Publications

Glasses are used extensively by the electronics industry for packaging and in components. Because glasses have such low fracture toughness, glass components must maintain low tensile stresses to avoid cracking and ensure product stability. Modeling is a key tool for developing designs with low tensile stresses. Thermoelastic analyses are ideal for modeling slow, oven controlled processes where the temperature varies uniformly. Many processing environments, however, involve rapid heating and cooling cycles that produce nonhomogeneous temperature fields causing the volume and stresses in the glass to relax at different rates. This structural relaxation is an important nonlinear material behavior that gives rise to a point-to-point variability in effective properties of the material. To accurately model such stresses, a thermal analysis must be coupled to a structural analysis that employs a viscoelastic model of glass. Laser sealing of glasses is an example of a process where thermal history is an important factor in determining the residual stress state. Recent needs to consider laser sealing methods for fiber optic connectors and flat panel displays have spurred the development of coupled, three-dimensional thermal and structural finite element codes. Analyses of the temperatures and stresses generated in a flat panel display during a laser sealing operation are presented, an the idiosyncrasies and importance of modeling coupled thermal/structural phenomena are discussed.

In the stereolithography process, three dimensional parts are built layer by layer using a laser to selectively cure slices of a photocurable resin, one on top of another. As the laser spot passes over the surface of the resin, the ensuing chemical reaction causes the resin to shrink and stiffen during solidification. When laser paths cross or when new layers are cured on top of existing layers, residual stresses are generated as the cure shrinkage of the freshly gelled resin is constrained by the adjoining previously-cured material. These internal stresses can cause curling in the compliant material. A capability for performing finite element analyses of the stereolithography process has been developed. Although no attempt has been made to incorporate all the physics of the process, a numerical platform suitable for such development has been established. A methodology and code architecture have been structured to allow finite elements to be birthed (activated) according to a prescribed order mimicking the procedure by which a laser is used to cure and build-up surface layers of resin to construct a three dimensional geometry. In its present form, the finite element code incorporates a simple phenomenological viscoelastic material model of solidification that is based on the shrinkage and relaxation observed following isolated, uncoupled laser exposures. The phenomenological material model has been used to analyze the curl in a simple cantilever beam and to make qualitative distinctions between two contrived build styles.

The use of glasses is widespread in making hermetic, insulating seals for many electronic components. Flat panel displays and fiber optic connectors are other products utilizing glass as a structural element. When glass is cooled from sealing temperatures, residual stresses are generated due to mismatches in thermal shrinkage created by the dissimilar material properties of the adjoining materials. Because glass is such a brittle material at room temperature, tensile residual stresses must be kept small to ensure durability and avoid cracking. Although production designs and the required manufacturing process development can be deduced empirically, this is an expensive and time consuming process that does not necessarily lead to an optimal design. Agile manufacturing demands that analyses be used to reduce development costs and schedules by providing insight and guiding the design process through the development cycle. To make these gains, however, viscoelastic models of glass must be available along with the right tool to use them. A viscoelastic model of glass can be used to simulate the stress and volume relaxation that occurs at elevated temperatures as the molecular structure of the glass seeks to equilibrate to the state of the supercooled liquid. The substance of the numerical treatment needed to support the implementation of the model in a 3-D finite element program is presented herein. An accurate second-order, central difference integrator is proposed for the constitutive equations, and numerical solutions are compared to those obtained with other integrators. Inherent convergence problems are reviewed and fixes are described. The resulting algorithms are generally applicable to the broad class of viscoelastic material models. First-order error estimates are used as a basis for developing a scheme for automatic time step controls, and several demonstration problems are presented to illustrate the performance of the methodology.

Compression seals are commonly used in electronic components. Because glass has such a low fracture toughness, tensile residual stresses must be kept low to avoid crackS. N. Burchett analyzed a variety of compression pin seals to identify mechanically optimal configurations when work hardened Alloy 52 conductor pins are sealed in a 304 stainless steel housing with a Kimble TM-9 glass insulator. Mechanical property tests on Alloy 52, have shown that the heat treatments encountered in a typical glass sealing cycle are capable of annealing the Alloy 52 pins, increasing ductility and lowering the yield strength. Since most seal analyses are routinely based on unannealed Alloy 52 properties, a limited study has been performed to determine the design impact of lowering the yield strength of the pins in a typical compression seal. Thermal residual stresses were computed in coaxial compression seals with annealed pins and the results then were used to reconstruct design guidelines following the procedures employed by Miller and Burchett. Annealing was found to significantly narrow the optimal design range (as defined by a dimensionless geometric parameter). The Miller-Burchett analyses which were based on very coarse finite element meshes and a 50 ksi yield strength fortuitously predicted an overly conservative design range that is a subset of the narrow design window prevalent when the yield strength is assumed to be 34 ksi. This may not remain true for lower yield strengths. The presence of pin wetting was shown to exacerbate the glass stress state. The time is right to develop a modern and enhanced set of design guidelines which could address new material systems, three dimensional geometries, and viscoelastic effects.

Glass-to-metal seals are an integral part of many electronic components. When seals are formed at elevated temperatures and cooled to room temperature, residual stresses are generated by the unequal thermal contractions of the constituent materials. The combination of high stress and low fracture resistance of glass makes it extremely difficult to design and build hermetic glass-to-metal seals. Rigorous and robust stress analyses must incorporate the complex and coupled changes in volumetric strain and stress relaxation which occur as glass passes through the liquid/solid temperature regime. The phenomenological behavior of glass can be modeled viscoelastically. The theory and numerical discretization of the viscoelastic equations is presented for use in finite element programs. Vectorizable integration schemes are derived for both the traditional hereditary integrals of viscoelasticity and the equivalent rate forms of the equations. The general behavior of glass is discussed and related to the viscoelastic model. Solutions to discretized viscoelastic equations are applied to an example problem and compared to results obtained from experimental data. The viscoelastic model of glass provides a new capability to analyze and design actual manufacturing processes by predicting, a priori, the effects of temperature history on the residual stress state.