Acta Metall. Sin.(Engl. Lett.) Vol.21 No.2 pp125-132 April 2008
FEM SIMULATION OF RESIDUAL STRESSES INDUCED BY LASER SHOCK WITH OVERLAPPING LASER SPOTS Y.X. Hu∗ and Z.Q. Yao State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, China Manuscript received 20 March 2007; in revised form 28 May 2007
The finite element method is presented to attain the numerical simulation of the residual stresses field in the material treated by laser shock processing. The distribution of residual stresses generated by a single laser shock with square and round laser spot is predicted and validated by experimental results. With the Finite Element Method (FEM) model, effects of different overlapping rates and impact sequences on the distribution of residual stresses are simulated. The results indicate that: (1) Overlapping laser shock can increase the compressive residual stresses. However, it is not effective on the growth of plastically affected depth; (2) Overlapping rate should be optimized and selected carefully for the large area treatment. Appropriate overlapping rate is beneficial to obtain a homogeneous residual stress field; (3) The impact sequence has a great effect on the residual stress field. It can greatly attenuate the phenomenon of the “residual stress hole” to obtain a homogeneous residual stress field. KEY WORDS Laser shock processing; Overlapping; Residual stress; Finite element method
1. Introduction Surface treatment technologies have become very more important in the industry to cut costs and avoid the need for expensive materials. Demonstrated approximately 30 years ago, laser shock processing (LSP) is now emerging as a viable surface treatment technique. The compressive residual stresses in the metal material treated by LSP can extend deeper below the surface than those from shot peening. LSP is well suited for precisely controlled treatment of localized fatigue critical areas, such as, holes, notches, fillets, and welds. It has been proposed as a competitive alternative technology to classical treatments for improving fatigue, corrosion, and wear resistance of metals[1] . It is practically impossible to investigate the residual stress field with an analytical model, because laser shock processing is a process of ultra-high speed impact. Finite element method (FEM) was first introduced by Braisted & Brockman, to investigate the mechanical behavior and to predict the residual stresses from the laser shocked materials[2] . It is very helpful to optimize the laser parameters and has been attracting a great deal of attention. However, most studies on simulation are still concentrated on single and ∗
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· 126 · multiple laser shocks on the same position. Overlapping LSP is very necessary to attain a large area of treatment for industrial application to provide a high-intensity laser, because spot diameter is usually smaller than 1 cm. More recently, there have been some numerical simulations and experiments on overlapping LSP. Peyre et al.[3] investigated the overlapping laser shock processing fatigue of notched samples with small size spot impacts. Sano et al.[4] found that it was possible to attain favorable compressive residual stress on the surface layer of 304 stainless steel with the use of overlapping LSP. Rubio-Gonzalez et al.[5] has extensively investigated the effect of overlapping laser shock processing on the fatigue crack growth, fracture toughness, and wear properties of the 6061-T6 aluminum alloy. Residual stress is one of the key effects induced by laser shock processing for the fatigue life of specimens. However, the investigation on the influence of different overlapping parameters on the residual stress distribution, such as, overlapping rate and impact sequence, is greatly limited. This article aims to propose a finite element model to simulate the residual stress by laser shock with overlapping laser spots. Effects of different overlapping rates and sequences of laser spots on the residual stresses distribution are analyzed to optimize processing parameters. 