Effects of simulation parameters on residual stresses for laser shock ...

Journal of Mechanical Science and Technology 27 (7) (2013) 2025~2034 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-1263-0

Effects of simulation parameters on residual stresses for laser shock peening finite element analysis† Ju Hee Kim1,*, Yun Jae Kim2 and Joung Soo Kim3 1

Department of Mechanical Engineering, Korea Military Academy, Seoul, P.O. Box 77-2, Korea 2 Department of Mechanical Engineering, Korea University, Seoul, 135-775, Korea 3 Korea Atomic Energy Research Institute (KAERI), Daejeon, 305-353, Korea

(Manuscript Received December 12, 2011; Revised April 18, 2012; Accepted October 3, 2012) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract By using finite element analysis, we proposed an applicable finite element method of laser shock peening (LSP) and discussed various parameters, such as solution time, stability limit, dynamic yield stress, peak pressure, pressure pulse duration, laser spot size, and multiple LSP. The effects of parameters related to the finite element simulation of the LSP process on the residual stresses of 35CD4 30HRC steel alloy are discussed. Parametric sensitivity analyses were performed to establish the optimum processing variables of the LSP process. In addition, we evaluated the effects of initial residual stress, such as welding-induced residual stress field. Keywords: Ablative layer; Dynamic yield strength; Finite element analysis (FEA); Infinite element; Laser shock peening (LSP); Plasma; Shot peening (SP); Water tamping layer ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Laser shock peening (LSP) is an innovative surface treatment technique which produces compressive residual stresses near the surface, thereby improving fatigue performance of metallic components [1, 2]. The fatigue strength and life of a metallic material can increase remarkably after LSP because of the presence of compressive residual stresses in the material [1, 3]. Compressive residual stresses induced by LSP enhance the mechanical properties of the material, including hardness, fatigue strength, and stress corrosion cracking resistance. Furthermore, the LSP process is clean and the surface roughness of the workpiece is essentially unaffected for steel components. The present study aims to predict the residual stress distribution along the metal surface and the depth of the target induced by single and multiple LSP processes by using finite element analysis (FEA). The simulations were performed by using a commercial FE package program (ABAQUS V6.9), both ABAQUS/Explicit and ABAQUS/Standard [4]. The simulation results were compared with experimental and other FE data. The current study focused on the sensitivity analysis of the influence of LSP simulation parameters on residual stress, such as solution time, stability limit, dynamic yield stress, peak pressure, pressure pulse duration, laser spot size, *

Corresponding author. Tel.: +82 2 2197 2965, Fax.: +82 2 977 5317 E-mail address: [email protected] † Recommended by Associate Editor Jeong Sam Han © KSME & Springer 2013

and multiple LSP. In addition, the effect of initial residual stress, such as welding-induced residual stress field, was evaluated.

2. FEA 2.1 Simulation procedures A schematic configuration of an LSP process on a metal plate is shown in Fig. 1. Through LSP processing, the surface of the metallic target is exposed to an intense laser beam with high density (in the GW/cm2 range) and short pulse duration (tens of nanoseconds). Simultaneously, the thermo-protective coating (black paint or tape) is vaporized because of the highenergy laser pulse, thereby forming plasma that reaches temperatures in excess of 10,000°C. Thus, an extremely high pressure (on the order of GPa) against the metal surface confined by a transparent overlay material, such as water or glass, is caused by the extremely rapid expansion of the heated plasma [1-3]. The high-pressure pulse will propagate into the material’s interior. As a result, plastic deformation occurs and a hardened layer forms on the surface of the metallic target. As the LSP process involves high-speed impact and dynamic wave propagation, explicit time integration FE codes need to be employed, as shown in Fig. 1. In this respect, the ABAQUS/Explicit code [4] is generally used to simulate the LSP process. The full development of plastic deformation in the material during the LSP process takes much longer than

2026

J. H. Kim et al. / Journal of Mechanical Science and Technology 27 (7) (2013) 2025~2034 xf Finite element

Laser spot size

xp

Infinite element

x

z

Fig. 1. Schematic of one-sided LSP [5].

(a) xf xp

p

x (Surface)

rf CAX4R

Finite element Infinite element CINAX4

z (Dpeth)

(b) Fig. 3. (a) Geometry of one-sided LSP; (b) 2D FE mesh.

