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A three-dimensional simulation of shot peening process using multiple shot impacts
Journal of Materials Processing Technology 164–165 (2005) 1226–1234
A three-dimensional simulation of shot peening process using multiple shot impacts G.H. Majzoobi ∗ , R. Azizi, A. Alavi Nia Mechanical Engineering Department, Faculty of Engineering, Bu-Ali Sina University, Hamadan, Iran
Abstract Shot peening is a complex cold-working process involving many disciplines of static and dynamic elasticity and plasticity. The experimental evaluation of shot peening mechanism is very difficult and costly. On the other hand, numerical simulations allow a parametric study of shot peening process and provide an insight into the mechanism, subject to the selection of an appropriate material model and numerical procedure. LS-DYNA code was employed for the numerical simulation in this work. The modeling of shot peening process was accomplished by simulation of multiple shot impacts on a target plate at different velocities. From the simulations, the compressive residual stress profiles were obtained and the effects of velocity and peening coverage were investigated. The results showed that, residual stress distribution was highly dependent on impact velocity and multiplicity. A uniform state of stress was achieved at a particular shots number which was found to be 25 in this work. The shots number corresponding to the state of uniform stress was not the same as that related to the maximum compressive residual stress which may occur at lower number of shots. Impact velocity significantly influences the residual stress profile. The increase of velocity improves the residual stress distribution up to a particular point. Further increase in the velocity may reduce the maximum residual stress. A close agreement between the numerical residual stress profiles obtained in this work was achieved with the experimental profiles reported by Torres and Voorwald. © 2005 Elsevier B.V. All rights reserved. Keywords: Shot peening; Finite element; Residual stress; Impact; Numerical simulation
1. Introduction Shot peening is a surface cold-working process which is usually employed to improve the fatigue strength of metallic part or members. This process is widely used in aerospace, automotive and power generation industries. Turbine and compressor discs, blades, rotor spindles, landing gear components, springs, gears, connecting rods, cam shafts and torsion bars are typical components which are usually surface treaded by shot peening. This process is accomplished by bombarding the surface of the members with small spherical shots made of hardened materials at high velocities. As a result of collision of a shot with the surface of a component, an indentation is created which is surrounded by a plastic region followed by an elastic zone. Upon the rebound of the shot, the recovery of elastic zone creates a large compressive ∗
Corresponding author. E-mail address: gh [email protected] (G.H. Majzoobi).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.139
residual stress on the surface. The profile of the residual stress created by shot peening is schematically depicted in Fig. 1 [1]. This layer of compressive residual stress postpones the crack propagation which usually initiates from the surface and becomes the source of fatigue failure of the components. The result of shot peening can be affected by the shot parameters such as shot size, shape, velocity, hardness and material and the component properties such as hardness, strength, coverage and other factors such as temperature, duration of shot peening, etc. The quantitative evaluation of these parameters has been the subject of numerous research programs over past several decades [2–4]. The evaluations, however, are largely based on experimental work that are generally costly, tedious, and time consuming. Shot peening is a hybrid process involving many disciplines of static and dynamic elasticity and plasticity. Therefore, the investigation of this process requires a thorough understanding of mechanical behavior of the shot
G.H. Majzoobi et al. / Journal of Materials Processing Technology 164–165 (2005) 1226–1234
Fig. 1. Schematic representation of a typical profile of compressive residual stress.
and the target, the two main elements in shot peening, at both low and high strain rates. Al-Obaid [5] studied the residual stress distribution in the target and developed a number of theoretical expressions for the parameters of the process based on a new model of spherical cavity expansion. However, Al-Obaid states at the end that “there is still a huge lack of knowledge and that we are only just entering the area of mechanics of shot peening”. Kobayashi et al. [6] investigated the mechanism of compressive residual stress by shot peening. They performed static compression tests and dynamic impact tests using a single steel ball against a flat steel plate. In the static tests, compression residual stress was created near the center of the ball indentation mark. In the dynamic tests, however, tensile stress was created near the center of the ball indentation mark and compression residual stress was created outside of the indentation. The disadvantages of experimental works along with the appearances of powerful finite element codes such as ANSYS, NASTRAN and ABAQUS, which can simulate dynamic processes and phenomena, have attracted the attention of the researchers to numerical simulation of shot peening process. The numerical simulation is not only cheap and easy to perform, but can also provide as insight into the mechanism of shot peening during the impact of the shot on the component surface. The finite element simulation of shot peening enables the user to carry out a parametric study of the process. Meguid et al. [1] developed a three-dimensional finite element model of dynamic single and twin shot impacts using rigid spherical shots and metallic targets. He examined the effects of shot velocity, size and shape and target characteristics on residual stress distribution in the target. Their results indicated that the effect of shot parameters were more profound than the strain-hardening rate of the target. In another work, Meguid et al. [7] conducted a comprehensive non-linear dynamic elasto-plastic finite element analysis of shot peening process. Their results revealed that multiple shot impacts result in a more uniform residual stress and plastic strain
