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Simulation on deforming progress and stress evolution during laser shock forming with finite element method
Journal of Materials Processing Technology 220 (2015) 27–35
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Simulation on deforming progress and stress evolution during laser shock forming with finite element method Xingquan Zhang ∗ , Jianping She, Shengzhi Li, Shiwei Duan, Yu Zhou, Xiaoliu Yu, Ru Zheng, Biao Zhang School of Mechanical Engineering, Anhui University of Technology, Ma’anshan 243002, Anhui, China
a r t i c l e
i n f o
Article history: Received 13 May 2014 Received in revised form 4 January 2015 Accepted 10 January 2015 Available online 19 January 2015 Keywords: Laser shock wave Metal sheet Finite element method Deformation Stress
a b s t r a c t Laser shock forming (LSF) employs laser shock wave to form metal sheet, which is similar to explosive forming. Finite element method (FEM) is an effective method to better understand mechanism of LSF and select appropriate parameters to shape metal sheet accurately with LSF. In this paper, FEM analysis model is developed to simulate LSF, which includes how to determine the pressure loading, material constitutive model, and solution time. The commercial code LS-DYNA is applied to simulation. A sequence of dynamic deformation behaviors of metal sheet at the end of different periods are presented and discussed in detail, and the peculiar phenomena in dynamic deformation processing are discovered, which do not appear in the traditional forming processing. The final static deformation and residual stress are also predicted. The predicted results are accordance with the experimental data. © 2015 Published by Elsevier B.V.
1. Introduction Laser shock processing (LSP) is being served as a competitive surface treatment technique to strengthen metal material. LSP can refine material structure (Lu et al., 2010), and squeeze the beneficial compressive stress into material to a deeper depth than that achieved by shot peening (Hammersley et al., 2000), so the treated workpiece has better resistance to stress corrosion (Lim et al., 2012), and has a longer fatigue life (Lavender et al., 2008). Laser shock can also induce plastic deformation, even fracture. Guo and Caslaru (2011) have fabricated micro dents on surface of titanium Ti–6Al–4V plate with pulse laser, which possesses average power ranged from 1 W to 4 W. The experiments show that the surface plastic dent depth increases with laser power increasing, and the deepest depth can be achieved 1 m. O’Keefe et al. (1973) have studied the stainless steel irradiated by the laser with a flux of 1.4 GW/cm2 . The results exhibit that one-sided laser shock can lead to permanent deformation in cross section of metal sheet with thickness 0.063 cm. Zheng et al. (2013) have conducted experiment with Fe78 Si9 B13 metallic glass shocked by laser. The experiment results show that strong pulse laser can lead to thin metallic glass failure. These investigations indicate that laser shock can shape metal sheet if its parameters are selected appropriately. In recent
∗ Corresponding author. Tel.: +86 5552316517; fax: +86 5552316515. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.jmatprotec.2015.01.004 0924-0136/© 2015 Published by Elsevier B.V.
years, laser shock has been proposed as a tool to form metal sheet, which is similar to explosive forming. It is called laser shock forming (LSF). Compared with explosive forming, LSF is a safe and precise forming technique, because the location to be processed and the intensity of shock wave can be controlled accurately. So it seems to be very promising in practical application. There have been lots of attempts in experiments and simulations to probe LSF basic peculiarities. Zhou et al. (2002) have employed experimental approach to deform a stainless-steel sheet with laser, and they discover some non-linear plastic deformation characteristics in LSF. Niehoff and Vollertsen (2005) have investigated the 50 m thick Al99.5 foils impacted by laser, and gained some uniform domes. They point out particularly that LSF is a non thermal stretch-forming technology. Cheng et al. (2007) have employed laser to deform a copper foil with thickness 15 m. Their investigations reveal that material grain has been refined and tensile stresses are distributed on both side surfaces of component after LSF. Fan et al. (2005) and Wang et al. (2005, 2007) have studied the copper stripes peened by laser. They report that the stripes bend upward and the compressive residual stresses are distributed on its both-sided surfaces after laser treatment. Sagisaka et al. (2010) have bended pure aluminum A1100-H18 (in JIS) with femtosecond laser. They claim that it is helpful to improve bending efficiency by means of elastic pre-bending and large laser spot during LSF. Nagarajan et al. (2013) have explored micro-dents array on copper thin film using LSF without mold. The experimental results demonstrate that it is feasible to implement fabricate
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X. Zhang et al. / Journal of Materials Processing Technology 220 (2015) 27–35 Table 1 Mechanical properties of LY12CZ.
Fig. 1. Schematic of the setup for LSF.
near-spherical microcraters on thin metallic surface with LSF. All these researches are very useful to understand the characteristics of LSF. However, these investigations mainly focus on the influence of parameters on the deformed workpiece quality, and scarcely refer to dynamic behaviors of metal sheet. Up to present, there have been rare researches touched on the dynamic behaviors during LSF, because the dynamic deformation behaviors of metal sheet under ultrahigh strain rate are very complicate, and extremely difficult to be measured in situ experimentally. Wielage and Vollertsen (2011) have bended metals foil, Al and Cu, with laser shock wave. They conclude that, under the action of shock wave pressure 2.3 MPa, the temporal deformation velocity can be reached 40 m/s, and its strain rate attains 2 × 103 s−1 . Gao et al. (2009) have used finite element method (FEM) to simulate LSF process and its failure, in which copper foils (3 –15 m thickness) were subjected to lasers with different intensities (0.5–1.2 GW/cm2 ). They have investigated the effects of the critical parameters on its deformation behaviors, and obtained some important findings. However, their researches are confined to LSF. Due to the effect of size, some dynamic behaviors in micro LSF are different from those in thicker plate LSF. Some dynamic forming characteristics are still unknown. Therefore, the dynamic deforming process of LSF is still worth research. The aim of current work is first to introduce FEM to simulate metal sheet ultrafast dynamic response to laser shock, and then to achieve a better understanding of transient behaviors during LSF and gain an insight into the mechanism of LSF. The FEM model based on the commercial code LS-DYNA (2010) is described in detail. Dynamic behaviors of metal sheet have been analyzed. The final deformation and residual stress obtained from FEM are compared with the experimental results. 2. Mechanism of LSF and experimental setup LSF employs mechanical force, a high pressure shock wave pulse, to deform metal sheet, while metal sheet is not affected thermally. It is different from laser forming, which uses laser to deform metal sheet by high temperature gradient between the irradiated surface and the neighboring material. The setup for LSF is shown in Fig. 1. Prior to laser irradiating, a candidate metal sheet is laid on the top of die, and some coverings are deposited onto it top surface in advance. First, an aluminum foil (or black paint), served as laser ablating layer, covers metal sheet top surface to protect it from thermal damage. Subsequently, an optical glass, K9-glass with thickness 4.5 mm to act as overlay, is set on the top surface of
Property
Value
Yield strength 0.2 (MPa) Tensile strength b (MPa) Elongation ı (%) Elastic modulus E (GPa)
275 435 11 68.9
