The residual stress distribution in bimaterial beams induced by multiple thermal loadings has been investigated. Three models for the nonlinear stress-strain material behavior were considered: bilinear elastic-plastic, power law elastic-plastic, and power law purely plastic. The equations governing equilibrium, compatibility of strain, and stress-strain for the bimaterial configuration make up a system of nonlinear algebraic equations which is solved numerically. The elastic-plastic power law model leads to stress discontinuity in the layers. The other two models have been verified with a finite element analysis. Several examples are included using materials common to the microelectronics industry.

Issue Section:
Technical Papers
Topics:
Algebra, Equilibrium (Physics), Finite element analysis, Microelectronic devices, Stress, Stress analysis (Engineering), Stress concentration, Strips
1.
ANSYS User’s Manual for Revision 5.0, 1993, Swanson Analysis Systems, Inc.
2.
Burden, R. L., and Faires, J. D., 1989, Numerical Analysis, PWS-Kent Publishing Co., Boston, MA, pp. 536–539.
3.
Chen, W. F., and Zhang, H., 1991, Structural Plasticity: Theory, Problems, and CAE software, Springer-Verlag Inc., pp. 7–14.
4.
Cifuentes
A. O.
,
1991
, “
Elastoplastic Analysis of Bimaterial Beams Subjected to Thermal Loads
,”
ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol.
113
, pp.
355
–
358
.
5.
Eischen, J. W., and Reagan, S. W., 1993, “Elastic Plastic Analysis of Bimaterial Beams With Strain Hardening,” Proceedings of the 10th Biennial Conference on Reliability, Stress Analysis, and Failure Prevention, DE-Volume 55, The American Society of Mechanical Engineers, pp. 289–296.
6.
Ramberg, W., and Osgood, W. R., 1943, “Description of Stress-Strain Curves by Three Parameters,” Technical Note No. 902, National Advisory Committee for Aeronautics (NACA).
7.
Stoltz, R. E., and Pelloux, R. M., 1977, “The Bauschinger Effect, Monotonic and Cyclic Hardening in Precipitation-Strengthened Aluminum Alloys,” Work Hardening in Tension and Fatigue (Proceedings), Mechanical Metallurgy Committee, pp. 224–239.
8.
Suhir
E.
,
1988
, “
An Approximate Analysis of Stresses in Multilayered Elastic Thin Films
,”
ASME Journal of Applied Mechanics
, Vol.
55
, pp.
143
–
148
.
9.
Sze, S. M., 1988, VLSI Technology, McGraw-Hill Book Co., NY, p. 385.
10.
Tierney, J. W., 1995, “Residual Stress Analysis of Bimaterial Strips Under Multiple Thermal Loading,” M.S. thesis, North Carolina State University at Raleigh, NC.
11.
Timoshenko
S.
,
1925
, “
Analysis of Bi-Metal Thermostats
,”
Journal of the Optical Society of America
, Vol.
11
, pp.
233
–
255
.
12.
Ugural, A. C., and Fenster, S. K., 1987, Advanced Strength and Applied Elasticity, Elsevier Science Publishing Co. Inc., NY, pp. 69–71.
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