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\title{Effects of Simulation Parameters on Residual Stresses in 3D Finite Element Laser Shock Peening Analysis}
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             \author[1]{Ju Hee  Kim}

             \affil[1]{  Dept. of Mechnical Engineering/Korea Military Academy}

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\date{\small \em Received: 13 December 2012 Accepted: 5 January 2013 Published: 15 January 2013}

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\begin{abstract}
        


Laser shock peening(LSP) is an  innovative  surface treatment technique, which is successfully applied to improve fatigue performance of metallic components. After the treatment, the fatigue strength and fatigue life of a metallic material can be increased remarkably owing to the presence of compressive residual stresses in the material.  Recently,  the incidences of cracking in Alloy 600 small-caliber penetration nozzles (CRDM (control rod drive mechanism)  and BMI(bottom mounted  instrument)) have increased significantly. The cracking mechanism has been attributed to primary water stress corrosion cracking (PWSCC) and has been shown to be driven by welding residual stresses and operational stresses in the weld region. For this reason, to mitigating weld  residual stress, preventive maintenance of BMI nozzles was considered application of laser shock peening process. Effects of parameters related to finite element simulation of laser shock peening process to determine  residual  stresses are discussed, in particular parameters associated with the LSP process, such as the maximum pressure, pressure pulse duration, laser spot size and number of shots.  It is found that certain ranges of the maximum pressure and pulse duration can produce maximum compressive residual stresses near the surface, and thus proper choices of these parameters are important.  For the laser spot size, residual stresses are not affected, provided it is  larger than a certain size.  Magnitudes of compressive residual stresses are found to increase with increasing number of shots, but the effect is less pronounced for more shots. 

\end{abstract}


\keywords{FE analysis, LSP (laser shock peening), residual stress.}

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\let\tabcellsep& 	 	 		 
\section[{Effects of Simulation Parameters on Residual}]{Effects of Simulation Parameters on Residual}\par
Stresses in 3D Finite Element Laser Shock Peening Analysis\par
Abstract-Laser shock peening (LSP) is an innovative surface treatment technique, which is successfully applied to improve fatigue performance of metallic components. After the treatment, the fatigue strength and fatigue life of a metallic material can be increased remarkably owing to the presence of compressive residual stresses in the material. Recently, the incidences of cracking in Alloy 600 small-caliber penetration nozzles (CRDM (control rod drive mechanism) and BMI (bottom mounted instrument)) have increased significantly.\par
The cracking mechanism has been attributed to primary water stress corrosion cracking (PWSCC) and has been shown to be driven by welding residual stresses and operational stresses in the weld region. For this reason, to mitigating weld residual stress, preventive maintenance of BMI nozzles was considered application of laser shock peening process. Effects of parameters related to finite element simulation of laser shock peening process to determine residual stresses are discussed, in particular parameters associated with the LSP process, such as the maximum pressure, pressure pulse duration, laser spot size and number of shots. It is found that certain ranges of the maximum pressure and pulse duration can produce maximum compressive residual stresses near the surface, and thus proper choices of these parameters are important. For the laser spot size, residual stresses are not affected, provided it is larger than a certain size. Magnitudes of compressive residual stresses are found to increase with increasing number of shots, but the effect is less pronounced for more shots.\par
Keywords: FE analysis, LSP (laser shock peening), residual stress. 
\section[{Introduction}]{Introduction}\par
aser shock peening (LSP) is an innovative surface treatment technique, producing compressive residual stresses near the surface and thus improving fatigue performance of metallic components \hyperref[b0]{[1,}\hyperref[b1]{2]}. Through the LSP processing, the surface of the metallic target is exposed to an intense laser beam with high density (in the GW/cm2 range) for short duration (tens of nanoseconds). The thermo-protective coating (black paint or taping) is vaporized because of the highenergy laser pulse, forming a plasma that reaches temperatures in excess of 10,000 °C. An extremely high pressure (the order of GPa) on the metal surface is generated bythe extremely rapid expansion of the heated plasma \hyperref[b0]{[1]}\hyperref[b1]{[2]}\hyperref[b2]{[3]}. The high pressure then propagatesinto the material interior. As a result, plastic deformation occurs and a hardened layer is formed on the surface of the metallic target, enhancing mechanical properties such as hardness, fatigue strength, and stress corrosion cracking resistance.\par
In the present work, effects of parameters related to finite element (FE) simulation of LSP process to determine residual stresses is discussed. Simulations were performed using the general purpose FE program ABAQUS \hyperref[b3]{[4]}. 
