Finite Element Thermal/Mechanical Analysis of Transmission Laser Microjoining of Titanium and Polyimide

Detailed analysis of a residual stress profile due to laser microjoining of two dissimilar biocompatible materials, polyimide (PI) and titanium (Ti), is vital for the long-term application of bio-implants. In this work, a comprehensive three-dimensional (3D) transient model for sequentially coupled thermal/mechanical analysis of transmission laser (laser beam with wavelength of 1100 nm and diameter of 0.2 mm) microjoining of two dissimilar materials has been developed by using the finite element code ABAQUS, along with a moving Gaussian laser heat source. First the model has been used to optimize the laser parameters like laser traveling speed and power to obtain good bonding (burnout temperature of $PI>maximum$ temperature of PI achieved during $heating>melting$ temperature of PI) and a good combination has been found to be 100 mm/min and 3.14 W for a joint-length of 6.5 mm as supported by the experiment. The developed computational model has been observed to generate a bonding zone that is similar in width (0.33 mm) to the bond width of the Ti/PI joint observed experimentally by an optical microscope. The maximum temperatures measured at three locations by thermocouples have also been found to be similar to those observed computationally. After these verifications, the residual stress profile of the laser microjoint (100 mm/min and 3.14 W) has been calculated using the developed model with the system cooling down to room temperature. The residual stress profiles on the PI surface have shown low value near the centerline of the laser travel, increased to higher values at about $165μm$ from the centerline symmetrically at both sides, and to the contrary, have shown higher values near the centerline on the Ti surface. Maximum residual stresses on both the Ti and PI surfaces are obtained at the end of laser travel, and are in the orders of the yield stresses of the respective materials. It has been explained that the patterned accumulation of residual stresses is due to the thermal expansion and contraction mismatches between the dissimilar materials at the opposite sides of the bond along with the melting and softening of PI during the joining process.