Interfacial Thermal Stresses in Trilayer Assemblies

Abstract

A two-dimensional model has been developed for the interfacial thermal stresses in short and long trilayer assemblies under both plane stress and plane strain conditions. Interfacial stresses are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Governing differential equations are linearized through a finite difference discretization procedure. The conditions of zero shear stress at the free edges and self-equilibrated peel stresses are satisfied. The approach is mathematically straightforward, can be extended to include inelastic behavior, and can be adapted to problems involving external loads and a variety of geometries. The results have been compared to available data in the literature and finite element analysis.

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

“…For instance, Mackerle (2002) gives a bibliography of 867 FEA papers in adhesive bonding, soldering, and brazing published in the period [1996][1997][1998][1999][2000][2001][2002]. Nevertheless, as shown by Glaser (1990), Basaran and Zhao (2001), Ghorbani and Spelt (2005), and many others, the predictions of elastic FEA are strongly mesh sensitive around the free corners of interlayers under thermal loading. This is a consequence of the underlying elasticity solutions which predict that peel stresses approach infinity at the free edges.…”

“…As mentioned above, the present 2D elasto-creep analytical model for trilayer assemblies extends an earlier elastic model for interfacial thermal stresses (Ghorbani and Spelt, 2005). The model is applicable to trilayers with any aspect ratio (i.e.…”

“…1016/j.ijsolstr.2006.02.003 Interfacial thermal stress and strain distributions in layered structures have been analyzed using three main approaches: two-dimensional elasticity solutions, finite element (FE) analysis, and elementary beam theory. Many references can be found in the recent papers of Shen and Suresh (1996), Suhir (2001), Wen and Basaran (2004), and Ghorbani and Spelt (2005).…”

“…It was assumed that stresses and strains varied only in the through-thickness direction (independent of longitudinal position), with the curvature being the same for all layers. This is an approximation since the radius of curvature is variable in both the longitudinal and transverse directions from one layer to another (Ghorbani and Spelt, 2005). Madras et al (1996), in an attempt to explain the permanent deformations observed experimentally in adhesively bonded optical coatings during thermal cycling, modeled the adhesive using a simple Maxwell (spring-dashpot) element with a temperature-dependent viscosity.…”

“…The present elasto-creep analysis is based on the structural mechanics model of Ghorbani and Spelt (2005) for the thermal stresses in long and short trilayer assemblies. This model satisfies all equilibrium and compatibility requirements using compliances defined through elasticity solutions for both plane stress and plane strain conditions.…”