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distribution and that the separation distance between shots significantly influences the residual stress field. They also showed that the average depth of the compressed layer increases with a decrease in the normalized separation distances C/R (C is the distance between the centers of two adjacent shots and R the shot radius) from 2 to 10 for C/R ≤ 2, the interaction between different shot impacts along the target surface are negligible. Meguid et al. [7] also revealed that variation of friction coefficient between shot and the target upon impact on the residual stress distribution was negligible. The numerical simulation of single and multiple shot impacts carried out by Al-Hassani [8] verified the significant role played by non-linear work hardening and strain rate dependency of the target on residual stress profile and extent of surface hardening. It is well known that most of the materials and in particular those with fcc crystalline structure are highly dependent on rate of deformation or strain rate. The effect of strain rate is represented by a parameter called strain rate hardening exponent which is incorporated in an appropriate constitutive equation of the material. Numerous constitutive equations can be found in literature [9–11]. Some of these equations such as Johnson–Cook [12], Zerilli–Armstrong [13] and Cowper–Symonds power law have gained more popularity for numerical modeling purposes. The Johnson–Cook constitutive relation is stated as follows: σ = (A + Bεn )(1 + C ln ε∗ )(1 − T ∗m )
(1)
in which A, B, n, C and m are material constants and are measured by experiment. The Cowper–Symonds power law is 1/p ε˙ σ = σ0 1 + (2) C in which σ 0 , C and p are constants. Zerilli–Armstrong model is more comprehensive than the other models. In addition to the strain and strain rate hardening and temperature it takes account of grain size and crystalline structure of the material, as well. As stated above, shot peening process is a non-linear dynamic contact problem and must be treated as an impact problem. Therefore, the parameters associated with an impact problem, such as stress wave propagation, strain and strain rate hardening must be taken into account in the modeling. These necessitate the use of an appropriate finite element code. Having considered the latter points, LS-DYNA was employed for numerical simulations in the present work. This numerical code has been widely used for numerical simulations of impact problems. However, most of the numerical simulations, reported in the literature, lack a validation by experiment. In this work, the experimental results obtained from a series of single-shot tests are used for validation of LS-DYNA code. The material constants of the target material for Johnson–Cook model are obtained at high strain rates. These constants are then used for numerical simulations of the single-shot experiments. After the code validation, numerical
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simulations of multiple shot impacts are performed and the residual stress profile is investigated.
2. LS-DYNA validation 2.1. Experimental results for validation Two single balls with a diameter of 3 and 5.5 mm were fired against a flat steel plate of dimensions 20 mm × 300 mm × 300 mm at velocities in the range of 100–400 m/s using explosive actuated gun launcher. The balls were made of Cr–Ni steel alloy with a hardness of 60 Rockwell C. The desired impact velocities were obtained using appropriate amount of explosive charge and impact distance. Ultrasonic velocity sensors were employed for velocity measurement. The profiles of indentations created on the target plate by the impact of the projectiles (balls) were used for validation. In order to obtain the profile, the indentations were molded with an acrylic wax material. The molds were then examined by optical microscopy and the profiles of the indentations were obtained. The target plate with some indentations is shown in Fig. 2. The mechanical properties of the target plate at high strain rates were necessary for numerical simulations. For the reasons stated above, Johnson–Cook model [12] was designated for the simulations. Having ignored the temperature effects, the strain and strain rate constants, A, B, n and C were measured from a number of tensile tests. The tests were conducted at velocities in the range of 0.01–250 mm/s using the universal Instron tensile testing machine. The higher rate tests within the range of 1000–1700 mm/s were carried out using flying wedge testing apparatus [14,15]. A general view of the apparatus is shown in Fig. 3. Flying wedge receives its energy of the impact from a gas gun. The specimen is pulled apart by a slider mechanism illustrated in Fig. 4. The specimen, as can be seen in Fig. 4, is hold between two sliders. The gas gun accelerates a wedge against the sliders. Upon the impact of the wedge on the sliders, the sliders are pulled apart leading to the tension of the specimen. The angle of the wedge matches up with that of sliders and is 28◦ [15]. The specimen’s geometry is shown in Fig. 5.
Fig. 2. A portion of the target plate with some indentations.
Fig. 3. A general view of flying wedge.
Fig. 4. Slider mechanism of flying wedge with a specimen installed between two sliders.
The stress–strain curve obtained from the experiments are illustrated in Fig. 6. The variation of stress versus the logarithmic scale of strain rate is depicted in Fig. 7. From the Figs. 6 and 7 the material constants for Johnson–Cook model were found to be: A = 320 MPa, B = 420 MPa, n = 0.47, C = 0.018. 2.2. Numerical simulations for validation In order to account for the effect of stress wave propagations which are induced by impact, the widely used Gruneisen
Fig. 5. Specimens geometries used for: (a) low strain rates and (b) high strain rates testing.
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Fig. 8. Finite element model for single-shot impact simulations.
Fig. 6. Stress–strain curves of the target plate material at various strain rates.
Fig. 9. Comparison between the experimental and numerical indentation profiles (V = 360 m/s, indentation depth = 1.25 mm, shot diameter = 5.5 mm).
Fig. 7. Stress–strain rate diagram of the target plate material.
equation of state (for compressed material) [16]: p=
ρ0 C 2 µ 1 + 1 −
γ0 a 2 2 µ − 2µ
µ 1 − (S1 − 1)µ − S2 µ+1 − S3
+(γ0 + aµ)E
2
µ3 (µ+1)2
2
Fig. 10. Comparison between the experimental and numerical indentation profiles (V = 270 m/s, indentation depth = 0.97 mm, shot diameter = 5.5 mm).
