A Mechanism for Inducing Compressive Residual Stresses on a Surface by Laser Peening without Coating

Laser peening without coating (LPwC) involves irradiating materials covered with water with intense laser pulses to induce compressive residual stress (RS) on a surface. This results in favorable effects, such as fatigue enhancement; however, the mechanism underlying formation of the compressive RS is not fully understood. In general, tensile RS is imparted on the surface of the material due to shrinkage after heating by laser irradiation. In this study, we assessed the thermomechanical effect of single laser pulse irradiation and introduce a phenomenological model to predict the outcome of LPwC. To validate this model, RS distribution across the laser-irradiated spot was analyzed using X-ray diffraction with synchrotron radiation. In addition, the RS was evaluated across a line and over an area, following irradiation by multiple laser pulses with partial overlapping. Large tensile RSs were found in the spot irradiated by the single pulse; however, compressive RSs appeared around the spot. In addition, the surface RS state shifted to the compressive side due to an increase in overlap between neighboring laser pulses on the line and over the area of irradiation. The compressive RSs around a subsequent laser spot effectively compensated the tensile component on the previous spot by controlling the overlap, which may result in compressive RSs on the surface after LPwC.

Through comprehensive experiments, we concluded that LPwC imparts compressive RSs on the top surface of a material. This is achieved through irradiating metallic components covered with water using laser pulses, with appropriate overlapping between neighboring pulses [8,25,26]. However, a full understanding has not yet been reached regarding the underlying mechanism of LPwC, whereby the top surface becomes compressive despite the intense thermal effect of laser irradiation on the exposed surface, leading to ablation of the top surface. If an overlay is applied to block a thermal effect on the top surface [27][28][29], the mechanism is easy to understand; sudden generation of high-pressure plasma due to the ablation produces a shock wave, which propagates into the material to cause a permanent strain; meanwhile, a compressive RS field remains on the surface due to the elastic constraint of the surrounding area [30][31][32][33]. However, in the case of LPwC, this mechanical effect competes with the thermal effect during each laser pulse, which can last for nanoseconds or tens of nanoseconds. In this context, Peyre et al. demonstrated that the RS state of the top surface must be tensile after direct irradiation of a single laser pulse to 55C1 medium carbon steel and 12% Cr martensitic stainless steel, experimentally [28] and in a thermo-mechanical simulation based on the finite element method (FEM) [29]. Morales et al. reported that compressive RSs appeared on the top surface in their full three-dimensional (3D) simulation of LPwC, which included interactions between adjacent laser pulses irradiated successively [34].
In this paper, we propose a phenomenological model of LPwC for inducing compressive RSs on the top surface of a material, which qualitatively explains how the surface becomes compressive with successive irradiating laser pulses. According to this model, the tensile region of the laser-irradiated spot is swept through subsequent laser pulses; the consequently increased overlapping results in the surface RS state changing from tensile to compressive [8]. To validate this model, we precisely analyzed the RS distribution on the top surface after single pulse (zero-dimensional (0D)), single line (one-dimensional (1D)), and area (two-dimensional (2D)) irradiation by means of X-ray diffraction (XRD). The analysis revealed large tensile RSs at the spot subjected to 0D single pulse irradiation; however, compressive RSs were observed on the circle-like area around the spot [35]. Furthermore, compression was attained on the laser-irradiated line and area after 1D and 2D irradiation [25], by increasing overlapping as predicted by the LPwC model.

Evolution of Surface Stress Due to Single Pulse Irradiation
During laser pulse irradiation of a surface, the laser energy is absorbed by the top surface, which expands rapidly; this causes a compressive stress at the position of the laser spot, pushing away the surrounding material. This effect is promoted by a shock wave generated by the sudden pressure rise of the laser-induced plasma. The resultant compressive stress is much higher than the yield strength of most metals and alloys, assuming that the coefficient of thermal expansion (CTE) is in the order of 10 −5 /K and the temperature rise is greater than 10 3 K. Therefore, plastic strain is generated at the position of the laser spot and the surrounding material. As the top surface begins to melt, the induced stresses and strains at the laser spot are released; however, the plastic strain remains in the unmelted surrounding material. Once the laser pulse is powered off and the plasma dissipates, cooling and solidification begin. This is followed by a tensile RS generated on the top surface of the material due to thermal shrinkage.
The time evolution of these phenomena and the respective stress states are summarized in Table  1. The laser-irradiated spot on the surface is initially compressive due to thermal expansion and the dynamic pressure of the shock wave, and then becomes tensile due to shrinkage caused by cooling following the dissipation of the plasma after switch-off of the laser pulse. As a result, the tensile RS remains on the laser spot and the compressive RS remains within the surrounding circular boundary (rim), without melting.

