| dc.description.abstract | High concentrations of interfacial stress near the adherend ends are primarily
responsible for the debonding failure of bonded joints, such as those structured extensively
in civil and structural engineering; aeronautical, ground, and marine vehicles; and flexible
electronics and microelectronic packaging. Accurate determination of these interfacial
stresses is crucial to improved structural design and optimization as well as health
monitoring of the structures in which such joints are found. A variety of joint models have
been available in the literature for joint strength analysis and structural design. Yet, a few
deficiencies still exist in most of these models in accurate prediction of joint stresses,
including the violation of the generalized Hooke's law of the adhesive layers and failure to
satisfy the physical traction conditions at the free edges of joint adherends.
In this thesis, a generalized stress-function variational method is developed for the
determination of the interfacial shear and normal stresses in general bonded bimaterial
joints subjected to mechanical and thermomechanical loads. Specifically, three types of
joints are considered in this study, including single-sided bonded joints, single-sided strap
joints, and single-lap joints. During the formulation, two unknown interfacial stress
functions are directly introduced to satisfy the traction boundary conditions of the joints;
the Euler-Bernoulli elementary beam theory and 2D elasticity are used to determine the
stress components of the adherends in terms of the interfacial stress functions. By utilizing the theorem of minimum complementary strain energy, the governing equations of the
bimaterial joint are obtained as a system of two coupled 4th-order ordinary differential
equations (ODEs) of the introduced stress functions. These ODEs are formatted into a
generalized eigenvalue problem, and are further solved numerically by designing robust
and efficient computational codes using MATLAB™. The results of the analysis are
validated by comparison with elementary mechanics of materials as well as detailed finite
element analysis (FEA) using ANSYS™; the current models can accurately satisfy the
shear stress-free boundary conditions at the adherend edges.
In addition, the proposed method is further applied to the analysis of progressive
cracking in hard coatings. In this analysis, a cracked hard coating layer bonded onto a
substrate is modeled as a single-sided bonded joint, and the expressions of strain energy
derived in this study are incorporated into energy-based cracking criteria of the system.
Using the above variational method, the critical loads (i.e., applied axial stress, shear force,
bending moment, or temperature change) for initial cracking can be determined. Thus, the
present method is also capable of modeling progressive cracking in hard coating systems. | en_US |