2. Mechanism of Laser Shock Processing Laser shock processing originates from the ability to drive a high amplitude shock wave into a material surface irradiated with very short, high energy laser pulses. Typical application of the process utilizes a pulsed Nd: YAG laser providing a high-intensity beam, up to several GW/cm2 . The duration of the laser pulses is generally within the range of 6 to 40 ns, with most in the range of 15 to 25 ns. A schematic of how the process of laser shock works is shown in Fig.1. The metallic surface to be treated is first locally coated with an overlay, opaque to the laser beam (typically a black paint) and then covered with a dielectric material transparent to the laser beam (such as water). The opaque overlay acts as a sacrificial material to avoid a thermal effect from the heating of the surface by the laser beam and a thin layer of it vaporizes on absorption of laser energy. The transparent overlay confines the thermally expanding vapor and plasma against the surface of the target material, thus generating higher pressure than in the direct ablation mode. The large amplitude shock waves induce plastic deformation and favorable residual compressive stresses at the surface, which can increase the fatigue life of the target Fig.1 Schematic of the laser shock processing. material[6] . 3. FEM Modeling 3.1 Modeling strategy FEM analysis procedure of laser shock processing should comprise of two distinct parts, dynamic analysis and static analysis, to obtain an absolutely stable residual stress field and surface deformation. Dynamic analysis is adopted to simulate the propagation of the shock
· 127 · wave and obtain the dynamic response of the material. When the dynamic stress state of the target material becomes approximately stable, all transient stress will be imported into implicit FEM codes to perform static analysis, and to obtain the residual stress field and spring-back deformation in static equilibrium. By simulating dynamic pressure impact explicitly, and then modeling elastic energy release implicitly, stringent tolerances can be attained for the distribution of residual stresses. 3.2 Constitutive model LSP can generate strain-rate exceeding 106 s−1 within the target material. At such rates, metals behave in a significantly different manner than under quasi-static conditions. As the strain-rate increases, materials will typically exhibit an increase in yield strength and the event becomes a shock wave phenomenon[2] . Under uniaxial strain conditions, the highest elastic stress level in the shock wave propagation is defined as the Hugoniot Elastic Limit (HEL), for the semi-infinite model. When the pressure is greater than HEL, permanent deformation occurs. Assuming that the yielding occurs when the stress in the direction of the wave propagation reaches the HEL, the dynamic yield strength σydyn under uniaxial strain conditions can be defined in terms of the HEL by: σydyn = HEL(1 − 2ν)/(1 − ν)
(1)
where ν represents Poisson s ratio[2,7] . The target material can be assumed to be perfectly elastic-plastic with isotropic and homogeneous characteristics. The plastic strain will be assumed to follow the Von Mises yielding criterion and the dynamic yield strength σydyn is calculated based on Eq.(1). It should be noted that a high, strain-rate, stress-strain relationship such as the Johnson-Cook model, is often a good estimate for the actual material response. However, incorporation of these more advanced constitutive models is based on the availability of accurate data for a specific material. There has been little or no actual material property data available in the strain-rate-range required for this type of modeling, until now. Therefore, calibration of the FEM model for experimental results within the range of interest, and then using this model for predictions over the rest of the range is the most practical and probably the most accurate means to achieve a useful model[8] . 3.3 Modeling and validation Ballard investigated the effect of laser shock treatment on the residual stress field and fatigue behavior of steel in his doctoral dissertation. A metal specimen (35CD4, 50HRC steel) was irradiated in a square spot of 5 mm×5 mm size, with a laser power density of 8 GW/cm2 for duration of 30 ns. The specimen surface was coated with black paint, and water was used as a transparent overlay. Stresses that generated on the top surface of the specimen were measured by XRD. The plastically affected depths were evaluated using successive electrolytical polishing and XRD. The pressure profile of the induced plasma was a Gaussian temporal shape with a full width at half maximum (FWHM) of 50 ns, and its peak pressure was 3 GPa[9] . Generally, the shock pressure was assumed to be uniform over the action zone of the spot. Because of the narrow duration of the shock pressure, the pressure time history was modeled as a triangular ramp, in which the pressure rose linearly to the peak value over the time of the shock pressure FWHM, and then decayed linearly to zero during the following FWHM. According to the assumptions in section 3.2,
