Traditional electronics assemblies are typically packaged using physically or chemically blown potted foams to reduce the effects of shock and vibration. These potting materials have several drawbacks including manufacturing reliability, lack of internal preload control, and poor serviceability. A modular foam encapsulation approach combined with additively manufactured (AM) silicone lattice compression structures can address these issues for packaged electronics. These preloaded silicone lattice structures, known as foam replacement structures (FRSs), are an integral part of the encapsulation approach and must be properly characterized to model the assembly stresses and dynamics. In this study, dynamic test data is used to validate finite element models of an electronics assembly with modular encapsulation and a direct ink write (DIW) AM silicone FRS. A variety of DIW compression architectures are characterized, and their nominal stress-strain behavior is represented with hyperfoam constitutive model parameterizations. Modeling is conducted with Sierra finite element software, specifically with a handoff from assembly preloading and uniaxial compression in Sierra/Solid Mechanics to linear modal and vibration analysis in Sierra/Structural Dynamics. This work demonstrates the application of this advanced modeling workflow, and results show good agreement with test data for both static and dynamic quantities of interest, including preload, modal, and vibration response.
Aging of silicon photovoltaic (PV) module packaging is one of the greatest limiters of PV module service lifetimes. Module characterization typically focuses on power degradation metrics, which do not convey the complexities of often simultaneous degradation mechanisms. In this work, PV modules with pristine references and known fielding histories were investigated by non-destructive and destructive methods. Modules from Canadian Solar, Mission Solar, and Hanwha Q-Cells were fielded for up to three years; select modules were removed from fielding each year for coring to allow for characterization of the encapsulant. Modules are commonly encapsulated with two protective layers of partially-crystalline ethylene vinyl acetate (EVA) polymer that must undergo a crosslinking reaction to achieve desired properties. The extent of crystallinity of the encapsulants as studied by differential scanning calorimetry showed differences between manufacturers and over time. Some encapsulants showed different magnitudes of crystal sizes which changed after fielding; encapsulants with the monodisperse crystal sizes did not change with fielding. This is due to differences in thermal history. These results have implications for stress development during module aging, since EVA crystal melting and crosslinking reactions can result in encapsulant density changes.
Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.
Understanding the stress development in fluids as they transition to solids is not well-understood. Computational models are needed to represent "birthing stress" for multiphysics applications such as polymer encapsulation around sensitive electronics and additive manufacturing where these stresses can lead to defects such as cracking and voids. The local stress state is also critical to understand and predict the net shape of parts formed in the liquid phase. In this one-year exploratory LDRD, we have worked towards a novel experimental diagnostic to measure the fluid rheology, degree of solidification, and the solid stress development simultaneously. We debugged and made viable a "first-generation" Rheo-Raman system and used it to characterize two types of solidifying systems: paraffin wax, which crystalizes as it solidifies, and thermoset polymers, which form a network of covalent bonds. We used the paraffin wax as a model system to perform flow visualization studies and did some preliminary modeling of the experiment, to demonstrate the inadequacy of the current modeling approaches. This work will inform an advanced fluid constitutive equation that includes a yield stress, temperature dependence, and an evolving viscosity when we pursue the full proposal, which was funded for FY20.
Ceramic fiber insulation materials are used in numerous applications (e.g. aerospace, fire protection, and military) for their stability and performance in extreme environments. However, the thermal properties of these materials have not been thoroughly characterized for many of the conditions that they will be exposed to, such as high temperatures, pressures, and alternate gaseous atmospheres. The resulting uncertainty in the material properties can complicate the design of systems using these materials. In this study, the thermal conductivity of two ceramic fiber insulations, Fiberfrax T-30LR laminate and 970-H paper, was measured as a function of atmospheric temperature and compression in an air environment using the transient plane source technique. Furthermore, a model is introduced to account for changes in thermal conductivity with temperature, compression, and ambient gas. The model was tuned to the collected experimental data and results are compared. The tuned model is also compared to published data sets taken in argon, helium, and hydrogen environments and agreement is discussed.
In this report, we investigate how manufacturing conditions result in the warpage of moderate density PMDI polyurethane foam (12-50 lb/ft3) when they are released from a mold. We have developed a multiphysics modeling framework to simulate the manufacturing process including resin injection, foaming and mold filling, gelation of the matrix, elevated cure, vitrification, cool down, and demolding. We have implemented this framework within the Sierra Mechanics Finite Element Code Suite. We couple Aria for flow, energy conservation, and foaming/curing kinetics with Adagio for the nonlinear viscoelastic solid response in a multi-staged simulation process flow. We calibrate a model for the PMDI-10S (10 lb/ft3 free rise foam) through a suite of characterization data presented here to calibrate the solid cure behavior of the foam. The model is then used and compared to a benchmark experiment, the manufacturing and warpage over 1 year of a 10 cm by 10 cm by 2.5 cm foam "staple". This component features both slender and thick regions that warp considerably differently over time. Qualitative agreement between the model and the experiment is achieved but quantitative accuracy is not.
