WELDING RESEARCH Fig. 18 — Failure analysis of the BMF in the Type IV joint in the 1.0/1.0/1.0 mm stack. Fig. 19 — Effect of joint design on the failure mode transition. per constructs a model for predicting the failure mode for the Type IV joint. From the above discussion, it can be known that in the DIF failure of the Type IV joint, one interface fails through the LCGZ while the other interface fails through the interior of the weld nugget, i.e., through the EGZ. For simplification, the deformation and the work hardening of the weld nugget were ignored. The maximum shear stress at each interface is Accordingly, the failure load at the DIF mode can be expressed where EGZ is the shear strength of the equiaxed grain zone, and LCGZ is the shear strength of the columnar grain with a large secondary dendrite arm spacing. In order to determine the mathematical equation of the failure load for the BMF mode, Fig. 18 depicted the failure analysis of the BMF in the Type IV joint. LO is the length of overlapping, which is equal to the width of the workpiece W. The failure location around the weld nugget of the BMF mode was the PMZ as shown in Fig. 12. Thus, the failure load for the BMF mode can be expressed as Note that the thickness t in Equation 14 is the thickness of the middle sheet, which was not influenced by the indentation. Combining Equations 13 and 14, the following equation can be obtained The solution for Equation 15 is ������������ Applying the linear relationship between the strength and hardness, and the linear approximation between the shear strength and tensile strength, Equation 16 can be rewritten as Using W = 25 mm, t = 1 mm, f = 0.6, HPMZ = 65 Hv, HBM = 95 Hv, HEGZ = 60 Hv, and HLCGZ = 55 Hv, the critical nugget diameter of the Type IV joint is Although the predicted value is smaller than the experimental result (about 6.25 mm), based on the experimental results, when the button size was about 6 mm (the corresponding welding parameters were 20 kA and 200 ms), both the peak load and energy absorption of weld joints were similar to the weld joints that failed in BMF mode. Accordingly, the predicted result is also acceptable for the Type IV joint. For the Type I joint of the 1.5/1.0/2.0 mm stack, the failure location in the PO mode was the SCGZ. The average hardness of the SCGZ was 85 Hv. The increased hardness in the SCGZ maybe due to the hard norm of welding parameters. The failure location in the IF mode was the EGZ. The average hardness of the EGZ was 60 Hv. The average indentation was about 85% of the uppersheet i.e., the tIN was about 1.3 mm. The rotation angle was nearly zero when the joint failed in the IF mode, while it was about 2 deg when the joint failed in the PO mode. �� 3 ��EGZ + �� 3 ��LGGZ ������ ������ d2 + 1 2 t��BM �� �� 2 t��PMZ ������ ������ d �� W 2 t��BM + 3W 4 t��BM ������ ������ = 0 (15) FBMF = 3 2 W 2 t��BM + ��d 2 t��PMZ +W �� d 2 t��BM (14) (DC )Type IV = = 1 2 t��BM �� �� 2 t��PMZ + 1 2 t��BM �� �� 2 t��PMZ ������ ������ 2 + 4+ 3 ��EGZ + 4+ 3 ��LCGZ ������ ������ W 2 t��BM + 3W 4 t��BM ������ ������ 2+ 3 ��EGZ + 2+ 3 ��LCGZ (DC )Type IV = 3 4 (��tHPMZ ��tHBM ) + 3 2 1 2 tHBM �� �� 2 tHPMZ ������ ������ 2 + 4+ 3 fHEGZ + 4+ 3 fHLCGZ ������ ������ W 2 tHBM + 3W 4 tfHBM ������ ������ ��fHEGZ + ��fHLCGZ (DC )Type IV ��6.0 mm τSIMAX = 3F / 2 2A = 3F πd2 12 ( ) FDIF = πdID ( 2 ) 3 τLCGZ + πdID ( 2 ) 3 τEGZ (13) 488-s WELDING JOURNAL / DECEMBER 2016, VOL. 95 (16) (17)
Welding Journal | December 2016
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