness is achieved with the least static force.The surface roughness that is resulted from the simulations is well matched with the experimental data. These results are in agreement with the experimentscarried out in parallel with this research, with the reported results in earlier work, and with the intuitive knowledge about the process.

Grain refinement has been one of the most important topics in surface engineering. Sever plastic deformation is a known method for changing the alloys microstructure into nano structure and there are multiple processes that use this technic including Equal Channel Angular Pressing (ECAP) [1,2] and mechanical alloying [3]. In recent decades, after introduction of nanotechnology, attentions are attracted toward the development of a nano crystalline layer on the surface of the materials. Ultrasonic Surface Nanocrystallization (USN) technology is a new process that improves the mechanical properties of metal alloys by producing a thin nano-structure layer on their surface using Surface Severe Plastic Deformation (SSPD). This technology has been introduced first by Suh et al. [4] and since then multiple publications has shown the potential of this process for improving different alloys [5–7].

USN process improves the mechanical properties of the Workpiece (WP), including its hardness, wear resistance, compressive residual stress, and fatigue strength.The improvement of the mechanical properties and changing the surface micro structure to nano structure in USN technology is due to the severe plastic deformation. Therefore, the best way for analyzing the process is by identifying the residual stress after the process. There are semi and non-destructive methods for the direct experimental measurement of the residual stresses, which are difficult, expensive and time consuming. The Finite Element Modeling (FEM) of USN process is a considerable contribution toward understanding the process and to study the effect of the involved parameters which has been overlooked in the available literature. Designing the ultrasonic system is itself a challenge [8,9]. There have been several FEM simulations for design of high frequency resonators, transducers, and ultrasonic systems [10,11]. However, the lack of a thorough investigation on the induced deformation during SSPD process is seen in the literature.

After introducing surface nano crystallization by Lu and Lu [12], two major groups of treatments have been innovated to cause severe plastic deformation at the surface of metals:Contact loading methods, and thermal methods. However, contact loading is more common which includes treatments such as surface mechanical attrition [13], shot peening [14], ultrasonic impact peening [15,16], ultrasonic surface rolling [17], and ultrasonic cold forging [4]. Most of these treatments have random nature; therefore, realistic simulation of them is almost impossible.

USN is a new technology similar to ultrasonic cold forging and has never been studied numerically before. However, there are similar treatments that have been simulated by FEM, including shot peening [18], ultrasonic surface rolling [19], and ultrasonic impact peening [16]. There is considerable literature on predicting the residual stress and roughness of surface after shot peening by FEM models [20–22]. In prior work, the suggested models and the performed simulations have considerable deviation from the real process. Most of these models simulate the process by considering only one ball impact, while in others special sequences of impact locations are considered.In the present work simulation, the tool moves on the WP exactly similar to what happens during USN process. In addition, instead of considering a single impact of the spherical tool on the WP surface, the simulation is performed for a length of the tool movement to ensure that the effect of the impact on the neighbor nodes has also been considered.

Ultrasonic Impact Peening (UIP) is another process that is almost similar to USN. UIP has been simulated by FEM in two research activities. In the first article, Mordyuk developed a 2D plane strain FE model to simulate the single indent profile on the sample that was impacted by a rigid pin [5]. In the second paper, WP was deformed by a single impact in vertical direction and in diagonal direction [6]. In these two papers, there were too many assumptions that deviated the performed simulation far away from the real UIP process. Here are some of these assumptions:
1. UIP was simulated by considering a dynamic impact of a rigid ball with an initial velocity.However, the real process is hammering the surface by a rigid pin with simultaneous constant static force and constant vibration amplitude produced by ultrasonic head.
2. In earlier simulations, just one impact was modeled, while in the UIP the tool hits the surface in ultrasonic frequency, and these impacts have cross effect on the final surface.
3. WP in both of these FE models wasmeshed by 2D plane strain elements. Even if 2D modeling is inevitable, axisymmetric elements are more accurate for ball impact than plane strainelements.
4. Friction was not considered in these simulations.
5. It was assumed that the tool hitthe surface in one point; however in reality the tool moves on the surface and impacts are on the whole surface.

Modeling of USN has complexities and challenges, including non-linearity due to material behavior, 3D contact between tool and WP, high frequency loading, simultaneous parallel and perpendicular loading on the surface, and extreme distortion of WP. The general goal of the present work is to study the effect of significant parameters of USN process on the residual stress and the roughness of the surface. In the present work, the unrealistic assumptions of the prior work are removed; hence, there is a better agreement between simulation and the real treatment in terms of geometry, frequency, loading, and other important parameters. Also, a numerical parameter study for the USN is presented for the first time.

