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The purpose of this project is to develop multi-layered co-extrusion (MLCE) capabilities at Sandia National Laboratories to produce multifunctional polymeric structures. Multi-layered structures containing layers of alternating electrical, mechanical, optical, or structural properties can be applied to a variety of potential applications including energy storage, optics, sensors, mechanical, and barrier applications relevant to the internal and external community. To obtain the desired properties, fillers must be added to the polymer materials that are much smaller than the end layer thickness. We developed two filled polymer systems, one for conductive layers and one for dielectric layers and demonstrated the potential for using MLCE to manufacture capacitors. We also developed numerical models to help determine the material and processing parameters that impact processing and layer stability.

The explicitly elliptic momentum equation (EEME) of King et al. is applied with adaptive mesh refinement and a mixed Galerkin finite-element method for two model problems: planar and axisymmetric sudden contraction flow of a Maxwell fluid. Meshes for these problems were of an unstructured triangular nature, and were refined based on the mean of the seven residual equations of interest. Elements with high residuals were bisected, forming two new elements, and the solution was recomputed on the new, more refined mesh. Depending on Weissenberg number this process can or cannot be continued. Results with this method were mixed. Using the EEME formulation with quadratic interpolation for the velocities and stresses and linear interpolation for pressure (QQL) we obtained a significant improvement over QQL interpolation with the traditional Cauchy form of the momentum equation (CME). The quality of the solution was better for the EEME—QQL and higher Weissenberg number limits were found. However, quadratic velocity, linear stress and pressure interpolation (QLL) gave results for which the quality was similar using EEME and CME. The economy of mesh refinement is an important benefit of this technique since good solutions have been obtained using a highly refined mesh only near the singularity. If we covered our mesh with elements the size of our smallest element, we would need over 200 000 elements, rather than the 473 actually used. The most important point about adaptive finite-element methods is that we add degrees of freedom only in regions where the solution tells us to.

In this report, we summarize our work on developing a production level foam processing computational model suitable for predicting the self-expansion of foam in complex geometries. The model is based on a finite element representation of the equations of motion, with the movement of the free surface represented using the level set method, and has been implemented in SIERRA/ARIA. An empirically based time- and temperature-dependent density model is used to encapsulate the complex physics of foam nucleation and growth in a numerically tractable model. The change in density with time is at the heart of the foam self-expansion as it creates the motion of the foam. This continuum-level model uses an homogenized description of foam, which does not include the gas explicitly. Results from the model are compared to temperature-instrumented flow visualization experiments giving the location of the foam front as a function of time for our EFAR model system.

A series of experiments has been performed to allow observation of the foaming process and the collection of temperature, rise rate, and microstructural data. Microfocus video is used in conjunction with particle image velocimetry (PIV) to elucidate the boundary condition at the wall. Rheology, reaction kinetics and density measurements complement the flow visualization. X-ray computed tomography (CT) is used to examine the cured foams to determine density gradients. These data provide input to a continuum level finite element model of the blowing process.

SUMMARY Little adaptive finite element work has been done in the area of viscoelastic flow in complex geometries. In this paper an adaptive finite element mesh refinement study is carried out on a Newtonian fluid and a Maxwell fluid in an axisymmetric 4: 1 contraction. The error indicator used for the refinement is the local norm of the residual in an element. For the Newtonian fluid, steady improvement with refinement is seen, though this is not the case for the Maxwell fluid, which never achieves a solution of good quality.

As part of an effort to reduce costs and improve quality control in encapsulation and potting processes the Technology Initiative Project ''Defect Free Manufacturing and Assembly'' has completed a computational modeling study of flows representative of those seen in these processes. Flow solutions are obtained using a coupled, finite-element-based, numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. In addition, two commercially available codes, ProCAST and MOLDFLOW, are also used on geometries representing encapsulation processes at the Kansas City Plant. Visual observations of the flow in several geometries are recorded in the laboratory and compared to the models. Wetting properties for the materials in these experiments are measured using a unique flowthrough goniometer.

