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Geometrical effects on residual stresses in 7050-T7451 aluminum alloy rods subject to laser shock peening
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
journal homepage: www.elsevier.com/locate/jmatprotec
Geometrical effects on residual stresses in 7050-T7451 aluminum alloy rods subject to laser shock peening Chunhui Yang a,∗ , Peter Damian Hodgson a , Qianchu Liu b , Lin Ye c a b c
Centre for Material and Fibre Innovation (CMFI), Deakin University, Geelong, Australia Air Vehicles Division, Defence Science and Technology Organisation (DSTO), Melbourne, Australia Centre for Advanced Materials Technology (CAMT), University of Sydney, Sydney, Australia
a r t i c l e
i n f o
a b s t r a c t
Keywords:
Laser shock peening (LSP) is an emerging surface treatment technology for metallic mate-
LSP process
rials, which appears to produce more significant compressive residual stresses than those
3-D FE modelling
from the conventional shot peening (SP) for fatigue, corrosion and wear resistance, etc.
Residual stress
The finite element method has been applied to simulate the laser shock peening treatment
7050-T7451 aluminium alloy
to provide the overall numerical assessment of the characteristic physical processes and transformations. However, the previous researchers mostly focused on metallic specimens with simple geometry, e.g. flat surface. The current work investigates geometrical effects of metallic specimens with curved surface on the residual stress fields produced by LSP process using three-dimensional finite element (3-D FEM) analysis and aluminium alloy rods with a middle scalloped section subject to two-sided laser shock peening. Specimens were numerically studied to determine dynamic and residual stress fields with varying laser parameters and geometrical parameters, e.g. laser power intensity and radius of the middle scalloped section. The results showed that the geometrical effects of the curved target surface greatly influenced residual stress fields. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Laser shock peening (LSP) is an innovative surface treatment method, which has been shown to greatly improve the fatigue life of many metallic components. Compared to conventional glass bead peening (GBP), the LSP process introduces a deeper layer of compressive residual stresses—about a millimetre deep than 250 m deep by GBP (Montross et al., 2002). Moreover, LSP produces very little or no modification of the original surface profile or dimensions of a metallic component in comparison to SP, and has been successfully applied to increase fatigue life, reduce fretting fatigue, enhance resistance to
∗
Corresponding author. E-mail addresses: [email protected] (C. Yang), [email protected] (P.D. Hodgson), [email protected] (Q. Liu), [email protected] (L. Ye). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.11.147
corrosion and increase foreign object damage resistance of compressor blades. It is shown that when LSP conditions are optimal for the material and specimen configuration, a three to four times increase in fatigue life over the as-machined specimens can be achieved. However, if the process parameters are not optimal, the fatigue lives of LSP treated specimens may not reach such an improvement. Studies of the LSP process have mainly focused on several key issues, which involve in the optimization of the confined interaction modes, the influence of the laser parameters and the relative analytical modelling of the mechanical processes. However during a LSP process, it is very difficult to monitor
304
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
and investigate dynamic and residual stresses in the target by experimental approaches. Meanwhile, the complexity of the process cannot easily be described using analytical models. Therefore, the finite element method (FEM) can be applied to simulate the LSP process for its exploration and development. Braisted and Brockman (1999) first employed 2-D FEM to investigate mechanical behaviours and predict the residual stresses of Ti-6Al-4V alloy and 35CD4 steel alloy subjected to LSP using a combination of explicit and implicit dynamic analysis algorithms with the FEA package—ABAQUS. Ding and Ye (2003a,b) extended and developed their approach from 2-D to 3-D cases to consider different LSP processing on different metal alloys using the Hugoniot elastic limit (HEL) plastic model. Peyre et al. (2003) also applied FEM to simulate the LSP process through 2-D axisymmetric FE models for 12% Cr martensitic stainless steel and 7075 aluminium alloy by applying Johnson–Cook plasticity model for the high strain rate during LSP. Ocana et al. (2003) developed an exact model for the laser-induced timedependent plasma pressure through fluid dynamics theory for FE modelling. Although these ABAQUS-based FE simulations provided a relatively close match with the measured residual stresses from experiments, further development is still required to accurately model the LSP process, especially for complicated three-dimensional (3-D) cases. In current study, 3-D finite element modelling technique was further applied to LSP processes using ABAQUS and the main focus of the study was to evaluate the geometrical effects of the scalloped section of aluminium rods subject to LSP with varying laser power intensity.