\section[{II.}]{II.} 
\section[{F Analysis a) Simulation Procedures}]{F Analysis a) Simulation Procedures}\par
As the LSP process involves high speed impact and dynamic wave propagation, explicit time integration FE codes need to be employed, for instance, using the ABAQUS/Explicit code \hyperref[b3]{[4]}. There can be two approaches to simulate the LSP process. The first approach is to use explicit time integration FE codes only(procedure ?). Although this approach is relatively easy to perform, it requires long computation times. This is because calculation times should be chosen to be sufficiently long, as full development of plastic deformation in the material during the LSP process takes much longer than the duration of the pulse pressure, due to reflection and interaction of shock waves propagating in the target.\par
The second, more efficient, approach is to combine ABAQUS/Explicit and ABAQUS/Implicit codes (procedure ?). In this approach, dynamic analysis is firstly performed using the ABAQUS/Explicit code. When the dynamic analysis is completed, the deformed element data with all transient stresses and strains information are then imported into the ABAQUS/Implicit code to calculate residual stress fields using static analysis. For cases considered in this paper, it is found that the above two approaches give the same results, and thus the latter (and more efficient) approach is used throughout the paper. 
\section[{b) Modeling Pressure Loading}]{b) Modeling Pressure Loading}\par
Assuming a constant absorbed laser power density Io in the confined ablation mode, the maximum peak pressure induced by plasma, Pmax, is given by \hyperref[b0]{[1,}\hyperref[b1]{2,}\hyperref[b4]{[5]}\hyperref[b5]{[6]}\hyperref[b6]{[7]} (1)\par
where ? is the efficiency of the interaction; and Z is the reduced shock impedance between the material and the confining layer \hyperref[b0]{[1,}\hyperref[b10]{8]}.\par
(\par
Although the pressure-time history for simulating LSP is usually described using a Gaussian temporal profile, it is in fact very close to a triangular ramp because of very short pressure pulse duration (order of 100ns), as shown in Fig.  {\ref 2}. Thus, in this wo rk, the pressure is assumed to increase linearly to the maximum pressure, Pmax, and then decrease linearly for a total pulse duration, 2tp, as shown in Fig.  {\ref 2}. 
\section[{c) Modeling Plastic Deformation Due to Shock Wave}]{c) Modeling Plastic Deformation Due to Shock Wave}\par
As the shock wave propagates into the metal, plastic deformation occurs up to a depth at which the peak stress equals the Hugoniot elastic limit (HEL) of the material. The HEL is related to the dynamic yield strength at high strain rates, ?y d , according to \hyperref[b0]{[1,}\hyperref[b1]{2,}\hyperref[b4]{[5]}\hyperref[b5]{[6]}\hyperref[b6]{[7]}\hyperref[b10]{[8]} (3) where ? is Poisson's ratio. 
\section[{III.}]{III.} 
\section[{Sensitivity Analysis for LSP Simulation a) Geometry and FE mesh}]{Sensitivity Analysis for LSP Simulation a) Geometry and FE mesh}\par
As a generic problem, the present work considers one-sided laser peening on an infinite plate. The impact zone is assumed to be rectangular with a half-length xp, as schematically shown in Fig.  {\ref 3a}.\par
Corresponding three-dimensional (3D) FE quarter model is shown in Fig.  {\ref 3b}. The FE analysis domain has a halflength xf (which is fixed to xf =5 mm in this work).\par
Outside the domain, infinite elements are used to simulate an infinite plate. For the element type, the first order elements (C3D8R for finite elements and CIN3D8 for infinite elements within ABAQUS) are used. 