Surface Residual Stress after Successive Laser Pulse Irradiation
Through extension of the model shown in Table 1, which describes the evolution of the surface stress state due to single pulse irradiation, an LPwC model was devised where compressive RSs are induced on the material surface through increasing the overlap between the neighboring laser pulses, as shown in Table 2. In the case of the 0D single pulse irradiation (pattern A in Table 2), the tensile region remained on the laser-irradiated spot. Meanwhile, under 1D line and 2D area irradiation, the tensile region formed by the previous pulse was eliminated by the compressive effect of subsequent neighboring pulses (pattern C). However, where the overlap between the adjacent laser pulses is small, the tensile region elimination is not sufficient (pattern B).
This model suggests that compressive RSs on the surface could be introduced by LPwC when the overlap between neighboring spots is sufficient (patterns C and E), with the exception of the final spot subjected to consecutive laser pulse irradiation. The degree of overlap required to obtain compressive RSs depends on the laser irradiation conditions and characteristics of the material, such as its CTE and mechanical properties.

Preparation of Specimens
To validate the proposed LPwC model, the materials used were HT1000 (1000 MPa grade high tensile strength steel) and SUS304 (type 304 austenitic stainless steel). HT1000 has fine grains of around 10 m or less and is therefore suitable for the precise measurement of RSs in a small area by XRD with a micro X-ray beam. As a result, HT1000 was used to obtain RS profiles across laserirradiated spots and lines using synchrotron radiation (SR) as the X-ray source [25]. SUS304 is widely used in various applications; however, it has relatively coarse grains. Thus, SUS304 was used to evaluate the average RS over a specific area with the laboratory X-ray source.
HT1000 specimens with dimensions of 28 × 30 × 17 mm 3 were annealed at 973 K for 3 h, followed by furnace cooling to relieve RSs by machining. RSs on the top surface after annealing were close to zero (0-50 MPa). SUS304 specimens with dimensions of 40 × 60 × 10 mm 3 were prepared from an SUS304 plate that had been 20% cold-worked by rolling. The SUS304 specimens were ground parallel to the rolling direction to create tensile stresses in the near-surface layer prior to the laser irradiation. The mechanical properties of HT1000 and SUS304 are summarized in Table 3.  Figure 1 shows a schematic of the experimental setup for laser irradiation of the specimen [12,13]. Laser pulses from a Q-switched and frequency-doubled Nd:YAG laser ( = 532 nm) irradiated a specimen underwater through an optical window. For the 1D line and 2D area irradiations, the specimen was driven by a tri-axial stage during laser irradiation, while it was fixed for 0D single pulse irradiation. The position, density, and pattern of laser irradiation of the specimen were controlled by the tri-axial stage. The temporal profile of the laser pulse was near-Gaussian and the pulse duration was 5-8 ns at full width-half maximum (FWHM), which was measured with a fastresponding photodiode and fed back along with other parameters to calculate the power density, etc., in each experiment.

Residual Stress Measurement by X-Ray Diffraction
To validate the phenomenological model of LPwC proposed in Section 2, RSs on the top surface were measured across spots (0D), lines (1D), and areas (2D) after laser irradiation. The RSs were estimated using the 2-sin 2  XRD method with SR at the Photon Factory (PF) of the High Energy Accelerator Research Organization (KEK). For measurement of the average RS over a specific area, laboratory Mn-k X-rays were used.
The parameters used in the XRD measurements are listed in Table 4. At KEK-PF, X-rays from beam line BL-3A, with an energy of 5.4 keV, were collimated to 0.2 mm in diameter with a pin-hole and irradiated the HT1000 specimen placed at the center of a goniometer, as shown in Figure 2. The -Fe (211) was selected as the diffraction plane, considering the intensity and 2 angle of diffracted X-rays, and detected by a handmade position-sensitive proportional counter (PSPC).

