Laser shock processing (LSP) has been studied since 1970s (Clauer, et al., 1981; Peyre, et al., 1998). Laser generated shock waves in a confining medium have been used to improve the mechanical properties of various metals such as aluminum, steel and copper. In particular, LSP can induce compressive residual stresses in the target and improve its fatigue life. The beam spot size used is in the order of millimeters and the compressive stress can typically reach a couple of millimeters into the target material. The technique has not been widely applied partially due to the fact that a high power laser source is needed for a beam size in the order of millimeter to produce the high laser intensity required. It is also perceived as inefficient when a large area of surface needs to be processed because each laser pulse only processes a small area.

Processes such as laser machining, on the other hand, often impart an undesirable residual stress distribution at the vicinity of the machined region. For instance, thermally induced stress in laser drilling and scribing of ceramics was shown in simulation to induce a very thin layer of compressive residual stress at the surface of the hole, while substantial tensile stresses develop over a thick layer below and parallel to the surface (Modest, 1997; Modest and Thomas, 1999). Numerical analysis of the heat affected zone and residual stress distributions for laser cutting of stainless steel shown that along the cutting edge there are high levels of tensile stress that sharply reverts to compressive stress once away from the edge (Li and Sheng, 1995; Sheng and Joshi, 1995). The sharp stress gradient was thought to make the cutting edge susceptible to micro/macro cracks.

In recent decades, significant progress has been made in the design and fabrication of micro electromechanical systems (MEMS) via various methods. When the MEMS fabrication technology matures, attention will turn to the mechanical properties of the MEMS components, for instance, the residual stress distribution of a micro gear of metallic material. Needs will arise to impart a desirable residual stress distribution or alter the existing distribution left by the fabrication process itself. Little studies have been done for such methods in the micro scale.

When a metallic target is irradiated by an intense (>1 GW/cm²) laser pulse, the surface layer instantaneously vaporizes into a high temperature and high pressure (1~10 GPa) plasma. This plasma induces shock waves during expansion from the irradiated surface, and mechanical impulses are transferred to the target. If the plasma is not confined, i.e., in open air, the pressure can only reach several tenth of one GPa. If it is confined by water or other media, the shock pressure can be magnified by a factor of 5 or more compared with the open-air condition (Fox, 1974). At the same time, the shock pressure lasts 2 to 3 times longer than the laser pulse duration. In most LSP a coating is used to protect the target from thermal effects so that nearly pure mechanical effects are induced. The coating could be metallic foil, organic paints or adhesives. These coatings can modify the surface loading transmitted to the substrate by acoustic impedance mismatch effects at the coating-substrate interface, and an additional 50% increase in the peak stress values can be achieved (Peyre, et al., 1998). Pressures above 1 GPa are above the yield stress of most metals, thus plastic deformation can be induced. As a result, if the peak shock pressure is over the HEL (Hugoniot Elastic Limit) of the target material for a suitable time duration, compressive stress distribution in the irradiated volume can be formed (Clauer, et al., 1981).

In LSP, the target is subjected to very strong shock pressures (>1 GPa), the interaction time is very short (<100 ns), and the strain rate is very high (>100,000 s^-1). A review of constitutive equations for such high strain rates was given by Meyer (1992). The simplest model to describe the work hardening behavior of metals is , where Y is the yield strength, n, A and B are material constants, and e is the equivalent plastic strain. The work hardening model was extended to include the influence of temperature T and strain rate (Johnson, et al., 1983). Johnson's model was based on experiments with strain rates from 0 to 400 s^-1 and it did not consider pressure effects, which are very important in laser shock processing. A constitutive model applicable to ultrahigh pressures was given by Steinberg, et al. (1980). Steinberg's model did not consider rate dependent effects, however. It was found that rate dependent effects played a minor role at pressures above 10 GPa and their rate independent model was verified to successfully reproduce shock experimental data in this range. But for shock pressures below 10 GPa, the rate dependent effects cannot be neglected. In laser shock processing, the pressure involved is fairly high (>1 GPa) but less than 10 GPa.

For laser shock processing, therefore, both the strain rate effects and ultrahigh pressure effects on material yield stress need to be considered. Based on the above mentioned models and assuming that the material compression is negligible in the range of working pressure (below 10 GPa), the following constitutive equations are suggested and used in this paper.

(5)

(6)

(7)

where G is the shear modulus, P is pressure, T is temperature, Y₀ and G₀ are values at reference state (T = 300 K, P = 1 atm, strain free), C is the logarithmic rate sensitivity at strain rate 1 s^-1, e is strain,is strain rate, B and n are material parameters describing work hardening effect.