\section[{b) Material Properties}]{b) Material Properties}\par
The material is assumed to be the 35CD4 50HRC steel alloy, of which physical and mechanical properties, taken from Ref. \hyperref[b0]{[1]}, are given in Table  {\ref 1}. Other parameters used in simulations are; c) Parameters for Sensitivity Analysis 
\section[{d) Validation}]{d) Validation}\par
Before presenting results of sensitivity analysis, the present analysis is validated by comparing with existing experimental data \hyperref[b7]{[9]}. The material was the 35CD4 50HRC steel alloy that is the same as the one considered in the present work. Laser peening parameters (Pmax, td, xp and n) were the same as the reference values given in Table \hyperref[tab_0]{2}. More detailed information on experiments can be found in Ref. \hyperref[b7]{[9]}.\par
Simulated residual stresses are compared with experimental results in Fig. \hyperref[fig_2]{4}. Figure \hyperref[fig_2]{4a} compares variations of ?x and ?y residual stresses in the surface (at y=z=0) with distance x. Variations of ?x and ?y residual stresses with depth z (at x=y=0) are compared in Fig. \hyperref[fig_2]{4b}. Experimental data show that both residual stresses, ?x and ?y, are similar. Despite differences between experimental and simulated residual stresses, overall trends in experimental data can be 1 Note that reference values for Pmax, td, xp and n were chosen to max (GPa) 0.01 23 o P Z I ? ? ? ? 1 2 2 1 1 Z Z Z ? ? (1 ) (1 2 ) d y HEL ? ? ? ? ? ?\par
compare with existing experimental data, as will be described in the next subsection captured by simulation.\par
There are many parameters possibly affecting FE simulation results of the LSP process. They can be broadly categorized into two groups. The first group includes parameters associated with dynamic FE analysis, such as the mesh size Le, solution time for dynamic analysis, ts, time step, Î?" ts and dynamic yield strength, ?y d . The other group includes parameters associated with the LSP process, such as the maximum pressure, Pmax, pressure pulse duration, td, laser spot size, rp and the number of shots, n. For sensitivity analysis, the reference values for these variables are chosen, as given in Table \hyperref[tab_0]{2}.1 Each variable is then systematically varied to see its effect on simulation results. ?=0.1, Z1=3.6 106(g/cm-2s-1) and Z2=0.165 106(g/cm-2s-1) \hyperref[b0]{[1,}\hyperref[b10]{8]} IV. 
\section[{Sensitivity Analysis Results}]{Sensitivity Analysis Results} 
\section[{a) Effect of the Mesh Size}]{a) Effect of the Mesh Size}\par
It is known that FE LSP simulation results are not affected by the element size, provided it is less than about 5\% of the spot size, xp [1, 5]. The critical element size is 125 problem. To see the effect of the mesh size, three different FE models were prepared, having the element size ranging from Le=100 µm to Le=250 µm, and results are shown in Fig.  {\ref 6}. In Fig.  {\ref 6} as well as in subsequent figures, two residual stress profiles are presented. The first one is variations of the ?x residual stresses at the surface (y=z=0) with distance x, shown in Fig.  {\ref 6a}. The second result is variations of the ?x residual stresses at the center of the laser spot (x=y=0) with depth z, shown in Fig.  {\ref 6b}.\par
Results in Fig.  {\ref 6} confirm the existing finding that simulated residual stresses are not affected when the element size is less than 5\% of the spot size, xp. 
\section[{b) Time Step for Stability}]{b) Time Step for Stability}\par
In dynamic analysis, the time step, ?ts, should be chosen to be smaller than the stability limit for numerical stability. The stability limit can be estimated from \hyperref[b0]{[1,}\hyperref[b8]{10,}\hyperref[b9]{11]} (4)\par
where Le denotes the smallest element size; Cd is the wave speed of material; E is Young's modulus; and ? is the mass density. For the present problem, Cd= 5.193x10 3 m/s with Le=125 µm gives ?ts ?5.78 ns. For the sake of space, results are not shown but simulated residual stress results are found not to be affected by the time step, provided that it is less than ?ts, given by Eq.(4). 
\section[{c) Solution time for dynamic analysis (ts)}]{c) Solution time for dynamic analysis (ts)}\par
To obtain residual stress fields due to dynamic wave propagation by LSP, the solution time in dynamic analysis must be taken much longer than the laser duration time. Figure  {\ref 7} shows dynamic stress profiles at four different times during dynamic analysis. Results show that simulated dynamic stress profiles are affected by ts.\par
After ts=2,000ns, the dynamic stress profile in the depth direction gradually becomes steady, but the dynamic stress profile at surface become steady only after ts=5,000ns. Results suggest that the solution time for dynamic analysis should be chosen to be larger than 5,000ns, which is about hundred times larger than the pulse duration td=50ns. 