(3)
with the constants, v0 = 0, E0 = 0, C = 5200, S1 = 1.488, S1 = S3 = 0, γ 0 = 2.02, and A = −1.5 was employed for the numerical simulations. The finite element model of the impact of a single shot on the target plate is illustrated in Fig. 8. In order to validate the LS-DYNA finite element code, the profiles of the indentations created by the experiments with those predicted by numerical simulations were compared. The results are shown in Figs. 9–12 for the different ball diameters and velocities of impact. For more clarity, the deformed and undeformed finite element meshes were superimposed on the indentation profile obtained from the experiments as explained in Section 2.1.
Fig. 11. Comparison between the experimental and numerical indentation profiles (V = 200 m/s, indentation depth = 0.38 mm, shot diameter = 3 mm).
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Fig. 12. Comparison between the experimental and numerical indentation profiles (V = 100 m/s, indentation depth = 0.22 mm, shot diameter = 3 mm).
A reasonable agreement between the experimental results and numerical prediction can be seen in Figs. 9–12. It is interesting to notice that even the rounded protuberances surrounding the indentations have been fairly predicted by the simulations. The slight difference between experimental and numerical results may be attributed to the errors which may originate from the experimental measurement of a variety of parameters such as shot velocity, material constants for Johnson–Cook model and numerical approximations. Fig. 13. Four-shot model.
3. Multiple shot impacts modeling 3.1. Numerical models and material properties In this section the effect of impact multiplicity and velocity on residual stress profile is investigated. Despite validation of the code, we used the experimental results given by Torres and Voorwald [17] for further evaluation of the accuracy of the numerical predictions obtained from the simulations of multiple shot impacts. Therefore, we performed some part of the simulation with the same material model and velocity as used by Torres and Voorwald [17] in their experiments. The simulations of shot peening process in this work were carried out using the models consisting of 4, 6, 8, 9, 13, and 25 shots. The shot radius of 0.4 mm, the target plate dimensions of 0.8 mm × 0.8 mm × 1.6 mm and the friction coefficient of 0.1 remained constant throughout the simulations. The material properties of the shots were: ρ (density) = 7800 kg/m3 , E (elasticity modulus) = 210 GPa and υ (Poisson’s ratio) = 0.3. The target plate was made of AISI 4340 steel. This material, as used by Torres and Voorwald [17], had the following particulars: ρ = 7800 kg/m3 , E = 210 GPa, υ = 0.3, σ y = 1500 MPa, H (plasticity modulus) = 1600 MPa. The Cowper–Symonds material model with c = 2 × 105 , p = 3.3 and σ0 = 1500 MPa (see Eq. (2)) was employed for the simulations. The shots were modeled with 192 six- and eight-node brick elements. The target plate discretization was performed using a mesh of 4500 eight-node brick elements. The simulations were carried out at impact velocities in the range of 50–100 m/s.
3.2. Numerical simulation of multiple shot impacts As stated above, numerical simulations of multiple shot impacts were carried out using 4, 6, 8, 9, 13, and 25 shots. In order to shorten the paper only the models for 4 and 9 shots are shown. Fig. 13 illustrates the four-shot model in which only 1/8 of each shot has been considered in the simulation. In this model four shots collide with the target plate simultaneously. In the nine-shot model shown in Fig. 14, the arrangement of the shots for successive impacts can be observed. The first impact occurs with 4 shots, as explained for the four-shot model. The second and third collisions take place with 2 shots within the time intervals of 18 and 34 s, respectively. The last impact is accomplished by collision of a single shot 50 s after the third impact. The time interval is calculated from H/v, in which H is the distance between shot centers and v the impact velocity. The variation of residual stress profile versus impact velocity and impact multiplicity has been studied at five distinct critical points on the target plate. The points shown in Fig. 15 are: 1. Point A, which is located at the center of a region, that never directly comes into contact with a shot, in other words, in the region, which remains intact during surface bombarding. 2. Point B, which is located in the region where some indentations, caused by successive impacts, overlap. 3. Point C, which is located at the center of an indentation, which is created upon the first impact of the shots on the target plate.
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Fig. 16. Residual stress profiles for various shot models at the center of the target plate at a velocity of 50 m/s.
Fig. 14. Nine-shot model.
4. Point D, which is a random point of the plate. 5. The center of the target plate. The residual stress distribution obtained from the simulations of four- to nine-shot models at center of the target plate and at a velocity of 50 m/s (see Fig. 15) is shown in Fig. 16. From the figure it can be deduced that the profile of residual stress changes rapidly as the number of shot impacts increases. It is evident that the each point on the surface of the target plate would experience a different residual stress
Fig. 15. The target plate with indentations created by shot impacts.
Fig. 17. Residual stress profiles for nine-shot model at a velocity of 50 m/s.
distribution. Fig. 17 represents the residual stress profiles at the three different points explained above. This figure clearly illustrates the non-uniformity of the stress, which obviously depends on the shot multiplicity and impact velocity. The results given in Fig. 18 for 13-shot simulations again represents the residual stress non-uniformity on the target plate after multiple impacts.