Fig. 2. LSP simulation procedure.

the duration of the pulse pressure. Calculation times should be sufficiently long because of the reflection and interaction of shock waves that propagate in the target. Two approaches can be used to simulate the LSP process [6]. The first approach is to use explicit time integration FE codes only (procedure ②), which is relatively simple to perform, yet requires long computation time. The second approach, which is more efficient, involves combining the ABAQUS/Explicit and ABAQUS/Implicit codes (procedure ①). In this approach, dynamic analysis is first performed by using the ABAQUS/Explicit code. When the dynamic analysis is complete, the deformed element data with all transient stresses and strain information are imported into the ABAQUS/Implicit code to calculate the residual stress field using statical analysis. For the cases considered in this paper, the two approaches yield similar results [1, 7], and the latter (and more efficient) approach is used throughout the paper. If initial residual stresses (σi) exist, as shown in Fig. 1, ABAQUS/Implicit code is used before the dynamic analysis to apply the initial residual stresses.

2.2 Model geometry and FE mesh One-sided laser peening on an infinite plate is considered a generic problem in the present work. The impact zone is assumed to be circular with a radius xp, and the geometry can be assumed to be axisymmetric, which is schematically depicted in Fig. 3(a). The corresponding axisymmetric FE model is shown in Fig. 3(b). The size of xp is assumed to be xp = 4 mm, and the FEA domain is the radius of xf = 6 mm. Outside the domain, infinite elements are used to simulate an infinite plate. Element type is CAX4R on finite elements and CINAX4 on infinite elements, as shown in Fig. 3(b). 2.3 Modeling of loading As reported in the literature, in the confined ablation mode, assuming a constant absorbed laser power density I0, the peak pressure induced by plasma is given by the following equation [2, 5]: P (GPa ) = 0.01

α Z I0 2α + 3

(1)

2027

J. H. Kim et al. / Journal of Mechanical Science and Technology 27 (7) (2013) 2025~2034

Table 1. Mechanical properties of the 35CD4 30HRC steel alloy [1]. Density ρ (kg/m3)

Poisson’s ratio ν

Elastic modulus E (GPa)

Dynamic yielding strength σyd (GPa)

Hugoniot elastic limit HEL (GPa)

7800

0.29

210

0.87

1.47

Table 2. Range of parameters for sensitivity analysis.

Fig. 4. Pressure-time history of a single LSP.

where I0 is the laser power density, α is the efficiency of the interaction, and Z (2/Z ≈ 1/Z1 + 1/Z2) is the reduced shock impedance between the material (Z1) and the confining layer (Z2). The pressure-time history is very important for the simulation of the LSP process. Although the pressure-time history is usually described as a Gaussian temporal profile, it is very close to a triangular ramp because of a very narrow pulse duration, as shown in Fig. 4. Thus, in this work, the pressure rises linearly to the peak pressure (Pmax) and then declines linearly during the following td [1, 2]. 2.4 Material properties The metal of the 35CD4 30HRC steel alloy was assumed to be an elastically perfect plastic with isotropic hardening. In the analysis, the plastic yielding is defined to follow the von Mises yield criterion. The finite elements can undergo nonlinearity with large deformation to cope with high-pressure impact, whereas the infinite elements were assumed to be elastic elements. As the shock wave propagates into the metal, plastic deformation occurs to a depth at which the peak stress no longer exceeds the Hugoniot elastic limit (HEL) of the material, which induces residual stresses throughout the affected depth. HEL is related to the dynamic yield strength according to [1, 2, 5-9] HEL =

(1 − ν ) d σy (1 − 2ν )

Parameter

Ref.

