Electro-optical devices often include glass-to-metal interfaces with materials having different coefficients of thermal expansion. Typically, such parts are processed at elevated temperatures; at room temperature, significant thermo-mechanical stress may arise, which can lead to leaking, cracking, or other failures that degrade performance.
Engineers building electro-optical systems face the challenge of measuring stress at these interfaces, typically using optical birefringence. Birefringent materials feature two orthogonal optical axes with distinct refractive indices. Light polarized parallel to one axis travels at a different speed through the sample than light polarized parallel to the orthogonal axis. As a result, these two light components, which were in phase when they entered the sample, exit the sample out of phase. We can use this phase retardance to determine the mechanical stress with:
where σ is stress in kg/mm2, R is retardance in nm, t is thickness in cm, and C is the stress-optic constant in (nm/cm)/(Kg/mm2). This conversion to mechanical stress is valid if we can assume uniform stress along the light path. This is usually the case if the thickness along the light path is small relative to the dimensions orthogonal to the light path.
Conventional approaches to measuring retardance use polarized light microscopes equipped with manually adjusted compensators that allow measurement of stress at single points in the field of view. Adjusting a compensator until the point of interest in the field of view is compensated to zero, then reading the compensator dial, provides a measure of the birefringence retardance at that point.
This process is rather slow and labor intensive when surveying a part to find stress concentrations, however. Often, engineers are interested in quickly understanding the distribution of stress around a particular trouble area to help guide design for higher durability. Beyond knowing where stress concentrations are, it is vital to know the actual stress levels to gauge margins from yield points.
The retardance pattern in the glass surrounding a wire electrode, imaged with a liquid-crystal-based system, shows a high degree of stress at interface; a pseudo color look-up table provides convenient discrimination of stress levels (top). A vector overlay of a grayscale birefringence image indicates birefringence axis orientation (bottom); these vectors indicate radial compression and/or circumferential tension.
New methods use electro-optic devices and PC-based digital imaging to automatically measure distributions of birefringence retardance. Methods include raster-scanned laser beams with electro-optic modulators, motorized rotating wave plates and polarizers, and the use of liquid-crystal compensators with CCD-based imaging. These systems also measure the orientation of retardance, which can be used to determine direction of stress. We can study the retardance distribution around a glass-to-metal interface, such as a conductor in glass (see figure).
A common expectation is that a retardance image can be converted directly to a map of stress using the equation given above; however, conversion of retardance values to stress values can be complicated because measured retardance relates to the difference between the stresses in orthogonal directions, not the absolute stresses. Isotropic stress, for example, does not produce retardance, regardless of stress levels. Determining actual stress levels in some cases requires analytical techniques or finite element analysis using boundary conditions to determine stresses in the middle of a sample.
Fortunately, there are simple and basic rules that allow the use of the equation above with certain sample geometries to relate retardance to the actual stress. This is the case with the sample in the figure because the signs of the stresses in orthogonal directions are reversed. Also, there may be locations on a sample at which stress is known to be zero or low in one direction, such as along an unconstrained edge. As long as we keep these considerations in mind, retardance mapping is a powerful tool for analyzing mechanical stress in glass and optimizing designs for higher performance and durability. oe
Clifford Hoyt is co-founder and chief technology officer at CRi Inc., Woburn, MA.