Fig. 18. Residual stress profiles for 13-shot model at a velocity of 50 m/s.
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Fig. 19. Residual stress profiles for 25-shot model at a velocity of 50 m/s.
The residual stress profiles provided in Fig. 19, indicate that a state of uniform stress have been achieved in the simulations of 25-shot impacts at the impact velocity of 50 m/s. An interesting point to be noticed is that the residual stress profile induced at a point by a shot collision is not affected considerably by further shot impacts surrounding the point. This can be observed in Fig. 20, in which the residual stress profiles for three different multiple shots at point D are illustrated. Another important aspect of shot peening process, which is investigated here, is the effect of impact velocity. The residual stress profiles obtained from the numerical simulation at point D and at the velocities of 50, 75, and 100 m/s have been depicted in Figs. 20–22, respectively. The figures clearly show that unlike the results obtained for 50 m/s, the higher velocities result in a non-uniform state of residual stress. This non-uniformity is significantly influenced by the number of shots, so that the maximum residual stress is attained for nine-shot model. However, further increase in the number of shots, as can be seen for 13- and 25-shot models, not only does not improve the results, but also deteriorate the situation. The residual stress profiles for 25 shots at the three velocities are produced in Fig. 23. Although, the
Fig. 20. Residual stress profiles at point D for three different shot models at a velocity of 50 m/s.
Fig. 21. Residual stress profiles at point D for three different shot models at a velocity of 75 m/s.
Fig. 22. Residual stress profiles at point D for three different shot models at a velocity of 100 m/s.
profiles are different, but the maximum residual stress for the three velocities are very close to each other. The variation of maximum residual stress versus impact velocity is depicted in Fig. 24. The figure implies that the maximum compressive residual stress rises as the velocity increases up to a point thereafter it begins to decline. Although, the maximum residual stress–velocity curve varies for different points on the
Fig. 23. The profiles of 25 shots at point D.
G.H. Majzoobi et al. / Journal of Materials Processing Technology 164–165 (2005) 1226–1234
Fig. 24. Variation of maximum residual stress vs. impact velocity.
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2. A uniform state of stress is achieved at a particular shots number which was found to be 25 in this work. 3. The shots number corresponding to the state of uniform stress is not the same as that related to the maximum compressive residual stress which may occur at lower number of shots. 4. Impact velocity significantly influences the residual stress profile. The increase of velocity improves the residual stress distribution up to a particular point, found to be 90 m/s in this work. Further increase in the velocity may reduce the maximum residual stress. 5. Numerical simulation allows a parametric study of shot peening process. This can provide insight into the process and a better understanding of shot peening mechanism. 6. The best compressive residual stress distribution was achieved for the simulation of 25-shot model at a velocity of 90 m/s.
Acknowledgements The authors wish to thank Dr. Maleki, the Dean of Faculty of Engineering, Bu-Ali Sina University for his support. They also like to thank research unit of Defense Industries for their contribution to this project and in particular testing the high velocity single-shot impacts. Thanks are due to Mr. Nemati, the technician of strength of material laboratory for his help in conducting the experiments.
Fig. 25. A comparison between the numerical and experimental residual stress profile.
target plate, but the trend of the curves is the same for all the points. From the results described above, it can be observed that the best residual stress distribution is obtained for 25 shots models at the velocity of 90 m/s. This is because, on one hand a nearly uniform stress distribution is achieved and on the other hand, the maximum compressive residual stress is attained. As stated in Section 3.1, the simulation’s conditions in the present work were adopted from the experimental work by Torres and Voorwald [17]. The numerical predictions of residual stress profile for 25-shot model at various points (given in Fig. 19) are compared with the experimental profiles reported by Torres and Voorwald [17] in Fig. 25. As the figure indicates, the numerical and experimental results are very close. The differences can be attributed to the material model, numerical approximation and measurements.
4. Conclusions 1. Shot peening process can successfully be simulated by LS-DYNA finite element code providing a proper material model is selected.
References [1] S.A. Meguid, G. Shagal, J.C. Stranart, J. Daly, Three-dimensional dynamic finite element analysis of shot-peening induced residual stresses, Finite Element Anal. Des. 31 (1999) 179– 191. [2] S. Kyriacou, Shot Peening Mechanics: A Theoretical Study, 6th ed., ICSP, 1996, pp. 505–516. [3] S.A. Meguid, Mechanics of shot peening, Ph.D. Thesis, UMIST, UK, 1975. [4] Y.F. Al-Obaid, A rudimentary analysis of improving fatigue life of metals by shot peening, J. Appl. Mech. 57 (1990) 307– 312. [5] Y.F. Al-Obaid, Shot peening mechanics: experimental and theoretical analysis, Mech. Mater. 19 (1995) 251–260. [6] M. Kobayashi, T. Matsui, Y. Murakami, Mechanics of creation of compressive residual stress by shot peening, Int. J. Fatigue 20 (1998) 351–357. [7] S.A. Meguid, G. Shagal, J.C. Stranart, Three-dimensional finite element analysis of peening of strain-rate sensitive materials using multiple impingement model, Int. J. Impact Eng. 27 (2002) 119– 134. [8] S.T.S. Al-Hassani, Numerical Simulation of Multiple Shot Peening, 7th ed., ICSP, 1999, pp. 217–227. [9] N. Cristescu, Dynamic Plasticity, North-Holland, 1967. [10] J.A. Zukas, High Velocity Impact Dynamics, Wiley, 1990. [11] A. Nemat-Naser, Engineering Solid Mechanics: Fundamentals and Applications, McGraw-Hill, 1982. [12] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, in:
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Proceedings of the Seventh International Symposium on Ballistics, The Huge, The Netherlands, 1973, pp. 541–547. [13] F.J. Zerilli, R.W. Armstrong, Constitutive relations for plastic deformations of metals, AIP Conf. Proc. 309 (1994) 989. [14] G.H. Majzoobi, Experimental and numerical studies of metals deformation and fracture at high strain rates, Ph.D. Thesis, Leeds University, Leeds, UK, 1990.
