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.