Surface Residual Stress after 0D Single Pulse Irradiation
A single laser pulse irradiated the HT1000 specimen with a spot diameter of 1.2 mm and an energy of 320 mJ. A pulse with a smaller spot size of 0.4 mm and energy of 34 mJ was also used to determine the effect of spot size; the power density was 4 GW/cm 2 for both irradiations. The resultant surface RSs were estimated by XRD with SR.
The RSs in the radial direction across the laser spots are plotted in Figure 3. The error bars in the plot correspond to the standard deviation in the RS estimation. Tensile components exist in the spots, which are attributed to shrinkage of the top surface following heating by the laser pulse. The absolute value of the tensile components decreases drastically with a reduction in spot size. This suggests that a reduction of the laser-irradiated area would enhance the cooling of the top surface, even if the laser power density is constant. Meanwhile, compressive components were observed outside the spots, as predicted by the model in Table 1. The range of compression outside the spot would be comparable to the spot diameter.
In real-world applications, each point on the specimen would typically experience several tens of hits by laser pulses [22][23][24]. In such cases, compression outside the spot would likely accumulate and reach a higher absolute value as laser pulses irradiate the area close to the point of interest. To confirm this, we performed experiments where multiple laser pulses irradiated the same area. Laser pulses irradiated the HT1000 specimen fixed underwater with 215 mJ pulse energy, 1.0 mm spot diameter, 4 GW/cm 2 power density, and 1, 4, 10, or 40 laser pulses on the same spot. The results are shown in Figure 4; the overall RS distribution shifts to the compressive side as the number of pulses increases. It is worth noting that even RSs in the laser spot shifted to the compressive side, despite the pulses resetting the surface RSs each time due to the melting of the surface. If the area around the spot is already in compression, the tensile strain due to solidification after laser irradiation may be offset to some extent by the existing compressive strain. In such cases, the tension in the spot may be reduced and it calls for further investigation.

Surface Residual Stress after 1D Line Irradiation
Inspired by the results shown in Figure 4, we proceeded to 1D line irradiation of the HT1000 specimen using a pulse energy of 215 mJ, spot diameter of 1.0 mm, and power density of 4 GW/cm 2 . The effects of pulse densities of 1, 5, 10, and 100 pulses/mm on the RS profile were determined. Figure  5 plots the surface RSs in the y-direction (perpendicular to the laser-irradiated lines) for pulse densities of 10 and 100 pulse/mm. As expected, the RS profile of the 100 pulse/mm line has a much lower RS distribution on the compression side compared to the 10 pulse/mm line. The compression outside the laser-irradiated lines exceeds the line width of 1 mm for both lines of 10 and 100 pulse/mm. These results are consistent with those obtained after multiple irradiations of the same spot, as described in Section 4.1 and Figure 4. The surface RSs in the x-direction (parallel to the laser-irradiated lines) were measured at the center of the laser irradiated lines. The results are plotted in Figure 6 for pulse densities of 1, 5, 10, and 100 pulse/mm. The surface RS changed significantly from tensile to compressive with increasing pulse density, in accordance with the LPwC model described in Table 2 (patterns B and C).

Surface Residual Stress after 2D Area Irradiation
As demonstrated in the previous sections, the laser pulse irradiation-induced compression around laser-irradiated spots and lines can accumulate with successive irradiations. In this section, we confirm the effect of overlap of neighboring laser pulses on RSs in a 2D area. Laser pulses with an energy of 100 mJ irradiated the SUS304 specimen. The focal spot size was 0.8 mm, and the pulse duration was 5 ns, resulting in a power density of about 4 GW/cm 2 . The laser pulse density was varied between 11 and 180 pulse/mm 2 . The surface RSs measured in the y-direction are plotted in Figure 7. For the surface-ground SUS304 specimens, the standard deviation of RS estimation was about 20 MPa and in most cases less than 40 MPa. In accordance with the LPwC model described in Table 2, a significant effect of pulse density on the RSs in the 2D area was seen. To compare the effects of isotropic and anisotropic irradiation, SUS304 specimens were irradiated using patterns E and F in Table 2. Successive laser pulses with an energy of 200 mJ converged to a diameter of 0.9 mm and irradiated the SUS304 specimen underwater, with a power density of about 4 GW/cm 2 . The pulse density was set to 36 pulses/mm 2 , for a coverage (C) of 2300%. The C indicates the average number of laser pulses that irradiated a given point within the laserirradiated area, and can be calculated by the following equation: C = (D 2 /4), where D is the spot diameter and  is the pulse density.
During isotropic irradiation, the interval between the neighboring laser spots was 0.17 mm in both the x-and y-directions, with an irradiation density of 36 pulses/mm 2 . During anisotropic irradiation, the interval was reduced by 1/2 or 1/4 in the x-direction and increased 2-or 4-fold in the y-direction, with the same pulse density. The patterns of laser irradiation and RSs are shown in Figure  8. As expected from the LPwC model, compressive RSs were observed on the surface with all irradiation patterns. These findings are important when willing to increase the processing speed in real-world applications. With anisotropic irradiation, the motion of an LPwC machine is slower than with isotropic irradiation. The time required for acceleration and deceleration of the machine can be reduced in the anisotropic irradiation, thus increasing the processing speed.