2. Some aspects of FE modelling of laser shock peening process for metal alloys 2.1.
Basics of laser shock peening
The laser shock peening process is based on producing shock waves using a high power pulsed laser, which involves the generation of confined plasma on the surface of the target material. In most LSP experiments, the laser system is a Q-switched neodymium (Nd)-glass laser with short pulse duration (around 30 ns) focused to produce laser power densities of several GW cm−2 at the target. When an intense pulsed laser impacts the target surface with this confinement, the surface layer is instantaneously vaporised to reach a temperature up to 10,000 ◦ C, then the ionization is transformed into plasma. Extremely high-pressure plasma (up to 10 GPa) is generated for a very short duration (about 20–30 ns). The
plasma pressure is transmitted into the target through shock waves that lead to plastic deformation on the target surface. The confinement is obtained when the irradiated surface is coated with an absorbent coating such as a black paint or a layer of aluminium foil, and covered with a transparent overlay, such as water or glass. Fig. 1(a) shows the configuration of confined ablation mode, in which water is usually used as the transparent overlay and the absorbent coating is a black paint. Consequently, on relaxation, the deformed surface layer is loaded in compression by the undeformed bulk material as shown in Fig. 1(b) and (c). Note that the laser shock peening process is a mechanical process, not a thermal process, and attempts to avoid all thermal effects.
2.2.
Mechanistic description of laser shock peening
A one-dimensional (1-D) model to predict the plasma pressure function of laser power density was established by Fabbro et al. (1998), assuming that laser irradiation is uniform and shock propagation in both the confining medium and the target is one-dimensional. The plasma pressure, P(t), the thickness of interface, L(t), have the following relationships: dL(t) 3 d + [P(t)L(t)] dt 2˛ dt
I(t) = P(t)
(1)
where I(t) is the laser power density and dL(t) 2 = P(t) dt Z
(2)
where ˛ is the fraction of the internal energy devoted to the thermal energy (typically, ˛ ≈ 0.1–0.2; for a water-confined mode, ˛ = 0.11); Z is the reduced shock impedance between the confining water (Zwater ) and target (Ztarget ) defined by the relation: 2 1 1 = + Z Zwater Ztarget
(3)
where Zwater and Ztarget are the shock impedance of the water and the target, respectively; for a water confined ablation mode, Zwater = 0.165 × 106 (g cm−2 s−1 ) and Ztarget = 1.5 × 106 (g cm−2 s−1 ) for an aluminium target. Considering a constant laser power density, I0 , and a water-confined ablation mode, the relationship between the laser power density and the peak plasma pressure, P0 , can be expressed by the following equation:
P0 = 0.01
˛ ZI0 2˛ + 3
Fig. 1 – Schematic of a typical LSP.
(4)
305
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
where P0 is the peak plasma pressure (GPa), I0 is the incident power density. For aluminum target in water confined ablation mode,
P0 = 1.0078
I0
(5)
2.3. Simplified LSP constitutive modelling—Hugoniot elastic limit (HEL) LSP generates strain-rates exceeding 106 s−1 within the target metal materials and at such high rates, metals have remarkably different responses than under quasi-static conditions. As the strain-rate increases, metals typically exhibit little change in their elastic modulus, and an increase in yield strength. As the strain-rate increases, the effect from laser shock peening becomes a shock wave phenomenon. Under uniaxial strain conditions, the highest elastic stress level in the direction of the shock wave propagation is defined as Hugoniot elastic limit (HEL). At pressures greater than HEL, permanent deformation occurs. If it is assumed that the yielding occurs when the stress in the direction of the shock wave propagadyn tion reaches the HEL, the dynamic yield strength Y can be defined in terms of the HEL by:
dyn
Y
= HEL
(1 − 2) (1 − )
(6)
where is the Poisson’s ratio.