an aluminum foil to increase the peak pressure of shock wave and prolong its action time. Finally, a blank holder, a thick plate with an axial hole at the center, is placed on K9-glass surface, which clamps tightly the above mentioned materials to die. These coverings are in place, and laser shock can be carried out. A high-power, Q-switched, pulsed neodymium-glass laser is used to produce a short-duration high-power pulse, which passes through k9-glass and illuminates vertically aluminum foil surface with a desired spot. The aluminum foil is partly vaporized immediately and generates plasma. The vapor and plasma proceed to absorbing the follow-up incident laser energy, and then expand and explode violently, which result in a strong pulse pressure on surfaces of K9-glass and metal sheet. The instant shock loading induces stress wave propagating into material and pushes metal sheet into die cavity. If metal sheet acquires sufficient momentum from shock wave, it deforms in line with the die, and the desired shape of metal sheet is obtained. In experiment, the material was a quenching and artificial aging of LY12CZ aluminum alloy, which was super hard and widely used in aircraft structure components for example, plane beam and frame rib. Its chemical composition (wt.%) was: 1.54 Mg, 0.58 Mn, 4.61 Cu, 0.29 Fe, 0.26 Si, 0.1 Zn, 0.024 Ni, and its mechanical properties were shown in Table 1. The specimen was 40 mm in diameter and 0.4 mm in thickness. It was irradiated by laser pulse with a full width at half maximum (FHWM) 23 ns, a wavelength 1.064 m, energy 34 J per pulse, a repetition rate 2 Hz and a spot size 8 mm in diameter. The axial hole in blank holder was 16 mm in diameter, and the size of hole in die was 14 mm in diameter. After laser shock, the profile of the cross section of the deformed metal sheet was measured with a contour meter PGI400 (Taylor Hobson, England), and the residual stress was measured by X-ray diffraction tester XTress3000 (Stresstech Oy, Finland). In order to allow direct comparison, some data of the experimental conditions were imported into FEM model to simulate metal sheet dynamic responses to laser shock. The experimental results were used as references to validate FEM results. 3. FEM 3.1. Calculation code choosing Numerical simulations of the material response to LSP with the commercial codes have been extensively reported. Braisted and Brockman (1999) first established 2-D FEM model to predict residual stresses. Ding and Ye (2003) also developed similar model to simulate metal material dynamic responses to different LSP treatment conditions and its final residual stresses. Yang et al. (2008) further utilized FEM to analyze effect of geometrical size on residual stresses induced by LSP. In these simulations, the commercial codes ABAQUS/Explicit and ABAQUS/Implicit were employed jointly. Hu and Yao (2008) utilized 3-D FEM with software LS-DYNA and ANSYS, instead of ABAQUS package explicit and implicit, to predict residual stresses of metal alloy subjected to LSP. These simulation processes all include explicit analysis step and subsequent implicit analysis step. The explicit analysis step is used to solve the dynamic response to LSP, and the following implicit analysis step is applied to making material become stable without long time. Peyre et al. (2007) applied ABAQUS to simulate LSP for 12% Cr martensitic
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stainless steel and 316 L austenitic stainless steel. However, compared with the above mentioned works, he did not carry out the relaxation step using implicit step, and the corresponding relaxation was also accomplished in dynamic analysis step at the cost of long time. He pointed out that there was no difference between the dynamic stresses after enough long time in pure explicit model and residual stresses obtained in dual explicit and implicit step model. In current case, metal sheet will be subjected to laser shock wave with sever GPa pressure loading, and material will undergo extremely high strain-rate (107 –109 s−1 ) during a short period of time and be dynamically yielded into a certain shape (Zhou et al., 2002), so the simulation firstly demands for figuring out shorttime, high speed nonlinearity problem, and then for releasing much elastic strain energy accompanied by ultrafast forming. The commercial code LS-DYNA (2010) is especially well-suited to solving this high-speed dynamic event. In order to calculate the entire event effectively and efficiently, the commercial code ANSYS (2010) should also be employed together. The code LS-DYNA solves the rapid dynamic responses to laser shock, and ANSYS is used to avoid material taking much long time to become stable state owing to releasing a large amount of stored strain energy. In dynamic analysis with LS-DYNA, Solid 164 explicit elements are always chosen for calculation, which are defined by eight nodes having the degrees of freedom at each node–displacement, stresses and so on in the x, y, and z directions. They will be converted automatically into companion implicit elements Solid 185 for subsequent static calculation with ANSYS. Nevertheless, due to big plastic deformation occurred in explicit analysis in present work, the elements Solid 185 cannot support some plasticity options in following implicit analysis. Namely, the dynamic calculated results extracted from LS-DYNA can’t be input into ANSYS to calculate smoothly the final static results. Therefore, the explicit analysis step is only used in entire event, and the corresponding relaxation is also accomplished in dynamic analysis step at the cost of long time, as above mentioned Peyre’s work to figure out residual stresses. In the following analysis, the code LS-DYNA is solely employed to predict deformation and stress.
LSF is a pressure forming, and the driving force is from laser shock wave pressure. The spatial and temporal distribution of the pressure is one of key parameters related to the effect of LSF. Fabbro et al. (1990) found that the generated shock wave pressure persisted two to three times longer than the duration of laser pulse in confine model. They also established mathematical model to describe the relation between the peak pressure of laser shock wave and laser pulse intensity, which can be expressed as following: P = 10−9
˛ 2˛ + 3
1 1 2 + = Z Z1 Z2
1/2
z 1/2 × I0 1/2
Fig. 2. Pressure pulse induced by a laser pulse.
3.3. Material constitutive model Laser shock induces high strain rate within metal material. Under such high rate condition, the material behavior is remarkably different from that under quasi-static condition, and the static stress-strain relation is essentially invalid to characterize material dynamic responses. Zhao et al. (2007) have experimentally investigated the dynamic constitutive model for LY12CZ aluminum alloy subjected to large strain, high strain rate. His experimental results show that the model established by Cowper and Symonds (1957) is more suitable for LY12CZ alloy under high strain rate deformation. The C–S model can be written as
y = ˇ 0 + EP εPoff
(1)
(2)
where P (GPa) is the peak pressure of shock wave, Z is the reduced shock impedance, Z1 is the target impedance = 1.38 × 107 kg/m2 /s (Al), Z2 is the confining medium impedance = 1.14 × 107 kg/m2 /s (K9-glass), and ˛ is the efficiency of interaction, where ˛E contributes to the pressure increase and (1 − ˛)E is devoted to generating and ionizing the plasma (˛ = 0.1 to 0.2), in current case, ˛ is 0.15. I0 is the incident laser power density = 0.252 × 1013 W/m2 , and P is the peak pressure about 4.6 GPa. According to above presentation, the pressure loaded on metal sheet surface is depicted in Fig. 2.
(3)
And ˇ =1+
3.2. Pressure loading conditions
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EP =
ε P1 C
Et E E − Et
(4) (5)
where y is the dynamic yield strength, εPoff is the strain, E is the material elastic modulus, EP is the plastic hardening modulus, C and P are constant, which correspond to a specific material, Et is tangent modulus. His experimental results determine, for LY12CZ aluminum alloy, 0 = 290 MPa, y = 515 MPa, C = 22,515.4, P = 4.843, E = 68.5 GPa, Et = 1530 MPa, EP = 1565 MPa. 3.4. Finite element model A three-dimensional FEM model is developed to simulate LSF, as displayed in Fig. 3. Since the geometric shape and pressure loading are symmetric, only a half of the configuration is employed to perform the finite element calculation instead of a full one to save the calculating time. In order to obtain accurate results and further save calculating cost, it is necessary to adopt different mesh densities to different regions. Therefore, the metal sheet is divided into three regions: I, II and III, as shown in Fig. 3. Region Iis shocked by laser, and it demands for the densest mesh density to capture stress wave. Region II, where the deformation gradient reaches the maximum value and stress concentration easily occurs, needs sufficient mesh density. Region III, the external surrounding region far away from the shocked zone, does not require dense mesh density. Then, we
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4. Simulating results and discussion 4.1. Plastic deformation progress
Fig. 3. Schematic diagram of model size in FEM.
can allocate different element sizes to different regions. In addition, both side surfaces of region III are restricted. Hence, the metal sheet is easily meshed into set of Solid 164 dynamic elements with different mesh densities in different regions. The number of total elements in model is 374,888.