Experimental methods

USN machine (Figure 1) is used for surface treatment of the metal alloys. During USN process, a spherical tool applies staticload (F), as well as dynamic ultrasonic deformation with amplitude (A) on the WP, while the tool moves with constant feed rate (V). As a result, the severe plastic deformation changes the microstructure of the surface of the sample. Details of this treatment can be found in Loeian et al. [7].

Figure 1. Schematic of USN process; the major components are: 1) WP; 2) Tool tip; 3) Horn; 4) Booster; 5) Transducer; and 6) Positioning machine.

In this research, a machine was designed and fabricated to perform USN treatmentat 20 KHz. Figure 2 shows the USN setup that has been used in this research. USN head includes the transducer, booster, horn, and the tip. Since the workspace is cylindrical, a lathe has been used to move the tip on the surface of the target part. Laser vibrometer has been used to measure the vibration amplitude at the tip of ultrasonic head. An ultrasonic generator is being used to excite the piezoelectric transducer at 20 KHz. A pneumatic actuator supporting the USN head is applying a static force during USN process on the WP surface.

Figure 2. USN Experimental setup, USN head including USN head includes the transducer, booster, horn, and the tip mounted on a lathe. Laser vibrometer is intended to measure the vibration amplitude.

By using this machine, a new layer with ultrafine and nano grains is developed on the surface of metal alloys.Previously, this system has developed nanostructure grains on the surface of AISI S1 steel [7]. Here AISI 4130 steel is being used as the work piece material since it has many applicationsincluding pressure vessels and airframe structure in aircrafts [23,24]. The most important parameters of USN process are initial properties of the material, Tool geometry, Vibration amplitude (A), Static force (F), and Feed velocity (V). The microstructure of AISI 4130 steel before and after the USN process is shown in Figure 3. For this sample, the utilized parameters are A=5 µm, F=500 N, and V=40 mm/s.The thickness of the affected layer separated by dash line is 100 µm. In other steel samples, similar observations were reported [4,5].

Plastic behavior, roughness, hardness and preprocess microstructure are the important properties of the samples that influence the USN process. From these properties, plastic behavior of the material and the friction coefficient are the most important factors. Ultrasonic vibration in parallel or perpendicular direction has a great influence on the friction coefficient between two sliding surfaces [25]. Considering earlier work reports and the observations in the performed experiments during this research, a friction coefficient of 0.05 has been imported to the model. For simplicity, the plastic behavior of the WP was modeled as elastic- full plastic material. Other properties of WP material are listed in Table 1.

Figure 3. Microstructure of AISI 4130 steel at the surface: (a) Before treatment; (b) After USN treatment. The thickness of new layer after the USN treatment is 100 µm. The utilized parameters for this process are A=5 µm, F=500 N, and V=40 mm/s.

Elastic module (GPa)

Yield strength (Mpa)

Density (kg/mm3)

Friction coefficient





Table 1. Material properties of AISI 4130 steel.

The utilized tool is a semi- sphere, made of carbide-tungsten, which is modeled as a rigid hemisphere. Different kinds of dynamic parameters influence USN process, including input vibration energy, vibration forces, and vibration amplitude of the tool. Among them, vibration amplitude is the most effective parameter to be studied, and it is easier to measure during the USN process. 5 and 10 µm are the vibration amplitudes of USN tool that is evaluated by laser vibrometer in different ultrasonic generator input energies and these values are considered as the vibration amplitude in the simulations.

In USN machine, pneumatic system maintains the static force steady during the process. In compliance with the performed experiments, 250 and 500 Newton wastaken for static force in the studied samples.

After applying USN process, the roughness of surface for all of samples was measured. Table 2 compares the roughness of samples surface before and after USN process. It is observed that the Ra of surface after applying USN process is less than the Ra surface after grinding and before the USN process. Also by decreasing the tool velocity (increasing the number of strikes), decreasing the vibration amplitude and decreasing the static force, the surface roughness is improved. The similar results were reported by Cao et al. [26].

Sample number

Static force (N)

Vibration amplitude (µm)

Tool velocity (mm/sec)

Surface roughness (Ra) (µm)


Without USN treatment


2 (process A)





3 (process B)





4 (process C)





5 (process D)





Table 2. Surface roughness of samples before and after USN treatment.