Ceramic fiber insulation materials, such as Fiberfrax and Min-K products, are used in a number of applications (e.g. aerospace, fire protection, and military) for their stability and performance in extreme conditions. However, the thermal properties of these materials have not been thoroughly characterized for many of the conditions that they will be exposed to, such as high temperatures and pressures. This complicates the design of systems using these insulations as the uncertainty in the thermal properties is high. In this study, the thermal conductivity of three ceramic fiber insulations, Fiberfrax T-30LR laminate, Fiberfrax 970-H paper, and Min-K TE1400 board, was measured as a function of atmospheric temperature and compression. Measurements were taken using the transient plane source technique. The results of this study are compared against three published data sets.
Polyurethane foams are used widely for encapsulation and structural purposes because they are inexpensive, straightforward to process, amenable to a wide range of density variations (1 lb/ft3 - 50 lb/ft3), and able to fill complex molds quickly and effectively. Computational model of the filling and curing process are needed to reduce defects such as voids, out-of-specification density, density gradients, foam decomposition from high temperatures due to exotherms, and incomplete filling. This paper details the development of a computational fluid dynamics model of a moderate density PMDI structural foam, PMDI-10. PMDI is an isocyanate-based polyurethane foam, which is chemically blown with water. The polyol reacts with isocyanate to produces the polymer. PMDI- 10 is catalyzed giving it a short pot life: it foams and polymerizes to a solid within 5 minutes during normal processing. To achieve a higher density, the foam is over-packed to twice or more of its free rise density of 10 lb/ft3. The goal for modeling is to represent the expansion, filling of molds, and the polymerization of the foam. This will be used to reduce defects, optimize the mold design, troubleshoot the processed, and predict the final foam properties. A homogenized continuum model foaming and curing was developed based on reaction kinetics, documented in a recent paper; it uses a simplified mathematical formalism that decouples these two reactions. The chemo-rheology of PMDI is measured experimentally and fit to a generalized- Newtonian viscosity model that is dependent on the extent of cure, gas fraction, and temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved via a stabilized finite element method. The equations are combined with a level set method to determine the location of the foam-gas interface as it evolves to fill the mold. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics, viscosity, and other material properties are all sensitive to temperature. Results from the model are compared to experimental flow visualization data and post-test X-ray computed tomography (CT) data for the density. Several geometries are investigated including two configurations of a mock structural part and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed for future work.
A three year LDRD was undertaken to look at the feasibility of using magnetic sensing to determine flows within sealed vessels at high temperatures and pressures. Uniqueness proofs were developed for tracking of single magnetic particles with multiple sensors. Experiments were shown to be able to track up to 3 dipole particles undergoing rigid-body rotational motion. Temperature was wirelessly monitored using magnetic particles in static and predictable motions. Finally high-speed vibrational motion was tracked using magnetic particles. Ideas for future work include using small particles for measuring vorticity and better calibration methods for tracking multiple particles.
We present selected results from a series of Open Stack thermal battery tests performed in FY14 and FY15 and discuss our findings. These tests were meant to provide validation data for the comprehensive thermal battery simulation tools currently under development in Sierra/Aria under known conditions compared with as-manufactured batteries. We are able to satisfy this original objective in the present study for some test conditions. Measurements from each test include: nominal stack pressure (axial stress) vs. time in the cold state and during battery ignition, battery voltage vs. time against a prescribed current draw with periodic pulses, and images transverse to the battery axis from which cell displacements are computed. Six battery configurations were evaluated: 3, 5, and 10 cell stacks sandwiched between 4 layers of the materials used for axial thermal insulation, either Fiberfrax Board or MinK. In addition to the results from 3, 5, and 10 cell stacks with either in-line Fiberfrax Board or MinK insulation, a series of cell-free “control” tests were performed that show the inherent settling and stress relaxation based on the interaction between the insulation and heat pellets alone.