According to above described model, the code LS-DYNA runs to simulate dynamic behaviors of metal sheet subjected to a single pulse laser. After the dynamic calculation accomplishment, the obtained results containing transient deformation, stress and so on are stored in a specified file, and can be read into code ANSYS with the powerful post-processing capabilities; so we can review the dynamic results and output them using ANSYS post-processing tools. In order to see clearly the obtained graphics in current case, the outer un-deformed part of sample is partially hidden purposely, and the central part within 20 mm region is only displayed in the following 3D figures. Fig. 4 displays the contours of metal sheet at the end of 500, 1800, 10,870 and 230,000 ns respectively. From Fig. 4, we can clearly see a series of 3D deforming processes of LSF. Under the shock wave pressure acting on metal sheet surface, the central part of metal sheet on the top of die hole is free, so this part easily falls into die cavity. Due to the round die hole and a circular laser spot, the sheet gradually develops into an axial symmetric bulge with broad rim. The metal sheet inside die hole experiences deeply stretching deformation by itself kinetic energy acquired from laser shock wave. As a result, its thickness decreases. Due to the constraint of the holder, the material underneath holder cannot follow and still maintains its original thickness, so a small terrace appears at the entrance of die cavity, as clearly shown in
Fig. 4. A series of the 3-D temporal deformations. (a) At the end of 500 ns, (b) at the end of 1800 ns, (c) at the end of 10,870 ns, (d) at the end of 230,000 ns.
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Fig. 5. Profiles of the cross-section of metal sheet at the end of different periods of solution time. (a) At the end of 50, 150, 350, 500, 550, 650 ns; (b) at the end of 800, 1800, 2800, 3400, 3750, 4175 ns; (c) at the end of 10,874, 22,872, 37,122, 120,000, 200,000, 230,000 ns.
partial detail magnification in Fig. 4(c) and (d) respectively. This phenomenon also appears in earlier study on Cu sheet deformed by Zheng et al. (2010) with laser shock. Fig. 5 further shows the evolution of metal sheet shape in light of the convex bottom surface. As illustrated in Fig. 5(a), there is no plastic deformation before 50 ns, because it needs time to generate stress higher than dynamic yield strength in material, and needs time for plastic stress wave to travel through the thickness of metal sheet. When the plastic stress wave arrives at metal sheet bottom, it starts to sink into die hole. Due to pressure uniformity in local laser spot, the metal sheet undergoes shear deformation around the border of laser impacting zone in initial stage. As a result, a bulge with plane bottom emerges, and its opening almost keeps constant before 650 ns. After that, its opening starts to enlarge progressively to 14 mm, the die hole diameter size, and then remains unchanged all the time. At the same time, the depth of bulge goes on increasing due to its inertia. It is interesting to note that the temporal reverse deformation occurs at the bottom of bulge from 500 ns to 4175 ns, as presented in Fig. 5(a) and (b). When the compressive stress waves travel though the thickness of material target, they are reflected by the opposite
free surface and then turned into tensile shock waves, which continue to propagate in material. This process repeats many times until stress waves vanish. When plastic deformation occurs, the dilatational and transverse waves also generate from the periphery of the round plastic boundary, which are also propagating outward from the loaded area and inward toward the centerline. These stress waves impinge on one another, reflect and propagate. As a result of action, the tensile pulses generate at the center of impacted region sheet and the reverse yielding deformation occurs. Much like in LSP using round laser spot, the tensile pulses, at the centre of the treated round zone, result from the focus of the surface stress waves, which generate around the perimeter of laser spot, and propagate radially inward. Large tensile pulses may eliminate the compressive residual stresses near the center of laser spot, which was reported previously by researchers, such as Braisted and Brockman (1999). Up to now, no literature has reported this unique phenomenon of the transient reverse deformation during LSF process, but Bassi et al. (2003) have reported the similar anomalous permanent plastic deformation of circular plate loaded by explosive shock wave. It can also be seen from Fig. 7(a) and (b) that, near the outer edge of laser shock region, the temporary pile-up appears in special initial
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time, which results from the material transverse flowing from the impacted zone induced by the transverse plastic wave. The similar pile-up phenomenon after LSP treatment was also seen in work done by Guo and Caslaru (2011). It can be seen from Fig. 5(c) that, at the end of 10,874 ns, the deepest depth of bulge reaches 1.79 mm, while, at the end of 22,872 ns, the maximum depth of bulge decreases to 1.416 mm. During a LSF process, the total work done by laser shock wave is first converted to kinetic energy of metal sheet, and then kinetic energy is mainly changed into the elastically stored energy and plastically dissipated energy. At the end of 10,874 ns, although the velocity of metal sheet is 0, a large sum of elastic strain energy is stored in target material, and the bulge is in unstable deformation condition. So it will spring back to release the stored elastic energy, and metal sheet acquires kinetic energy again. After several times energy exchange, the elastically stored energy gradually exhausts, which is mainly attributed to damping. At the end of 0.20 ms and 0.23 ms, the profiles of bulge entirely overlap, which indicates the plastic deformation in metal sheet is saturated and metal sheet has reached the final static state. Fig. 6 reveals the history of central node displacement at the bottom surface of metal sheet. From Fig. 6, it can be seen that the displacement of central node constantly varies, which imply that metal sheet experiences several reverberations to exhaust elastic energy stored in ultrafast deformation material. The similar vibration of metal foil impacted by laser shock was also observed by
Fig. 6. History of central node displacement.
Peyre et al. (1998) with VISA in LSP treatment. After 0.23 ms, the metal sheet stops vibrating and the displacement keeps constant value 1.58 mm. Therefore, the state of metal sheet at the end of 0.23 ms can be regarded as the final static state, and solution time
Fig. 7. Contour of the Von Mises stress at the end of different periods of solution time. (a) At the end of 6000 ns, (b) at the end of 10,874 ns, (c) at the end of 22,872 ns, (d) at the end of 230,000 ns.
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Fig. 8. Surface dynamic stress (S33 ) profiles at different periods of solution time. (a) At the end of 50, 150, 500, 800, 875 ns; (b) at the end of 10,874, 22,872, 37,122, 120,000, 200,000, 230,000 ns.
Fig. 9. Contours of the residual stress in the Z-axis direction. (a) The impacted side surface, (b) the un-impacted side surface.
in the case is set to 0.23 ms. Compared with the dynamic solution time, 6500 ns, set by Hu and Yao (2008) in LSP simulation, the solution time in the case is two to three orders of the magnitude longer than that in LSP simulation. 4.2. Stress evolution Fig. 7 illustrates that a series of the typical Von Mises stress distributions at the end of different times, in which Maximum Von Mises stresses are highlighted with locations and values. It can be seen clearly from Fig. 7 that Maxmum Von Mises stresses are 654, 539, 459 and 298 MPa at the end of 6000, 10,874, 22,872 and 230,000 ns, respectively. The longer the solution time is, the smaller Maxmum Von Mises stress is. Maxmum Von Mises stress always occurs around the peripheral of the cavity, where the fillet of die and friction block the plastic flowing smoothly. At the end of 22872 ns, Maxmum Von Mises stress 459 MPa is greater than material yield stress 290 MPa, which indicates that the metal sheet needs more time to decrease stress gradient. At the end of 230,000 ns, Maximum Von Mises stress is 298 MPa, which quite approaches to material static yield stress, because the overwhelming majority of elastic strain energy stored in material releases after long time.