2.4.
Three-dimensional finite element modelling of LSP
In the LSP simulation, numerical simulation using ABAQUS (2007) can be generally classified into three stages: (a) explicit dynamics analysis for laser shock peening analysis; (b) static equilibrium analysis for springback deformation analysis; and (c) post-processing analysis for residual stress analysis. In the first stage, an explicit dynamic analysis was performed using the ABAQUS/Explicit to determine the steady-state solutions and calculate the short duration shock waves until the saturation of plastic deformation occurs in the target. In the second stage, the deformed body with all transient stress and strain states was imported into the ABAQUS/Standard to finally determine the residual stress field at static equilibrium. ABAQUS provides the control options to transfer the deformed mesh and its associated material state between ABAQUS/Explicit and ABAQUS/Standard (ABAQUS, 2007). After this static analysis is performed, a stable residual stress and spring-back deformation field will be obtained ready for the final stage, in which the related residual stresses and plastically affected depth can be determined.
Fig. 2 – Schematic configurations of AA7050 specimen (unit: mm).
3. Metal alloy rods with scalloped middle section and their FE models 3.1.
Design of metal specimens
A series of the hourglass-type specimen geometry was designed for the investigation of effects from variant surface curvature on LSP. The specimens were with continuous radius at their central area, which was scalloped with about 0, 1, 2, 3 and 4 mm depth (h) and 35 mm width (l); the diameter in the central section was 4, 6, 8, 10 and 12 mm as shown in Fig. 2. The scalloped area was the laser shock peened region. Note that the ‘straight surface’ cases of h = 0 mm and d = 12 mm are applied as benchmark cases for comparison. Aluminium alloy AA7050-T7451 was chosen for the metal rods and its main mechanical properties are listed in Table 1.
3.2. Finite element models of metal alloy rods of curved surface 3-D finite element models were developed to simulate the process, which two laser pulses simultaneously impact on both sides of the target and thus only a quarter of the original specimen are simulated in FEA. FE models were also devised as a trunk from the original one by applying both finite elements, C3D8R, and infinite elements, CIN3D8, as nonreflecting boundaries as shown in Fig. 3. The impulsive loads are applied in the treated surface through the distributed load and the plasma peak pressures P0 are calculated using Eq. (5) and listed in Table 2. Note that the impact zone is 2 mm × 2 mm in the x–y plane (XP = YP = 2 mm) as the same for all the cases.
Table 1 – Mechanical properties of AA7050-T7451 Yield stress (MPa) 443
Tensile stress (MPa) 512
Young’s modulus (GPa) 72.2
Density (kg/m3 ) 2830
HEL (GPa) 1.1
Dynamic yield stress (GPa) 0.56
Elongation (%)
Poisson’s ratio
11
0.33
306
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
Fig. 3 – 3-D finite element models with symmetrical boundary conditions. (a) FE model and (b) Plasma pressure history.
4.
Numerical results and discussions
4.1.
