## 2 Materials and Methods
### Experimental Principles and Equipment  
During the cold extrusion experiment, the compacted assembly of bushing and lug is tightened in a vise to prevent the movement of the lugs. The equipment section of the mandrel is clamped through the bushing on a fixed pulling device. The extrusion of the mandrel bushing-lug subassembly is achieved with the contraction of the mandrel by the pulling device, which results in the application of the load. After the cold extrusion experiments, the mandrel is dismantled in reverse installation order. Then, the residual stress test of the lugs can be carried out. Figure 2a is a schematic diagram of the measurement of residual stresses in lug plates using X-ray diffraction, and the coordinate system for the determination of the X-ray diffraction method is shown in Figure 2b, where \(2\theta\) is the diffraction angle, and \(\Psi\) is the azimuthal angle normal to the diffracted crystal plane. Figure 1: Cold expansion structure, finite element lug, and compression bushing model. **(a)** Schematic diagram of cold expansion strengthening. **(b)** Finite element model. In summary, determining residual stresses on the surface of lug plates using X-ray diffraction is a matter of determining the diffraction angle at different azimuths and calculating it separately. The sample of this study is a reinforced structure after the expansion of compression bushing and lug plates, in which the material of the compression bushing is PH13-8 Mo stainless steel and the material of the lug plates is TC4-DT titanium alloy. As the residual stress distribution of the reinforced structure of the compression bushing-lug plate, the stress state of the lug plate plays a decisive influence on the life of the entire reinforced structure, so this time, the main determination of the residual stress distribution is along the path of the TC4-DT titanium alloy lug plate. The modulus of elasticity of the TC4-DT titanium alloy lug plate is 109 GPa, and the Poisson's ratio is 0.34. In the preliminary pre-experiment and pre-simulation, as well as relevant references, it is known that the transition region between the rectangle and semicircle of the part is the region of maximum circumferential stress, so this region is selected for radial stress analysis. Moreover, the destruction of the bushing occurs first at the shaft end face, which is the location of the greatest axial stress. Figure 3a shows a schematic diagram of the location of the test point and the test direction of the sample. The stress measurement point was set as the direction of the extruded surface of the lug along the smallest cross-section in the figure. As to the residual stress in the thickness direction of the lug plate, it is usually determined by the geometrical requirement of the mechanical structure, which is lower than that at the shaft end face from the simulation results. Considering the experimental measurement and key issue of the application, the stress effect of the thickness direction is neglected in the simulation. The distances of the measurement points from the aperture wall of the lug plate were 0.5 mm, 1.5 mm, 2.5 mm, 3.5 mm, and 5.5 mm, respectively, and the radial and circumferential stresses were measured at each measurement point, as shown in Figure 3b. Figure 3c shows a sample of a lug plate of titanium alloy material determined in this study. The area to be determined was electrolytically polished to reduce the degree of influence of surface machining on the determination of cold expansion residual stresses. Figure 2: Principle of X-ray diffraction method for measuring residual stresses in lug plates. (**a**) Schematic diagram of the X-ray diffraction method for measuring residual stresses in a lug plate. (**b**) Determination of the coordinate system for the X-ray diffraction method. Currently, there are many techniques used for stress measurement, among which X-ray diffraction is the most used in high-precision measurement methods [32], so X-ray diffraction equipment was also chosen for this experiment.