Fig. 8 represents the distributions of instant dynamic stresses S33 along the z-axis direction in cross section at the end of different periods. At the end of initial period of 50 ns, the profile of stress is more regular, which results from the evenly distributed compressive dynamic stress induced by the uniform shock wave pressure. Subsequently, the initial downward compressive stress wave is reflected by the opposite free surface and switched into tensile stress wave, and the change-in-shape of metal sheet leads to multiple dynamic stress waves in material, so the profile of stress continuously changes remarkably. As the solution time increases, the magnitude of dynamic stress in deformed zone drops progressively, and its influence region expands outward little by little. At the end of 0.2 ms and 0.23 ms, the profiles of dynamic stress overlap, which indicates that interaction of various stress waves in material is quite feeble, even vanishes. It is consistent with the above analysis in terms of central node displacement, and validates the solution time choosing again. Fig. 9 exhibits the contour of residual stress in the Z-axis direction on both side surfaces of bulge. From Fig. 9, it can be seen that the maximum value of tensile stress occurs near the die edge, because the material plastic flowing is confined by the holder. On each side deformed region surface, there is a complicate residual stress state, which may be explained by LSF that combines the plastic
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Fig. 10. A bulge with broad rim. (a) The side surface of laser irradiation and (b) the opposite side surface of laser irradiation.
Fig. 12. Comparisons of numerical and experimental stresses in the Z-axis direction along the cross-section of the bulge.
available test results, and the FEM model established for LSF is verified. The residual surface stress was measured by X-ray diffraction method, and distribution of residual stresses is shown in Fig. 12. As exhibited in Fig. 12, between the test values of residual stresses and the calculation ones on deformed region surfaces, there exist deviations, which may be attributed to its original stress −20 MPa on both side surfaces before LSF. If its original stress is taken into account, the test and calculation results are close generally.
Fig. 11. Comparison of numerical and experimental profiles of the cross-section of the bulge.
deformation with LSP. On the one hand, the mental sheet is deeply pulled by shock wave and plastic deformation takes place. The tensile residual stress should occur on both deformed surfaces. On the other hand, the material is processed by laser shock, the compressive stress always emerges in laser shocked zone. These two mechanisms interact simultaneously and lead to complicate stress on both-sided surfaces. 5. Experiments According to the above described specimen size in Section 3.4, it was cut from the 0.4 mm thick plate with wire cut electrical discharge machining (WEDM). The specimen was irradiated by laser with the same parameters mentioned in simulation. After laser irradiation, the specimen was taken out from the die, and the reminder ablative layer was first removed, and then ultrasound in ethanol was used to degrease its surface. As a result of laser shock, a uniform bulge with broad rim was formed, as shown in Fig. 10. As seen in Fig. 10, the irradiated surface shows no melting, which manifests that LSF is real a cold plastic forming technology. Compared with the surrounding original surfaces of bulge, the deformed region surfaces are bright, and fine scratches disappear, which imply that LSF can obviously improve the surface roughness of material. The profile of the cross-section of bulge measured with a Taylor Hobson contour meter is described in Fig. 11. The profile obtained from the test is similar to that from the calculation. The maximum depth from the test is about 1.75 mm, 11% bigger than that from the calculation. The calculation data are well consistent with the
6. Conclusions A FEM model with the commercial code LS-DYNA has been built to simulate LSF process. LSF displays some unique characteristics, which don’t display in quasi-static forming. The following conclusions are obtained: (1) In order to gain the accurate results in LSF simulation with code LS-DYNA, the solution time should be set to ms level, which is two to three orders of the magnitude longer than that in LSP. (2) During the dynamic deformation progress, the metal sheet initially experiences the shearing deformation at the border of the local shocked area, and then it is deeply stretched by itself momentum obtained from laser shock. (3) The opening of bulge gradually increases to die hole diameter and subsequently keeps constant. The depth of bulge firstly lasts increasing and then undergoes several spring backs, and the evolution of bulge experiences successively flat bottom, reverse deformation, and tip bottom. (4) The complicate residual stress state exists on both side surfaces of the deformed region. The lower magnitude of compressive residual stress and the relative higher magnitude of tensile stress emerge on both-sided surfaces. However, the current work is not involved in the conditions that metal sheet is impacted successively by multiple laser shots and deformed into the intricate 3D shape according to die. These works will be carried out in the future. Obviously, we are only just touching the entrance of LSF, and it needs us longer term efforts to realize LSF to act as a realistic tool in practical applications.
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Acknowledgement We gratefully acknowledge support for this work was supported by the National Natural Science Foundation of China under Grant no. 51175002, and the National Natural Science Foundation of Anhui province under Grant no. 090414156. References ANSYS, 2010. Software-Version 12 User’s Manual. Swanson Analysis Systems Inc. Bassi, A., Genna, F., Symonds, P.S., 2003. Anomalous elastic–plastic responses to short pulse loading of circular plates. Int. Impact Eng. 28 (1), 65–91. Braisted, W., Brockman, R., 1999. Finite element simulation of laser shock peening. Int. J. Fatigue 21 (7), 719–724. Cheng, G.J., Pirzada, D., Zhou, M., 2007. Microstructure and mechanical property characterizations of metal foil after microscale laser dynamic forming. J. Appl. phys. 101 (6), 063108–063115. Cowper, G.R., Symonds, P.S., 1957. Strain hardening and strain rate effect in the impact loading of cantilever beams. In: Tech. Rep. Brown University Division of Applied Mathematics, Providence. Ding, K., Ye, L., 2003. Three-dimensional dynamic finite element analysis of multiple laser shock peening processes. Surf. Eng. 19 (5), 351–358. Fabbro, R., Fournier, J., Ballard, P., Devaux, D., Virmont, J., 1990. Physical study of laser-produced plasma in confined geometry. J. Appl. Phys. 68 (2), 775–784. Fan, Y., Wang, Y., Vukelic, S., Yao, Y.L., 2005. Wave–solid interactions in laser-shockinduced deformation processes. J. Appl. Phys. 98 (10), 104904–104914. Gao, H., Ye, C., Cheng, G.J., 2009. Deformation behaviors and critical parameters in microscale laser dynamic forming. J. Manuf. Sci. Eng. Trans. ASME 131 (5), 0510111–05101111. Guo, Y.B., Caslaru, R., 2011. Fabrication and characterization of micro dent arrays produced by laser shock peening on titanium Ti–6Al–4V surfaces. J. Mater. Process. Technol. 211 (4), 729–736. Hammersley, G., Hackel, L., Harris, F., 2000. Surface prestresing to improve fatigue strength of components by laser shot peening. Opt. Laser Eng. 34 (4–6), 327–337. Hu, Y.X., Yao, Z.Q., 2008. Numerical simulation and experimentation of overlapping laser shock processing with symmetry cell. Int. J. Mach. Tools Manuf. 48 (2), 152–162. Lavender, C.A., Hong, S.T., Smith, M.T., Johnson, R.T., Lahrman, D., 2008. The effect of laser shock peening on the life and failure mode of a cold pilger die. J. Mater. Process. Technol. 204 (1–3), 486–491.