Dynamic stresses
The LSP-induced stress waves have a constant velocity in the same material. The stress waves from the treated surface reach the centre of the rods where they meet the waves from the other side and complex interaction occurs, lead-
ing to an increase in amplitude of the compressive stresses and a decrease in amplitude of the tensile stresses. Then the stress waves start their attenuating due to the plastic deformation formed in the specimens. After the shock waves have dispersed the plastic deformation, compressive and tensile residual stresses remain. The dynamic stresses, xx , yy and zz , propagating along the radial direction z and longitudinal direction y of AA7050 rod, subject to laser power density I0 = 2 GW/cm2 at six solu-
Fig. 4 – Dynamic stresses of AA7050 rods at Laser power density I0 = 2 GW/cm2 . (a) d = 4 mm, (b) d = 6 mm, (c) d = 8 mm and (d) d = 10 mm.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
Fig. 4 – (Continued )
307
308
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
Table 2 – Peak plasma pressure P0 (˛ = 0.11) in AA7050. Laser power density I0 (GW/cm2 ) Peak plasma pressure P0 (GPa)
2 1.4252
3 1.7455
tion time intervals from 200 ns to 2000 ns are depicted in Fig. 4. From the variations of the dynamic stresses along the longitudinal direction y (from y = 0 to 4 mm), the shock waves mainly propagate along the radial direction z (from z = 2/3/4/5 to 0 mm) and also focus mostly on the zone of the laser spot. It also demonstrates the shock stress waves are mainly propagating along the in-depth direction z and the dominating in-plane (x–y plane) stresses are xx , yy . The geometrical effects of curved surfaces are found from the maximum dynamic stresses along the radial direction z and for the cases d = 4, 6, 8 and 10 mm, the maximum
4 2.0156
5 2.2535
6 2.4685
7 2.6663
tensile/compression xx and yy (unit: MPa) are 899/−1012, 1164/−1486 (4 mm), 1548/−604, 527/−1117 (6 mm), 959/−748, 852/−810 (8 mm) and 758/−803, 758/−763 (10 mm), respectively.
4.2.
Residual stresses
Below the impact, the induced plastic strains depend on the depth, z and their absolute value is a function of z. In order to determine the residual stress field in the target along the in-depth direction in the target, the plastic depth Lp for the
Fig. 5 – Residual stresses of AA7050 rods at laser power density I0 = 4 GW/cm2 . (a) Scalloped section of d = 4 mm and cylindrical section of radius 6 mm, (b) scalloped section of d = 10 mm and cylindrical section of radius 6 mm and (c) cylindrical section of radius 6 mm.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
given loading conditions is one of important parameters. The residual stresses xx and yy , along the radial direction z and longitudinal direction y of the rods are plotted in Fig. 5 for laser power density I0 = 4 GW/cm2 . The geometrical effect of the curved treated surface is also found through comparing the maximum residual compressive stresses xx and yy (MPa) of these three cases along the radial direction z and they are −302, −397 (4 mm), −318, −302 (10 mm) and −320, −285 (12 mm). Meanwhile, the plastic affected depth Lp is around 1 mm for xx in all the cases but for yy , the Lp is 1.45 mm for the case of d = 4 mm. Moreover, the maximum residual compressive stresses xx and yy (MPa) in longitudinal direction y are −305, −394 (4 mm), −314, −284 (10 mm) and −305, −235 (12 mm), respectively.
5.
Summary
In this study, a systematic procedure of finite element modelling and analysis combined the explicit dynamic and implicit static analysis techniques using commercial FEA package—ABAQUS was developed for laser shock peening process of metal alloys. The proposed nonlinear FEA procedure and algorithm were successfully applied to investigate the geometrical effects of the treated surface of AA7050 rods and numerical results showed the existence of curved surface greatly influenced the distribution of dynamic/residual stress fields. Therefore, the optimization design of laser shock peening procedure for metal specimens with complex shape is necessary to obtain better surface treatment.
309
Acknowledgements C. Yang and P.D. Hodgson would like to appreciate the financial support from the Australia Research Council (ARC) through Prof. Hodgson’s Australian Federation Fellowship (FF0455846).
