Objective As the core technology which leads the future development direction of the manufacturing industry, laser additive manufacturing (LAM) of functionally gradient materials (FGMs) has attracted significant attention recently. This technology can achieve the gradient change of component composition, microstructure, and properties by adjusting the proportion of powder conveying and laser-forming process. TC4/TC11 gradient titanium alloy has broad application prospects in the manufacture of large and complex key titanium alloy components such as aircraft frame beams and engine blisks. However, because of the periodic, unsteady thermal cycling and the constrained rapid solidification of the moving molten pool in the additive manufacturing process, there is a high residual stress in the formed component. The nonuniformity of the composition of the gradient structure material further complicates the problem. Therefore, studying the temperature and stress fields in the LAM process is particularly important. In this study, the residual stress field of TC4/TC11 FGM fabricated via LAM was analyzed using the finite element method (FEM). The hemispherical heat source function and forced convection model were written in FORTRAN language and loaded into the model using DFLUX and FILM subroutines to achieve the thermal-mechanical coupling finite element analysis of the LAM process. This research has important reference significance for the measurement, control, and reasonable suppression of the residual stress in the additive manufacturing of FGM.
Methods The residual stress of TC4/TC11 FGM fabricated via LAM was investigated using FEM. First, the hemispherical heat source model was used as the loading function of the laser heat source. The basic theory and method of composite materials were used to calculate the density, elastic modulus, Poisson’s ratio, yield strength, coefficient of thermal expansion, and specific heat capacity of gradient materials. Second, in the actual modeling analysis, to save the computational cost, half of the model was taken for modeling and symmetry constraints were set on the symmetry plane. Considering the size of the model and computational efficiency, a double-precision grid was selected. The fine grid was set in and near the sedimentary area, while the grid was sparse and far away from the sedimentary area. Finally, the birth-death element technology was used to simulate the additive manufacturing process. The synchronous loading of the moving heat source was achieved by killing and activating the element. The standard thermal-mechanical coupling analysis method was used to calculate the final residual stress.
Results and Discussions Temperature and stress fields of the LAM process are calculated using FEM. The temperature distribution of each layer at different time is presented. The temperature of the laser action center is about 1600 ℃. The temperature distribution can approximately describe the situation of the molten pool. The temperature in the center of the molten pool is higher, and the temperature gradient is larger. In the region far away from the laser source, the temperature is lower and the distribution is flat (Fig. 2). The residual stress calculation results show that the residual stress mainly appears in the deposition area, the stress distribution in the middle area is uniform, the stress on the substrate is small, and there is a stress concentration effect at the junction of the substrate and sample. The residual stress along the laser scanning direction is larger than that in the other two directions. Most of the residual stress along the stacking direction is compressive stress; there is a small tensile stress around the specimen and substrate (Fig. 4). The maximum tensile and compressive stresses are 563 and -103 MPa, respectively, which appear in the transition mode Ⅲ. Results show that the stress discontinuity at the interface of the transition mode Ⅲ is obvious; the maximum stress jump value is 200 MPa. The stress distribution tends to be stable, and the stress jump value is smaller under the other two transition modes (Fig. 6).
Conclusions In this study, the thermal-mechanical coupling finite element model for residual stress analysis of LAM is established based on the hemispherical heat source model, birth-death element technology, and composite theory. The temperature field calculation results show that the temperature gradient in the laser region is large and the temperature distribution is small and flat in the region far away from the laser source. The results show that the variation in the temperature field under different transition modes is similar. The temperature peak value at the interface of the transition mode Ⅱ is relatively small, whereas that at the interface of the transition mode Ⅲ is relatively large. The residual stress in the LAM process is mainly tensile stress. The residual stress along the laser scanning direction is larger than that in the other two directions. The results show that the distribution of residual stress at the interface of the three transition modes is similar, and the distribution is with the inverted bowl shape. The tensile stress is larger in the middle and then decreases sharply toward both ends; the compressive stress is smaller at both ends. The distribution of residual stress at the interface of different material components is discontinuous. The stress near the side with high TC11 content is larger than that on the other side. The residual tensile stress increases with the increase in TC11 content.
