This SAND report fulfills the completion requirements for the ASC Physics and Engineering Modeling Level 2 Milestone 7836 during Fiscal Year 2021. The Sandia Simplified potential energy clock (SPEC) non-linear viscoelastic constitutive model was developed to predict a whole host of polymer glass physical behaviors in order to provide a tool to assess the effects of stress on these materials over their lifecycle. Polymer glasses are used extensively in applications such as electronics packaging, where encapsulants and adhesives can be critical to device performance. In this work, the focus is on assessing the performance of the model in predicting material evolution associated with long-term physical aging, an area that the model has not been fully vetted in. These predictions are key to utilizing models to help demonstrate electronics packaging component reliability over decades long service lives, a task that is very costly and time consuming to execute experimentally. The initiating hypothesis for the work was that a model calibration process can be defined that enables confidence in physical aging predictions under ND relevant environments and timescales without sacrificing other predictive capabilities. To test the hypothesis, an extensive suite of calibration and aging data was assembled from a combination of prior work and collaborating projects (Aging and Lifetimes as well as the DoD Joint Munitions Program) for two mission relevant epoxy encapsulants, 828DGEBA/DEA and 828DGEBA/T403. Multiple model calibration processes were developed and evaluated against the entire set of data for each material. A qualitative assessment of each calibration's ability to predict the wide range of aging responses was key to ranking the calibrations against each other. During this evaluation, predictions that were identified as non-physical, i.e., demonstrated something that was qualitatively different than known material behavior, were heavily weighted against the calibration performance. Thus, unphysical predictions for one aspect of aging response could generate a lower overall rating for a calibration process even if that process generated better quantitative predictions for another aspect of aging response. This insurance that all predictions are qualitatively correct is important to the overall aim of utilizing the model to predict residual stress evolution, which will depend on the interplay amongst the different material aging responses. The DSC-focused calibration procedure generated the best all-around aging predictions for both materials, demonstrating material models that can qualitatively predict the whole host of different physical aging responses that have been measured. This step forward in predictive capability comes from an unanticipated source, utilization of calorimetry measurements to specify model parameters. The DSC-focused calibration technique performed better than compression-focused techniques that more heavily weigh measurements more closely related to the structural responses to be predicted. Indeed, the DSC-focused calibration procedure was only possible due to recent incorporation of the enthalpy and heat capacity features into SPEC that was newly verified during this L2 milestone. Fundamentally similar aspects of the two material model calibrations as well as parametric studies to assess sensitives of the aging predictions are discussed within the report. A perspective on the next steps to the overall goal of residual stress evolution predictions under stockpile conditions closes the report.
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.
The Henkel technical data sheet (TDS) for Stycast 2651/Catalyst 11 lists three alternate cure schedules for the material, each of which would result in a different state of reaction and different material properties. Here, a cure schedule that attains full reaction of the material is defined. The use of this cure schedule will eliminate variance in material properties due to changes in the cure state of the material, and the cure schedule will serve as the method to make material prior to characterizing properties. The following recommendation was motivated by (1) a desire to cure at a single temperature for ease of manufacture and (2) a desire to keep the cure temperature low (to minimize residual stress build-up associated with the cooldown from the cure temperature to room temperature) without excessively limiting the cure reaction due to vitrification (i.e., material glass transition temperature, Tg, exceeding cure temperature).
The Emerson & Cuming technical data sheet (TDS) for Stycast 2651/Catalyst 9 lists three alternate cure schedules for the material, each of which would result in a different state of reaction and different material properties. Here, a cure schedule that attains full reaction of the material is defined. The use of this cure schedule will eliminate variance in material properties due to changes in the cure state of the material, and the cure schedule will serve as the method to make material prior to characterizing properties. The following recommendation uses one of the schedules within the TDS and adds a “post cure” to obtain full reaction.
Develop an understanding of the evolution of glassy polymer mechanical response during aging and the mechanisms associated with that evolution. That understanding will be used to develop constitutive models to assess the impact of stress evolution in encapsulants on NW designs.
When diethanolamine (DEA) is used as a curative for a DGEBA epoxy, a rapid “adduct-forming” reaction of epoxide with the secondary amine of DEA is followed by a slow “gelation” reaction of epoxide with hydroxyl and with other epoxide. Through an extensive review of previous investigations of simpler, but chemically similar, reactions, it is deduced that at low temperature the DGEBA/DEA gelation reaction is “activated” (shows a pronounced induction time, similar to autocatalytic behavior) by the tertiary amine in the adduct. At high temperature, the activated nature of the reaction disappears. The impact of this mechanism change on the kinetics of the gelation reaction, as resolved with differential scanning calorimetry, infrared spectroscopy, and isothermal microcalorimetry, is presented. It is shown that the kinetic characteristics of the gelation-reaction of the DGEBA/DEA system are similar to other tertiary-amine activated epoxy reactions and consistent with the anionic polymerization model previously proposed for this class of materials. Principle results are the time-temperature-transformation diagram, the effective activation energy, and the upper stability temperature of the zwitterion initiator of the activated gelation reaction. It is established that the rate of epoxide consumption cannot be generically represented as a function only of temperature and degree of epoxy conversion. The complex chemistry active in the material requires specific consideration of the dilute intermediates in the reaction sequence in order to define a model of the reaction kinetics applicable to all time-temperature cure histories.