references
ABAQUS user’s manual version 6.7, 2007. SIMULIA. Braisted, W., Brockman, R., 1999. Finite element simulation of laser shock peening. Int. J. Fatigue 211, 719–724. Ding, K., Ye, L., 2003a. FEM simulation of two sided laser shock peening of thin sections of Ti-6Al-4V alloy. Surf. Eng. 19 (2), 127–133. Ding, K., Ye, L., 2003b. Three-dimensional dynamic finite element analysis of multiple laser shock peening processes. Surf. Eng. 19 (5), 351–358. Fabbro, R., Peyre, P., Berthe, L., Scherpereel, X., 1998. Physics and applications of laser-shock processing. J. Laser Appl. 10 (6), 265–279. Montross, C.S., Wei, T., Ye, L., Clark, G., Mai, Y.W., 2002. Laser shock processing and its effects on microstructure and properties of metal alloys: a review. Int. J. Fatigue 24, 1021–1036. Ocana, J.L., Morales, M., Molpeceres, C., Torres, J., 2003. Numerical simulation of surface deformation and residual stresses fields in laser shock processing experiments. Appl. Surf. Sci. 238, 242–248. Peyre, P., Sollier, A., Chaieb, I., Berthe, L., Bartnicki, E., Braham, C., Fabbro, R., 2003. FEM simulation of residual stress induced by laser peening. Eur. Phys. J. AP 23, 83–88.
journal homepage: www.elsevier.com/locate/jmatprotec
Geometrical effects on residual stresses in 7050-T7451 aluminum alloy rods subject to laser shock peening Chunhui Yang a,∗ , Peter Damian Hodgson a , Qianchu Liu b , Lin Ye c a b c
Centre for Material and Fibre Innovation (CMFI), Deakin University, Geelong, Australia Air Vehicles Division, Defence Science and Technology Organisation (DSTO), Melbourne, Australia Centre for Advanced Materials Technology (CAMT), University of Sydney, Sydney, Australia
a r t i c l e
i n f o
a b s t r a c t
Keywords:
Laser shock peening (LSP) is an emerging surface treatment technology for metallic mate-
LSP process
rials, which appears to produce more significant compressive residual stresses than those
3-D FE modelling
from the conventional shot peening (SP) for fatigue, corrosion and wear resistance, etc.
Residual stress
The finite element method has been applied to simulate the laser shock peening treatment
7050-T7451 aluminium alloy
to provide the overall numerical assessment of the characteristic physical processes and transformations. However, the previous researchers mostly focused on metallic specimens with simple geometry, e.g. flat surface. The current work investigates geometrical effects of metallic specimens with curved surface on the residual stress fields produced by LSP process using three-dimensional finite element (3-D FEM) analysis and aluminium alloy rods with a middle scalloped section subject to two-sided laser shock peening. Specimens were numerically studied to determine dynamic and residual stress fields with varying laser parameters and geometrical parameters, e.g. laser power intensity and radius of the middle scalloped section. The results showed that the geometrical effects of the curved target surface greatly influenced residual stress fields. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Laser shock peening (LSP) is an innovative surface treatment method, which has been shown to greatly improve the fatigue life of many metallic components. Compared to conventional glass bead peening (GBP), the LSP process introduces a deeper layer of compressive residual stresses—about a millimetre deep than 250 m deep by GBP (Montross et al., 2002). Moreover, LSP produces very little or no modification of the original surface profile or dimensions of a metallic component in comparison to SP, and has been successfully applied to increase fatigue life, reduce fretting fatigue, enhance resistance to
∗
Corresponding author. E-mail addresses: [email protected] (C. Yang), [email protected] (P.D. Hodgson), [email protected] (Q. Liu), [email protected] (L. Ye). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.11.147
corrosion and increase foreign object damage resistance of compressor blades. It is shown that when LSP conditions are optimal for the material and specimen configuration, a three to four times increase in fatigue life over the as-machined specimens can be achieved. However, if the process parameters are not optimal, the fatigue lives of LSP treated specimens may not reach such an improvement. Studies of the LSP process have mainly focused on several key issues, which involve in the optimization of the confined interaction modes, the influence of the laser parameters and the relative analytical modelling of the mechanical processes. However during a LSP process, it is very difficult to monitor
304
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
and investigate dynamic and residual stresses in the target by experimental approaches. Meanwhile, the complexity of the process cannot easily be described using analytical models. Therefore, the finite element method (FEM) can be applied to simulate the LSP process for its exploration and development. Braisted and Brockman (1999) first employed 2-D FEM to investigate mechanical behaviours and predict the residual stresses of Ti-6Al-4V alloy and 35CD4 steel alloy subjected to LSP using a combination of explicit and implicit dynamic analysis algorithms with the FEA package—ABAQUS. Ding and Ye (2003a,b) extended and developed their approach from 2-D to 3-D cases to consider different LSP processing on different metal alloys using the Hugoniot elastic limit (HEL) plastic model. Peyre et al. (2003) also applied FEM to simulate the LSP process through 2-D axisymmetric FE models for 12% Cr martensitic stainless steel and 7075 aluminium alloy by applying Johnson–Cook plasticity model for the high strain rate during LSP. Ocana et al. (2003) developed an exact model for the laser-induced timedependent plasma pressure through fluid dynamics theory for FE modelling. Although these ABAQUS-based FE simulations provided a relatively close match with the measured residual stresses from experiments, further development is still required to accurately model the LSP process, especially for complicated three-dimensional (3-D) cases. In current study, 3-D finite element modelling technique was further applied to LSP processes using ABAQUS and the main focus of the study was to evaluate the geometrical effects of the scalloped section of aluminium rods subject to LSP with varying laser power intensity.