\section[{Dynamic Yield Strength (?y d )}]{Dynamic Yield Strength (?y d )}\par
As the strain rate during the LSP process is faster than 10 -6 s -1 , plastic deformation is determined by the dynamic yield strength, ?y d . As information on ?y d may have uncertainty, the effect of ?y d is investigated by varying ?y d from 1.0GPa to 1.5GPa, and the results are shown in Fig. \hyperref[fig_4]{8}. Results show that magnitudes of compressive residual stresses decrease almost linearly with increasing ?y d , due to the fact that increasing the material yield strength tends to increase material resistance against plastic deformation \hyperref[b9]{[11]}. e) Maximum Pressure (Pmax,, see Fig.  {\ref 2})\par
The plasma pressure pulse induced by LSP depends on the laser power density, as shown in Eq. (1). Increasing laser power density increases the magnitude of the pressure pulse on the material surface. The plastic deformation in the material depends mainly on the HEL. No plastic deformation occurs in the material for Pmax <HEL. The plastic strain occurs with a purely elastic reverse strain for HEL< Pmax <2×HEL, and the plastic strain fully occurs for Pmax >2×HEL \hyperref[b0]{[1,}\hyperref[b1]{2,}\hyperref[b5]{6]}.\par
To see the effect of the laser power density on residual stresses, simulations are performed for Pmax, ranging from 2.5GPa to 5GPa, and results are shown in Fig.  {\ref 9}. Note HEL=2.1GPa for the present problem.\par
Results show that magnitudes of compressive residual stresses near the surface increase with increasing Pmax up to Pmax =4GPa. For Pmax =5GPa, the magnitudes of compressive residual stresses in the surface are overall smaller than those for Pmax =4GPa.\par
Along the depth direction, the plastically affected zone size increases with increasing Pmax. For Pmax =2.5GPa and 3GPa, magnitudes of compressive residual stresses decrease monotonically. However, for Pmax =4GPa and 5GPa, they increase near the surface and then decrease. Results in Fig.  {\ref 9} suggest that the case of Pmax =4GPa can produce optimum laser peening treatment, which is fully consistent to the existing finding that materials can be optimally treated with Pmax = (2-2.5)×HEL range \hyperref[b0]{[1,}\hyperref[b5]{6]}. Results show that the choice of the laser power density is important in the LSP process to produce desired residual stress profiles.\par
f) Pressure Duration (td)\par
In addition to the laser power density, the pressure duration is another important parameter associated with the LSP process. Figure  {\ref 10} shows the a 3D profile of predicted residual stresses (von Mises stress) on the surface and in the depth directions, impacted at a spot size of xp=2.5mm. measurement, results in Fig. \hyperref[fig_2]{4} suggest that FE simulation of the LSP process is reliable. Figure  {\ref 5}  effect of the pressure duration of laser pulse on residual stresses decrease monotonically with the depth. For td =100ns, they increase near the surface and then decrease. For larger td, such trend is more pronounced. Results in Fig.  {\ref 10} suggest that the pressure duration should be chosen properly to obtain desired residual stress profiles. 
\section[{g) Laser Spot Size ( xp )}]{g) Laser Spot Size ( xp )}\par
To see the effect of the laser spot size, simulations are performed for various laser spot sizes (rp) ranging from 0.5mm to 2.5mm, with the fixed Pmax=3GPa and pulse duration of td=50 ns, and results are shown in Fig.  {\ref 11}. The affected zone size of compressive residual stresses in the surface obviously increases with increasing laser spot size. However, residual stresses in the depth direction are not affected by the laser spot size, provided it is larger than 1.5mm. 
\section[{h) Number of Shots (n)}]{h) Number of Shots (n)}\par
In practice, the multiple LSP process can be performed to produce more compressive residual stresses. The effect of multiple LSP process (from single to four times) on simulated residual stresses is shown in Fig.  {\ref 12}. In simulation, the parameters associated with the LSP process are fixed; Pmax=3GPa, xp=2.5mm and td=50ns. Multiple LSP is applied to the same area.\par
Results show that magnitudes of compressive residual stresses increase with increasing number of shots, but the effect on residual stresses is less pronounced for more shots. 
