Robert S. Chambers

Stresses during thermoset cure

Production problems attributed to excessive stresses generated during the cure of epoxies led us to develop a formalism to predict these stresses. In our first studies, we developed a fundamental understanding of the complex evolution of viscoelasticity as the cure progresses. We then incorporated these results into a proper tensorial constitutive equation that was integrated into our finite element codes and validated using more complicated geometries, thermal histories, and strain profiles. The formalism was then applied to the original production problem to determine cure schedules that would minimize stress generation during cure. During the pursuit of these activities, several interesting and puzzling phenomena were discovered that have stimulated further investigation. {copyright} {ital 1998 Materials Research Society.}

Verification of the capability for quantitative stress prediction during epoxy cure

We previously developed a formalism to calculate the evolution of stresses during the cure of crosslinking polymers. In the present study, we characterized the chemical kinetics and cure-dependent thermophysical properties for two epoxy systems, the diglycidyl ether of bisphenol A cured by either diethanolamine or a mixture of aromatic amines. Well-defined experiments were performed in which the cure stresses for these two epoxies were measured as a function of time. The stresses predicted by our formalism, using the material parameters obtained for the two systems, agreed well with the measured stresses.

A thermodynamically consistent, nonlinear viscoelastic approach for modeling thermosets during cure

Our previous, extensively validated, nonlinear viscoelastic formalism for glassy polymers is extended to include the effects of chemical reaction. Two modifications are necessary. First, the extent of reaction represents an additional degree of freedom that must be included in the free energy series expansion. Second, simultaneous reaction and deformation can lead to “compression set” that is represented by an evolving stress-free configuration in the cross-linked solid. The material clock, which is based on potential energy and must also incorporate these modifications, naturally predicts the increase in glass transition with cure.

Potential energy clock model: Justification and challenging predictions

A recent, nonlinear viscoelastic theory for predicting the thermomechanical response of glassy polymers has been shown to predict behaviors from enthalpy relaxation to temperature-dependent mechanical yield in various modes of deformation quite well. The foundation of this theory rests on a “material clock” that depends on the potential energy of the system. The molecular basis for the clock and the Rational Mechanics framework for the constitutive equation are briefly reviewed. The theory is then used to predict and explain much more complicated behavior of glassy polymers: the change in compressive yield stress during physical aging at different temperatures, the peculiar enthalpic response of glassy polymers previously compressed to different strains, “volumetric implosion” on samples subjected to tensile strains, and the dependence of the shift factor on aging time and applied stress.

Predicting the Initiation of Thermoset De-Bonding

Napkin ring adhesion tests over a broad range of experimental conditions suggested a de-bonding mechanism for glassy thermosets associated with “run-away” nonlinear viscoelasticity. Finite element analyses of these tests using a high fidelity, nonlinear constitutive equation were used to identify a single, scalar metric that consistently predicted the initiation of de-bonding, a critical value of the maximum principal strain in the “interphase” zone. In principle, such a de-bonding metric enables evaluation of design margins in practical components.

Time-Dependence of Epoxy Debonding

Test geometries with well-defined stresses at the initiation of adhesive failure (failure in adhesion) were used to examine debonding of epoxies in controlled ramp and creep tests. Little effect of substrate, curative, or filler content was seen in failure initiation for the variations studied. The time-to-fail in creep tests depended sensitively on the applied load. Sinusoidal shear loads were also applied in both single (zero to max) and double-sided (− max to + max) mode. Whereas the single-sided, oscillatory loaded samples failed much later than samples loaded in creep to the same maximum stress, double-sided times-to-fail were similar to those in creep.

Critical tractions for initiating adhesion failure at interfaces in encapsulated components

ABSTRACT Determining the initiation of adhesive failure at a surface buried deep within the bulk of an epoxy is qualitatively different from measuring the propagation of an existing surface crack. Most current tests are shown to be unsuitable for assessing the critical traction at initiation. A new test geometry is presented that initiates failure away from an air interface, produces a slowly varying stress distribution near the initiation site and minimal contributions from thermal residual stresses, and enables tests with mixed modes of loading. This new geometry is used to examine temperature-dependent adhesive failure in tensile, shear, and mixed modes of loading for both smooth and rough surfaces. Some of the experimental results are unexpected. As examples, the critical traction at initiation of adhesive failure is apparently insensitive to surface roughness, and the critical normal traction is independent of temperature while the critical tangential traction tracks the shear yield stress.

