CHAPTER 7: MULTI-SCAN LASER BENDING OF MAGNESIUM M1A ALLOY SHEETS
8.8 Effect of Pre-displacement .1 Bending mechanism
8.8 Effect of Pre-displacement
B. Stress distribution
As discussed in earlier chapters, for TGM, the increase in temperature causes a thermal expansion in the heated region that is restricted by the surrounding material, which is at relatively low temperature. This induces compressive stresses in the heated region and tensile stresses in the surrounding region. Figure 8.17 shows the x-direction stress histories at Point A and Point B for laser bending and laser assisted bending process. The stress distribution in laser bending and laser assisted bending is quite different.
Figure 8.17. Comparison of x-direction stress histories for laser and laser assisted bending.
From Figure 8.17, it can be observed that the tensile stresses at bottom (Point B) and compressive stresses at top (Point A) surfaces increase gradually from time 0 to 0.5 second (Point a). During this period (0 to a) the initial pre-displacement (PD) is applied at the corner of the worksheet. Once the desired pre-displacement is achieved, the laser beam irradiates and the mechanical load moves along the free edge simultaneously with the laser beam. The tensile and compressive stresses at the top and bottom surfaces increase slightly from a to b. It is because as the moving pre-displacement reaches near to Point A, the vertical displacement increases at Point A. The stresses at both top and bottom surfaces decrease gradually due to heating of the material (b to c). When the laser beam reaches at Point A, the temperature of the material is high, and hence stiffness of the material reduces to a very low value. Therefore, the stresses are very less at ‘c’. As the laser beam moves forward, stresses increase at Point A and Point B as shown between c and d. At the end, on removal of laser energy and mechanical pre- displacement, the stresses at top and bottom surfaces (from d and e) reduce. Laser beam and mechanical load have completely been removed from the worksheet at e. It can be seen that
residual stresses remain in the worksheet material at the end of the process. Residual stresses are minimum when the pre-displacement is not applied and they increase with the increase in applied pre-displacement.
From Figure 8.17, it can also be observed that significant tensile stresses are generated at the bottom surface due to the application of pre-displacement. However, in case of pure laser bending, compressive stresses are induced at the bottom surface. Thus, the mechanism of laser assisted bending differs from that of laser bending.
Figure 8.18. Comparison of von-Mises stress histories for laser and laser assisted bending.
Figure 8.18 shows the von-Mises stress histories at Point A and Point B for laser bending and laser assisted bending of magnesium alloy. It can be seen that the peak stresses are quite high in laser assisted bending. In case of laser bending without pre-displacement, von- Mises residual stresses are higher at the top and lower at the bottom surface. The peak residual stress increases with the increase in pre-displacement. It can also be observed that after the irradiation, the residual von-Mises stresses in the worksheet are almost similar at the top surface for both 5 mm and 10 mm pre-displacements. At the bottom surface, the von-Mises stresses are low for the case of 5 mm pre-displacement in comparison with those of 10 mm pre- displacement. The von-Mises stress is the highest at the top surface and the lowest at the bottom surface, when pre-displacement is not applied.
Figure 8.19 shows x-directional components of the residual stresses along the scanning line for chosen process conditions. It can be seen that the residual stresses are compressive at start of the scanning line. The residual stresses decrease along the scanning line and finally become tensile. The tensile stresses attain a peak and then slightly decrease towards the end of
scanning line. At bottom surface, stresses increase slightly along the scanning line, and then decrease to become compressive in nature. The compressive stresses increase towards the end of the scanning line. At bottom surface, the compressive stresses are the highest at the end of scanning line, while at the top surface, these are the highest at the start of scanning line.
Figure 8.19. Residual stresses along the scanning line.
The trends of residual stress distribution along the scanning line is different for laser bending with and without application of the pre-displacement. For laser bending without pre- displacement, the residual stresses are near to zero all along the scanning line except at the edges. During laser assisted bending with both 5 mm and 10 mm pre-displacement, the residual stresses are compressive at start, then become tensile. They attain a peak at middle of the scanning line, and then decrease towards the end of the scanning line.