\section[{i) FE results using LSP optimal process parameters}]{i) FE results using LSP optimal process parameters}\par
The surface and depth residual stress distributions resulting from the optimum parameters of LSP system are shown in Fig.  {\ref 13}. Then optimum LSP parameters such as peak pressure (2×HEL=4.2GPa), laser spot size (2.5mm), and laser pulse duration (100ns) are used in same conditions. As shown in Fig.  {\ref 13a}, after one impact using optimum LSP parameters on same area, the surface residual stresses have increased remarkably. It shows that the maximum compressive residual stresses increase to about 567MPa, which is 62\% higher than that for Pmax=3GPa, td=50ns. The distributions of the depth residual stresses plotted in Fig.  {\ref 13b}. Along the depth direction, the plastically affected zone size(Lp) decreases to about 1.42mm, which is 136\% higher than that for Pmax=3GPa, td=50ns. Therefore, residual stresses due to the LSP optimal process parameters result in a more effective residual stress.\par
V. 
\section[{Conclusions}]{Conclusions}\par
In the present work, effects of parameters related to finite element (FE) simulation of LSP process to determine residual stresses are discussed. Two groups of parameters are considered: one those associated with dynamic FE analysis, such as the mesh size, solution time for dynamic analysis, time step and dynamic yield strength; and the other associated with the LSP process, such as the maximum pressure, pressure pulse duration, laser spot size and number of shots.\par
Conclusions can be summarized as follows. ? The mesh size should be chosen to be smaller than 5\% of the spot size. ? The solution time for dynamic analysis should be chosen to be sufficiently long, about hundred times larger than the pulse duration. ? The effect of the dynamic yield strength on simulated residual stresses is almost linear. ? Certain ranges of the maximum pressure and pulse duration can produce maximum compressive residual stresses near the surface, and thus proper choices of these parameters are important. ? Residual stresses in the depth direction are not affected by the laser spot size, when it is larger than a certain size. ? Magnitudes of compressive residual stresses increase with increasing number of shots, but the effect is less pronounced for more shots.\par
However, for td =100ns, residual stresses near the center become less compressive. For td =150ns, they can be even tensile. Along the depth direction, the plastically affected zone size increases with increasing td. For td =30ns and 50ns, magnitudes of compressive simulated residual stresses. In the surface, residual stress profiles for td =30ns and 50ns are similar.\par
and Quantum Electronics, Vol. 27, pp. 1213-1229, 1995.      Table  {\ref 1} : Mechanical properties of the 35CD4 50HRC steel alloy [1]   Global Journal of Researches in Engineering   
\section[{Volume XIII Issue IX Version I ( )}]{Volume XIII Issue IX Version I ( )}
\begin{quote}
A Year\end{quote}
\begin{figure}[htbp]
\noindent\textbf{123}\includegraphics[]{image-2.png}
\caption{\label{fig_1}Figure 1 :Figure 2 :Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-3.png}
\caption{\label{fig_2}Figure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{567}\includegraphics[]{image-4.png}
\caption{\label{fig_3}Figure 5 :Figure 6 :Figure 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8}\includegraphics[]{image-5.png}
\caption{\label{fig_4}Figure 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{910}\includegraphics[]{image-6.png}
\caption{\label{fig_5}Figure 9 :Figure 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1112}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Figure 11 :Figure 12 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_7}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.6142123287671233\textwidth}P{0.020376712328767123\textwidth}P{0.07277397260273973\textwidth}P{0.14263698630136987\textwidth}}
Parameter\tabcellsep \tabcellsep Ref.\tabcellsep Ranges\\
\multicolumn{2}{l}{Mesh size, L e (mm)}\tabcellsep 0.125\tabcellsep 0.25-0.1\\
\multicolumn{2}{l}{Solution time for dynamic analysis, t p (ns)}\tabcellsep 5,000\tabcellsep 500-5,000\\
Dynamic yield strength, ? y\tabcellsep d (GPa)\tabcellsep 1.24\tabcellsep 1-1.5\\
\multicolumn{2}{l}{Maximum pressure, P max (GPa)}\tabcellsep 3\tabcellsep 2.5-5\\
\multicolumn{2}{l}{Pressure pulse duration, t d (ns)}\tabcellsep 50\tabcellsep 30-150\\
\multicolumn{2}{l}{Laser spot size, x p (mm)}\tabcellsep 2.5\tabcellsep 0.5-2.5\\
\multicolumn{2}{l}{Number of shots, n (shot)}\tabcellsep 1\tabcellsep 1-4\end{longtable} \par
 
\caption{\label{tab_0}Table 2 :}\end{figure}
 			\footnote{© 2013 Global Journals Inc. (US)} 		 		\backmatter  			 
\subsection[{( )}]{( )}\par
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