Guidelines for predicting stress in cemented doublets undergoing temperature change: theory, practice, and data

Abstract

This work explores quick predictive methods for calculating potentially risky stresses and deflections in cemented doublets experiencing temperature change that agree well with finite element analysis. There are three failure modes of interest: cohesive failure of the adhesive, delamination (surface bond failure or debonding), and glass fracture. Adhesive theory, confirmed by finite element analysis, predicts stress singularities that complicate interpretation of the stress calculations. The presence of a stress singularity indicates the breakdown of linear elastic assumptions, but damage initiation and stress singularities are related. The authors find that geometry details near a bond edge can exacerbate or minimize damage initiation and stress concentrations. Because the interpretation of the stress results is complicated, the authors investigated predicted stresses in doublets that have been successfully tested between −40°C and 85°C. This study found that the thermal strain ðΔT • ΔαÞ should be less than 189 ppm, where ΔT is the temperature excursion and Δα is the difference in the two glass coefficients of thermal expansion. If the thermal strain is equal to or greater than 189 ppm, further analysis and testing is warranted. But the authors also show that the fabrication process can significantly influence stress failure, particularly with large diameter doublets.