To analyze the stresses and strains generated during the solidification of glass-forming materials, stress and volume relaxation must be predicted accurately. Although the modeling attributes required to depict physical aging in organic glassy thermosets strongly resemble the structural relaxation in inorganic glasses, the historical modeling approaches have been distinctly different. To determine whether a common constitutive framework can be applied to both classes of materials, the nonlinear viscoelastic simplified potential energy clock (SPEC) model, developed originally for glassy thermosets, was calibrated for the Schott 8061 inorganic glass and used to analyze a number of tests. A practical methodology for material characterization and model calibration is discussed, and the structural relaxation mechanism is interpreted in the context of SPEC model constitutive equations. SPEC predictions compared to inorganic glass data collected from thermal strain measurements and creep tests demonstrate the ability to achieve engineering accuracy and make the SPEC model feasible for engineering applications involving a much broader class of glassy materials.
Glass forming materials like polymers exhibit a variety of complex, nonlinear, time-dependent relaxations in volume, enthalpy and stress, all of which affect material performance and aging. Durable product designs rely on the capability to predict accurately how these materials will respond to mechanical loading and temperature regimes over prolonged exposures to operating environments. This cannot be achieved by developing a constitutive framework to fit only one or two types of experiments. Rather, it requires a constitutive formalism that is quantitatively predictive to engineering accuracy for the broad range of observed relaxation behaviors. Moreover, all engineering analyses must be performed from a single set of material model parameters. The rigorous nonlinear viscoelastic Potential Energy Clock (PEC) model and its engineering phenomenological equivalent, the Simplified Potential Energy Clock (SPEC) model, were developed to fulfill such roles and have been applied successfully to thermoplastics and filled and unfilled thermosets. Recent work has provided an opportunity to assess the performance of the SPEC model in predicting the viscoelastic behavior of an inorganic sealing glass. This presentation will overview the history of PEC and SPEC and describe the material characterization, model calibration and validation associated with the high Tg (~460 °C) sealing glass.
The degradation in the strength of napkin-ring (NR) joints bonded with an epoxy thermoset is evaluated in a humid environment. While adherend composition (stainless steel and aluminum) and surface preparation (polished, grit blasted, primed, coupling agent coated) do not affect virgin (time=0) joint strength, they can significantly affect the role of moisture on the strength of the joint. Adherend surface abrasion and corrosion processes are found to be key factors in determining the reliability of joint strength in humid environments. In cases where surface specific joint strength degradation processes are not active, decreases in joint strength can be accounted for by the glass transition temperature, Tg, depression of the adhesive associated with water sorption. Under these conditions, joint strength can be rejuvenated to virgin strength by drying. In addition, the decrease in joint strength associated with water sorption can be predicted by the Simplified Potential Energy Clock (SPEC) model by shifting the adhesive reference temperature, Tref, by the same amount as the Tg depression. When surface specific degradation mechanisms are active, they can reduce joint strength below that associated with adhesive Tg depression, and joint strength is not recoverable by drying. A critical relative humidity (or, potentially, critical water sorption concentration), below which the surface specific degradation does not occur, appears to exist for the polished stainless steel joints.
The thermal-mechanical properties of three potential underfill candidate materials for PBGA applications are characterized and reported. Two of the materials are a formulations developed at Sandia for underfill applications while the third is a commercial product that utilizes a snap-cure chemistry to drastically reduce cure time. Viscoelastic models were calibrated and fit using the property data collected for one of the Sandia formulated materials. Along with the thermal-mechanical analyses performed, a series of simple bi-material strip tests were conducted to comparatively analyze the relative effects of cure and thermal shrinkage amongst the materials under consideration. Finally, current knowledge gaps as well as questions arising from the present study are identified and a path forward presented.
Cracks in glass-to-metal seals can be a threat to the hermeticity of isolated electronic components. Design and manufacturing of the materials and processes can be tailored to minimize the residual stresses responsible for cracking. However, this requires high fidelity material modeling accounting for the plastic strains in the metals, mismatched thermal shrinkage and property changes experienced as the glass solidifies during cooling of the assembly in manufacturing. Small plastic strains of just a few percent are typical during processing of glass-to-metal seals and yet can generate substantial tensile stresses in the glass during elastic unloading in thermal cycling. Therefore, experimental methods were developed to obtain very accurate measurements of strain near and just beyond the proportional limit. Small strain tensile characterization experiments were conducted with varying levels and rates of strain ratcheting over the temperatures range of -50 to 550 °C, with particular attention near the glass transition temperature of 500 °C. Additional experiments were designed to quantify the effects of stress relaxation and reloading. The experimental techniques developed and resulting data will be presented. Details of constitutive modeling efforts and glass material experiments and modeling can be found in Chambers et al. (Characterization & modeling of materials in glass-to-metal seals: Part I. SAND14-0192. Sandia National Laboratories, January 2014).
The material characterization tests conducted on 304L VAR stainless steel and Schott 8061 glass have provided higher fidelity data for calibration of material models used in Glass - To - Metal (GTM) seal analyses. Specifically, a Thermo - Multi - Linear Elastic Plastic (thermo - MLEP) material model has be endefined for S S304L and the Simplified Potential Energy Clock nonlinear viscoelastic model has been calibrated for the S8061 glass. To assess the accuracy of finite element stress analyses of GTM seals, a suite of tests are proposed to provide data for comparison to model predictions.