Ranges

Mesh size Le (µm)

30

20 to 50

Solution time for dynamic analysis tp (ns)

5,000

100 to 5,000

Stability limit time ts (ns)

ts

ts/2 - ts

Dynamic yield stress σyd (GPa)

0.87

0.8 to 1.0

Maximum peak pressure Pmax (GPa)

2.8

1.8 to 4.8

Pressure pulse duration td (ns); FWHM

50

5 to 75

Laser spot size xp (mm)

4

2 to 4

Multiple LSP n (shot)

1

1 to 4

Initial residual stress σi (MPa)

0

About 250

2.6 Parameters for sensitivity analysis Many parameters may affect the FE simulation results of the LSP process. They can be broadly categorized into two groups. The first group, which is related to convergence and accuracy of dynamic analysis, includes parameters associated with the dynamic FEA technique, such as the mesh size Le, solution time for dynamic analysis, and tp, stable limit time, ts. The other group, which is related to material properties and laser systems, includes parameters associated with the material property and the LSP process, such as the dynamic yield strength, σyd , maximum pressure, Pmax, pressure pulse duration, td, laser spot size, xp and the number of shots, n. For sensitivity analysis, the reference values for these variables are chosen, as given in Table 2.1 Each variable is then systematically varied to observe its effect on the simulation results.

3. Validation of FE simulation (2)

where νis the Poisson’s ratio, and σyd is the dynamic yield strength at high strain rates. The mechanical properties of the 35CD4 30HRC steel alloy are summarized in Table 1. 2.5 Boundary condition The infinite elements are used as non-reflecting boundaries for the finite element area [4]. This provides quiet boundaries for the numerical simulations that minimize reflection of propagating stress waves back into the finite element area [1, 2]. Displacement along the radial direction of the center axis nodes (at depth z) is limited because of the axisymmetric model.

Before presenting the results of sensitivity analysis, the present analysis is validated through a comparison with existing experimental data [10]. The same material, the 35CD4 30HRC steel alloy, was used for both studies. Laser peening parameters (Pmax, td, xp and n) were the same as the reference values given in Table 2. The detailed information on the experiments is found in Ref. [9]. Simulated residual stresses are compared with experimental results in Fig. 5. Fig. 5(a) compares variations of σx residual stresses on the surface (at y = z = 0) with distance x. Variations of σx residual stresses with depth z (at x = 3.5 mm) are com-

1

Reference values for Pmax, td, xp and n were chosen to compare with existing experimental data, as will be described in the next sub-section.

2028


(a)

(a)

(b)

(b) Fig. 5. Comparison between simulated FE results with experimental data.

pared in Fig. 5(b). Experimental data show that the residual stresses, σx, are similar. Despite differences between experimental and simulated residual stresses, overall trends in experimental data can be captured by the simulation. Considering uncertainties in measuring experimental residual stress, the results in Fig. 5 suggest that FE simulation of the LSP process is reliable. However, the experimental data indicate that the compressive residual stress is approximately zero at the center of the spot and that compressive and tensile residual stresses at the center area of the target zone are absent. For a circular laser spot, this phenomenon may have resulted from the simultaneous focusing of shockwaves at the center of the impact zone that emit from the edge of the area under impact [1-3, 10].

4. Sensitivity analysis results 4.1 Sensitivity analyses for FEA technique parameters 4.1.1 Mesh sensitivity In the FEA, results can be normal to sensitive to the size of the finite element mesh. To evaluate the effects of mesh size, three FE models with a mesh size of Le = 20, 30, and 50 µm, respectively, are selected (Fig. 6).

Fig. 6. Effect of the mesh size on simulated residual stress profiles.

The stresses (σxx) on the surface and depth of the target affected by mesh refinement are shown in Figs. 5(a) and 5(b). The result of surface and depth from Le = 20 µm is almost the same as that from Le = 30 µm, but it is quite different from Le = 50 µm. Thus, to ensure computational efficiency, Le = 30 µm is selected for further evaluation. Generally, the analysis employs a square mesh with an average element edge length of about 0.5% from the spot radius [5]. 4.1.2 Stability limit (ts) In ABAQUS/Explicit analysis, the time increment (∆t) affects the convergence and accuracy of results. If the time increment is larger than the stability limit, ts, a numerical instability can occur, thereby leading to an unbounded solution. A simple estimate based on element-by-element calculation can be used; this method is efficient and conservative in practice. Using the smallest element length, Le, and the wave speed of the material, Cd, ts can be estimated by using [1, 11, 12] ∆ts =

Le ρ = Le Cd E

(3)


2029

(a)

(a)

(b)

(b)

Fig. 7. Effect of the stability limit time on simulated residual stress profiles.

