The capability of the Simplified Potential Energy Clock Model (SPEC) to represent the uniaxial compression yield strength evolution under isothermal aging conditions is evaluated for a widely used epoxy thermoset encapsulation material, 828 DGEBA/DEA. A baseline model calibration is used. We note that this calibration did not consider yield strength behavior close to the glass transition temperature (Tg), but in this work, the model is exercised in this temperature range to evaluate the ability to predict changes in material response with aging as equilibrium is approached. Some model alterations were needed to remove negative Prony weights in the thermal and bulk relaxation function (f1), which is chiefly responsible for aging in this analysis, but otherwise, the model was not altered. Model predictions of yield stress evolution are quantitatively different compared with experiments, but the rate of change of yield stress with respect to aging time is in reasonable agreement with respect to experiments for the first 1000 hours of aging. After this aging time, the measured yield stress stops evolving, but the model continues to evolve for several more decades in time. Parametric studies and model alterations are considered to investigate how yield strength evolution predictions are affected by modeling choices. It is clear that the baseline calibration must be re-examined in order to represent the aging data quantitatively.
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.
Damage mechanisms in elastomeric syntactic foams filled with glass microballoons (GMB) and resulting effects on the macroscale elastic constants have been investigated. Direct numerical simulations of the material microstructure, composite theory analyses, and uniaxial compression tests across a range of filler volume fractions were conducted. The room temperature and elastic behavior of composites with undamaged, fully debonded, and fully crushed GMBs were investigated for syntactic foams with a polydimethylsiloxane matrix. Good agreement was obtained between numerical studies, composite theory, and experiments. Debonding was studied via finite element models due to the difficulty of isolating this damage mechanism experimentally. The predictions indicate that the bulk modulus is insensitive to the state of debonding at low-GMB-volume fractions but is dramatically reduced if GMBs are crushed. The shear behavior is affected by both debonding and crush damage mechanisms. The acute sensitivity of the bulk modulus to crushed GMBs is further studied in simulations in which only a fraction of GMBs are crushed. We find that the composite bulk modulus drops severely even when just a small fraction of GMBs are crushed. Various material parameters such as GMB wall thickness, volume fraction, and minimum balloon spacing are also investigated, and they show that the results presented here are general and apply to a wide range of microstructure and GMB filler properties.
The ability to relax a macroscopically applied stress is often associated with molecular mobility, or the possibility for a molecule to move outside the confines of its current position, within the material of which the stress is applied. Here, a viscoelastic constitutive analysis is used to investigate the counter-intuitive experimental observation of “mobility decrease with increased deformation through yield” [1] for a glass forming polymer during stress relaxation while under compressive and tensile loading conditions. The behavior of an epoxy thermoset is examined using an extensively validated, thermorheologically simple, material “clock” model, the Simplified Potential Energy Clock (SPEC) model.[2] This methodology allows for a comparison between the linear viscoelastic (LVE) limit and the true non-linear viscoelastic (NLVE) representation and enables exploration of a wide range of conditions that are not practical to investigate experimentally. The model predicts the behavior previously described as “mobility decrease with increased deformation” in the LVE limit and at low strain rates for NLVE. Only when loading rates are sufficient to decrease the material shift factor by multiple orders of magnitude is the anticipated deformation induced mobility or “mobility increase with increased deformation” observed. While the model has not been “trained” for these behaviors, it also predicts that the normalized stress relaxation response is indistinguishable amongst strain levels in the “post-yield” region, as has been experimentally reported. At long time, which has not been examined experimentally, the model predicts that even the normalized relaxation curves that exhibit “mobility increase with increased deformation” “cross back over” and return to the LVE ordering. These findings demonstrate the ability of rheologically simple models to represent the counter-intuitive experimentally measured material response and present predictions at long time scales that could be tested experimentally.
Sylgard® 184/Glass Microballoon (GMB) potting material is currently used in many NW systems. Analysts need a macroscale constitutive model that can predict material behavior under complex loading and damage evolution. To address this need, ongoing modeling and experimental efforts have focused on study of damage evolution in these materials. Micromechanical finite element simulations that resolve individual GMB and matrix components promote discovery and better understanding of the material behavior. With these simulations, we can study the role of the GMB volume fraction, time-dependent damage, behavior under confined vs. unconfined compression, and the effects of partial damage. These simulations are challenging and push the boundaries of capability even with the high performance computing tools available at Sandia. We summarize the major challenges and the current state of this modeling effort, as an exemplar of micromechanical modeling needs that can motivate advances in future computing efforts.
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.