Remote temperature sensing is essential for applications in enclosed vessels, where feedthroughs or optical access points are not possible. A unique sensing method for measuring the temperature of multiple closely spaced points is proposed using permanent magnets and several three-axis magnetic field sensors. The magnetic field theory for multiple magnets is discussed and a solution technique is presented. Experimental calibration procedures, solution inversion considerations, and methods for optimizing the magnet orientations are described in order to obtain low-noise temperature estimates. The experimental setup and the properties of permanent magnets are shown. Finally, experiments were conducted to determine the temperature of nine magnets in different configurations over a temperature range of 5 °C to 60 °C and for a sensor-to-magnet distance of up to 35 mm. To show the possible applications of this sensing system for measuring temperatures through metal walls, additional experiments were conducted inside an opaque 304 stainless steel cylinder.
Physical property measurements including viscosity, density, thermal conductivity, and heat capacity of low-molecular weight polydimethylsiloxane (PDMS) fluids were measured over a wide temperature range (-50°C to 150°C when possible). Properties of blends of 1 cSt and 20 cSt PDMS fluids were also investigated. Uncertainties in the measurements are cited. These measurements will provide greater fidelity predictions of environmental sensing device behavior in hot and cold environments.
We present a new collection of data on the load-stress relaxation-unload behavior of MinK and FiberFrax Board (FF) insulation materials used as pellets in-line with thermal battery electrochemical stacks. Both materials were subjected to standard thermal preparations, and then tested at room temperature. Intermediate term stress relaxation tests are presented (order 104 minutes of relaxation) showing that FF relaxation is not significantly stress or deformation dependent, but MinK is moderately so. Moreover, stress-strain curves associated with specimen unloading, reloading, and unloading again are presented for both materials. FF and MinK are substantially different here. Acute material variability is observed though test conditions and material preparations are standardized. A modeling approach is presented to empirically estimate the amount of stress relaxation at room temperature, and from this state, represent the unloading stress-strain behavior of both materials. This effort provides a complete framework for representing (in an engineering sense) both materials in thermal battery performance simulations.
Polyurethane is a complex multiphase material that evolves from a viscous liquid to a system of percolating bubbles, which are created via a CO2 generating reaction. The continuous phase polymerizes to a solid during the foaming process generating heat. Foams introduced into a mold increase their volume up to tenfold, and the dynamics of the expansion process may lead to voids and will produce gradients in density and degree of polymerization. These inhomogeneities can lead to structural stability issues upon aging. For instance, structural components in weapon systems have been shown to change shape as they age depending on their molding history, which can threaten critical tolerances. The purpose of this project is to develop a Cradle-to-Grave multiphysics model, which allows us to predict the material properties of foam from its birth through aging in the stockpile, where its dimensional stability is important.
The transient transport of electrolytes in thermally-activated batteries is studied using electron probe micro-analysis (EPMA), demonstrating the robust capability of EPMA as a useful tool for studying and quantifying mass transport within porous materials, particularly in difficult environments where classical flow measurements are challenging. By tracking the mobility of bromine and potassium ions from the electrolyte stored within the separator into the lithium silicon anode and iron disulfide cathode, we are able to quantify the transport mechanisms and physical properties of the electrodes including permeability and tortuosity. Due to the micron to submicron scale porous structure of the initially dry anode, a fast capillary pressure driven flow is observed into the anode from which we are able to set a lower bound on the permeability of 10-1 mDarcy. The transport into the cathode is diffusion-limited because the cathode originally contained some electrolyte before activation. Using a transient one-dimensional diffusion model, we estimate the tortuosity of the cathode electrode to be 2.8 ± 0.8.
We are developing computational models to elucidate the expansion and dynamic filling process of a polyurethane (PMDI) foam used to encapsulate electronic components or to produce lightweight structural parts. The polyurethane of interest is a chemically blown foam, where carbon dioxide is produced via the reaction of water, a blowing agent, and isocyanate. Here, we take a careful look at the evolution of the bubble sizes during blowing. This information will help the development of subgrid models to predict bubble formation, growth, coalescence and collapse, drainage, and, hence, eventually the development of engineering models to predict foam expansion into a mold. Close-up views of bubbles at a transparent wall of a narrow, temperature-controlled channel are recorded during the foaming reaction and analyzed with image processing. Because these bubbles are pressed against the wall, the bubble sizes in the last frames after the expansion has stopped are compared to scanning electron microscope (SEM) images of the interior of some of the cured samples to determine if the presence of the wall significantly changes the bubble sizes. In addition, diffusing wave spectroscopy (DWS) is used to determine the average bubble sizes across the width of a similar channel as the bubbles change with time. DWS also gives information about microstructural changes as bubbles rearrange upon bubble collapse or coalescence. In this paper we conclude qualitatively that the bubble size distribution is heavily dependent on the formulation of foam being tested, temperature, the height in the foam bar, the proximity to a wall, and the degree of over-packing.