Small Strain Plasticity Behavior of 304L Stainless Steel in Glass-to-Metal Seal Applications

Cracks in glass-to-metal seals can be a threat to the hermeticity of isolated electronic components. Design and manufacturing of the materials and processes can be tailored to minimize the residual stresses responsible for cracking. However, this requires high fidelity material modeling accounting for the plastic strains in the metals, mismatched thermal shrinkage and property changes experienced as the glass solidifies during cooling of the assembly in manufacturing. Small plastic strains of just a few percent are typical during processing of glass-to-metal seals and yet can generate substantial tensile stresses in the glass during elastic unloading in thermal cycling. Therefore, experimental methods were developed to obtain very accurate measurements of strain near and just beyond the proportional limit. Small strain tensile characterization experiments were conducted with varying levels and rates of strain ratcheting over the temperatures range of −50 to 550 °C, with particular attention near the glass transition temperature of 500 °C. Additional experiments were designed to quantify the effects of stress relaxation and reloading. The experimental techniques developed and resulting data will be presented. Details of constitutive modeling efforts and glass material experiments and modeling can be found in Chambers et al. (Characterization & modeling of materials in glass-to-metal seals: Part I. SAND14-0192. Sandia National Laboratories, January 2014).

Temperature-Dependent Small Strain Plasticity Behavior of 304L Stainless Steel

Glass-to-metal seals are used extensively to protect and isolate electronic components. Small strains of just a few percent are typical in the metal during processing of seals, but generate substantial tensile stresses in the glass during the solidification portion of the process. These tensile stresses can lead to glass cracking either immediately or over time, which results in a loss of hermiticity of the seal. Measurement of the metal in the small strain region needs to be very accurate as small differences in the evolving state of the metal have significant influence on the stress state in the glass and glass-metal interfaces. Small strain tensile experiments were conducted over the temperatures range of 25–800 °C. Experiments were designed to quantify stress relaxation and reloading combined with mid-test thermal changes. The effect of strain rate was measured by directly varying the applied strain rate during initial loading and reloading and by monitoring the material response during stress relaxation experiments. Coupled thermal mechanical experiments were developed to capture key features of glass-to-metal seal processing details such as synchronized thermal and mechanical loading, thermal excursions at various strain levels, and thermal cycling during stress relaxation or creep loadings. Small changes in the processing cycle parameters were found to have non-insignificant effect on the metal behavior. The resulting data and findings will be presented.

Viscoelasticity of Glass-Forming Materials: What About Inorganic Sealing Glasses?

Glass forming materials like polymers exhibit a variety of complex, nonlinear, time-dependent relaxations in volume, enthalpy and stress, all of which affect material performance and aging. Durable product designs rely on the capability to predict accurately how these materials will respond to mechanical loading and temperature regimes over prolonged exposures to operating environments. This cannot be achieved by developing a constitutive framework to fit only one or two types of experiments. Rather, it requires a constitutive formalism that is quantitatively predictive to engineering accuracy for the broad range of observed relaxation behaviors. Moreover, all engineering analyses must be performed from a single set of material model parameters. The rigorous nonlinear viscoelastic Potential Energy Clock (PEC) model and its engineering phenomenological equivalent, the Simplified Potential Energy Clock (SPEC) model, were developed to fulfill such roles and have been applied successfully to thermoplastics and filled and unfilled thermosets. Recent work has provided an opportunity to assess the performance of the SPEC model in predicting the viscoelastic behavior of an inorganic sealing glass. This presentation will overview the history of PEC and SPEC and describe the material characterization, model calibration and validation associated with the high Tg (~460 °C) sealing glass.