Finite Element Model

In this research, the USN process is simulated by means of ABAQUS/EXPLICIT software [27], using a half space model with a symmetry plane in the middle of the WP and the tool (Figure 4). The tool is a part of a sphere that its radius is 2.5 mm and WP is a cube that its dimensions are 1×2×4 mm3. This model has two steps in explicit based solver and consists of a rigid tool and a deformable WP. WP is an elastic- full plastic material, with properties as shown in Table 1.

The WP is meshed by explicit 3D Reduced Integration Elements [27].The elements are hexahedron explicit linear elements with reduced integration. Also distortion control and hourglass control is applied on the elements [27].The size of cubes is 30 µm in the origin which is the target area. For investigating the results at the end of the process, three paths are defined on the WP, as shown in Figure 5.

Figure 4. Assembled model of finite element model. The radius of rigid toll is 2.5 mm and the dimensions of the WP are 1 × 2 × 4 mm3.

Figure 5. Definition of paths for extracting the results. Path 1 is along the moving path of the tool. Path 2 is along the depth and path 3 is along the width of deformed area.

The tool is defined as analytical rigid and the loadings are applied on its reference point. The static force and vibration amplitude should be applied on tool reference point simultaneously. Since it is not possible to apply simultaneous force and displacement, two static simulations were carried out to find the static displacements that produce 250 and 500 Newton reaction forces on the tool. Table 3 shows the result of these two static simulations.

Static simulation




Reaction force on the tool (Newton)




Displacement of tool (µm)




Table 3. Static simulations results.

In order to have estimation about the size of the WP in simulation, the third static model was developed for finding the maximum radius of deformed area. In this model, addition of maximum static displacement (26 µm) and maximum vibration amplitude (10 µm) was imported as the displacement of the tool. The variation of Plastic Equivalent Strain (PEEQ) along path 1 and normal stress along path 2 are shown in the Figures 6 and 7, respectively. The static displacement is applied on the reference point of rigid tool that is in the position 1 mm on the path 1.

Figure 6. PEEQ along path 1, for static models. Static models 1 and 2 are simulating the deformation of WP caused by 250 and 500 N. Static model 3 super impose the penetration of 500 N and 10 µm vibration amplitude.

Figure 7. Normal stress along path 2, for the static models. Maximum compressive residual stress is not at the surface.

According to Figure 6, the maximum distancefrom the impact position that has been deformed plastically is 1 mm. Therefore, for the simulation of USN process, it suffices to simulate 2 mm of the tool movement, and then observe the results in the plane which is in the middle of this path. It was observed that the maximum stress and strain had not happened at the surface. Similar results have been reported for shot peening, where one impact of a rigid ball has been simulated [28,29]. Of course, when there is more than one impact, the maximum stress and strain will be at the surface [4] and the same results are gained from the simulations.

Four models have been constructed to study the effect of USNparameters on theprocess. The first model is considered as the reference model, while tool velocity, vibration amplitude and static displacement are changed in the other three models, respectively. In Table 4, theparameters of the models are explainedbriefly.

Process simulation

Tool velocity (mm/s)

Vibration amplitude (µm)

Static displacement (µm)

















Table 4. Process simulations parameters.

Model (A): Reference model

The first model is considered as the reference model for comparison. The reaction force, the normal stress at the origin of the coordinate system, and the displacement of the tool during the process are shown in Figures 8-10, respectively.

In the model (A), the first step that static load is applied lasts 0.01 s and the second step that ultrasonic vibration is applied lasts 0.05 s. In Figure 8, it is shown that the reaction force rises extremely at the beginning of the second step, due to sudden movement of the tool in the x-direction. The reaction force during the process changes disorderly due to severe contact and deformation of WP.

Figure 9 shows the variation of the normal stress in the x-direction at the origin of the coordinate system during the process. At the beginning of the second step, there is a small change in the stress around the origin of the coordinate system. As the tool gets closer to the origin point, the stress raises irregularly. When the tool reaches the middle of the path 1, the stresses decrease, and after 0.03 s of the second step, the deformations are in elastic zone again. However, unlike of the beginning of the second step, the average value of the stress is not zero, and is a negative value. This is the compressive residual stress that remains in the WP after the USN process.

Figure 8. Reaction force on the tool during process model (A). Large force at the beginning of vibration impacts are noticeable.

Figure 9. Normal stress in x direction at the origin of Cartesian coordinate of WP during process model (A). The difference of the mean value of the stress between the beginning and end of process shows the residual stress.