Fig. 8. Effect of the solution time for dynamic analysis on simulated dynamic stress profiles.

where E is the Young’s modulus of the material, and ρ is the mass density of the material. For the finite element size (Le) of 0.03 mm and the undamped, elastic wave speed of the material, Cd = 5.193103m/s, ts is about 5.78 ns. Fig. 7 shows the surface and depth residual stress profiles at the stability limit (ts and ts/2) selected by Eq. (3). The results are almost identical to other time increments. To avoid numerical instability, the ABAQUS/Explicit code sets the time increment (∆t) to be less than the stability limit (ts). 4.1.3 Solution time (tp) To obtain the residual stress field of the specimen, the solution time must be longer than the laser duration time. Fig. 8 shows the surface and depth residual stress profiles at the end of the six solution time periods. The residual stress profile is clearly different between the solution times of 100 ns and 5,000 ns. After the solution time of 2,000 ns, the surface residual stress profile gradually becomes steady. However, the depth residual stress profile becomes steady after the solution time of 500 ns. These results indicate that the solution time for dynamic analysis should be greater than 2,000 ns.

4.2 Sensitivity analyses for LSP optimal process parameters 4.2.1 Dynamic yield strength (σyd) At strain rate of less than 10-6 s-1, the plastic deformation during the LSP process is determined by the dynamic yield strength, σyd. As information on σyd may still be uncertain, the effect of σyd is investigated by varying σyd from 0.8 GPa to 1.0 GPa, and the results are shown in Fig. 9. An increase in the dynamic yield strength results in a decrease in the surface and depth residual stresses except at the center of the laser spot on the surface. Increasing the material yield strength is generally known to increase the material resistance for plastic deformation. In this way, the stability time is shortened, and the shock-affected zone and the plastic deformation depth are decreased [13]. 4.2.2 Maximum peak pressure (Pmax, see Fig. 4) The plasma pressure pulse induced by LSP is a function of laser power density. An increase in the laser power density increases the magnitude of pressure pulse on the material surface. To evaluate effects on the residual stress field relative to changes in peak pressures, Pmax of 1.8 GPa to 4.8 GPa is used according to an increase in the laser power density from Eq. (1).

2030


(a)

(a)

(b)

(b)

Fig. 9. Effect of the dynamic yield strength on simulated residual stress profiles.

Fig. 10. Effect of the peak pressure on simulated residual stress profiles.

Fig. 10 shows the results; HEL = 1.47 GPa stands for the present metal material. Results show that magnitudes of compressive residual stresses near the surface increase with increasing Pmax up to Pmax = 2.8 GPa. For Pmax = 3.8 GPa and 4.8 GPa, the total magnitude of compressive residual stresses on the surface is smaller than that for Pmax = 2.8 GPa. Along with depth direction, the plastically affected zone size increases with increasing Pmax. For Pmax = 1.8 GPa, magnitudes of compressive residual stresses decrease monotonically. However, for Pmax = 2.8 GPa, 3.8 GPa, and 4.8 GPa, they increase near the surface and then decrease. Results in Fig. 10 suggest that the case of Pmax = 2.8 GPa can produce optimum LSP results, which is fully consistent with existing findings that materials can be optimally treated with Pmax = (22.5)×HEL range [1, 6]. The choice of laser power density is important to produce desired residual stress profiles in the LSP process.

periods of pressure pulse duration were introduced in the FEA. Fig. 11(a) shows increased maximum compressive residual stress for td = 5 ns and 25 ns. However, for over td = 25 ns, residual stresses near the center become less compressive. For over td = 50 ns, they can be even tensile. Along with depth direction, the plastically affected depth size increases with increasing td, as shown in Fig. 11(b). For td = 5 ns and 25 ns, magnitudes of compressive residual stresses decrease monotonically with depth. For td = 50 ns and 75 ns, they increase near the surface and then decrease. The results shown in Fig. 11 suggest that the pressure pulse duration should be selected properly to obtain desired residual stress profiles.

