Publications

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Experiments were performed to characterize the mechanical response of a 15 pcf flexible polyurethane foam to large deformation at different strain rates and temperatures. Results from these experiments indicated that at room temperature, flexible polyurethane foams exhibit significant nonlinear elastic deformation and nearly return to their original undeformed shape when unloaded. However, when these foams are cooled to temperatures below their glass transition temperature of approximately -35 o C, they behave like rigid polyurethane foams and exhibit significant permanent deformation when compressed. Thus, a new model which captures this dramatic change in behavior with temperature was developed and implemented into SIERRA with the name Flex_Foam to describe the mechanical response of both flexible and rigid foams to large deformation at a variety of temperatures and strain rates. This report includes a description of recent experiments. Next, development of the Flex Foam model for flexible polyurethane and other flexible foams is described. Selection of material parameters are discussed and finite element simulations with the new Flex Foam model are compared with experimental results to show behavior that can be captured with this new model.

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Experiments were performed to characterize the mechanical response of several different rigid polyurethane foams to large deformation. In these experiments, the effects of load path, loading rate, and temperature were investigated. Results from these experiments indicated that rigid polyurethane foams exhibit significant damage, volumetric and deviatoric plasticity when they are compressed. Rigid polyurethane foams were also found to be extremely strain-rate and temperature dependent. These foams are also rather brittle and crack when loaded to small strains in tension or to larger strains in compression. Thus, a phenomenological Unified Creep Plasticity Damage (UCPD) model was developed to describe the mechanical response of these foams to large deformation at a variety of temperatures and strain rates. This paper includes a description of recent experiments and experimental findings. Next, development of a UCPD model for rigid, polyurethane foams is described. Finite element simulations with the new UCPD model are compared with experimental results to show behavior that can be captured with this model.

Numerous experiments were performed to characterize the mechanical response of several different rigid polyurethane foams (FR3712, PMDI10, PMDI20, and TufFoam35) to large deformation. In these experiments, the effects of load path, loading rate, and temperature were investigated. Results from these experiments indicated that rigid polyurethane foams exhibit significant volumetric and deviatoric plasticity when they are compressed. Rigid polyurethane foams were also found to be very strain-rate and temperature dependent. These foams are also rather brittle and crack when loaded to small strains in tension or to larger strains in compression. Thus, a new Unified Creep Plasticity Damage (UCPD) model was developed and implemented into SIERRA with the name Foam Damage to describe the mechanical response of these foams to large deformation at a variety of temperatures and strain rates. This report includes a description of recent experiments and experimental findings. Next, development of a UCPD model for rigid, polyurethane foams is described. Selection of material parameters for a variety of rigid polyurethane foams is then discussed and finite element simulations with the new UCPD model are compared with experimental results to show behavior that can be captured with this model.

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Accurate material models are fundamental to predictive structural finite element models. Because potting foams are routinely used to mitigate shock and vibration of encapsulated components in electro/mechanical systems, accurate material models for foams are needed. A viscoplastic foam constitutive model has been developed to represent the large nonlinear and rate dependent crush of a polyurethane foam throughout an application space defined by temperature, strain rate and strain levels. Validation of this viscoplastic model, which is implemented in the transient dynamic Presto finite element code, is being achieved by modeling and testing a series of structural geometries of increasing complexity that have been designed to ensure sensitivity to material parameters. Both experimental and analytical uncertainties are being quantified to ensure fair assessment of model validity. Quantitative model validation metrics are being developed to provide a means of comparing analytical model predictions with experimental observations. This paper focuses on model validation of foam/component behavior over a wide temperature, strain rate, and strain level range using a Presto viscoplastic finite element model. Experiments include simple foam/component test articles crushed in a series of drop table tests. Material variations of density have been included. A double blind validation process is described that brings together test data with model predictions.

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Using molecular dynamics simulations, a constitutive model for the chemical aging of polymer networks was developed. This model incorporates the effects on the stress from the chemical crosslinks and the physical entanglements. The independent network hypothesis has been modified to account for the stress transfer between networks due to crosslinking and scission in strained states. This model was implemented in the finite element code Adagio and validated through comparison with experiment. Stress relaxation data was used to deduce crosslinking history and the resulting history was used to predict permanent set. The permanent set predictions agree quantitatively with experiment.

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Constitutive models for chemically reacting networks are formulated based on a generalization of the independent network hypothesis. These models account for the coupling between chemical reaction and strain histories, and have been tested by comparison with microscopic molecular dynamics simulations. An essential feature of these models is the introduction of stress transfer functions that describe the interdependence between crosslinks formed and broken at various strains. Efforts are underway to implement these constitutive models into the finite element code Adagio. Preliminary results are shown that illustrate the effects of changing crosslinking and scission rates and history.

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.