The transient thermal and residual stress in the metal-to-ceramic brazed joints were analyzed by using the modified linear two-dimensional finite element model. The solution domain possessing one element in the longitudinal direction was introduced to allow the change of the longitudinal total strain along the width and depth of the longitudinal total strain. To determine the longitudinal total strain, the compatibility equation, force and moment equilibrium equations were considered.
For the comparision of the simulation results, the residual stress in the brazed joints was measured by using the X-ray diffraction method. The results calculated by the FEM analysis showed a similar tendency as the results measured by the X-ray diffraction method.
The thermal and residual stresses which were induced mainly by the difference in the thermal expansion coefficients between the brazed materials were successively calculated. The high tensile residual stress occurred in the brazed joints interface which has a potential to cause internal cracks in the brazed joints. The effects of the design variables such as filler metal thickness, joint shape and specimen size were also investigated by using the modified linear model.
In order to reduce the tensile residual stress in the brazed joints, the two types of mechanical loading cycle were adopted during the brazing thermal cycle. And the effect of the mechanical loading times was also calculated. In the case of brazed joints with 0.1mm thick filler metal, the measured residual stress in the ceramic part after the mechanical loading cycle showed a lower tensile stress compared to that of the brazed joints without mechanical loading cycle. The larger the applied load was, the smaller was the tensile residual stress occurring in the metal-to-ceramic brazed joint. The calculation results revealed that the tensile residual stress in the brazed ceramics can be reduced by the mechanical loading cycle, and that the magnitude of the applied load and the temperature at which the mechanical loading cycle started greatly influence the reduction amount of the tensile residual stress. In the multi-loading condition, the type II loading condition showed more reduction effect of the tensile residual stress in the ceramic interface edge than that of the type I condition. But the difference of the mechanical loading type in single loading condition was not shown clearly.
To improve the analysis result by using the modified linear finite element model in metal-to-ceramic brazed joint, the modified multi-step two-dimensional model was adopted for determination of the longitudinal boundary condition. The longitudinal total strain in the modified multi-step model was separately calculated each brazed materials by considering the compatibility equation, force and moment equilibrium equation and displacement continuity conditions at the brazed interface such as metal/filler metal and filler metal/ceramic interface. The computed results were compared with those by the modified linear model and the XRD results. The calculation results revealed that the modified multi-step model could more reasonably describe the residual stress than the modified linear model.