4.2.3 Pressure duration (td) In addition to laser power density, pressure duration is another important parameter associated with the LSP process. To determine the relationship between the residual stress and the pressure duration of laser pulse, as shown in Fig. 11, four

4.2.4 Laser spot size (xp) The simulation is also performed to verify changes in residual stresses corresponding to variations in the laser spot size (xp) under the same peak pressure of 2.8 GPa and the same laser pulse duration of 50 ns. The radii of the laser spot are assumed to be 2 mm to 4 mm. The results from the FE simulation are shown in Fig. 12. The results in Fig. 12(a) show that surface residual stress distributions are quite similar to the variation of the laser spot size, and the maximum compressive residual stress level re-


2031

(a)

(a)

(b)

(b)

Fig. 11. Effect of the pressure durations on simulated residual stress profiles.

Fig. 12. Effect of the laser spot size on simulated residual stress profiles.

mained almost steady at about 360 MPa. The distributions of the depth residual stresses with respect to changes in the laser spot size are plotted in Fig. 12(b), which indicates that the plastic affected depth and the maximum compressive residual stresses remain almost stable. Therefore, the maximum compressive residual stress and the plastically affected depth are unrelated to the laser spot size.

creased from 420 MPa to 520 MPa. The maximum plastically affected depth (Lp1) reached 0.76 mm after one impact. After four impacts on the same spot, the plastically affected depth (Lp4) increased up to 1.5 mm. Therefore, multiple LSP can have a beneficial effect on the residual stress distributions for depth direction.

4.2.5 Multiple LSP (n) The surface and depth residual stress distributions that result from the multiple LSP are shown in Fig. 13. The LSP parameters, such as peak pressure (2.8 GPa), laser spot size (4 mm), and laser pulse duration (50 ns), are used in similar conditions. As shown in Fig. 13(a), after four impacts on the same area, the surface residual stresses gradually became almost steady. In general, the peak compressive residual stress is slightly changed. Further improving the surface residual stresses under the same LSP conditions is difficult because LSP can increase the metal surface hardness over the entire region of the laser impact area [9]. However, as shown in Fig. 13(b), depth compressive residual stresses increase with the number of impact on the same area. The peak compressive residual stress in-

4.3 FE results using LSP optimal process parameters The surface and depth residual stress distributions that result from the optimum parameters of the LSP system are shown in Fig. 14. Then optimum LSP parameters such as peak pressure (2×HEL), laser spot size (4 mm), and laser pulse duration (25 ns) are used in the same conditions. As shown in Fig. 14(a), after one impact by using optimum LSP parameters on the same area, surface residual stresses increased remarkably. The maximum compressive residual stresses increased to about 510 MPa, which is 42% higher than that of Pmax = 2.8 GPa, td = 50 ns. The distributions of the depth residual stresses are plotted in Fig. 14(b). Along with depth direction, the plastically affected zone size (Lp) decreased to about 0.42 mm, which is 138% lower than that for Pmax = 2.8 GPa, td = 50 ns. However, as

2032


(a)

(a)

(b)

(b)

Fig. 13. Effect of the multiple laser impacts on simulated residual stress profiles.

Fig. 14. Comparison between the experimental results and FE simulated results by optimum parameters.

shown in Fig. 13(b) the maximum plastically affected depth (Lp1) increased in the multiple LSP process. Therefore, residual stresses due to the LSP optimal process parameters result in a more effective residual stress.

state of initial tensile residual stress (σi = 250 MPa). Significantly, a compressive residual stress is also generated even if initial tensile residual stresses exist in the target area. As a result, the LSP technique can produce a compressive residual stress field on the metal surfaces, which existed before the tensile residual stress.

4.4 Effect of initial residual stress (σi) To evaluate the effect of initial tensile residual stress, such as welding residual stress, in the metal, the initial condition option is used in the FE code (ABAQUS). Corresponding to the general welding residual stress [4], initial residual stresses σi are assumed to be about 250 MPa. When the initial condition option is used, a proportional integral adjustment, which is widely used in automatic control, can be used to modify the input initial stress values to reproduce a desired residual stress distribution [13]. As shown in Fig. 15, initial tensile residual stresses σi are assumed to be about 250 MPa. The simulation is performed under LSP parameters such as Pmax = 2.8 GPa, xp = 4 mm, td = 500 ns and single shot, n = 1. In Fig. 16, the amplitudes of the compressive residual stresses on surface and in-depth directions are both compared with the absence of initial residual stress (σi = 0 MPa) and the

5. Conclusions The present work discussed the effects of parameters for FE simulation of the LSP process to determine residual stresses. A two-dimensional FE simulation of single and multiple LSP on a 35CD4 steel alloy was conducted by using the simulation methodology. The conclusions can be summarized as follows. • The selected mesh size should be smaller than about 0.5% of the spot size. • The solution time for dynamic analysis should be sufficiently long at about hundred times longer than the laser pulse duration. • The time increment for dynamic analysis should be less than the stability limit time to be decided by element size. • The effect of the dynamic yield strength on simulated residual stresses is almost linear.