[15] G.H. Majzoobi, Flying wedge tensile testing apparatus, Research Report No. 264, Faculty of Engineering, Bu-Ali Sina University, Hamadan, Iran, 1994 (in Persian). [16] LS-DYNA Keyword User’s Manual, Version 950, 1999. [17] M.A.S. Torres, H.J.C. Voorwald, An evaluation of shot peening, residual stress and stress relaxation on the fatigue life of AISI 4340 steel, Int. J. Fatigue 24 (2002) 877–886.
A three-dimensional simulation of shot peening process using multiple shot impacts G.H. Majzoobi ∗ , R. Azizi, A. Alavi Nia Mechanical Engineering Department, Faculty of Engineering, Bu-Ali Sina University, Hamadan, Iran
Abstract Shot peening is a complex cold-working process involving many disciplines of static and dynamic elasticity and plasticity. The experimental evaluation of shot peening mechanism is very difficult and costly. On the other hand, numerical simulations allow a parametric study of shot peening process and provide an insight into the mechanism, subject to the selection of an appropriate material model and numerical procedure. LS-DYNA code was employed for the numerical simulation in this work. The modeling of shot peening process was accomplished by simulation of multiple shot impacts on a target plate at different velocities. From the simulations, the compressive residual stress profiles were obtained and the effects of velocity and peening coverage were investigated. The results showed that, residual stress distribution was highly dependent on impact velocity and multiplicity. A uniform state of stress was achieved at a particular shots number which was found to be 25 in this work. The shots number corresponding to the state of uniform stress was not the same as that related to the maximum compressive residual stress which may occur at lower number of shots. Impact velocity significantly influences the residual stress profile. The increase of velocity improves the residual stress distribution up to a particular point. Further increase in the velocity may reduce the maximum residual stress. A close agreement between the numerical residual stress profiles obtained in this work was achieved with the experimental profiles reported by Torres and Voorwald. © 2005 Elsevier B.V. All rights reserved. Keywords: Shot peening; Finite element; Residual stress; Impact; Numerical simulation
1. Introduction Shot peening is a surface cold-working process which is usually employed to improve the fatigue strength of metallic part or members. This process is widely used in aerospace, automotive and power generation industries. Turbine and compressor discs, blades, rotor spindles, landing gear components, springs, gears, connecting rods, cam shafts and torsion bars are typical components which are usually surface treaded by shot peening. This process is accomplished by bombarding the surface of the members with small spherical shots made of hardened materials at high velocities. As a result of collision of a shot with the surface of a component, an indentation is created which is surrounded by a plastic region followed by an elastic zone. Upon the rebound of the shot, the recovery of elastic zone creates a large compressive ∗
Corresponding author. E-mail address: gh [email protected] (G.H. Majzoobi).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.139
residual stress on the surface. The profile of the residual stress created by shot peening is schematically depicted in Fig. 1 [1]. This layer of compressive residual stress postpones the crack propagation which usually initiates from the surface and becomes the source of fatigue failure of the components. The result of shot peening can be affected by the shot parameters such as shot size, shape, velocity, hardness and material and the component properties such as hardness, strength, coverage and other factors such as temperature, duration of shot peening, etc. The quantitative evaluation of these parameters has been the subject of numerous research programs over past several decades [2–4]. The evaluations, however, are largely based on experimental work that are generally costly, tedious, and time consuming. Shot peening is a hybrid process involving many disciplines of static and dynamic elasticity and plasticity. Therefore, the investigation of this process requires a thorough understanding of mechanical behavior of the shot
G.H. Majzoobi et al. / Journal of Materials Processing Technology 164–165 (2005) 1226–1234
Fig. 1. Schematic representation of a typical profile of compressive residual stress.
