2-D Modeling of Moisture and Heat Diffusion in Adhesively Bonded Joints

In this dissertation research, a novel two-dimensional model is proposed for adhesively-bonded Single Lap Joints (SLJ) under combined mechanical loads and moisture/heat diffusion. Governing partial differential equations of the constitutive stress-diffusion model are formulated and solved numerically. Various scenarios for individual and combined diffusion of moisture and heat through the joint substrates and directly into the adhesive layer are analyzed. The resulting location-dependent material model is fed into the governing partial differential equations. Shear and peel stresses in the adhesive layer are investigated. Results are presented, with a focus on the improvements brought by the capability of the proposed model to predict the effects of diffusive patterns that are perpendicular to the axial tensile-shear load.Moisture diffusion across the joint width is found to have a significant effect on the shear stress distribution for structural epoxy adhesives with high elastic modulus. Numerical comparison with a linear Finite Elements Analysis is provided. Material properties are derived from experimental testing of commercially available two-component epoxy and polyurethane adhesives. This document is organized as follows: Chapter One "Introduction and Literature Review" includes a description of the analytical, numerical, and experimental work that serves as foundation for this dissertation. A previous one-dimensional analytical model is revised, and the motivations driving this research effort are illustrated. Chapter Two "Modeling of Heat and Moisture Diffusion" lays the groundwork for the analysis of diffusive patterns in the joint substrates and in the adhesive layer. Multiple scenarios of moisture and heat diffusion are explored, and their effect on the elastic properties of the adhesive is investigated. Governing partial differential equations are derived, and solution strategies are discussed. Chapter Three "Elastic Model" includes the formulation of coupled stress-diffusion partial differential equations for the shear and peel stresses in the adhesive layer, resulting from the application of an external tensile-shear load on the two adherends. Equilibrium considerations, stress-strain, and strain-displacement relationships are used to generate the constitutive equations, with adequate assumptions and simplifications. Chapter Four "Elastic Modulus of Structural Adhesives: Relationship to Bulk Material Temperature" contains the experimental procedure and results for the bulk adhesive tests. The elastic moduli of two-component epoxy and polyurethane adhesives are measured using a DMA Q800, and a linear law relating temperature to material properties is inferred. Chapters Five, Six, and Seven present the results of the shear and peel stress models for adhesive joints subjected to two-dimensional moisture-only, heat-only, and combined moisture/heat diffusion, respectively. A convergence study is performed on the two-dimensional solution to the heat equation governing moisture and heat diffusion in the adhesive layer. Stress gradients along the length and width of the bondline are analyzed, and the results are compared to the previous one-dimensional coupled stress-diffusion model. The results of the two-dimensional model are compared with a Finite Elements Analysis in Chapter Eight "FEA Comparison". Chapter Nine "Conclusions and Future Work" summarizes the major findings of this dissertation research, and outlines the potential for future work.