Surface Residual Stress on the Final Laser-Irradiated Spot in the 2D Area
The results presented in Sections 4.1 to 4.3 confirm the validity of the LPwC model described in Table 2, by showing that successive laser pulse irradiation with appropriate overlapping can induce compressive RSs on the surface. Based on the results of the 0D single pulse experiment and the predictions of the LPwC model, the RS state of the final spot should be tensile. To confirm this, we made precise measurements of RSs across the final spot irradiated in the 2D area.
Laser pulses with an energy of 200 mJ were focused to 1.0 mm and irradiated the HT1000 specimen underwater in an isotropic manner (pattern E in Table 2). The power density was 3.2 GW/cm 2 and the pulse density was 100 pulses/mm 2 . The pitch between the neighboring laser spots was 0.1 mm in both the x-and y-directions. The RSs under the final laser spot were estimated by XRD with SR at KEK-PF, as described in Section 3.3. Figure 9 shows the distributions of RSs in the radial direction across the final spot irradiated in the 2D area. As predicted by the LPwC model, large tensile RSs appeared in the final spot, which was surrounded by a region of compressive RSs. The depth of the tensile region was estimated as less than 10 m considering thermal diffusion length, L, which could be evaluated from the following equation: L = 2 (Datp) 0.5 , where Da is the thermal diffusivity and tp is the interaction time between the high-temperature plasma and the top surface. The thermal diffusivity, Da, is in the order of 10 mm 2 /s for steels. The interaction time, tp, is considered to be no more than 1 s; the plasma illumination completely disappeared within 1 s in our experiments [7]. Actually, tensile RSs were observed to a depth of about 10 m for high-strength steel SHY685 [36] and about 5 m for SUS304 [8] in our experiments. This was confirmed through electrolytic polishing and XRD.
We were concerned that, if the final spot was inadvertently positioned in an area susceptible to fatigue, SCC, etc., cracks may initiate from it due to the tensile RSs. However, we have not yet observed cracks emanating from the final spot subjected to LPwC. This is likely due to the tensile region being extremely shallow compared to the compressive region beneath the spot (typically 1 mm), and to the width of the surrounding compressive region. However, considering the RS state in the final spot, laser irradiation sequence should be terminated outside areas susceptible to fatigue, SCC, etc.

Conclusions
We introduced a phenomenological model of LPwC to assess the thermo-mechanical effect of single pulse (0D) irradiation, and the interaction between successive laser pulses in line (1D) and area (2D) irradiations. The model qualitatively predicts RS states on the top surface after LPwC. To validate the proposed LPwC model, specimens of HT1000 and SUS304 were subjected to 0D, 1D, and 2D irradiation. The RS distributions were evaluated by XRD with SR and a laboratory X-ray source. The experiments revealed that after LPwC, the top surface can become compressive through increasing the overlap between adjacent laser pulses as predicted by the LPwC model. The results obtained in the experiments are summarized as follows: (1) With 0D single pulse irradiation, large tensile RSs were observed within spots irradiated by the single laser pulse, but compressive RSs appeared in the area outside the spots over a distance comparable to the spot diameters. By increasing the number of pulses irradiating the same area, the compressive state outside the spot was enhanced.
(2) With 1D line irradiation, tensile RSs were observed in the laser-irradiated line in the case of low pulse density. However, the RS state changed from tensile to compressive with increasing pulse density. Outside the laser-irradiated lines, compressive RSs were observed over a distance greater than the line width.
(3) With 2D area irradiation, tensile RSs were observed after irradiation with low pulse density, but, similar to the results obtained with 1D line irradiation, the RS state changed from tensile to compressive with increasing pulse density. Under anisotropic irradiation, compressive RSs close to those observed under isotropic irradiation were obtained, even when the pulse interval was reduced by 1/2 or 1/4 times in the x-direction and increased by 2-or 4-fold in the y-direction.

Conflicts of Interest:
The authors declare no conflict of interest.