Temperature monitoring is essential in automation, mechatronics, robotics and other dynamic systems. Wireless methods which can sense multiple temperatures at the same time without the use of cables or slip-rings can enable many new applications. A novel method utilizing small permanent magnets is presented for wirelessly measuring the temperature of multiple points moving in repeatable motions. The technique utilizes linear least squares inversion to separate the magnetic field contributions of each magnet as it changes temperature. The experimental setup and calibration methods are discussed. Initial experiments show that temperatures from 5 to 50 °C can be accurately tracked for three neodymium iron boron magnets in a stationary configuration and while traversing in arbitrary, repeatable trajectories. This work presents a new sensing capability that can be extended to tracking multiple temperatures inside opaque vessels, on rotating bearings, within batteries, or at the tip of complex endeffectors.
We are studying PMDI polyurethane with a fast catalyst, such that filling and polymerization occur simultaneously. The foam is over-packed to tw ice or more of its free rise density to reach the density of interest. Our approach is to co mbine model development closely with experiments to discover new physics, to parameterize models and to validate the models once they have been developed. The model must be able to repres ent the expansion, filling, curing, and final foam properties. PMDI is chemically blown foam, wh ere carbon dioxide is pr oduced via the reaction of water and isocyanate. The isocyanate also re acts with polyol in a competing reaction, which produces the polymer. A new kinetic model is developed and implemented, which follows a simplified mathematical formalism that decouple s these two reactions. The model predicts the polymerization reaction via condensation chemis try, where vitrification and glass transition temperature evolution must be included to correctly predict this quantity. The foam gas generation kinetics are determined by tracking the molar concentration of both water and carbon dioxide. Understanding the therma l history and loads on the foam due to exothermicity and oven heating is very important to the results, since the kinetics and ma terial properties are all very sensitive to temperature. The conservation eq uations, including the e quations of motion, an energy balance, and thr ee rate equations are solved via a stabilized finite element method. We assume generalized-Newtonian rheology that is dependent on the cure, gas fraction, and temperature. The conservation equations are comb ined with a level set method to determine the location of the free surface over time. Results from the model are compared to experimental flow visualization data and post-te st CT data for the density. Seve ral geometries are investigated including a mock encapsulation part, two configur ations of a mock stru ctural part, and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Thoughts on m odel improvements are also discussed.
A model system was developed for enabling a multiscale understanding of centrifugal-contactor liquid–liquid extraction.The system consisted of Nd(III) + xylenol orange in the aqueous phase buffered to pH =5.5 by KHP, and dodecane + thenoyltrifluroroacetone (HTTA) + tributyphosphate (TBP) in the organic phase. Diffusion constants were measured for neodymium in both the organic and aqueous phases, and the Nd(III) partition coefficients were measured at various HTTA and TBP concentrations. A microfluidic channel was used as a high-shear model environment to observe mass-transfer on a droplet scale with xylenol orange as the aqueous-phase metal indicator; mass-transfer rates were measured quantitatively in both diffusion and reaction limited regimes on the droplet scale. Lastly, the microfluidic results were comparable to observations made for the same system in a laboratory scale liquid–liquid centrifugal contactor, indicating that single drop microfluidic experiments can provide information on mass transfer in complicated flows and geometries.
We present a phenomenological constitutive model that describes the macroscopic behavior of pressed-pellet materials used in molten salt batteries. Such materials include separators, cathodes, and anodes. The purpose of this model is to describe the inelastic deformation associated with the melting of a key constituent, the electrolyte. At room temperature, all constituents of these materials are solid and do not transport cations so that the battery is inert. As the battery is heated, the electrolyte, a constituent typically present in the separator and cathode, melts and conducts charge by flowing through the solid skeletons of the anode, cathode, and separator. The electrochemical circuit is closed in this hot state of the battery. The focus of this report is on the thermal-mechanical behavior of the separator, which typically exhibits the most deformation of the three pellets during the process of activating a molten salt battery. Separator materials are composed of a compressed mixture of a powdered electrolyte, an inert binder phase, and void space. When the electrolyte melts, macroscopically one observes both a change in volume and shape of the separator that depends on the applied boundary conditions during the melt transition. Although porous flow plays a critical role in the battery mechanics and electrochemistry, the focus of this report is on separator behavior under flow-free conditions in which the total mass of electrolyte is static within the pellet. Specific poromechanics effects such as capillary pressure, pressure-saturation, and electrolyte transport between layers are not considered. Instead, a phenomenological model is presented to describe all such behaviors including the melting transition of the electrolyte, loss of void space, and isochoric plasticity associated with the binder phase rearrangement. The model is appropriate for use finite element analysis under finite deformation and finite temperature change conditions. The model reasonably describes the stress dependent volume and shape change associated with dead load compression and spring-type boundary conditions; the latter is relevant in molten salt batteries. Future work will transition the model towards describing the solid skeleton of the separator in the traditional poromechanics context.
