Edge Stresses in a Composite Strip Subjected to Axial Temperature Gradients Part II: Evaluation of Numerical Results

Abstract

In Part I of this paper, a combination of Airy stress functions and direct displacement functions was utilized to obtain the plane elasticity solution for the stresses and displacements in a multilayer laminated orthotropic strip subjected to a temperature gradient that is arbitrarily symmetric in the longitudinal direction. The solution is exact for the specific boundary conditions associated with satisfaction of zero slope of transverse displacement at the strip ends and shear traction free edges at the strip ends.

In Part II of this paper, numerical results are presented for several examples and compared to detailed finite element analyses for approximate zero edge slope and free edge boundary conditions. The results indicate the shear and peel stress concentrations and axial stress distributions for the boundary condition are in excellent agreement with the finite element analysis results for the zero edge slope case and correlate with the free edge boundary condition over a broad range of temperature gradient cases. This correlation with the free edge numerical analysis indicates the theoretical approach is feasible as a conceptual design tool for a reasonable range of free edge engineering problems.

Get full access to this article

View all access options for this article.

References

1. Eischen, J. W. , C. Chung and J. H. Kim . 1990. "Realistic Modeling of Edge Stresses in Bimaterial Elements," ASME Journal of Electronic Packaging, 112:16-23.

2. Mirman, I. B. 1991. "Effects of Peeling Stresses in Bimaterial Assembly," ASME Journal of Electronic Packaging, 113:431.

3. Swett, D. W. and G. R. Shiffett . 1997. "Edge Stresses in a Laminated Elastic Strip Subjected to Axial Temperature Gradients, Part II: Evaluation of Numerical Results," ASME Journal of Electronic Packaging, March 1997.

4. Wang, A. S. D. and F. W. Crossman . 1977. "Edge Effects on Thermally Induced Stresses in Composite Laminates," Journal of Composite Materials, 11:300-312.

5. Wolfram, S. 1990. Mathematica: A System for Doing Mathematics by Computer, 2nd edition, Addison-Wesley, Redwood City, CA.

6. Yin, W.-L. 1991. "Thermal Stresses and Free-Edge Effects in Laminated Beams: A Variational Approach Using Stress Functions," ASME Journal of Electronic Packaging, 113:68-75.

7. Yin, W.-L. 1992. "Refined Variational Solutions of the Interfacial Thermal Stresses in a Laminated Beam," ASME Journal of Electronic Packaging, 114:193-198.

8. Yin, W.-L. 1993. "Thermal Stresses in Anisotropic Multilayered Structures," in Thermal Stress and Strain in Microelectronics Packaging, J. H. Lau, ed ., Van Nostrand Reinhold, New York, pp. 95-138.