In the stress analysis, work hardening, strain rate and pressure effects on yield strength are considered while temperature is taken as room temperature. This is reasonable because only the coating is vaporized and minimal thermal effects are felt by the sample. Shock pressure is computed and used as loading for the 2D axisymmetric stress analysis. A commercial FEM code, ABAQUS, is used to compute the deformation and stress distribution of the sample under the shock pressure. The simulation is a dynamic implicit nonlinear process. Single and multiple pulses at single and multiple locations are simulated. The boundary conditions for the axisymmetric stress model are as follows.

Figure 1 (a) and (b) show a typical simulation result of radial strain E11(E_r) and the in-depth strain E22(E_z), respectively. Both are total strains that consist of elastic and plastic strains. For laser shock processing of copper, plastic strains are dominant. Deformation (dent) is clearly seen on the top surface near the centerline. As shown in Figure 1 (b), the maximum compressive strain of E22 occurs 10 microns below the top surface along the centerline, and the region of compressive strain expands from this point. On the top surface, a very thin layer of about 2 microns of tensile strain is observed. When the shock wave is acting on the sample, the material beneath the shocked area undergoes both plastic and elastic deformations. The shock pressure is attenuated as it propagates downwards and outwards. When the shock wave reaches the bottom, it is bounced back. The upward and downward shock pressure cancels each other. This explains the flat shape of the contour lines near the bottom. When the shock pressure is over, the top surface becomes traction free and stress relaxation occurs. The plastic deformation induced compressive strain under the top surface adjusts itself and finally balances the relaxation effects. This explains why the maximum compressive strain is not on the top surface. The radial strain (Figure 1 (a)) is tensile in the region where the in-depth strain is compressive. This is understandable because the material is isotropic and the in-depth strain will cause an in-plane (x-y) strain in the opposite sign under the principle of constant volume. The depth of plastic deformation reached about 70 microns in the sample of 90 microns thick. The simulation results were indirectly validated in the following geometry comparison.

Figure 2 shows a typical distribution of residual stresses for a single pulse at the energy level E = 240 m J. The computation domain is 90 microns by 1000 microns, and the region shown is 90 microns by 200 microns for clear view of the results. As seen from Figure 2 (a), radial stress S11 is compressive in a wide region below the top surface with the maximum of 165 MPa reached along the centerline and about 70 microns into the sample. On the top surface, S11 is compressive within 10 microns from the center and is tensile in the range of 10 to 38 microns, and then becomes compressive again. Such tensile radial stress near the edge of laser irradiation was also observed in LSP using large beam sizes (Clauer, et al., 1981). This thin layer (about 2.5 microns deep) of tensile stress is undesirable, but it may be altered by overlapping laser pulses at proper spacing, as illustrated in Section 4.4. The wide range of compressive radial stress distribution near the top surface is desired for the prevention of crack formation and propagation. Figure 2 (b) shows the distribution of in-depth residual stress S22. S22 is close to zero near the top surface as expected from the equilibrium requirement, and becomes compressive at the lower center part of the sample. The locations of the maximum tensile and compressive in-depth residual stresses are close to the bottom surface instead of the top surface. One explanation is that the bottom surface is fixed in position, while the top surface is traction free when the shock load is removed. The top part of the sample will have nearly zero in-depth stress after sufficient stress relaxation, but the center bottom part cannot relax as the top surface does because both the centerline and the bottom surface are fixed in position. As a result, the in-depth residual stress accumulates near the center bottom region.

Figure 3 illustrates the distribution of residual stresses on the top surface and at 70 microns below the top surface. The distance from the center is normalized to the radius of laser beam r₀, where r₀ = 6 microns. Stress distribution within 1.75 r₀ was shown to view the laser-irradiated region and its vicinity in detail. Under all conditions, the radial stress S11 (equivalent to in-plane (x-y) stress if equal-biaxial is assumed) on the surface is compressive within the 1.75 r₀ range and the compressive radial stress reaches around 160 MPa 70 microns below the top surface. When r/ r₀ approaches 1.75 and is greater than 1.75 for that matter, the radial stress on the top surface rises and eventually becomes tensile (Figure 2 (a)), which is undesirable but may be alleviated by overlapping pulses at proper spacing as discussed in the previous paragraph. As to the in-depth stress S22, it is all very close to zero on the top surface for the reason already stated in the previous paragraph. It is interesting to note that the radial stress S11 on the top surface is more sensitive to the number of pulses (Figure 3 (a)) while S11 deep below the top surface (70 microns) is more sensitive to the pulse energy level (Figure 3 (c)). It is easy to understand why S11 increases with the energy level below the top surface but its insensitivity to the energy level at the top surface is due to the fact that relaxation took place near the top surface after the shock pressure is over therefore regardless of the energy level the relaxation will always take place and as a result, S11 at the top surface seems less sensitive to the energy level. The same reasoning can be used to explain why the increase in the number of pulses causes appreciable increase in S11 at the top surface. The reason that S11 70 microns below the top surface is less sensitive the number of pulses is due to the work-hardening effect.