To reduce costs and hazardous wastes associated with the production of lead-based active ceramic components, an injection molding process is being investigated to replace the current machining process. Here, lead zirconate titanate (PZT) ceramic particles are suspended in a thermoplastic resin and are injected into a mold and allowed to cool. The part is then bisque fired and sintered to complete the densification process. To help design this new process we use a finite element model to describe the injection molding of the ceramic paste. Flow solutions are obtained using a coupled, finite-element based, Newton-Raphson numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. Thermal, rheological, and wetting properties of the PZT paste are measured for use as input to the model. The viscosity of the PZT is highly dependent both on temperature and shear rate. One challenge in modeling the injection process is coming up with appropriate constitutive equations that capture relevant phenomenology without being too computationally complex. For this reason we modelmore » the material as a Carreau fluid and a WLF temperature dependence. Two-dimensional (2D) modeling is performed to explore the effects of the shear in isothermal conditions. Results indicate that very low viscosity regions exist near walls and that these results look similar in terms of meniscus shape and fill times to a simple Newtonian constitutive equation at the shear-thinned viscosity for the paste. These results allow us to pick a representative viscosity to use in fully three-dimensional (3D) simulation, which because of numerical complexities are restricted to using a Newtonian constitutive equation. Further 2D modeling at nonisothermal conditions shows that the choice of representative Newtonian viscosity is dependent on the amount of heating of the initially room temperature mold. An early 3D transient model shows that the initial design of the distributor is sub-optimal. However, these simulations take several months to run on 4 processors of an HP workstation using a preconditioner/solver combination of ILUT/GMRES with fill factors of 3 and PSPG stabilization. Therefore, several modifications to the distributor geometry and orientations of the vents and molds have been investigated using much faster 3D steady-state simulations. The pressure distribution for these steady-state calculations is examined for three different distributor designs to see if this can indicate which geometry has the superior design. The second modification, with a longer distributor, is shown to have flatter, more monotonic isobars perpendicular to the flow direction indicating a better filling process. The effects of the distributor modifications, as well as effects of the mold orientation, have also been examined with laboratory experiments in which the flow of a viscous Newtonian oil entering transparent molds is recorded visually. Here, the flow front is flatter and voids are reduced for the second geometry compared to the original geometry. A horizontal orientation, as opposed to the planned vertical orientation, results in fewer voids. Recently, the Navier-Stokes equations have been stabilized with the Dohrman-Bochev PSPP stabilization method, allowing us to calculate transient 3D simulations with computational times on the order of days instead of months. Validation simulations are performed and compared to the experiments. Many of the trends of the experiments are captured by the level set modeling, though quantitative agreement is lacking mainly due to the high value of the gas phase viscosity necessary for numerical stability, though physically unrealistic. More correct trends are predicted for the vertical model than the horizontal model, which is serendipitous as the actual mold is held in a vertical geometry. The full, transient mold filling calculations indicate that the flow front is flatter and voids may be reduced for the second geometry compared to the original geometry. The validated model is used to predict mold filling for the actual process with the material properties for the PZT paste, the original distributor geometry, and the mold in a vertical orientation. This calculation shows that voids may be trapped at the four corners of the mold opposite the distributor.« less

Solidification and blood flow seemingly have little in common, but each involves a fluid in contact with a deformable solid. In these systems, the solid-fluid interface moves as the solid advects and deforms, often traversing the entire domain of interest. Currently, these problems cannot be simulated without innumerable expensive remeshing steps, mesh manipulations or decoupling the solid and fluid motion. Despite the wealth of progress recently made in mechanics modeling, this glaring inadequacy persists. We propose a new technique that tracks the interface implicitly and circumvents the need for remeshing and remapping the solution onto the new mesh. The solid-fluid boundary is tracked with a level set algorithm that changes the equation type dynamically depending on the phases present. This novel approach to coupled mechanics problems promises to give accurate stresses, displacements and velocities in both phases, simultaneously.