According to Figure 10, in the first step the tool penetrates in the WP toward its depth. In the second step, the tool vibrates in y direction (along path 2) and moves on the surface in the x direction (along path 1). The tool does not move in z direction (along path 3) during the process.

Figure 10. Displacement of the tool during process model (A). The frequency of y displacement vibration in step 2 is 20 KHz.

Figure 11 compares the equivalent plastic strain (PEEQ) on path 2 between static and ultrasonic loadings. It is shown that the PEEQ at the surface after applying ultrasonic loading is much more than static loading, which is the key point of the generation of the nano crystalline surface. Umemoto et al.[30] showed from the measured shear strain that the necessary PEEQ to produce nano crystalline region is about 3. In Figure 11, the maximum PEEQ at the surface of WP after USN process is 7.51. Based on the Umemoto’s theory, a micro structure change at the surface should happen in a layer with thickness of about 100 micrometer, which is called "severely deformed area". The same thickness was observed in our experimental sample while we used the same parameters for USN sample (Figure 3).

Figure 11. Comparison of equivalent plastic strain (PEEQ) under static and ultrasonic loading. There are a lot of difference in the residual equivalent plastic strain between process A and static model 3 at the surface.

Figure 12 shows the 3D image of work piece residual stress for process (A). The highest residual stress is at the origin where the target point in these simulations is. Also it can be observed that the height of surface nodes around the deformed area is higher that the initial location due to the deformation.

Figure 12. 3D residual stress on sample after process A. The maximum residual compression stress is at the origin point at the surface while it decreases significantly toward the depth of sample.

Model (B): Reduced feed rate

Model (B) is similar to model(A), but the duration of the second step has been doubled (0.1 s), which corresponds to half feed rate(20 mm/s). For comparison, the results of models (A) and (B) are shown in Figures 13-16.

Figure 13 show that by decreasing the tool velocity, the compressive residual stress at the surface has a great reduction. However, in model (A) the residual stress decreases rapidly toward the depth. The depth of existence of residual stress in both models is the same.

Figure 13. Normal stress in the x direction along path 2 for process (A) and (B). Having higher feed rate causes lower residual stress at the surface.

In spite of residual stress, PEEQ and the depth of severely deformed area and consequently the depth of nanostructure surface are increased by reducing the feed rate. By reducing the feed rate, the displacement of the nodes at the surface in the y direction has increased, according to Figures 15 and 16. However the surface of WP in lower feed rate (model B) is smoother.

As a result of decreasing the tool velocity, the tool moves on the surface smoother and steadier, and the residual stress at the surface is decreased. However, ultrasonic vibration has more time to deform the surface and PEEQ is increased. Also roughness of the surface is better due to lower distance between loading points, and higher overlap between deformed areas.

Figure 14. PEEQ along path 2 for process (A) and (B). Decreasing the feed rate causes higher strain and thicker layer with new structure at the surface.

Figure 15. Displacement of surface nodes in the y direction versus distance on path 1. The surface roughness for the simulation with lower feed rate is smaller and it has a smoother surface.

Figure 16. Displacement of surface nodes in the y direction versus distance on path 3. The width of deformation is a little larger when the feed rate is decreased.

Model(C): Higher vibration amplitude

The only difference between models A and C is in the value of vibration amplitude. The vibration amplitude in (C) is 10 micrometer, while it was 5 µm in (A). The results of these two situations are compared in Figures 17-20.

As expected, by increasing the vibration amplitude, the residual stress at the surface is increased and the compressive residual stress decreases slowly toward the depth. However, the depth of compressive residual stress at the surface is similar at both simulations.

Increasing the vibration amplitude has resulted in higher PEEQ at the surface and higher depth of severely deformed area. It is observed that the higher the vibration amplitude, the higher the displacement of surface nodes on paths 1 and 3. The roughness of the surface is increased by increasing the vibration amplitude, as expected.

By increasing the vibration amplitude, deformation and contact is more intense. Consequently, compressive residual stress, PEEQ, the depth of severely deformed area, and the roughness of the surface are increased.

Figure 17. Plastic equivalent strain versus depth for process A and C along path 2. Higher plastic strain and thicker nanostructure layer is the result of increasing vibration amplitude.

Figure 18. Normal stress in the x direction along path 2. The residual stress at the surface for simulation with larger vibration amplitude is higher.

Figure 19. Displacement of surface nodes in y direction versus distance on path 1. After utilizing higher vibration amplitude, the surface roughness of sample is increased

Figure 20. Displacement of surface nodes in y direction versus distance on path 3. The width of deformed are is increased in the simulation with higher vibration amplitude.