It is shown that for a laser beam of 6 microns in radius and pulse energy of 240 m J, in-plane (x-y) compressive residual stress is imparted on the surface of copper samples within a region of about two radii of the laser beam, and over 150 MPa compressive stress is imparted 70 microns into the target material. A small region around the edge of the dented area is seen as tensile, which may be alleviated by overlapping laser pulses at proper spacing. It is shown that it is possible to impart desirable residual stress distributions into micro scale metallic components by properly choosing laser intensity, number of pulses and spacing. The micro scale laser shock processing has the potential to alter mechanical properties of small metallic components such as micro gears fabricated using the MEMS technology. It may also be combined with laser micromachining processes, which alone often leave an undesirable residual stress distribution in the machined components, to allow the net residual stress distributions in favor of improved fatigue life of the components.

Berthe, L., et al., 1998, "Experimental study of the transmission of breakdown plasma generated during laser shock processing," The European Physical Journal Applied Physics, 1998, Vol. 3, pp 215-218.

Clauer, A. H., et al., 1981, "Effects of laser induced shock waves on metals," Shock Waves and High Strain Phenomena in Metals-Concepts and Applications, New York, Plenum, 1981, pp. 675-702.

Fabbro, R., et al., 1990, "Physical study of laser-produced plasma in confined geometry," J. Appl. Phys., July, 1990, Vol. 68(2), pp. 775-784.

Fox, J. A., 1974," Effect of water and paint coatings on laser-irradiated targets," Appl. Phys. Lett., 15 May 1974, Vol.24, No. 10, pp. 461-464.

Johnson, G. R., et al., 1983, "Response of various metals to large torsional strain over a large range of strain rates," J. Eng. Mat. Techn., Jan. 1983, Vol. 105, pp. 42-53.

Li, K. and Sheng, P. S., 1995, "Computational model for laser cutting of steel plates," Manufacturing Science and Engineering, ASME 1995, MED-Vol. 2(1), pp.3-14.

Meyer, L. W., 1992, "Constitutive equations at high strain rates," Shock-wave and High-Strain-Rate Phenomena in Metals, Marcel Dekker, Inc., New York, 1992, pp. 49-68.

Modest, M. F., 1997, "Thermal elastic and viscoelastic thermal stresses during laser drilling of ceramics," J. Heat Transfer, 1997, Vol. 120, pp. 892-898.

Modest M. F., and Mallison, T. M., 1999, "Transient elastic thermal stresse development during laser scribing of ceramics," ICALEO 1999, pp. B118-127.

Noyan, I. C. and Cohen J. B, 1986, Residual Stress, Springer-Verlag NewYork Inc., New York, 1986, pp.135.

Peyre, X. S., et al., 1998, "Current trends in laser shock processing," Surface Engineering, 1998, Vol. 14 No. 5, pp. 377-380.

Peyre, P., et al., 1996, "Laser shock processing of materials, physical processes invloved and examples of applications," Journal of Laser Applications, 1996, Vol. 8, pp.135-141.

Sheng, P. S. and Joshi, V. S., 1995, "Analysis of heat-affected zone formation for laser cutting of stainless steel," Journal of Materials Processing Technology, 1995, Vol. 53, pp. 879-892.

Steinberg, D. J., et al., 1980, "A constitutive model for metals applicable at high-strain rate," J. Appl. Phys., March 1980, Vol. 51(3), pp. 1498-1504.

Figure 1 Typical distribution of total strain at the end of a shock pulse (a) Radial strain E11; and (b) In-depth strain E22. Pulse energy E = 240 m J (I = 4.24 GW/cm²), beam diameter is 12 microns, plasma absorption coefficient AP = 0.545 and interaction coefficient a = 0.2. Axisymmetry is assumed. Computation domain is 90 microns by 1000 microns, and the region shown is 90 microns by 100 microns for clear view of the results. Deformation in the dented region is magnified by a factor of 3 for viewing clarity.

(a)

(b)

Figure 2 Typical distribution of residual stresses (a) radial residual stress S11and (b) in-depth residual stress S22, E = 240 m J, beam diameter = 12 microns. Stress unit: Pascal. Axisymmetry is assumed. Computation domain is 90 microns by 1000 microns, and the region shown is 90 microns by 200 microns for clear view of the results. Deformation in the dented region is magnified by a factor of 3 for viewing clarity.

Figure 3 Distribution of residual stresses on the top surface and at 70 microns below the top surface (a) radial residual stress S11, E = 240 m J, 2 to 4 pulses; (b) in-depth residual stress S22, E = 240 m J, 2 to 4 pulses; (c) radial residual stress S11, 2 pulses, E = 180, 200 and 240 m J; and (d) in-depth residual stress S22, 2 pulses, E = 180, 200 and 240 m J. Distance from the center is normalized to the radius of laser beam r₀, where r₀ = 6 microns.

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