2. Some aspects of FE modelling of laser shock peening process for metal alloys 2.1.
Basics of laser shock peening
The laser shock peening process is based on producing shock waves using a high power pulsed laser, which involves the generation of confined plasma on the surface of the target material. In most LSP experiments, the laser system is a Q-switched neodymium (Nd)-glass laser with short pulse duration (around 30 ns) focused to produce laser power densities of several GW cm−2 at the target. When an intense pulsed laser impacts the target surface with this confinement, the surface layer is instantaneously vaporised to reach a temperature up to 10,000 ◦ C, then the ionization is transformed into plasma. Extremely high-pressure plasma (up to 10 GPa) is generated for a very short duration (about 20–30 ns). The
plasma pressure is transmitted into the target through shock waves that lead to plastic deformation on the target surface. The confinement is obtained when the irradiated surface is coated with an absorbent coating such as a black paint or a layer of aluminium foil, and covered with a transparent overlay, such as water or glass. Fig. 1(a) shows the configuration of confined ablation mode, in which water is usually used as the transparent overlay and the absorbent coating is a black paint. Consequently, on relaxation, the deformed surface layer is loaded in compression by the undeformed bulk material as shown in Fig. 1(b) and (c). Note that the laser shock peening process is a mechanical process, not a thermal process, and attempts to avoid all thermal effects.
2.2.
Mechanistic description of laser shock peening
A one-dimensional (1-D) model to predict the plasma pressure function of laser power density was established by Fabbro et al. (1998), assuming that laser irradiation is uniform and shock propagation in both the confining medium and the target is one-dimensional. The plasma pressure, P(t), the thickness of interface, L(t), have the following relationships: dL(t) 3 d + [P(t)L(t)] dt 2˛ dt
I(t) = P(t)
(1)
where I(t) is the laser power density and dL(t) 2 = P(t) dt Z
(2)
where ˛ is the fraction of the internal energy devoted to the thermal energy (typically, ˛ ≈ 0.1–0.2; for a water-confined mode, ˛ = 0.11); Z is the reduced shock impedance between the confining water (Zwater ) and target (Ztarget ) defined by the relation: 2 1 1 = + Z Zwater Ztarget
(3)
where Zwater and Ztarget are the shock impedance of the water and the target, respectively; for a water confined ablation mode, Zwater = 0.165 × 106 (g cm−2 s−1 ) and Ztarget = 1.5 × 106 (g cm−2 s−1 ) for an aluminium target. Considering a constant laser power density, I0 , and a water-confined ablation mode, the relationship between the laser power density and the peak plasma pressure, P0 , can be expressed by the following equation:
P0 = 0.01
˛ ZI0 2˛ + 3
Fig. 1 – Schematic of a typical LSP.