Model (D): Reduced static force

In the final model, the effect of reducing the static load is investigated. Therefore, all parameters except the static displacement in this model are identical withprocess (A). Figures 21-24 shows the results obtained results from this model.

In Figure 21, it is shown that by decreasing the static displacement, the residual stress at the surface is declined, which is expected. However, the depth of compressive residual stress is the same at both models.

Figure 21. Normal stress in x direction along path 2. Decreasing the static force from 500N to 250N caused 50% decrease in surface residual stress.

PEEQ and the depth of the severely deformed area are decreased by inserting less static force. The thickness of the area that it’s PEEQ is more than 3 (i.e., Umemoto’s criterion) in process (D) is 50 µm.

Figure 22. Plastic equivalent strain versus depth for process A and D along path 2. The plastic strain at the surface is decreased about 30% by reducing the static force from 500 to 250 N.

The displacements of the surface nodes on path 1 and 3 in y direction at the final model are decreased. However, the surface in this model is excellent and the roughness of the WP is the least among 4 models.

Figure 23. Displacement of surface nodes in y direction versus distance on path 1. The process with lowest static force has the minimum surface roughness.

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Figure 24. Displacement of surface nodes in y direction versus distance on path 3. The width of deformed area for the simulation with 250 N static forces is reduced significantly.

Displacement of surface nodes in y-direction versus distance on path 3. The width of deformed area for the simulation with 250 N static forces is reduced significantly

These results show that by decreasing the static force, contact situation and deformation of WP is less intensive. Consequently, the residual stress at the surface, PEEQ, the depth of severely deformed area, and the roughness are decreased. Table 5 summarizes comparisons between four models.


The least

The most

Residual stress at the surface (MPa)

Model B (-193.5)

Model C (-441)

PEEQ at the surface

Model D (5.3)

Model C (8.3)

Depth of severely deformed area (mm)

Model D (50)

Model C (140)

Displacement of surface nodes in y direction (μm)

Model D (4)

Model C (7)

Pick to valley of displacement of surface nodes (μm)

Model D (1.5)

Model A (3)

The wide of tool trace (mm)

Model D (0.3)

Model C (0.42)

Table 5. Results of process simulations.






Roughness of simulated samples (µm)





Roughness of experimental samples (µm)





Table 6. Comparing the surface roughness (Ra) obtained from experiments and simulation.

A 3D finite element study has been performed to analysis the effect of input parameters on the result of Ultrasonic Surface Nanocrystallization process. Significant and constructive results were obtained, which are in compliance with the intuitive knowledge about the process, with the reported results in earlier works [4,7], and with the experimental observation carried out in parallel with this research. Based on Umemoto’s theory [30], when the steel samples are going through severe plastic deformation, there will be a new structure in the area that had been applied plastic strain more than 3. For process A, the results in Figures 3 and 11 from experiment and simulation showed that there is a new layer with thickness of 100 μm at the surface of sample. This can be a proof for showing the agreement of these simulations with experimental results. Also the same pattern can be observed for surface roughness of simulation and experiment samples. For both experimental and simulation results, Process A has the roughest surface while process D has the lowest surface roughness (Table 6) .

By increasing the vibration amplitude, the residual stress at the surface was increased, while the residual stress was decreased by decreasing the tool velocity and static force. In all of studied models, the depth of compressive residual stress was equal. The residual stress from the surface toward the depth is declined in all four models. However,the reference model and the model with reduced static force had the fastest rate of declining, while the model with half feed rate had the slowest rate of declining. It was observed that the tool velocity had the highest effect on the rate of residual stress decreasing toward the depth. It was also observed that increasing the vibration amplitude and decreasing the tool velocity lead to increasing the amount of plastic deformation and PEEQ. The smoothest surface was achieved where the least static force had been applied. By increasing the vibration amplitude, the surface roughness was increased, and the nodes at the surface had the highest displacement toward the depth. This has to be taken into account for the work pieces that their dimension tolerance is in the range of 0.05-0.5 mm.

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Citation: Farhadi F, Behbahani S, Karimzadeh F, Loeianc MS (2017) Finite Element Modeling of Ultrasonic Surface Nanocrystallization Process. Int J Nanotechnol Nanomed Res 1:007.

Published: 14 September 2017

Reviewed By : Dr. Vijay K. Varadan, Dr Xiubo Zhao,

Copyright: © 2017 Loeianc MS . This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.