2033

• Residual stresses in the depth direction are unaffected by the laser spot size. • Magnitudes of compressive residual stresses increase with the increase in the number of shots, but this effect is less pronounced with more shots.

Acknowledgments This work was supported by a grant from the Korea Atomic Energy Research Institute funded by the Ministry of Knowledge Economy, Republic of Korea (No. R1100161).

Nomenclature-----------------------------------------------------------------------Fig. 15. Initial residual stress distributions for LSP FEA.

I0

α Z HEL σyd Le tp ts Pmax td xp n Cd

: Laser power density : Laser efficiency : Reduced shock impedance : Hugoniot elastic limit : Dynamic yield strength : Length of element : Solution time for dynamic analysis : Stability time limit : Maximum peak pressure : Pressure pulse duration : Laser spot size : Number of laser shot : Wave speed of material

References (a)

(b) Fig. 16. Effect of the different initial residual stresses on simulated residual stress profiles.

• The maximum peak pressure (about 2×HEL) can produce maximum compressive residual stresses near the surface and depth. Thus, the maximum peak pressure should be selected. • Certain pulse duration ranges can produce maximum compressive residual stresses near the surface. Thus, the proper choice of this parameter is important.

[1] K. Ding and L. Ye, Laser shock peening Performance and process simulation, CRC Press (2006) 47-118. [2] K. Ding and L. Ye, Simulation of multiple laser shock peening of a 35CD4 steel alloy, J. of Materials Processing Technology, 178 (2006) 162-169. [3] J. E. Masse and G. Barreau, Laser generation of stress waves in metal, Surface and Coating Technology, 70 (1995) 231234. [4] ABAQUS Version 6.7 and 6.9, User’s manual, Dassault Systemes (2008). [5] W. Braisted and R. Brockman, Finite element simulation of laser shock peening, Int. J. of Fatigue, 21 (1999) 719-724. [6] X. Ling, W. Peng and G. Ma, Influence of Laser Peening Parameters on Residual Stress Field of 304 Stainless Steel, J. of Pressure Vessel Technology, 130 (021120) (2008) 1-8. [7] J. H. Kim, Y. J. Kim, H. Y. Bae, C. Y. Oh, J. S. Kim and J. S. Kim, Numerical simulation of two-sided laser shock peening using finite element method, Korean Society of Pressure Vessel and Piping Spring Conference (2011) 127-128. [8] P. Peyre and R. Fabbro, Laser shock processing: a review of the physics and applications, Optical and Quantum Electronics, 27 (1995) 1213-1229. [9] C. Yang, P. D. Hodgson, Q. Liu and L. Ye, Geometrical effects on residual stresses in 7050-T7451 aluminum alloy rods subject to laser shock peening, J. of Material Processing Technology, 201 (2008) 303-309.

2034


[10] P. Ballard, J. Fournier, R. Fabbro and J. Frelat, Residual stresses induced by laser-shocks, J. de Physique IV, 1 (1991) 487-581. [11] Y. Hu and Z. Yao, Numerical simulation and experimentation of overlapping laser shock processing with symmetry cell, Int. J. of Machine Tools & Manufacture, 48 (2008) 152162. [12] B. W. Bang, S. K. Son, J. M. Kim and C. D. Cho, Residual Stress Prediction in LSP Surface Treatment by Using FEM, KSME-A, 33 (8) (2009) 776-772. [13] Y. Lei, N. P. O’Dowd and G. A. Webster, Fracture me-

chanics analysis of a crack in a residual stress field, Int. J. of Fracture, 106 (2000) 195-216.

Ju Hee Kim is an assistant professor of the Department of Mechanical Engineering, Korea Military Academy, Seoul, Korea. His main research interests are residual stress analysis for welding and LSP simulation.