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 $165 μm$ 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.

1.
Steen
,
W. M.
,
Dowden
,
J.
,
Davis
,
M.
, and
,
P.
, 1988, “
A Point and Line Source Model of Laser Keyhole Welding
,”
J. Phys. D
0022-3727,
21
, pp.
1255
1260
.
2.
Mazumder
,
J.
, and
Steen
,
W. M.
, 1980, “
Heat Transfer Model for CW Laser Material Processing
,”
J. Appl. Phys.
0021-8979,
51
, pp.
941
947
.
3.
Goldak
,
J.
, 1990, “
Keynote Address: Modeling Thermal Stresses and Distortions in Welds
,”
Recent Trends in Welding Science and Technology
,
ASM
,
Metals Park, OH
.
4.
Mahmood
,
T.
,
Mian
,
A.
,
Amin
,
M.
,
Auner
,
G.
,
Witte
,
R.
,
Herfurth
,
H.
, and
Newaz
,
G.
, 2007, “
Finite Element Modeling of Transmission Laser Microjoining Process
,”
J. Mater. Process. Technol.
0924-0136,
186
(
1–3
), pp.
37
44
.
5.
Xing
,
W.
,
Chenglin
,
P.
,
Zhiqiang
,
Z.
,
Xiaogang
,
L.
,
Ning
,
H.
, and
Huiquan
,
Z.
, 2005, “
Research Progress of Subretinal Implant Based on Electronic Stimulation
,”
Proceedings of the 27th IEEE Engineering in Medicine and Biology Annual Conference
, Shanghai, China, pp.
1289
1292
.
6.
Georgiev
,
D. G.
,
Baird
,
R. J.
,
Newaz
,
G.
,
Auner
,
G.
,
Herfurth
,
H.
, and
Witte
,
R.
, 2004, “
An XPS Study of Laser-Fabricated Polyimide/Titanium Interface
,”
Appl. Surf. Sci.
0169-4332,
236
(
1–4
), pp.
71
76
.
7.
Burgener
,
M. L.
, and
Reedy
,
R. E.
, 1982, “
Temperature Distributions Produced in a Two Layer Structure by a Scanning CW Laser or Electron Beam
,”
J. Appl. Phys.
0021-8979,
53
, pp.
4357
4363
.
8.
Habbitt, Karlesson and Sorensen, Inc.
, 2004, ABAQUS version 6.5 User’s Manual and Documentations.
9.
Cook
,
R.
,
Malkus
,
D.
,
Plesha
,
M.
, and
Witt
,
R.
, 2004,
Concepts and Applications of Finite Element Analysis
, 4th ed.,
Wiley
,
New York
.
10.
Zienkiwicz
,
O. C.
, and
Taylor
,
R. L.
, 1991,
The Finite Element Method
,
McGraw-Hill
,
New York
, Chap. 5.
11.
Labudovic
,
M.
, and
Burka
,
M.
, 2003, “
Heat Transfer and Residual Stress Modeling of a Diamond Film Heat Sink for High Power Laser Diodes
,”
IEEE Trans. Compon. Packag. Technol.
1521-3331,
26
(
3
), pp.
575
581
.
12.
Monteiro
,
S. N.
, and
Reed-Hill
,
R. E.
, 1973, “
An Empirical Analysis of Titanium Stress-Strain Curves
,”
Metall. Mater. Trans. B
1073-5615,
4
(
4
), pp.
1011
1015
.
13.
Kuo
,
C. T.
,
Yip
,
M. C.
,
Chiang
,
K. N.
, and
Tsou
,
C.
, 2005, “
Characterization Study of Time- and Temperature-Dependent Mechanical Behavior of Polyimide Materials in Electronics Packaging Applications
,”
J. Electron. Mater.
0361-5235,
34
(
3
), pp.
272
281
.
14.
Yovanovich
,
M. M.
, 2005, “
Four Decades of Research on Thermal Contact, Gap, and Joint Resistance in Microelectronics
,”
IEEE Trans. Compon. Packag. Technol.
1521-3331,
28
(
2
), pp.
182
206
.
15.
Sultana
,
T.
, 2007, “
Bond Quality and Failure Mode Assessment for Polymer-Metal and Polymer-Glass Transmission Laser Joints
,” Ph.D. thesis, Wayne State University, Detroit, MI.