· 128 · the material properties of 35CD4 50HRC steel required for FEM simulations are density ρ=7.8×103 kg·m−3 , Poisson s ratio ν=0.29, elastic modulus E=210 GPa and Hugoniot elastic limit HEL=2.1 GPa. LS-DYNA and ANSYS were chosen to accomplish full FEM simulation of LSP. A threedimensional, semi-infinite finite element model, with the size of 15 mm×15 mm×3 mm was developed for simulation. Solid 164 explicit elements, defined by eight nodes having the following degrees of freedom at each node: translations, velocities, and accelerations in the nodal x, y, and z directions, were chosen for dynamic analysis. They would be converted into corresponding companion implicit elements Solid 185 for static analysis according to the ANSYS user s manual. The densely meshed region was meshed with the element edge length in the order of 2.5% of the spot size, and the number of total finite elements was 259, 200. Time steps for explicit analysis were about 5 ns and solution time for a single impact was set to be 5 µs. Fig.2 shows a schematic configuration of this model including the boundary conditions. A detailed discussion on the simulation strategy can be found in the authors latest study presented in the literature[10] . Fig.3 shows the simulated distribution of residual stresses induced by a single laser shock compared with the experimental results on the top surface and at a depth, respectively. A close match between these simulated results and experimentally measured residual stresses was found. Modeling strategy for this condition can be expected to be much better on the simulation of laser shock with overlapping laser spots, with all laser conditions and modeling parameters remainFig.2 Schematic of the FEM model configuing consistent. ration.
Fig.3 FEM simulation of residual stresses induced by single LSP: (a) along x-axis on top surface; (b) along z-axis in depth.
A round spot, 5 mm in diameter, was also simulated for laser shock, with the other laser conditions for processing remaining consistent. These results are also shown in Fig.3. As shown in these figures, it is much easier to induce a residual stress drop in round laser spots than at the center of the treated zone, which is the so-called “residual stress hole”.
· 129 · This is in accordance with the phenomenon given by Peyre et al.[11] . The reason for this nonhomogeneity of the compressive stress field at this particular point may be attributed to a radial relief wave coming from the edge of the impact after the interaction and focalizing simultaneously to its center, as shown in Fig.4. This focalization results in a reverse strain state and stress drop. Results of experiments on the material A356T6 alloy also show that the phenomenon of the “residual stress hole” also exists when the power density exceeds a given value[12] . It Fig.4 Mechanism for the generation of residwill be unfavorable for the material to obtain ual stress drop. a uniform fatigue resistance because a great stress gradient will exist in the impact area if there is a residual stress drop at the center. For some reason, laser condition that will induce the “residual stress hole” should be chosen for processing. For example, the round laser spot is widely used and is much easier to achieve than the rectangular spot, increasing the incident power density for a larger amplitude of the compressive residual stress. Therefore, an effective method to attenuate the “residual stress hole” has to be found. 4. Parameter Analysis of Overlapping Laser Spots The FEM modeling strategy discussed earlier was adopted for the analysis of residual stress induced by shocks, with overlapping laser spots. All the following FEM simulations were performed with round laser spots to analyze the function of overlapping LSP, to attenuate the residual stress drop. Moreover, the residual stress field in the region covered by the spot in the middle was selected to assess the effect of different overlapping parameters. 4.1 Overlapping rate Overlapping rate is a parameter to describe the overlap of two adjacent laser spots, which can be defined by the equation: η=∆/D, where η is the overlapping rate, ∆ the overlap length of two laser spots, and D the spot diameter, as shown in Fig.5. Simulations were successively conducted with another two laser shocks on both sides of the first treated zone by 25%, 50%, and 75% overlapping. The simulated residual stress
Fig.5 Arrangement of laser spots for overlapping LSP.
· 130 · distributions on the surface layer are given in Fig.6. As shown in these figures, following observations can be made when compared with a single laser shock:
Fig.6 FEM simulation of residual stresses induced by different overlapping rates: (a) along x-axis on top surface; (b)along z-axis in depth.