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Lim, H., Kim, P., Jeong, H., Jeong, S., 2012. Enhancement of abrasion and corrosion resistance of duplex stainless steel by laser shock peening. J. Mater. Process. Technol. 212 (6), 1347–1354. LS-DYNA, 2010. Software-Version 12 User’s Manual. Swanson Analysis Systems Inc. Lu, J.Z., Luo, K.Y., Zhang, Y.K., Cui, C.Y., Sun, G.F., Zhou, J.Z., Zhang, L., You, J., Chen, K.M., Zhong, J.W., 2010. Grain refinement of LY2 aluminum alloy induced by ultra-high plastic strain during multiple laser shock processing impacts. Acta Mater. 58 (11), 3884–3894. Nagarajan, B., Castagne, S., Wang, Z.K., 2013. Mold-free fabrication of 3D microfeatures using laser-induced shock pressure. Appl. Surf. Sci. 268, 529–534. Niehoff, H.S., Vollertsen, F., 2005. Non-thermal laser stretch-forming. Adv. Mater. Res. 6–8, 433–440. O’Keefe, J.D., Skeen, C.H., York, C.M., 1973. Laser-induced deformation modes in thin metal targets. J. Appl. Phys. 44 (10), 4622–4626. Peyre, P., Berthe, L., Scherpereel, X., Fabbro, R., 1998. Laser-shock processing of aluminium-coated 55C1 steel in water-confinement regime, characterization and application to high-cycle fatigue behaviour. J. Mater. Sci. 33 (6), 1421–1429. Peyre, P., Chaieb, I., Braham, C., 2007. FEM calculation of residual stresses induced by laser shock processing in stainless steels. Modell. Simul. Mater. Sci. Eng. 15 (3), 205–211. Sagisaka, Y., Kamlya, M., Matsuda, M., Ohta, Y., 2010. Thin-sheet-metal bending by laser peen forming with femtosecond laser. J. Mater. Process. Technol. 210 (15), 2304–2309. Wang, Y., Fan, Y., Vukelic, S., Yao, Y.L., 2007. Energy-level effects on the deformation mechanism in microscale laser peen forming. J. Manuf. Processes 9 (1), 1–12. Wielage, H., Vollertsen, F., 2011. Classification of laser shock forming within the field of high speed forming processes. J. Mater. Process. Technol. 211 (5), 953–957. Yang, C.H., Hodgson, P.D., Liu, Q.C., Ye, L., 2008. Geometrical effects on residual stresses in 7050-T7451 aluminum alloy rods subject to laser shock peening. J. Mater. Process. Technol. 201 (1–3), 303–309. Zhao, S.G., He, Z., Yang, J.L., Cheng, W., 2007. Experiment investigation of dynamic material property of aluminium alloy. J. Beijing Univ. Aeronaut. Astronaut. 33 (8), 982–984. Zheng, C., Sun, S., Song, L.B., Zhang, G.F., Luan, Y.G., Ji, Z., Zhang, J.H., 2013. Dynamic fracture characteristics of Fe78 Si9 B13 metallic glass subjected to laser shock loading. Appl. Surf. Sci. 286, 121–125. Zheng, C., Sun, S., Ji, Z., Wang, W., Liu, J., 2010. Numerical simulation and experimentation of micro scale laser bulge forming. Int. J. Mach. Tools Manuf. 50, 1048–1056. Zhou, M., Zhang, Y.K., Cai, L., 2002. Investigation of the effect of laser treatment on the longitudinal and transverse velocity of an aluminum alloy. J. Appl. Phys. 91 (9), 5775–5781.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Simulation on deforming progress and stress evolution during laser shock forming with finite element method Xingquan Zhang ∗ , Jianping She, Shengzhi Li, Shiwei Duan, Yu Zhou, Xiaoliu Yu, Ru Zheng, Biao Zhang School of Mechanical Engineering, Anhui University of Technology, Ma’anshan 243002, Anhui, China
a r t i c l e
i n f o
Article history: Received 13 May 2014 Received in revised form 4 January 2015 Accepted 10 January 2015 Available online 19 January 2015 Keywords: Laser shock wave Metal sheet Finite element method Deformation Stress
a b s t r a c t Laser shock forming (LSF) employs laser shock wave to form metal sheet, which is similar to explosive forming. Finite element method (FEM) is an effective method to better understand mechanism of LSF and select appropriate parameters to shape metal sheet accurately with LSF. In this paper, FEM analysis model is developed to simulate LSF, which includes how to determine the pressure loading, material constitutive model, and solution time. The commercial code LS-DYNA is applied to simulation. A sequence of dynamic deformation behaviors of metal sheet at the end of different periods are presented and discussed in detail, and the peculiar phenomena in dynamic deformation processing are discovered, which do not appear in the traditional forming processing. The final static deformation and residual stress are also predicted. The predicted results are accordance with the experimental data. © 2015 Published by Elsevier B.V.
1. Introduction Laser shock processing (LSP) is being served as a competitive surface treatment technique to strengthen metal material. LSP can refine material structure (Lu et al., 2010), and squeeze the beneficial compressive stress into material to a deeper depth than that achieved by shot peening (Hammersley et al., 2000), so the treated workpiece has better resistance to stress corrosion (Lim et al., 2012), and has a longer fatigue life (Lavender et al., 2008). Laser shock can also induce plastic deformation, even fracture. Guo and Caslaru (2011) have fabricated micro dents on surface of titanium Ti–6Al–4V plate with pulse laser, which possesses average power ranged from 1 W to 4 W. The experiments show that the surface plastic dent depth increases with laser power increasing, and the deepest depth can be achieved 1 m. O’Keefe et al. (1973) have studied the stainless steel irradiated by the laser with a flux of 1.4 GW/cm2 . The results exhibit that one-sided laser shock can lead to permanent deformation in cross section of metal sheet with thickness 0.063 cm. Zheng et al. (2013) have conducted experiment with Fe78 Si9 B13 metallic glass shocked by laser. The experiment results show that strong pulse laser can lead to thin metallic glass failure. These investigations indicate that laser shock can shape metal sheet if its parameters are selected appropriately. In recent
∗ Corresponding author. Tel.: +86 5552316517; fax: +86 5552316515. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.jmatprotec.2015.01.004 0924-0136/© 2015 Published by Elsevier B.V.
years, laser shock has been proposed as a tool to form metal sheet, which is similar to explosive forming. It is called laser shock forming (LSF). Compared with explosive forming, LSF is a safe and precise forming technique, because the location to be processed and the intensity of shock wave can be controlled accurately. So it seems to be very promising in practical application. There have been lots of attempts in experiments and simulations to probe LSF basic peculiarities. Zhou et al. (2002) have employed experimental approach to deform a stainless-steel sheet with laser, and they discover some non-linear plastic deformation characteristics in LSF. Niehoff and Vollertsen (2005) have investigated the 50 m thick Al99.5 foils impacted by laser, and gained some uniform domes. They point out particularly that LSF is a non thermal stretch-forming technology. Cheng et al. (2007) have employed laser to deform a copper foil with thickness 15 m. Their investigations reveal that material grain has been refined and tensile stresses are distributed on both side surfaces of component after LSF. Fan et al. (2005) and Wang et al. (2005, 2007) have studied the copper stripes peened by laser. They report that the stripes bend upward and the compressive residual stresses are distributed on its both-sided surfaces after laser treatment. Sagisaka et al. (2010) have bended pure aluminum A1100-H18 (in JIS) with femtosecond laser. They claim that it is helpful to improve bending efficiency by means of elastic pre-bending and large laser spot during LSF. Nagarajan et al. (2013) have explored micro-dents array on copper thin film using LSF without mold. The experimental results demonstrate that it is feasible to implement fabricate
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X. Zhang et al. / Journal of Materials Processing Technology 220 (2015) 27–35 Table 1 Mechanical properties of LY12CZ.
