# Residual Stress in Laser Welding of TC4 Titanium Alloy Based on Ultrasonic laser Technology
## 3 Experimental Process
### Ultrasonic laser for Measurement of Residual Stress in Laser Welding
#### 3.2.3 Measurement of Residual Stress  
The residual stress during the laser welding of TC4 titanium alloy was measured using ultrasonic laser technology. The experimental program and the location of the measurement lines are shown in Figure 5, where \(M_{0}\) is the measurement point, and all the measurement points are arranged in the measuring line; \(N_{1}\) and \(N_{2}\) are the location of the excitation laser and detection laser, respectively; \(l_{0}\) is the measurement line (black line) arranged on the center axis of the specimen; and \(l_{1}\), \(l_{2}\) and \(l_{3}\) are the auxiliary lines (blue line). Notably, the stress at the measuring point is actually the average residual stress within the travel distance of the surface wave. Therefore, when there is a large stress gradient or stress concentration, the distance between the measurement points must be refined to improve the measuring accuracy. The transverse propagation velocity \(v_{x}\) was obtained using the same experimental program, and the residual stress of measurement point \(M_{0}\) was determined using Equations (1) and (2).  
Figure 6 shows the residual stress distribution of weld 1 with a welding power of 2800 W, welding speed of 6.0 m/min, and heat input of 28 kJ/m. Since the boundary conditions at both ends of the weld centerline were similar, a symmetric approach was assumed in the residual stress profile. It was  
Figure 4: The relationship between velocity ratio and tensile stress. The slopes of the linear fitting curve correspond to the acoustoelastic coefficients.  
Figure 5: (**a**) Experimental specimen and (**b**) layout of measuring line when measuring the velocity \(v_{y}\), where \(M_{0}\) is a measurement point; \(l_{0}\) is the measuring line; \(l_{1}\), \(l_{2}\), and \(l_{3}\) are the auxiliary lines; and \(N_{1}\) and \(N_{2}\) are the positions of the laser beam.  
reasonable to assume that data points at the same distance but at either sides of the centerline would have the same value of residual stress. These types of symmetric approaches were adopted in a number of research studies on welds [3,4]. The longitudinal residual stress was greater than the transverse residual stress. The longitudinal residual stress was high tensile stress near the welding seam, and the maximum values of longitudinal and transverse residual stresses were 297.7 MPa and 72.4 MPa near the HAZ, respectively. The longitudinal stress decreased rapidly with increasing distance from the weld centerline, passing through zero at a distance near to the weld centerline and leading to the balancing of the compressive stress at approximately \(-15.7\) MPa in the far field. The welding residual stress reached one-third of the yield strength of the material. If residual stress is superimposed with external forces, it easily exceeds the yield strength, resulting in plastic deformation and failure of the components. The longitudinal residual stresses measured by the hole-drilling method and ultrasonic laser method were basically the same. However, error and uncertainty in measurement are inevitable. For the hole-drilling technique, the stress uncertainty mainly depends on the absolute value of the strain. For the ultrasonic laser technique, the uncertainty mainly depends on the propagation velocity of the ultrasonic waves. Considering the maximum longitudinal residual stress, corresponding to the ultrasonic laser and hole-drilling techniques, the uncertainty of measurements were 1.2 MPa and 2.4 MPa, respectively.