(4)
305
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
where P0 is the peak plasma pressure (GPa), I0 is the incident power density. For aluminum target in water confined ablation mode,
P0 = 1.0078
I0
(5)
2.3. Simplified LSP constitutive modelling—Hugoniot elastic limit (HEL) LSP generates strain-rates exceeding 106 s−1 within the target metal materials and at such high rates, metals have remarkably different responses than under quasi-static conditions. As the strain-rate increases, metals typically exhibit little change in their elastic modulus, and an increase in yield strength. As the strain-rate increases, the effect from laser shock peening becomes a shock wave phenomenon. Under uniaxial strain conditions, the highest elastic stress level in the direction of the shock wave propagation is defined as Hugoniot elastic limit (HEL). At pressures greater than HEL, permanent deformation occurs. If it is assumed that the yielding occurs when the stress in the direction of the shock wave propagadyn tion reaches the HEL, the dynamic yield strength Y can be defined in terms of the HEL by:
dyn
Y
= HEL
(1 − 2) (1 − )
(6)
where is the Poisson’s ratio.
2.4.
Three-dimensional finite element modelling of LSP
In the LSP simulation, numerical simulation using ABAQUS (2007) can be generally classified into three stages: (a) explicit dynamics analysis for laser shock peening analysis; (b) static equilibrium analysis for springback deformation analysis; and (c) post-processing analysis for residual stress analysis. In the first stage, an explicit dynamic analysis was performed using the ABAQUS/Explicit to determine the steady-state solutions and calculate the short duration shock waves until the saturation of plastic deformation occurs in the target. In the second stage, the deformed body with all transient stress and strain states was imported into the ABAQUS/Standard to finally determine the residual stress field at static equilibrium. ABAQUS provides the control options to transfer the deformed mesh and its associated material state between ABAQUS/Explicit and ABAQUS/Standard (ABAQUS, 2007). After this static analysis is performed, a stable residual stress and spring-back deformation field will be obtained ready for the final stage, in which the related residual stresses and plastically affected depth can be determined.
Fig. 2 – Schematic configurations of AA7050 specimen (unit: mm).
3. Metal alloy rods with scalloped middle section and their FE models 3.1.
Design of metal specimens
A series of the hourglass-type specimen geometry was designed for the investigation of effects from variant surface curvature on LSP. The specimens were with continuous radius at their central area, which was scalloped with about 0, 1, 2, 3 and 4 mm depth (h) and 35 mm width (l); the diameter in the central section was 4, 6, 8, 10 and 12 mm as shown in Fig. 2. The scalloped area was the laser shock peened region. Note that the ‘straight surface’ cases of h = 0 mm and d = 12 mm are applied as benchmark cases for comparison. Aluminium alloy AA7050-T7451 was chosen for the metal rods and its main mechanical properties are listed in Table 1.
3.2. Finite element models of metal alloy rods of curved surface 3-D finite element models were developed to simulate the process, which two laser pulses simultaneously impact on both sides of the target and thus only a quarter of the original specimen are simulated in FEA. FE models were also devised as a trunk from the original one by applying both finite elements, C3D8R, and infinite elements, CIN3D8, as nonreflecting boundaries as shown in Fig. 3. The impulsive loads are applied in the treated surface through the distributed load and the plasma peak pressures P0 are calculated using Eq. (5) and listed in Table 2. Note that the impact zone is 2 mm × 2 mm in the x–y plane (XP = YP = 2 mm) as the same for all the cases.
Table 1 – Mechanical properties of AA7050-T7451 Yield stress (MPa) 443
Tensile stress (MPa) 512
Young’s modulus (GPa) 72.2
Density (kg/m3 ) 2830
HEL (GPa) 1.1
Dynamic yield stress (GPa) 0.56
Elongation (%)
Poisson’s ratio
11
0.33
306
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
Fig. 3 – 3-D finite element models with symmetrical boundary conditions. (a) FE model and (b) Plasma pressure history.
4.
Numerical results and discussions
4.1.