C. Strain distribution
When induced thermal stresses exceed temperature dependent flow stress, the plastic deformation occurs. The x-direction plastic strain histories for laser bending and laser assisted bending with 5 mm and 10 mm pre-displacements are shown in Figure 8.20. In laser bending, compressive deformation occurs at both top and bottom surfaces and the worksheet bends due to the difference between plastic deformation at top and bottom surfaces. However, in laser assisted bending, the deformation behavior is different. In laser assisted bending, the tensile deformation occurs at the bottom surface while the compressive deformation occurs at the top surface. This results in a large difference between plastic deformations at the top and bottom surfaces, which leads to a significant increase in the bend angle. The magnitude of compressive deformation at the top surface increases due to the application of external mechanical load. The
tensile deformation at the bottom surface and compressive deformation at the top surface increases with the increase in pre-displacement. This leads to the increase in bend angle with the increase in pre-displacement as shown in Figure 8.21.
Figure 8.20. Comparison of x-direction strain histories for laser and laser assisted bending.
Figure 8.21. Comparison of bending histories for laser and laser assisted bending.
Figure 8.21 shows a comparison between bending histories at the middle of the scanning line for the laser bending and laser assisted bending. It can be seen that on employing the pre-displacements, larger bend angles are obtained. The bend angle increases with the increase in pre-displacement. It is because the pre-displacement is applied towards the bending direction (laser source), and hence the mechanical stresses support the thermal stresses to bend the worksheet. It can also be seen that an elastic recovery of the bend angle occurs when the
pre-displacement is removed from the worksheet. This elastic recovery is called spring-back effect, and it increases with the increase in pre-displacement. In laser bending, the elastic recovery does not exist. It is because the mechanical stresses are not present.
8.8.2 Bend angle
The pre-displacement bends the worksheet in the upward (towards laser head) direction. Due to this, compressive stresses induce on the top surface and tensile stresses on the bottom surface. These mechanical stresses induced along with thermal stresses bend the worksheet.
Effects of pre-displacement on the bend angle are shown in Figure 8.22 to Figure 8.25. The bend angle increases with the increase in pre-displacement. It is because the pre-displacement generates large plastic compressive deformation at the top surface and tensile deformation at the bottom surface (see Figure 8.20). The bend angle is a result of the difference between plastic deformation at the top and bottom surfaces. Thus, a larger bend angle is obtained when a higher pre-displacement is applied.
Figure 8.22. Effect of pre-displacement on bend angle at P=300 W and D=3.87 mm.
Figure 8.23. Effect of pre-displacement on bend angle at P=400 W and D=3.87 mm.
From Figure 8.22 to Figure 8.24, it can be observed that the bend angle decreases with the increase in scan speed. It is because the energy absorbed by the worksheet surface is less at a faster scan speed. It results in a lower peak temperature, and relatively higher yield strength.
The rate of increase in the bend angle with pre-displacement is more at a slower scan speed in comparison with that observed for medium to fast scan speeds. It is because the pre- displacement produces a higher plastic deformation when the temperature of the scanning surface is more.
Figure 8.24. Effect of pre-displacement on bend angle at P=500 W and D=3.87 mm.
Figure 8.25. Effect of pre-displacement on bend angle at P=300 W and V=1000 mm/min.
From Figure 8.22 to Figure 8.24, it can also be seen that the bend angle increases with the increase in laser power. It is because the peak temperature in the irradiated region is more at higher laser power. It reduces the yield strength and results in a higher plastic deformation when the pre-displacement is applied. Figure 8.25 shows that the bend angle decreases with the increase in beam diameter. It is due to decrease in the heat flux density at a larger beam diameter, which reduces the peak temperature at the scanning surface.
It is to be noted that in this section the effects of variation in the laser power and scan speed on the bend angle are discussed for the beam diameter of 3.87 mm. However, a full factorial study was carried out with the other two levels of beam diameters (viz., 5.81 mm and 7.74 mm). During this study, similar trends were observed for medium and large beam diameters. These are reported in the Appendix 8.3.
8.8.3 Spring-back effect
The induced stresses in the worksheet varies from the tensile stresses at the bottom surface to the compressive stresses at the top surface. This variation in stresses results in the spring-back during laser assisted bending process. The highest tensile stresses occur at the bottom surface of the worksheet. These stresses decrease along the worksheet thickness and become zero at the neutral axis. The neutral axis is stressed to a value below the elastic limit which creates a narrow elastic band on both sides of the neutral axis. The metal away from the neutral axis is stressed beyond the yield strength, and is plastically deformed. When external pre- displacement is removed, the elastically deformed material at the neutral axis tries to return to the original flat condition. However, it could not come to the original condition due to
restrictions provided by the plastically deformed surrounding material. Elastic recovery occurs up to the equilibrium of elastic and plastic zones. This elastic recovery is called spring-back.