Fig. 1. Schematic of the setup for LSF.
near-spherical microcraters on thin metallic surface with LSF. All these researches are very useful to understand the characteristics of LSF. However, these investigations mainly focus on the influence of parameters on the deformed workpiece quality, and scarcely refer to dynamic behaviors of metal sheet. Up to present, there have been rare researches touched on the dynamic behaviors during LSF, because the dynamic deformation behaviors of metal sheet under ultrahigh strain rate are very complicate, and extremely difficult to be measured in situ experimentally. Wielage and Vollertsen (2011) have bended metals foil, Al and Cu, with laser shock wave. They conclude that, under the action of shock wave pressure 2.3 MPa, the temporal deformation velocity can be reached 40 m/s, and its strain rate attains 2 × 103 s−1 . Gao et al. (2009) have used finite element method (FEM) to simulate LSF process and its failure, in which copper foils (3 –15 m thickness) were subjected to lasers with different intensities (0.5–1.2 GW/cm2 ). They have investigated the effects of the critical parameters on its deformation behaviors, and obtained some important findings. However, their researches are confined to LSF. Due to the effect of size, some dynamic behaviors in micro LSF are different from those in thicker plate LSF. Some dynamic forming characteristics are still unknown. Therefore, the dynamic deforming process of LSF is still worth research. The aim of current work is first to introduce FEM to simulate metal sheet ultrafast dynamic response to laser shock, and then to achieve a better understanding of transient behaviors during LSF and gain an insight into the mechanism of LSF. The FEM model based on the commercial code LS-DYNA (2010) is described in detail. Dynamic behaviors of metal sheet have been analyzed. The final deformation and residual stress obtained from FEM are compared with the experimental results. 2. Mechanism of LSF and experimental setup LSF employs mechanical force, a high pressure shock wave pulse, to deform metal sheet, while metal sheet is not affected thermally. It is different from laser forming, which uses laser to deform metal sheet by high temperature gradient between the irradiated surface and the neighboring material. The setup for LSF is shown in Fig. 1. Prior to laser irradiating, a candidate metal sheet is laid on the top of die, and some coverings are deposited onto it top surface in advance. First, an aluminum foil (or black paint), served as laser ablating layer, covers metal sheet top surface to protect it from thermal damage. Subsequently, an optical glass, K9-glass with thickness 4.5 mm to act as overlay, is set on the top surface of
Property
Value
Yield strength 0.2 (MPa) Tensile strength b (MPa) Elongation ı (%) Elastic modulus E (GPa)
275 435 11 68.9
an aluminum foil to increase the peak pressure of shock wave and prolong its action time. Finally, a blank holder, a thick plate with an axial hole at the center, is placed on K9-glass surface, which clamps tightly the above mentioned materials to die. These coverings are in place, and laser shock can be carried out. A high-power, Q-switched, pulsed neodymium-glass laser is used to produce a short-duration high-power pulse, which passes through k9-glass and illuminates vertically aluminum foil surface with a desired spot. The aluminum foil is partly vaporized immediately and generates plasma. The vapor and plasma proceed to absorbing the follow-up incident laser energy, and then expand and explode violently, which result in a strong pulse pressure on surfaces of K9-glass and metal sheet. The instant shock loading induces stress wave propagating into material and pushes metal sheet into die cavity. If metal sheet acquires sufficient momentum from shock wave, it deforms in line with the die, and the desired shape of metal sheet is obtained. In experiment, the material was a quenching and artificial aging of LY12CZ aluminum alloy, which was super hard and widely used in aircraft structure components for example, plane beam and frame rib. Its chemical composition (wt.%) was: 1.54 Mg, 0.58 Mn, 4.61 Cu, 0.29 Fe, 0.26 Si, 0.1 Zn, 0.024 Ni, and its mechanical properties were shown in Table 1. The specimen was 40 mm in diameter and 0.4 mm in thickness. It was irradiated by laser pulse with a full width at half maximum (FHWM) 23 ns, a wavelength 1.064 m, energy 34 J per pulse, a repetition rate 2 Hz and a spot size 8 mm in diameter. The axial hole in blank holder was 16 mm in diameter, and the size of hole in die was 14 mm in diameter. After laser shock, the profile of the cross section of the deformed metal sheet was measured with a contour meter PGI400 (Taylor Hobson, England), and the residual stress was measured by X-ray diffraction tester XTress3000 (Stresstech Oy, Finland). In order to allow direct comparison, some data of the experimental conditions were imported into FEM model to simulate metal sheet dynamic responses to laser shock. The experimental results were used as references to validate FEM results. 3. FEM 3.1. Calculation code choosing Numerical simulations of the material response to LSP with the commercial codes have been extensively reported. Braisted and Brockman (1999) first established 2-D FEM model to predict residual stresses. Ding and Ye (2003) also developed similar model to simulate metal material dynamic responses to different LSP treatment conditions and its final residual stresses. Yang et al. (2008) further utilized FEM to analyze effect of geometrical size on residual stresses induced by LSP. In these simulations, the commercial codes ABAQUS/Explicit and ABAQUS/Implicit were employed jointly. Hu and Yao (2008) utilized 3-D FEM with software LS-DYNA and ANSYS, instead of ABAQUS package explicit and implicit, to predict residual stresses of metal alloy subjected to LSP. These simulation processes all include explicit analysis step and subsequent implicit analysis step. The explicit analysis step is used to solve the dynamic response to LSP, and the following implicit analysis step is applied to making material become stable without long time. Peyre et al. (2007) applied ABAQUS to simulate LSP for 12% Cr martensitic
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stainless steel and 316 L austenitic stainless steel. However, compared with the above mentioned works, he did not carry out the relaxation step using implicit step, and the corresponding relaxation was also accomplished in dynamic analysis step at the cost of long time. He pointed out that there was no difference between the dynamic stresses after enough long time in pure explicit model and residual stresses obtained in dual explicit and implicit step model. In current case, metal sheet will be subjected to laser shock wave with sever GPa pressure loading, and material will undergo extremely high strain-rate (107 –109 s−1 ) during a short period of time and be dynamically yielded into a certain shape (Zhou et al., 2002), so the simulation firstly demands for figuring out shorttime, high speed nonlinearity problem, and then for releasing much elastic strain energy accompanied by ultrafast forming. The commercial code LS-DYNA (2010) is especially well-suited to solving this high-speed dynamic event. In order to calculate the entire event effectively and efficiently, the commercial code ANSYS (2010) should also be employed together. The code LS-DYNA solves the rapid dynamic responses to laser shock, and ANSYS is used to avoid material taking much long time to become stable state owing to releasing a large amount of stored strain energy. In dynamic analysis with LS-DYNA, Solid 164 explicit elements are always chosen for calculation, which are defined by eight nodes having the degrees of freedom at each node–displacement, stresses and so on in the x, y, and z directions. They will be converted automatically into companion implicit elements Solid 185 for subsequent static calculation with ANSYS. Nevertheless, due to big plastic deformation occurred in explicit analysis in present work, the elements Solid 185 cannot support some plasticity options in following implicit analysis. Namely, the dynamic calculated results extracted from LS-DYNA can’t be input into ANSYS to calculate smoothly the final static results. Therefore, the explicit analysis step is only used in entire event, and the corresponding relaxation is also accomplished in dynamic analysis step at the cost of long time, as above mentioned Peyre’s work to figure out residual stresses. In the following analysis, the code LS-DYNA is solely employed to predict deformation and stress.