When thermosetting polymers are used to bond or encapsulate electrical, mechanical or optical assemblies, residual stress, which often affects the performance and/or reliability of these devices, develops within the structure. The Thin-Disk-on-Cylinder structural response test is demonstrated as a powerful tool to design epoxy encapsulant cure schedules to reduce residual stress, even when all the details of the material evolution during cure are not explicitly known. The test's ability to (1) distinguish between cohesive and adhesive failure modes and (2) demonstrate methodologies to eliminate failure and reduce residual stress, make choices of cure schedules that optimize stress in the encapsulant unambiguous. For the 828/DEA/GMB material in the Thin-Disk-on-Cylinder geometry, the stress associated with cure is significant and outweighs that associated with cool down from the final cure temperature to room temperature (for measured lid strain, IεcureI > IεthermalI). The difference between the final cure temperature and the temperature at which the material gels, Tf-Tgel, was demonstrated to be a primary factor in determining the residual stress associated with cure. Increasing Tf-Tgel leads to a reduction in cure stress that is described as being associated with balancing some of the 828/DEA/GMB cure shrinkage with thermal expansion. The ability to tune residual stress associated with cure by controlling Tf-Tgel would be anticipated to translate to other thermosetting encapsulation materials, but the times and temperatures appropriate for a given material may vary widely.
The performance and reliability of many mechanical and electrical components depend on the integrity of po lymer - to - solid interfaces . Such interfaces are found in adhesively bonded joints, encapsulated or underfilled electronic modules, protective coatings, and laminates. The work described herein was aimed at improving Sandia's finite element - based capability to predict interfacial crack growth by 1) using a high fidelity nonlinear viscoelastic material model for the adhesive in fracture simulations, and 2) developing and implementing a novel cohesive zone fracture model that generates a mode - mixity dependent toughness as a natural consequence of its formulation (i.e., generates the observed increase in interfacial toughness wi th increasing crack - tip interfacial shear). Furthermore, molecular dynamics simulations were used to study fundamental material/interfa cial physics so as to develop a fuller understanding of the connection between molecular structure and failure . Also reported are test results that quantify how joint strength and interfacial toughness vary with temperature.
The degradation in the strength of napkin-ring (NR) joints bonded with an epoxy thermoset is evaluated in a humid environment. While adherend composition (stainless steel and aluminum) and surface preparation (polished, grit blasted, primed, coupling agent coated) do not affect virgin (time=0) joint strength, they can significantly affect the role of moisture on the strength of the joint. Adherend surface abrasion and corrosion processes are found to be key factors in determining the reliability of joint strength in humid environments. In cases where surface specific joint strength degradation processes are not active, decreases in joint strength can be accounted for by the glass transition temperature, Tg, depression of the adhesive associated with water sorption. Under these conditions, joint strength can be rejuvenated to virgin strength by drying. In addition, the decrease in joint strength associated with water sorption can be predicted by the Simplified Potential Energy Clock (SPEC) model by shifting the adhesive reference temperature, Tref, by the same amount as the Tg depression. When surface specific degradation mechanisms are active, they can reduce joint strength below that associated with adhesive Tg depression, and joint strength is not recoverable by drying. A critical relative humidity (or, potentially, critical water sorption concentration), below which the surface specific degradation does not occur, appears to exist for the polished stainless steel joints.
Liquid foams are viscoelastic liquids, exhibiting a fast relaxation attributed to local bubble motions and a slow response due to structural evolution of the intrinsically unstable system. In this work, these processes are examined in unique organic foams that differ from the typically investigated aqueous systems in two major ways: the organic foams (1) posses a much higher continuous phase viscosity and (2) exhibit a coarsening response that involves coalescence of cells. The transient and dynamic relaxation responses of the organic foams are evaluated and discussed in relation to the response of aqueous foams. The change in the foam response with increasing gas fraction, from that of a Newtonian liquid to one that is strongly viscoelastic, is also presented. In addition, the temporal dependencies of the linear viscoelastic response are assessed in the context of the foam structural evolution. These foams and characterization techniques provide a basis for testing stabilization mechanisms in epoxy-based foams for encapsulation applications.
Many weapons components (e.g. firing sets) are encapsulated with blown foams. Foam is a strong lightweight material--good compromise between conflicting needs of structural stability and electronic function. Current foaming processes can lead to unacceptable voids, property variations, cracking, and slipped schedules which is a long-standing issue. Predicting the process is not currently possible because the material is polymerizing and multiphase with changing microstructure. The goals of this project is: (1) Produce uniform encapsulant consistently and improve processability; (2) Eliminate metering issues/voids; (3) Lower residual stresses, exotherm to protect electronics; and (4) Maintain desired properties--lightweight, strong, no delamination/cracking, and ease of removal. The summary of achievements in the first year are: (1) Developed patentable chemical foaming chemistry - TA; (2) Developed persistent non-curing foam for systematic evaluation of fundamental physics of foams--Initial testing of non-curing foam shows that surfactants very important; (3) Identified foam stability strategy using a stacked reaction scheme; (4) Developed foam rheology methodologies and shear apparatuses--Began testing candidates for shear stability; (5) Began development of computational model; and (6) Development of methodology and collection of property measurements/boundary conditions for input to computational model.