The subject of this work is the development of models for the numerical simulation of matter, momentum, and energy balance in heterogeneous materials. These are materials that consist of multiple phases or species or that are structured on some (perhaps many) scale(s). By computational mechanics we mean to refer generally to the standard type of modeling that is done at the level of macroscopic balance laws (mass, momentum, energy). We will refer to the flow or flux of these quantities in a generalized sense as transport. At issue here are the forms of the governing equations in these complex materials which are potentially strongly inhomogeneous below some correlation length scale and are yet homogeneous on larger length scales. The question then becomes one of how to model this behavior and what are the proper multi-scale equations to capture the transport mechanisms across scales. To address this we look to the area of generalized stochastic process that underlie the transport processes in homogeneous materials. The archetypal example being the relationship between a random walk or Brownian motion stochastic processes and the associated Fokker-Planck or diffusion equation. Here we are interested in how this classical setting changes when inhomogeneities or correlations in structure are introduced into the problem. Aspects of non-classical behavior need to be addressed, such as non-Fickian behavior of the mean-squared-displacement (MSD) and non-Gaussian behavior of the underlying probability distribution of jumps. We present an experimental technique and apparatus built to investigate some of these issues. We also discuss diffusive processes in inhomogeneous systems, and the role of the chemical potential in diffusion of hard spheres is considered. Also, the relevance to liquid metal solutions is considered. Finally we present an example of how inhomogeneities in material microstructure introduce fluctuations at the meso-scale for a thermal conduction problem. These fluctuations due to random microstructures also provide a means of characterizing the aleatory uncertainty in material properties at the mesoscale.
We show that it is possible to manufacture strong macroporous ceramic films that can be backfilled with electrolyte to form rigid separator pellets suitable for use in thermal batteries. Several new ceramic manufacturing processes are developed to produce sintered magnesium oxide foams with connected porosities of over 80% by volume and with sufficient strength to withstand the battery manufacturing steps. The effects of processing parameters are quantified, and methods to imbibe electrolyte into the ceramic scaffold demonstrated. Preliminary single cell battery testing show that some of our first generation pellets exhibit longer voltage life with comparable resistance at the critical early times to that exhibited by a traditional pressed pellets. Although more development work is needed to optimize the processes to create these rigid separator pellets, the results indicate the potential of such ceramic separator pellets to be equal, if not superior to, current pressed pellets. Furthermore, they could be a replacement for critical material that is no longer available, as well as improving battery separator strength, decreasing production costs, and leading to shorter battery stacks for long-life batteries.
Ceramic foams with porosities over 90% are created by drying and sintering particle stabilized oil-water emulsions. This technique is optimized for the creation of magnesium oxide (MgO) porous scaffolds. Processing parameters such as emulsion mixing speed, particle concentration, and drying time are related to final properties such as porosity, permeability, and mechanical strength. The hydroxylation of magnesium oxide to form a gel can also be used to create green ceramics with very low densities directly without the additional steps to form an emulsion. The quality of these ceramic foams compares well to porous ceramics produced by other methods, specifically tape casting of an MgO slip with added poreformers and sponge impregnation of reticulated foam with a slip in a replication process.
We examine several methods to create a sheet of magnesium oxide (MgO) macroporous ceramic material via tape casting. These methods include the approach pioneered by Akartuna et al. in which an oil/water emulsion is stabilized by surface-modified metal oxide particles at the droplet interfaces. Upon drying, a scaffold of the self-assembled particles is strong enough to be removed from the substrate material and sintered. We find that this method can be used with MgO particles surface modified by short amphiphilic molecules. This approach is compared with two more traditional methods to induce structure into a green ceramic: 1) creation of an MgO ceramic slip with added pore formers, and 2) sponge impregnation of a reticulated foam with the MgO slip. Green and sintered samples made using each method are hardness tested and results compared for several densities of the final ceramics. Optical and SEM images of the materials are shown.