LSF is a pressure forming, and the driving force is from laser shock wave pressure. The spatial and temporal distribution of the pressure is one of key parameters related to the effect of LSF. Fabbro et al. (1990) found that the generated shock wave pressure persisted two to three times longer than the duration of laser pulse in confine model. They also established mathematical model to describe the relation between the peak pressure of laser shock wave and laser pulse intensity, which can be expressed as following: P = 10−9
˛ 2˛ + 3
1 1 2 + = Z Z1 Z2
1/2
z 1/2 × I0 1/2
Fig. 2. Pressure pulse induced by a laser pulse.
3.3. Material constitutive model Laser shock induces high strain rate within metal material. Under such high rate condition, the material behavior is remarkably different from that under quasi-static condition, and the static stress-strain relation is essentially invalid to characterize material dynamic responses. Zhao et al. (2007) have experimentally investigated the dynamic constitutive model for LY12CZ aluminum alloy subjected to large strain, high strain rate. His experimental results show that the model established by Cowper and Symonds (1957) is more suitable for LY12CZ alloy under high strain rate deformation. The C–S model can be written as
y = ˇ 0 + EP εPoff
(1)
(2)
where P (GPa) is the peak pressure of shock wave, Z is the reduced shock impedance, Z1 is the target impedance = 1.38 × 107 kg/m2 /s (Al), Z2 is the confining medium impedance = 1.14 × 107 kg/m2 /s (K9-glass), and ˛ is the efficiency of interaction, where ˛E contributes to the pressure increase and (1 − ˛)E is devoted to generating and ionizing the plasma (˛ = 0.1 to 0.2), in current case, ˛ is 0.15. I0 is the incident laser power density = 0.252 × 1013 W/m2 , and P is the peak pressure about 4.6 GPa. According to above presentation, the pressure loaded on metal sheet surface is depicted in Fig. 2.
(3)
And ˇ =1+
3.2. Pressure loading conditions
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EP =
ε P1 C
Et E E − Et
(4) (5)
where y is the dynamic yield strength, εPoff is the strain, E is the material elastic modulus, EP is the plastic hardening modulus, C and P are constant, which correspond to a specific material, Et is tangent modulus. His experimental results determine, for LY12CZ aluminum alloy, 0 = 290 MPa, y = 515 MPa, C = 22,515.4, P = 4.843, E = 68.5 GPa, Et = 1530 MPa, EP = 1565 MPa. 3.4. Finite element model A three-dimensional FEM model is developed to simulate LSF, as displayed in Fig. 3. Since the geometric shape and pressure loading are symmetric, only a half of the configuration is employed to perform the finite element calculation instead of a full one to save the calculating time. In order to obtain accurate results and further save calculating cost, it is necessary to adopt different mesh densities to different regions. Therefore, the metal sheet is divided into three regions: I, II and III, as shown in Fig. 3. Region Iis shocked by laser, and it demands for the densest mesh density to capture stress wave. Region II, where the deformation gradient reaches the maximum value and stress concentration easily occurs, needs sufficient mesh density. Region III, the external surrounding region far away from the shocked zone, does not require dense mesh density. Then, we
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4. Simulating results and discussion 4.1. Plastic deformation progress
Fig. 3. Schematic diagram of model size in FEM.
can allocate different element sizes to different regions. In addition, both side surfaces of region III are restricted. Hence, the metal sheet is easily meshed into set of Solid 164 dynamic elements with different mesh densities in different regions. The number of total elements in model is 374,888.
According to above described model, the code LS-DYNA runs to simulate dynamic behaviors of metal sheet subjected to a single pulse laser. After the dynamic calculation accomplishment, the obtained results containing transient deformation, stress and so on are stored in a specified file, and can be read into code ANSYS with the powerful post-processing capabilities; so we can review the dynamic results and output them using ANSYS post-processing tools. In order to see clearly the obtained graphics in current case, the outer un-deformed part of sample is partially hidden purposely, and the central part within 20 mm region is only displayed in the following 3D figures. Fig. 4 displays the contours of metal sheet at the end of 500, 1800, 10,870 and 230,000 ns respectively. From Fig. 4, we can clearly see a series of 3D deforming processes of LSF. Under the shock wave pressure acting on metal sheet surface, the central part of metal sheet on the top of die hole is free, so this part easily falls into die cavity. Due to the round die hole and a circular laser spot, the sheet gradually develops into an axial symmetric bulge with broad rim. The metal sheet inside die hole experiences deeply stretching deformation by itself kinetic energy acquired from laser shock wave. As a result, its thickness decreases. Due to the constraint of the holder, the material underneath holder cannot follow and still maintains its original thickness, so a small terrace appears at the entrance of die cavity, as clearly shown in
Fig. 4. A series of the 3-D temporal deformations. (a) At the end of 500 ns, (b) at the end of 1800 ns, (c) at the end of 10,870 ns, (d) at the end of 230,000 ns.
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Fig. 5. Profiles of the cross-section of metal sheet at the end of different periods of solution time. (a) At the end of 50, 150, 350, 500, 550, 650 ns; (b) at the end of 800, 1800, 2800, 3400, 3750, 4175 ns; (c) at the end of 10,874, 22,872, 37,122, 120,000, 200,000, 230,000 ns.
partial detail magnification in Fig. 4(c) and (d) respectively. This phenomenon also appears in earlier study on Cu sheet deformed by Zheng et al. (2010) with laser shock. Fig. 5 further shows the evolution of metal sheet shape in light of the convex bottom surface. As illustrated in Fig. 5(a), there is no plastic deformation before 50 ns, because it needs time to generate stress higher than dynamic yield strength in material, and needs time for plastic stress wave to travel through the thickness of metal sheet. When the plastic stress wave arrives at metal sheet bottom, it starts to sink into die hole. Due to pressure uniformity in local laser spot, the metal sheet undergoes shear deformation around the border of laser impacting zone in initial stage. As a result, a bulge with plane bottom emerges, and its opening almost keeps constant before 650 ns. After that, its opening starts to enlarge progressively to 14 mm, the die hole diameter size, and then remains unchanged all the time. At the same time, the depth of bulge goes on increasing due to its inertia. It is interesting to note that the temporal reverse deformation occurs at the bottom of bulge from 500 ns to 4175 ns, as presented in Fig. 5(a) and (b). When the compressive stress waves travel though the thickness of material target, they are reflected by the opposite
free surface and then turned into tensile shock waves, which continue to propagate in material. This process repeats many times until stress waves vanish. When plastic deformation occurs, the dilatational and transverse waves also generate from the periphery of the round plastic boundary, which are also propagating outward from the loaded area and inward toward the centerline. These stress waves impinge on one another, reflect and propagate. As a result of action, the tensile pulses generate at the center of impacted region sheet and the reverse yielding deformation occurs. Much like in LSP using round laser spot, the tensile pulses, at the centre of the treated round zone, result from the focus of the surface stress waves, which generate around the perimeter of laser spot, and propagate radially inward. Large tensile pulses may eliminate the compressive residual stresses near the center of laser spot, which was reported previously by researchers, such as Braisted and Brockman (1999). Up to now, no literature has reported this unique phenomenon of the transient reverse deformation during LSF process, but Bassi et al. (2003) have reported the similar anomalous permanent plastic deformation of circular plate loaded by explosive shock wave. It can also be seen from Fig. 7(a) and (b) that, near the outer edge of laser shock region, the temporary pile-up appears in special initial
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time, which results from the material transverse flowing from the impacted zone induced by the transverse plastic wave. The similar pile-up phenomenon after LSP treatment was also seen in work done by Guo and Caslaru (2011). It can be seen from Fig. 5(c) that, at the end of 10,874 ns, the deepest depth of bulge reaches 1.79 mm, while, at the end of 22,872 ns, the maximum depth of bulge decreases to 1.416 mm. During a LSF process, the total work done by laser shock wave is first converted to kinetic energy of metal sheet, and then kinetic energy is mainly changed into the elastically stored energy and plastically dissipated energy. At the end of 10,874 ns, although the velocity of metal sheet is 0, a large sum of elastic strain energy is stored in target material, and the bulge is in unstable deformation condition. So it will spring back to release the stored elastic energy, and metal sheet acquires kinetic energy again. After several times energy exchange, the elastically stored energy gradually exhausts, which is mainly attributed to damping. At the end of 0.20 ms and 0.23 ms, the profiles of bulge entirely overlap, which indicates the plastic deformation in metal sheet is saturated and metal sheet has reached the final static state. Fig. 6 reveals the history of central node displacement at the bottom surface of metal sheet. From Fig. 6, it can be seen that the displacement of central node constantly varies, which imply that metal sheet experiences several reverberations to exhaust elastic energy stored in ultrafast deformation material. The similar vibration of metal foil impacted by laser shock was also observed by
Fig. 6. History of central node displacement.