To support higher fidelity modeling of residual stresses in glass-to-metal (GTM) seals and to demonstrate the accuracy of finite element analysis predictions, characterization and validation data have been collected for Sandia’s commonly used compression seal materials. The temperature dependence of the storage moduli, the shear relaxation modulus master curve and structural relaxation of the Schott 8061 glass were measured and stress-strain curves were generated for SS304L VAR in small strain regimes typical of GTM seal applications spanning temperatures from 20 to 500 C. Material models were calibrated and finite element predictions are being compared to measured data to assess the accuracy of predictions.
Decisions on material selections for electronics packaging can be quite complicated by the need to balance the criteria to withstand severe impacts yet survive deep thermal cycles intact. Many times, material choices are based on historical precedence perhaps ignorant of whether those initial choices were carefully investigated or whether the requirements on the new component match those of previous units. The goal of this program focuses on developing both increased intuition for generic packaging guidelines and computational methodologies for optimizing packaging in specific components. Initial efforts centered on characterization of classes of materials common to packaging strategies and computational analyses of stresses generated during thermal cycling to identify strengths and weaknesses of various material choices. Future studies will analyze the same example problems incorporating the effects of curing stresses as needed and analyzing dynamic loadings to compare trends with the quasi-static conclusions.
Polymers and fiber-reinforced polymer matrix composites play an important role in many Defense Program applications. Recently an advanced nonlinear viscoelastic model for polymers has been developed and incorporated into ADAGIO, Sandia's SIERRA-based quasi-static analysis code. Standard linear elastic shell and continuum models for fiber-reinforced polymer-matrix composites have also been added to ADAGIO. This report details the use of these models for advanced adhesive joint and composites simulations carried out as part of an Advanced Simulation and Computing Advanced Deployment (ASC AD) project. More specifically, the thermo-mechanical response of an adhesive joint when loaded during repeated thermal cycling is simulated, the response of some composite rings under internal pressurization is calculated, and the performance of a composite container subjected to internal pressurization, thermal loading, and distributed mechanical loading is determined. Finally, general comparisons between the continuum and shell element approaches for modeling composites using ADAGIO are given.
Polymer stresses around sharp corners and in constrained geometries of encapsulated components can generate cracks leading to system failures. Often, analysts use maximum stresses as a qualitative indicator for evaluating the strength of encapsulated component designs. Although this approach has been useful for making relative comparisons screening prospective design changes, it has not been tied quantitatively to failure. Accurate failure models are needed for analyses to predict whether encapsulated components meet life cycle requirements. With Sandia's recently developed nonlinear viscoelastic polymer models, it has been possible to examine more accurately the local stress-strain distributions in zones of likely failure initiation looking for physically based failure mechanisms and continuum metrics that correlate with the cohesive failure event. This study has identified significant differences between rubbery and glassy failure mechanisms that suggest reasonable alternatives for cohesive failure criteria and metrics. Rubbery failure seems best characterized by the mechanisms of finite extensibility and appears to correlate with maximum strain predictions. Glassy failure, however, seems driven by cavitation and correlates with the maximum hydrostatic tension. Using these metrics, two three-point bending geometries were tested and analyzed under variable loading rates, different temperatures and comparable mesh resolution (i.e., accuracy) to make quantitative failure predictions. The resulting predictions and observations agreed well suggesting the need for additional research. In a separate, additional study, the asymptotically singular stress state found at the tip of a rigid, square inclusion embedded within a thin, linear elastic disk was determined for uniform cooling. The singular stress field is characterized by a single stress intensity factor K{sub a} and the applicable K{sub a} calibration relationship has been determined for both fully bonded and unbended inclusions. A lack of interfacial bonding has a profound effect on inclusion-tip stress fields. A large radial compressive stress is generated in front of the inclusion-tip when the inclusion is well bonded, whereas a large tensile hoop stress is generated when the inclusion is unbended, and frictionless sliding is allowed. Consequently, an epoxy disk containing an unbended inclusion appears more likely to crack when cooled than a disk containing a fully bonded inclusion. A limited number of tests have been carried out to determine if encapsulant cracking can be induced by cooling a specimen fabricated by molding a square, steel insert within a thin, epoxy disk. Test results are in qualitative agreement with analysis. Cracks developed only in disks with mold-released inserts, and the tendency for cracking increased with inclusion size.
Viscoelastic materials are often characterized in terms of stress relaxation moduli which decay in time. Finite element programs which model viscoelastic materials frequently require that these relaxation functions be defined as an exponential series (i.e., Prony Series) to exploit the numerical advantages of developing recursive equations for evaluating hereditary integrals. Obtaining these data fits can be extremely difficult when the data is spread over many decades in the logarithm of time. RELFIT is a nonlinear optimization program that iteratively determines the Prony series coefficients and relaxation times so as to minimize the least squares error in the data fit. An overview of the code, a description of the required inputs (i.e., users`s instructions), and a demonstration problem are presented.
Experimental work conducted by D. B. Adolf has shown that a separable K-BKZ constitutive equation works reasonable well in predicting the stress relaxation observed in single step strain experiments for carbon black filled rubber. However, the memory requirements and numerical efficiency of the K-BKZ equation do not make it well suited for use in a production, three-dimensional finite element code. As an alternative, D. J. Segalman, K. Zuo, and D. Parsons have developed a "damage-like" constitutive equation which is computationally attractive. This formalism has been installed in the JAS3D finite element code. The requisite code inputs and numerical details of the constitutive integration are discussed, and solutions to selected problems are presented. Comparisons are made to data collected from both single and double step strain experiments.
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.