and the target, the two main elements in shot peening, at both low and high strain rates. Al-Obaid [5] studied the residual stress distribution in the target and developed a number of theoretical expressions for the parameters of the process based on a new model of spherical cavity expansion. However, Al-Obaid states at the end that “there is still a huge lack of knowledge and that we are only just entering the area of mechanics of shot peening”. Kobayashi et al. [6] investigated the mechanism of compressive residual stress by shot peening. They performed static compression tests and dynamic impact tests using a single steel ball against a flat steel plate. In the static tests, compression residual stress was created near the center of the ball indentation mark. In the dynamic tests, however, tensile stress was created near the center of the ball indentation mark and compression residual stress was created outside of the indentation. The disadvantages of experimental works along with the appearances of powerful finite element codes such as ANSYS, NASTRAN and ABAQUS, which can simulate dynamic processes and phenomena, have attracted the attention of the researchers to numerical simulation of shot peening process. The numerical simulation is not only cheap and easy to perform, but can also provide as insight into the mechanism of shot peening during the impact of the shot on the component surface. The finite element simulation of shot peening enables the user to carry out a parametric study of the process. Meguid et al. [1] developed a three-dimensional finite element model of dynamic single and twin shot impacts using rigid spherical shots and metallic targets. He examined the effects of shot velocity, size and shape and target characteristics on residual stress distribution in the target. Their results indicated that the effect of shot parameters were more profound than the strain-hardening rate of the target. In another work, Meguid et al. [7] conducted a comprehensive non-linear dynamic elasto-plastic finite element analysis of shot peening process. Their results revealed that multiple shot impacts result in a more uniform residual stress and plastic strain
1227
distribution and that the separation distance between shots significantly influences the residual stress field. They also showed that the average depth of the compressed layer increases with a decrease in the normalized separation distances C/R (C is the distance between the centers of two adjacent shots and R the shot radius) from 2 to 10 for C/R ≤ 2, the interaction between different shot impacts along the target surface are negligible. Meguid et al. [7] also revealed that variation of friction coefficient between shot and the target upon impact on the residual stress distribution was negligible. The numerical simulation of single and multiple shot impacts carried out by Al-Hassani [8] verified the significant role played by non-linear work hardening and strain rate dependency of the target on residual stress profile and extent of surface hardening. It is well known that most of the materials and in particular those with fcc crystalline structure are highly dependent on rate of deformation or strain rate. The effect of strain rate is represented by a parameter called strain rate hardening exponent which is incorporated in an appropriate constitutive equation of the material. Numerous constitutive equations can be found in literature [9–11]. Some of these equations such as Johnson–Cook [12], Zerilli–Armstrong [13] and Cowper–Symonds power law have gained more popularity for numerical modeling purposes. The Johnson–Cook constitutive relation is stated as follows: σ = (A + Bεn )(1 + C ln ε∗ )(1 − T ∗m )
(1)
in which A, B, n, C and m are material constants and are measured by experiment. The Cowper–Symonds power law is 1/p ε˙ σ = σ0 1 + (2) C in which σ 0 , C and p are constants. Zerilli–Armstrong model is more comprehensive than the other models. In addition to the strain and strain rate hardening and temperature it takes account of grain size and crystalline structure of the material, as well. As stated above, shot peening process is a non-linear dynamic contact problem and must be treated as an impact problem. Therefore, the parameters associated with an impact problem, such as stress wave propagation, strain and strain rate hardening must be taken into account in the modeling. These necessitate the use of an appropriate finite element code. Having considered the latter points, LS-DYNA was employed for numerical simulations in the present work. This numerical code has been widely used for numerical simulations of impact problems. However, most of the numerical simulations, reported in the literature, lack a validation by experiment. In this work, the experimental results obtained from a series of single-shot tests are used for validation of LS-DYNA code. The material constants of the target material for Johnson–Cook model are obtained at high strain rates. These constants are then used for numerical simulations of the single-shot experiments. After the code validation, numerical
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simulations of multiple shot impacts are performed and the residual stress profile is investigated.
2. LS-DYNA validation 2.1. Experimental results for validation Two single balls with a diameter of 3 and 5.5 mm were fired against a flat steel plate of dimensions 20 mm × 300 mm × 300 mm at velocities in the range of 100–400 m/s using explosive actuated gun launcher. The balls were made of Cr–Ni steel alloy with a hardness of 60 Rockwell C. The desired impact velocities were obtained using appropriate amount of explosive charge and impact distance. Ultrasonic velocity sensors were employed for velocity measurement. The profiles of indentations created on the target plate by the impact of the projectiles (balls) were used for validation. In order to obtain the profile, the indentations were molded with an acrylic wax material. The molds were then examined by optical microscopy and the profiles of the indentations were obtained. The target plate with some indentations is shown in Fig. 2. The mechanical properties of the target plate at high strain rates were necessary for numerical simulations. For the reasons stated above, Johnson–Cook model [12] was designated for the simulations. Having ignored the temperature effects, the strain and strain rate constants, A, B, n and C were measured from a number of tensile tests. The tests were conducted at velocities in the range of 0.01–250 mm/s using the universal Instron tensile testing machine. The higher rate tests within the range of 1000–1700 mm/s were carried out using flying wedge testing apparatus [14,15]. A general view of the apparatus is shown in Fig. 3. Flying wedge receives its energy of the impact from a gas gun. The specimen is pulled apart by a slider mechanism illustrated in Fig. 4. The specimen, as can be seen in Fig. 4, is hold between two sliders. The gas gun accelerates a wedge against the sliders. Upon the impact of the wedge on the sliders, the sliders are pulled apart leading to the tension of the specimen. The angle of the wedge matches up with that of sliders and is 28◦ [15]. The specimen’s geometry is shown in Fig. 5.