Peyre et al. (1998) with VISA in LSP treatment. After 0.23 ms, the metal sheet stops vibrating and the displacement keeps constant value 1.58 mm. Therefore, the state of metal sheet at the end of 0.23 ms can be regarded as the final static state, and solution time
Fig. 7. Contour of the Von Mises stress at the end of different periods of solution time. (a) At the end of 6000 ns, (b) at the end of 10,874 ns, (c) at the end of 22,872 ns, (d) at the end of 230,000 ns.
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Fig. 8. Surface dynamic stress (S33 ) profiles at different periods of solution time. (a) At the end of 50, 150, 500, 800, 875 ns; (b) at the end of 10,874, 22,872, 37,122, 120,000, 200,000, 230,000 ns.
Fig. 9. Contours of the residual stress in the Z-axis direction. (a) The impacted side surface, (b) the un-impacted side surface.
in the case is set to 0.23 ms. Compared with the dynamic solution time, 6500 ns, set by Hu and Yao (2008) in LSP simulation, the solution time in the case is two to three orders of the magnitude longer than that in LSP simulation. 4.2. Stress evolution Fig. 7 illustrates that a series of the typical Von Mises stress distributions at the end of different times, in which Maximum Von Mises stresses are highlighted with locations and values. It can be seen clearly from Fig. 7 that Maxmum Von Mises stresses are 654, 539, 459 and 298 MPa at the end of 6000, 10,874, 22,872 and 230,000 ns, respectively. The longer the solution time is, the smaller Maxmum Von Mises stress is. Maxmum Von Mises stress always occurs around the peripheral of the cavity, where the fillet of die and friction block the plastic flowing smoothly. At the end of 22872 ns, Maxmum Von Mises stress 459 MPa is greater than material yield stress 290 MPa, which indicates that the metal sheet needs more time to decrease stress gradient. At the end of 230,000 ns, Maximum Von Mises stress is 298 MPa, which quite approaches to material static yield stress, because the overwhelming majority of elastic strain energy stored in material releases after long time.
Fig. 8 represents the distributions of instant dynamic stresses S33 along the z-axis direction in cross section at the end of different periods. At the end of initial period of 50 ns, the profile of stress is more regular, which results from the evenly distributed compressive dynamic stress induced by the uniform shock wave pressure. Subsequently, the initial downward compressive stress wave is reflected by the opposite free surface and switched into tensile stress wave, and the change-in-shape of metal sheet leads to multiple dynamic stress waves in material, so the profile of stress continuously changes remarkably. As the solution time increases, the magnitude of dynamic stress in deformed zone drops progressively, and its influence region expands outward little by little. At the end of 0.2 ms and 0.23 ms, the profiles of dynamic stress overlap, which indicates that interaction of various stress waves in material is quite feeble, even vanishes. It is consistent with the above analysis in terms of central node displacement, and validates the solution time choosing again. Fig. 9 exhibits the contour of residual stress in the Z-axis direction on both side surfaces of bulge. From Fig. 9, it can be seen that the maximum value of tensile stress occurs near the die edge, because the material plastic flowing is confined by the holder. On each side deformed region surface, there is a complicate residual stress state, which may be explained by LSF that combines the plastic
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Fig. 10. A bulge with broad rim. (a) The side surface of laser irradiation and (b) the opposite side surface of laser irradiation.
Fig. 12. Comparisons of numerical and experimental stresses in the Z-axis direction along the cross-section of the bulge.
available test results, and the FEM model established for LSF is verified. The residual surface stress was measured by X-ray diffraction method, and distribution of residual stresses is shown in Fig. 12. As exhibited in Fig. 12, between the test values of residual stresses and the calculation ones on deformed region surfaces, there exist deviations, which may be attributed to its original stress −20 MPa on both side surfaces before LSF. If its original stress is taken into account, the test and calculation results are close generally.
Fig. 11. Comparison of numerical and experimental profiles of the cross-section of the bulge.
deformation with LSP. On the one hand, the mental sheet is deeply pulled by shock wave and plastic deformation takes place. The tensile residual stress should occur on both deformed surfaces. On the other hand, the material is processed by laser shock, the compressive stress always emerges in laser shocked zone. These two mechanisms interact simultaneously and lead to complicate stress on both-sided surfaces. 5. Experiments According to the above described specimen size in Section 3.4, it was cut from the 0.4 mm thick plate with wire cut electrical discharge machining (WEDM). The specimen was irradiated by laser with the same parameters mentioned in simulation. After laser irradiation, the specimen was taken out from the die, and the reminder ablative layer was first removed, and then ultrasound in ethanol was used to degrease its surface. As a result of laser shock, a uniform bulge with broad rim was formed, as shown in Fig. 10. As seen in Fig. 10, the irradiated surface shows no melting, which manifests that LSF is real a cold plastic forming technology. Compared with the surrounding original surfaces of bulge, the deformed region surfaces are bright, and fine scratches disappear, which imply that LSF can obviously improve the surface roughness of material. The profile of the cross-section of bulge measured with a Taylor Hobson contour meter is described in Fig. 11. The profile obtained from the test is similar to that from the calculation. The maximum depth from the test is about 1.75 mm, 11% bigger than that from the calculation. The calculation data are well consistent with the
6. Conclusions A FEM model with the commercial code LS-DYNA has been built to simulate LSF process. LSF displays some unique characteristics, which don’t display in quasi-static forming. The following conclusions are obtained: (1) In order to gain the accurate results in LSF simulation with code LS-DYNA, the solution time should be set to ms level, which is two to three orders of the magnitude longer than that in LSP. (2) During the dynamic deformation progress, the metal sheet initially experiences the shearing deformation at the border of the local shocked area, and then it is deeply stretched by itself momentum obtained from laser shock. (3) The opening of bulge gradually increases to die hole diameter and subsequently keeps constant. The depth of bulge firstly lasts increasing and then undergoes several spring backs, and the evolution of bulge experiences successively flat bottom, reverse deformation, and tip bottom. (4) The complicate residual stress state exists on both side surfaces of the deformed region. The lower magnitude of compressive residual stress and the relative higher magnitude of tensile stress emerge on both-sided surfaces. However, the current work is not involved in the conditions that metal sheet is impacted successively by multiple laser shots and deformed into the intricate 3D shape according to die. These works will be carried out in the future. Obviously, we are only just touching the entrance of LSF, and it needs us longer term efforts to realize LSF to act as a realistic tool in practical applications.
X. Zhang et al. / Journal of Materials Processing Technology 220 (2015) 27–35
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