Publications

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In this work, we investigated microstructural features of elastomeric foam with the goal of identifying descriptors other than porosity that have a significant effect on the macroscale mechanical response. X-ray computed tomography (XCT) provided three-dimensional images of several flexible polyurethane foam samples prior to mechanical testing. The samples were then compressed to approximately 80% engineering strain. Stereo digital image correlation was used to measure the three-dimensional surface displacement data, from which strain was determined. The strain data, which were calculated with respect to the undeformed coordinates, were then overlaid on the corresponding surface generated from XCT. Heterogeneities in the strain-field were cross-correlated with topological quantities such as pore size distribution. A statistically significant correlation was identified between the distance transform of the pore phase and strain fluctuations.

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To elucidate the damage mechanisms in syntactic foams with hollow glass microballoon (GMB) reinforcement and elastomer matrices, in situ X-ray computed tomography mechanical testing was performed on syntactic foams with increasing GMB volume fraction. Image processing and digital volume correlation techniques identified very different damage mechanisms compared to syntactic foams with brittle matrices. In particular, the prevailing mechanism transitioned from dispersed GMB collapse at low volume fraction to clustered GMB collapse at high volume fraction. Moreover, damage initiated and propagated earlier in closely-packed GMBs for all specimens. Both of these trends were attributed to increased interaction between closely-packed GMBs. This was confirmed by statistical analysis of GMB damage, which identified a consistent, inverse relationship between the probability of survival and the local coordination number (Nneighbor) across all specimens.

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Accurate modeling of viscoelasticity remains an important consideration for a variety of materials (e.g. polymers and inorganic glasses). As such, over the previous decades a substantial body of work has been dedicated to developing appropriate constitutive models for viscoelasticity ranging from initial considerations of linear thermoviscoelasticity to more complex non-linear formulations incorporating fictive temperatures or potential energy clocks including the use of both internal state variable(ISV) and hereditary integral representations. Nonetheless, relatively limited (in comparison to plasticity) attention has been paid to the numerical integration of such schemes. In terms of integral based formulations, Taylor et al. first considered the problem of the integration of a linear viscoelasticity model. That work focused on the integration of the hereditary integrals and demonstrated improved performance of the new scheme with a custom finite element code over an existing finite difference reference. Chambers and Becker, using a free volume based shift factor, also considered the integration of the hereditary integrals and the impact on the problem of a pressurized thick-walled cylinder and developed an adaptive scheme to bound the error. Chambers later developed three-point Gauss and composite integration schemes for the hereditary integrals and noted improved accuracy. With respect to ISV-based schemes, formulations for the non-linear Schapery model have been proposed. However, in those efforts greater attention was paid to convergence of the non-linear solution scheme than impact of numerical integration. Various authors (e.g. Holzapfel and Simo and Hughes) have also studied the use of convolution integrals with differential forms of ISVs for temperature-independent formulations. Regardless, while the "potential energy clock" (PEC) and "simplified potential energy clock"(SPEC) models have been used to study a variety of non-linear responses (e.g.), limited attention has been paid to the numerical performance. As will be discussed later, the "clock" at the center of the formulations includes temperature and complex history dependence making the numerical integration of such a model even more challenging. Thus, in the current work an initial effort towards characterizing the numerical integration of the constitutive model through simplified problems is performed. To that end, in Section 2 the theory of the model is briefly presented while the numerical integration is discussed in Section 3. Results of various studies characterizing the numerical behavior and performance are then given in Section 4. Finally, some concluding remarks and thoughts for follow on works are provided in Section 5.

Silicone elastomer filled with glass micro balloons (GMB) is an elastomeric syntactic foam used in electronics and component packaging for encapsulation, potting, stress-relief layer, and electrical insulation purposes. Under mechanical loading, the reinforcing phase, namely the GMBs embedded in the elastomer matrix, may break or delaminate, leading to internal damage and macroscale stiffness degradation, which can alter the material's protective capacity against mechanical shock and vibration. The degree of damage is controlled by the loading history, delamination, and failure behavior of the GMBs. We investigate the GMB failure behavior in this work wherein we present an indentation experiment to measure the force required to fail individual GMBs that are either embedded in the elastomer matrix or adhered to the surface of an elastomer layer. The indentation apparatus is augmented with an inverted optical microscope to enable in situ imaging of the GMB. Failure modes for the embedded or non-embedded GMBs are discussed based on the morphology of the broken GMBs and the measured failure forces. We also measure the adhesion energy between the glass balloon and the elastomer, based on which the possibility of delamination between the GMB and the surrounding elastomer matrix during the failure process is evaluated. Our results can facilitate the development of a failure criterion of GMBs which is necessary for establishing a physics-based constitutive model to describe the macroscopic damage mechanics of elastomeric syntactic foams.

Glass-ceramics are a unique class of materials in which the growth of a ceramic phase(s) may be induced in an inorganic glass resulting in a microstructurally heterogeneous material with both glass and ceramic phases. This specialized processing is often referred to as "ceramming''. A wide variety of such materials have been developed through the use of different initial glass compositions and thermomechanical processing routes and that have enabled applications in dentistry, consumer kitchenware, and telescopes mirrors. These materials may also exhibit large apparent coefficients of thermal expansion making them attractive for consideration in glass-ceramic seals. These large apparent coefficients of thermal expansion often arise from silica polymorphs, such as cristobalite, undergoing a solid-to-solid phase transformations producing additional non-linearity in the effective material response.

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A parallel, adaptive overlay grid procedure is proposed for use in generating all-hex meshes for stochastic (SVE) and representative (RVE) volume elements in computational materials modeling. The mesh generation process is outlined including several new advancements such as data filtering to improve mesh quality from voxelated and 3D image sources, improvements to the primal contouring method for constructing material interfaces and pillowing to improve mesh quality at boundaries. We show specific examples in crystal plasticity and syntactic foam modeling that have benefitted from the proposed mesh generation procedure and illustrate results of the procedure with several practical mesh examples.

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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 (T_g), 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.

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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.