5. Unified momentum equation approach for laser heat treatment
5.3. Numerical and experimental results
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Figure 67. Numerical results considering fluid flow (left) and without considering fluid flow (right) for Case A at the top surface during the laser process. (a) Normal stress in the x-direction, (b) Solid- state phase, (c) Temperature.
Figure 68. Numerical results considering fluid flow (left) and without considering fluid flow (right) for Case A at the top surface after the material has been completely cooled down to the ambient temperature. (a) Normal stress in the x-direction, (b) Solid-state phase, (c) Temperature.
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In Figure 69 and Figure 70, the cross-section view of stress, solid-state phase, and temperature distributions for Case A is presented. The temperature distribution is further enlarged to closely observe the fluid flow in the melt pool. The figures in the cross-section show more clearly the differences between the numerical results with and without fluid flow. In the results considering fluid flow, the shape of HAZ is long in the horizontal direction due to melt flow driven by thermocapillary force. On the other hand, if the fluid flow is not taken into account, the shape of HAZ becomes circular and deep. Changes in temperature distribution affect the solid-state phase transformation and eventually alters residual stress distribution. In addition, the fluid-structure interactions in the mushy zone during melting and solidification influences stress development.
Figure 69. Numerical results considering fluid flow (left) and without considering fluid flow (right) for Case A at the cross-section during the laser process. (a) Normal stress in the x-direction, (b) Solid- state phase, (c) Temperature.
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Figure 70. Numerical results considering fluid flow (left) and without considering fluid flow (right) for Case A at the cross-section after the material has been completely cooled down to the ambient temperature. (a) Normal stress in the x-direction, (b) Solid-state phase, (c) Temperature.
In Figure 71, the solid-state phase distribution of numerical results for Case A is compared with the experimental measurements by optical microscopy at the cross-section. In the numerical result, martensite, bainite, and ferrite/pearlite (initial phase) phases are represented as red, green, and blue colors. Two black solid lines indicate solidus temperature and A1 temperature where the solid-state transformation begins. At the bottom of the figure, high magnification optical micrographs are presented to observed solid-state phases. In Case A, only the austenite to martensite transformation occurs after laser irradiation is finished due to the rapid cooling rate. At the position a, the martensite is well observed. As it goes down, the size of the martensitic phase becomes smaller and the ferrite/pearlite phase fraction increases while the martensite phase fraction decreases as shown at the position b. At the position c, no solid-state phase transformation occurs and only the initial phase exists. Figure 72 shows residual stresses (normal stress in the x-direction) of numerical results and experimental measurements for Case A. The black solid and dotted lines present the numerical results with and without fluid flow. The red solid line is the experimental result. The residual stresses are compared along the z-direction at the centerline and along the y-direction at a distance of 2.4 mm from the top surface. The numerical result without considering fluid flow do not fit well with the experimental measurement since the size of HAZ is deeper than actual result.
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Figure 71. Optical micrograph of cross-section (left) and simulation result of solid-state phase (right) for Case A. High magnification optical micrographs at positions a, b, and c are at the bottom of the figure.
Figure 72. Comparison of residual stresses obtained by numerical simulation and experimental measurement at cross-section for Case A. (a) along the z-direction at the centerline, (b) along the y- direction at a distance of 2.4 mm from the top surface.
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Optical micrograph and solid-state phase distribution obtained by numerical simulation for Case B are shown in Figure 73. In this case, the applied laser intensity is lower, and the scanning speed is slower than Case A. The big difference from Case A is the smaller size of HAZ but the cooling rate is still fast and only the austenite to martensite transformation is observed. Similar to Case A, as it goes down, the size of the martensitic phase becomes smaller and martensite phase fraction decreases.
Figure 74 shows residual stress distributions of numerical and experimental results for Case B.
Because of the different sizes of HAZ, the two turning points (z=5.7 mm, 2.2 mm) shown in Figure 74.
(b) are located above than in Case A (z=5.6 mm, 1.8 mm). Also, the maximum magnitude of residual stress in Case B is smaller than in Case A.
Figure 73. Optical micrograph of cross-section (left) and simulation result of solid-state phase (right) for Case B. High magnification optical micrographs at positions a, b, and c are at the bottom of the figure.
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Figure 74. Comparison of residual stresses obtained by numerical simulation and experimental measurement at cross-section for Case B. (a) along the z-direction at the centerline, (b) along the y- direction at a distance of 2.4 mm from the top surface.
Figure 75 shows the optical micrograph and the numerical result of solid-state phase distribution for Case C. The laser scanning speed of Case C is very slow compared to previous cases and it takes a long time for the material to cool down. Consequently, in this case, the austenite to bainite transformation also takes place and the martensite and bainite coexist in the HAZ. In the numerical result, the martensite and bainite fractions are 31 % and 69 % at the point of surface center. In Figure 76, the residual stresses for Case C obtained by experiment and numerical simulation are compared.
The overall trend of the residual stress distribution is similar to the previous cases, but low stress level is observed.
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Figure 75. Optical micrograph of cross-section (left) and simulation result of solid-state phase (right) for Case C. High magnification optical micrographs at positions a, b, and c are at the bottom of the figure.
Figure 76. Comparison of residual stresses obtained by numerical simulation and experimental measurement at cross-section for Case C. (a) along the z-direction at the centerline, (b) along the y- direction at a distance of 2.4 mm from the top surface.
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