In order to deeply investigate the tensile properties and fracture behaviors that are obtained by tensile tests of welded joints, constitutive and damage models are imperative for analyzing the tensile behaviors. In this work, the tensile tests are conducted on the T-welded joint specimens of aluminum alloy 6061-T6, which were cut from the T-welded joints of thin-walled parts under different welding currents of Tungsten Inert Gas Welding (TIGW). A modified Johnson-Cook (J-C) model based on the original J-C equation, Swift model, Voce model, and Hockett-Sherby (H-S) model, their linear combination model, and fracture failure model are constructed and applied to simulate tensile behaviors, combined with tensile test data. What is more, the finite element (FE) simulation of tension tests is executed with the VUMAT and VUSDFLD subroutines. Compared to those results simulated with different fracture criteria and tensile experiments, the tensile strength and yield strength of T-welded joint thin-walled parts under different welding currents were achieved, and their best mean errors were only about 1%. Furthermore, the accuracy of different fracture criteria is also evaluated by the correlation coefficient and mean squared error. The results show that the combination model can accurately predict the tensile properties and fracture behaviors of T-welded joints better than the single model, especially the results simulated with the Swift-H-S model and H-S-Voce model, which are in good agreement with tensile test results, which will provide an analysis foundation for enhancing the welding assembly quality and preventing fracture failure for complex thin-walled antenna structures.