The rheology of curing composite materials is important to many manufacturing processes. At Sandia, we work with particle-filled epoxy systems for a variety of applications. One particular system, designated as “459,” exhibits complex, counter-intuitive rheological dependence on temperature, flow history and particle-concentration. Despite the particles being relatively large (10 μm), 459 exhibits shear-thinning hysteretic behavior reminiscent of colloidal systems. It is hypothesized that the thixotropy arises from reaction of the 459 curative with the surface of the particulates. Under certain conditions, the addition of filler offsets the effect of epoxy polymerization on the viscosity, resulting in a viscosity that is constant with time. For this reason, we have developed an experimental model system that can be used to separate the effects of particle aggregation from the effects of cure on the viscosity. We have done experiments with this model suspension to determine its time-dependent response in step shear. In addition, we are working on a computational model that can be used to predict the behavior of the aggregating suspension. Preliminary modeling efforts focus on using a generalized Newtonian constitutive equation that relates the viscosity to the local aggregate concentration, defined by a dimensionless structure factor, to capture the time-dependence. Results from this constitutive equation are presented and compared to the experimental data from step-shear experiments in a Couette viscometer. Modeling results are also presented for a transient fiber spinning problem where the free surface evolves as the viscosity develops over time.Copyright © 2003 by ASME

Manufacturing applications for filled polymers include encapsulation of microelectronics and injection molding of composite parts. Predictive tools for simulating these manufacturing processes require knowledge of time- and temperature-dependent rheology of the polymer as well as information about local particle concentration. The overall system rheology is highly dependent on the particle concentration. The local particle concentration can change due to gravity, convection and shear-induced migration. For the epoxy systems of interest, an extent of reaction can be used to track the degree of cure. We couple the curing model with a diffusive flux suspension model [Zhang and Acrivos 1994] to determine the particle migration. This results in a generalized Newtonian model that has viscosity as a function of temperature, cure and concentration. Using this model, we examine settling of the particulate phase in both flowing and quiescent curing systems. We focus on settling in molds and flow in wide-gap counter-rotating cylinders. The heat transfer, including the exothermic polymerization reaction, must be modeled to achieve accurate results. The model is validated with temperature measurements and post-test microscopy data. Particle concentration is determined with x-ray microfocus visualization or confocal microscopy. Agreement between the simulations and experimental results is fair.Copyright © 2003 by ASME

Encapsulation is a common process used in manufacturing most non-nuclear components including: firing sets, neutron generators, trajectory sensing signal generators (TSSGs), arming, fusing and firing devices (AF and Fs), radars, programmers, connectors, and batteries. Encapsulation is used to contain high voltage, to mitigate stress and vibration and to protect against moisture. The purpose of the ASCI Encapsulation project is to develop a simulation capability that will allow us to aid in the encapsulation design process, especially for neutron generators. The introduction of an encapsulant poses many problems because of the need to balance ease of processing and properties necessary to achieve the design benefits such as tailored encapsulant properties, optimized cure schedule and reduced failure rates. Encapsulants can fail through fracture or delamination as a result of cure shrinkage, thermally induced residual stresses, voids or incomplete component embedding and particle gradients. Manufacturing design requirements include (1) maintaining uniform composition of particles in order to maintain the desired thermal coefficient of expansion (CTE) and density, (2) mitigating void formation during mold fill, (3) mitigating cure and thermally induced stresses during cure and cool down, and (4) eliminating delamination and fracture due to cure shrinkage/thermal strains. The first two require modeling ofmore » the fluid phase, and it is proposed to use the finite element code GOMA to accomplish this. The latter two require modeling of the solid state; however, ideally the effects of particle distribution would be included in the calculations, and thus initial conditions would be set from GOMA predictions. These models, once they are verified and validated, will be transitioned into the SIERRA framework and the ARIA code. This will facilitate exchange of data with the solid mechanics calculations in SIERRA/ADAGIO.« less

Theoretical models describing the dynamic behavior of the expansion and contraction of polyelectrolyte gels present numerically challenging problems. This paper describes how a method of weighted residuals approach has been used to solve the two-dimensional governing system of equations by finite element analysis. The modulation of the imbibition/expulsion of solvent by a gel disk is studied as an example.