(1) The maximum compressive residual stress on the top surface is about 330.6 MPa with the first impact. However, after two successive impacts on both sides, it is greatly increased. It is about 25.5% increasing to 414.8 MPa for 25% overlapping rate, 34.8% to 445.7 MPa for 50% overlapping rate, and 40.2% to 463.6 MPa for 75% overlapping rate. (2) With the 50% overlapping rate, the fluctuation of residual stress in the interesting region is decreased by 40.4% from 89.9 MPa to 53.6 MPa. However, the fluctuation was increased by 37.9% to 124 MPa for 25% overlapping rate and by 11.7% to 100.5 MPa for 75% overlapping rate. The results indicate that the overlapping rate should be optimized for the treatment, to obtain a homogeneous residual stress field. And impacts with 50% overlapping rate can be used to attenuate the “residual stress hole” for the treatment of 35CD4 steel. (3) As shown in Fig.6b, plastically affected depth is increased from 0.640 mm to 0.750 mm for 25% overlapping rate, to 0.701 mm for 50% overlapping rate, and to 0.750 mm for 75% overlapping rate. Impact with 50% overlapping rate has the smallest increase in the plastically affected depth. However, all the three overlapping rates are not effective enough to increase the plastically affected depth. Hence, proper selection of overlapping rate is of great importance for the treatment of large area processing, which can induce a better residual stress field in the specimen to enhance the performance of the material. 4.2 Impact sequence The impact sequence of overlapping LSP is well correlated with the scanning path laser spots, which should be optimized if the impact sequence has a great effect on the residual stress field. The impact sequences with 50% overlapping rate as shown in Fig.5 were designed for simulations to investigate the residual stress field. The arrangements of impact sequences for three laser spots were: a) middle→left→right (M-L-R); b) left→middle→right (L-M-R); c) left→right→middle (L-R-M). Simulated residual stress fields are shown in Fig.7. As shown in these figures, the following observations can be made:
· 131 ·
Fig.7 FEM simulation of residual stresses induced by different overlapping sequences: (a) along x-axis on top surface; (b) along z-axis in depth.
(1) The maximum compressive residual stresses are 445.7 MPa for the sequence of ML-R, 460 MPa for the sequence of L-M-R, and 435.5 for the sequence of L-R-M. It has been greatly increased compared with that in 330.6 MPa, induced by a single laser shock. There is only little difference among these three impact sequences for the maximum compressive residual stress. (2) Impact with the sequence of M-L-R can greatly decrease the fluctuation of residual stress in the center, which is from 89.9 MPa to 53.6 MPa. However, the other two impact sequences have increased the fluctuation to 126.2 MPa for the sequence of L-M-R and to 154.8 MPa for the sequence of L-R-M. The “Residual stress hole” becomes more severe for these two impact sequences when compared with the single impact, especially for the sequence of L-R-M. It indicates that the radial relief wave will be enhanced when there is an initial residual stress in the material. (3) As shown in Fig.7b, plastically affected depth is increased from 0.640 mm to 0.701 mm for the sequence of M-L-R, to 0.739 mm for the sequence of L-M-R, and to 0.785 mm for the sequence of L-R-C. All impact sequences are not effective to increase the plastically affected depth. It is similar to the effect of overlapping rate. 5. Conclusions (1) The overlapping laser shock can increase the compressive residual stresses induced by laser shock. However, it is not effective on the growth of plastically affected depth. This can be overcome by incorporating it with the multiple LSP in the same position. (2) The overlapping rate should be optimized and selected carefully for large area treatment. An appropriate overlapping rate is beneficial to obtain a homogeneous residual stress field. And 50% overlapping rate can be selected for the treatment of the material, 35CD4 steel. (3) The impact sequence has a great effect on the residual stress field. Impacting the key area first can greatly attenuate the phenomenon of “residual stress hole” to obtain a homogeneous residual stress field. Nevertheless, it will make the design of the scanning path of laser spots become complex. FEM simulation is an effective method to investigate overlapping LSP and optimize overlapping parameters. Furthermore, experimental investigation should be performed
· 132 · incorporating the FEM method. And the treatment efficiency and scanning path design should also be considered in the selection of overlapping parameters.
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