Dynamic stresses
The LSP-induced stress waves have a constant velocity in the same material. The stress waves from the treated surface reach the centre of the rods where they meet the waves from the other side and complex interaction occurs, lead-
ing to an increase in amplitude of the compressive stresses and a decrease in amplitude of the tensile stresses. Then the stress waves start their attenuating due to the plastic deformation formed in the specimens. After the shock waves have dispersed the plastic deformation, compressive and tensile residual stresses remain. The dynamic stresses, xx , yy and zz , propagating along the radial direction z and longitudinal direction y of AA7050 rod, subject to laser power density I0 = 2 GW/cm2 at six solu-
Fig. 4 – Dynamic stresses of AA7050 rods at Laser power density I0 = 2 GW/cm2 . (a) d = 4 mm, (b) d = 6 mm, (c) d = 8 mm and (d) d = 10 mm.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
Fig. 4 – (Continued )
307
308
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
Table 2 – Peak plasma pressure P0 (˛ = 0.11) in AA7050. Laser power density I0 (GW/cm2 ) Peak plasma pressure P0 (GPa)
2 1.4252
3 1.7455
tion time intervals from 200 ns to 2000 ns are depicted in Fig. 4. From the variations of the dynamic stresses along the longitudinal direction y (from y = 0 to 4 mm), the shock waves mainly propagate along the radial direction z (from z = 2/3/4/5 to 0 mm) and also focus mostly on the zone of the laser spot. It also demonstrates the shock stress waves are mainly propagating along the in-depth direction z and the dominating in-plane (x–y plane) stresses are xx , yy . The geometrical effects of curved surfaces are found from the maximum dynamic stresses along the radial direction z and for the cases d = 4, 6, 8 and 10 mm, the maximum
4 2.0156
5 2.2535
6 2.4685
7 2.6663
tensile/compression xx and yy (unit: MPa) are 899/−1012, 1164/−1486 (4 mm), 1548/−604, 527/−1117 (6 mm), 959/−748, 852/−810 (8 mm) and 758/−803, 758/−763 (10 mm), respectively.
4.2.
Residual stresses
Below the impact, the induced plastic strains depend on the depth, z and their absolute value is a function of z. In order to determine the residual stress field in the target along the in-depth direction in the target, the plastic depth Lp for the
Fig. 5 – Residual stresses of AA7050 rods at laser power density I0 = 4 GW/cm2 . (a) Scalloped section of d = 4 mm and cylindrical section of radius 6 mm, (b) scalloped section of d = 10 mm and cylindrical section of radius 6 mm and (c) cylindrical section of radius 6 mm.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 303–309
given loading conditions is one of important parameters. The residual stresses xx and yy , along the radial direction z and longitudinal direction y of the rods are plotted in Fig. 5 for laser power density I0 = 4 GW/cm2 . The geometrical effect of the curved treated surface is also found through comparing the maximum residual compressive stresses xx and yy (MPa) of these three cases along the radial direction z and they are −302, −397 (4 mm), −318, −302 (10 mm) and −320, −285 (12 mm). Meanwhile, the plastic affected depth Lp is around 1 mm for xx in all the cases but for yy , the Lp is 1.45 mm for the case of d = 4 mm. Moreover, the maximum residual compressive stresses xx and yy (MPa) in longitudinal direction y are −305, −394 (4 mm), −314, −284 (10 mm) and −305, −235 (12 mm), respectively.
5.
Summary
In this study, a systematic procedure of finite element modelling and analysis combined the explicit dynamic and implicit static analysis techniques using commercial FEA package—ABAQUS was developed for laser shock peening process of metal alloys. The proposed nonlinear FEA procedure and algorithm were successfully applied to investigate the geometrical effects of the treated surface of AA7050 rods and numerical results showed the existence of curved surface greatly influenced the distribution of dynamic/residual stress fields. Therefore, the optimization design of laser shock peening procedure for metal specimens with complex shape is necessary to obtain better surface treatment.
309
Acknowledgements C. Yang and P.D. Hodgson would like to appreciate the financial support from the Australia Research Council (ARC) through Prof. Hodgson’s Australian Federation Fellowship (FF0455846).
references
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