Fig. 2. A portion of the target plate with some indentations.
Fig. 3. A general view of flying wedge.
Fig. 4. Slider mechanism of flying wedge with a specimen installed between two sliders.
The stress–strain curve obtained from the experiments are illustrated in Fig. 6. The variation of stress versus the logarithmic scale of strain rate is depicted in Fig. 7. From the Figs. 6 and 7 the material constants for Johnson–Cook model were found to be: A = 320 MPa, B = 420 MPa, n = 0.47, C = 0.018. 2.2. Numerical simulations for validation In order to account for the effect of stress wave propagations which are induced by impact, the widely used Gruneisen
Fig. 5. Specimens geometries used for: (a) low strain rates and (b) high strain rates testing.
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Fig. 8. Finite element model for single-shot impact simulations.
Fig. 6. Stress–strain curves of the target plate material at various strain rates.
Fig. 9. Comparison between the experimental and numerical indentation profiles (V = 360 m/s, indentation depth = 1.25 mm, shot diameter = 5.5 mm).
Fig. 7. Stress–strain rate diagram of the target plate material.
equation of state (for compressed material) [16]: p=
ρ0 C 2 µ 1 + 1 −
γ0 a 2 2 µ − 2µ
µ 1 − (S1 − 1)µ − S2 µ+1 − S3
+(γ0 + aµ)E
2
µ3 (µ+1)2
2
Fig. 10. Comparison between the experimental and numerical indentation profiles (V = 270 m/s, indentation depth = 0.97 mm, shot diameter = 5.5 mm).
(3)
with the constants, v0 = 0, E0 = 0, C = 5200, S1 = 1.488, S1 = S3 = 0, γ 0 = 2.02, and A = −1.5 was employed for the numerical simulations. The finite element model of the impact of a single shot on the target plate is illustrated in Fig. 8. In order to validate the LS-DYNA finite element code, the profiles of the indentations created by the experiments with those predicted by numerical simulations were compared. The results are shown in Figs. 9–12 for the different ball diameters and velocities of impact. For more clarity, the deformed and undeformed finite element meshes were superimposed on the indentation profile obtained from the experiments as explained in Section 2.1.
Fig. 11. Comparison between the experimental and numerical indentation profiles (V = 200 m/s, indentation depth = 0.38 mm, shot diameter = 3 mm).
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Fig. 12. Comparison between the experimental and numerical indentation profiles (V = 100 m/s, indentation depth = 0.22 mm, shot diameter = 3 mm).
A reasonable agreement between the experimental results and numerical prediction can be seen in Figs. 9–12. It is interesting to notice that even the rounded protuberances surrounding the indentations have been fairly predicted by the simulations. The slight difference between experimental and numerical results may be attributed to the errors which may originate from the experimental measurement of a variety of parameters such as shot velocity, material constants for Johnson–Cook model and numerical approximations. Fig. 13. Four-shot model.
3. Multiple shot impacts modeling 3.1. Numerical models and material properties In this section the effect of impact multiplicity and velocity on residual stress profile is investigated. Despite validation of the code, we used the experimental results given by Torres and Voorwald [17] for further evaluation of the accuracy of the numerical predictions obtained from the simulations of multiple shot impacts. Therefore, we performed some part of the simulation with the same material model and velocity as used by Torres and Voorwald [17] in their experiments. The simulations of shot peening process in this work were carried out using the models consisting of 4, 6, 8, 9, 13, and 25 shots. The shot radius of 0.4 mm, the target plate dimensions of 0.8 mm × 0.8 mm × 1.6 mm and the friction coefficient of 0.1 remained constant throughout the simulations. The material properties of the shots were: ρ (density) = 7800 kg/m3 , E (elasticity modulus) = 210 GPa and υ (Poisson’s ratio) = 0.3. The target plate was made of AISI 4340 steel. This material, as used by Torres and Voorwald [17], had the following particulars: ρ = 7800 kg/m3 , E = 210 GPa, υ = 0.3, σ y = 1500 MPa, H (plasticity modulus) = 1600 MPa. The Cowper–Symonds material model with c = 2 × 105 , p = 3.3 and σ0 = 1500 MPa (see Eq. (2)) was employed for the simulations. The shots were modeled with 192 six- and eight-node brick elements. The target plate discretization was performed using a mesh of 4500 eight-node brick elements. The simulations were carried out at impact velocities in the range of 50–100 m/s.
3.2. Numerical simulation of multiple shot impacts As stated above, numerical simulations of multiple shot impacts were carried out using 4, 6, 8, 9, 13, and 25 shots. In order to shorten the paper only the models for 4 and 9 shots are shown. Fig. 13 illustrates the four-shot model in which only 1/8 of each shot has been considered in the simulation. In this model four shots collide with the target plate simultaneously. In the nine-shot model shown in Fig. 14, the arrangement of the shots for successive impacts can be observed. The first impact occurs with 4 shots, as explained for the four-shot model. The second and third collisions take place with 2 shots within the time intervals of 18 and 34 s, respectively. The last impact is accomplished by collision of a single shot 50 s after the third impact. The time interval is calculated from H/v, in which H is the distance between shot centers and v the impact velocity. The variation of residual stress profile versus impact velocity and impact multiplicity has been studied at five distinct critical points on the target plate. The points shown in Fig. 15 are: 1. Point A, which is located at the center of a region, that never directly comes into contact with a shot, in other words, in the region, which remains intact during surface bombarding. 2. Point B, which is located in the region where some indentations, caused by successive impacts, overlap. 3. Point C, which is located at the center of an indentation, which is created upon the first impact of the shots on the target plate.