The spring-back effect is a limitation of laser assisted bending. The information of the spring-back angle is important to produce accurate bend angles in laser assisted bending. The spring-back is quantified in terms of elastic recovery of bend angle and calculated as a difference of the maximum bend angle observed during laser scanning and the final bend angle obtained after completion of the process.
Figure 8.26 to Figure 8.29 show the effect of various process parameters on spring-back angle and percentage spring-back angle. The percentage spring-back angle is calculated as
% Spring-back angle = Spring-back angle
Final bend angle 100. (8.1)
The spring-back does not occur in the laser bending process as mechanical stresses are not present. Figure 8.26 to Figure 8.29 show the variation of spring back and % spring back angle with the increase in pre-displacement for various laser conditions. It can be observed that the spring-back angle increases with the increase in pre-displacement. It is because the higher pre-displacement results in higher elastic and plastic deformation. The elastic deformation recovers in the form of spring-back angle, and therefore the spring-back angle increases with the pre-displacement. The rate of increase in spring-back angle is less at higher pre- displacement (10 mm). It may be due to the fact that the percentage spring-back angle decreases with the increase in pre-displacement. The plastic deformation is more as compared with the elastic deformation when a higher pre-displacement is applied. Also in case of higher pre- displacement, the induced stresses are higher those deform the worksheet material plastically.
Figure 8.26. Effect of pre-displacement on spring-
back effect at P=300 W and D=3.87 mm. Figure 8.27. Effect of pre-displacement on spring- back effect at P=400 W and D=3.87 mm.
Figure 8.28. Effect of pre-displacement on spring-back effect at P=500 W and D=3.87 mm.
Figure 8.29. Effect of pre-displacement on spring- back effect at P=300 W and V=1000 mm/min.
The spring-back angle increases with the increase in scan speed, beam diameter and decreases with the increase in laser power. The increase in scan speed and beam diameter reduces the peak temperature of the worksheet while the increase in laser power increases the peak temperature. Therefore, it can be concluded that the spring-back angle decreases with the increase in peak temperature. It is because the yield strength decreases at higher temperature which leads to a higher plastic deformation in the heated region.
The percentage of spring-back angle is also affected by the laser process parameters. It increases with the increase in scan speed and beam diameter and decreases with the increase in laser power. It is because when energy input or heat flux density increases, the peak temperature in the heated region increases. It reduces the yield strength and a larger amount of material undergoes the plastic deformation. This decreases the ratio of elastic deformation to the plastic deformation, and hence the percentage of spring-back angle increases with the increase in scan speed and beam diameter, and decreases with the increase in laser power.
Figure 8.26 to Figure 8.28 are plotted for the chosen process parameters for beam diameter of 3.87 mm. However, a full factorial study was carried out with the other two levels of beam diameters (viz., 5.81 mm and 7.74 mm) also. During this study, similar trends of were observed for medium and large beam diameters. These are reported in the Appendix 8.4.
8.8.4 Edge effect
Edge effect is a performance parameter which is quantified in terms of the relative variation in bend angle per unit length (RVBA) as given in Equation (4.29). The effect of pre-displacement on RVBA is discussed in detail in this section.
Figure 8.30. Effect of pre-displacement on edge effect at P=300 W and D=3.87 mm.
Figure 8.31. Effect of pre-displacement on edge effect at P=400 W and D=3.87 mm.
Figure 8.32. Effect of pre-displacement on edge effect at P=500 W and D=3.87 mm.
Figure 8.33. Effect of pre-displacement on edge effect at P=300 W and V=1000 mm/min.
Figure 8.30 to Figure 8.33 show the effect of pre-displacement on the edge effect. It can be seen that the edge effect is less when 5 mm pre-displacement is applied as compared to that obtained in the cases of no external mechanical load (pre-displacement=0 mm) and pre- displacement of 10 mm. It may be due to the fact that the applied pre-displacement is uniform along the irradiation line that tends to obtain uniform bending of the worksheet along the scanning line. However, due to elastic recovery, the required bend angle cannot be achieved.
The elastic recovery (spring-back) is not uniform along the scanning line. It is because when scanning starts, heated region is small, and hence the restriction to the pre-displacement is more. When the laser beam is about to leave the worksheet, the heated region is large, and therefore the mechanical constraint provided by the worksheet material is negligible. This non- uniform distribution of the temperature and the mechanical constraint provided by the