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Fig. 16. Residual stress profiles for various shot models at the center of the target plate at a velocity of 50 m/s.
Fig. 14. Nine-shot model.
4. Point D, which is a random point of the plate. 5. The center of the target plate. The residual stress distribution obtained from the simulations of four- to nine-shot models at center of the target plate and at a velocity of 50 m/s (see Fig. 15) is shown in Fig. 16. From the figure it can be deduced that the profile of residual stress changes rapidly as the number of shot impacts increases. It is evident that the each point on the surface of the target plate would experience a different residual stress
Fig. 15. The target plate with indentations created by shot impacts.
Fig. 17. Residual stress profiles for nine-shot model at a velocity of 50 m/s.
distribution. Fig. 17 represents the residual stress profiles at the three different points explained above. This figure clearly illustrates the non-uniformity of the stress, which obviously depends on the shot multiplicity and impact velocity. The results given in Fig. 18 for 13-shot simulations again represents the residual stress non-uniformity on the target plate after multiple impacts.
Fig. 18. Residual stress profiles for 13-shot model at a velocity of 50 m/s.
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Fig. 19. Residual stress profiles for 25-shot model at a velocity of 50 m/s.
The residual stress profiles provided in Fig. 19, indicate that a state of uniform stress have been achieved in the simulations of 25-shot impacts at the impact velocity of 50 m/s. An interesting point to be noticed is that the residual stress profile induced at a point by a shot collision is not affected considerably by further shot impacts surrounding the point. This can be observed in Fig. 20, in which the residual stress profiles for three different multiple shots at point D are illustrated. Another important aspect of shot peening process, which is investigated here, is the effect of impact velocity. The residual stress profiles obtained from the numerical simulation at point D and at the velocities of 50, 75, and 100 m/s have been depicted in Figs. 20–22, respectively. The figures clearly show that unlike the results obtained for 50 m/s, the higher velocities result in a non-uniform state of residual stress. This non-uniformity is significantly influenced by the number of shots, so that the maximum residual stress is attained for nine-shot model. However, further increase in the number of shots, as can be seen for 13- and 25-shot models, not only does not improve the results, but also deteriorate the situation. The residual stress profiles for 25 shots at the three velocities are produced in Fig. 23. Although, the
Fig. 20. Residual stress profiles at point D for three different shot models at a velocity of 50 m/s.
Fig. 21. Residual stress profiles at point D for three different shot models at a velocity of 75 m/s.
Fig. 22. Residual stress profiles at point D for three different shot models at a velocity of 100 m/s.
profiles are different, but the maximum residual stress for the three velocities are very close to each other. The variation of maximum residual stress versus impact velocity is depicted in Fig. 24. The figure implies that the maximum compressive residual stress rises as the velocity increases up to a point thereafter it begins to decline. Although, the maximum residual stress–velocity curve varies for different points on the
Fig. 23. The profiles of 25 shots at point D.
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Fig. 24. Variation of maximum residual stress vs. impact velocity.
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2. A uniform state of stress is achieved at a particular shots number which was found to be 25 in this work. 3. The shots number corresponding to the state of uniform stress is not the same as that related to the maximum compressive residual stress which may occur at lower number of shots. 4. Impact velocity significantly influences the residual stress profile. The increase of velocity improves the residual stress distribution up to a particular point, found to be 90 m/s in this work. Further increase in the velocity may reduce the maximum residual stress. 5. Numerical simulation allows a parametric study of shot peening process. This can provide insight into the process and a better understanding of shot peening mechanism. 6. The best compressive residual stress distribution was achieved for the simulation of 25-shot model at a velocity of 90 m/s.
Acknowledgements The authors wish to thank Dr. Maleki, the Dean of Faculty of Engineering, Bu-Ali Sina University for his support. They also like to thank research unit of Defense Industries for their contribution to this project and in particular testing the high velocity single-shot impacts. Thanks are due to Mr. Nemati, the technician of strength of material laboratory for his help in conducting the experiments.
Fig. 25. A comparison between the numerical and experimental residual stress profile.
target plate, but the trend of the curves is the same for all the points. From the results described above, it can be observed that the best residual stress distribution is obtained for 25 shots models at the velocity of 90 m/s. This is because, on one hand a nearly uniform stress distribution is achieved and on the other hand, the maximum compressive residual stress is attained. As stated in Section 3.1, the simulation’s conditions in the present work were adopted from the experimental work by Torres and Voorwald [17]. The numerical predictions of residual stress profile for 25-shot model at various points (given in Fig. 19) are compared with the experimental profiles reported by Torres and Voorwald [17] in Fig. 25. As the figure indicates, the numerical and experimental results are very close. The differences can be attributed to the material model, numerical approximation and measurements.
4. Conclusions 1. Shot peening process can successfully be simulated by LS-DYNA finite element code providing a proper material model is selected.
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