Arbitrary Thermal History Research Articles

Assessment of unexplored isoconversional methods to predict epoxy-based composite curing under arbitrary thermal histories

The mass manufacturing of composite products is hindered by long curing times, and composite manufacturers demand shorter curing cycles while keeping material properties. This requires reliable methods to predict the curing kinetics of each resin formulation. Isoconversional methods are easy to implement and able to deal with complex processes. However, scientists still limit their isoconversional predictions of curing degree to isothermal or constant heating programs. In this study, we perform combined dynamic and isothermal DSC measurements for two different commercial epoxies for aerospace applications (M18 and VTC401). Based on the isoconversional kinetic analysis, we show the feasibility of predicting the evolution of an epoxy resin cure for an arbitrary and complex temperature program using two different unexplored methods for this purpose. Because of the versatility of both prediction methods, they are especially suited to deal with actual conditions in industrial processes. The proposed approach is validated experimentally by comparing predictions against the curing degree of these epoxies during a temperature program that comprises isothermal and dynamic stages. These reliable and straightforward predictions open the door to optimize curing times and increase productivity in composites.

Mean Field Modeling of Grain Growth and Zener Pinning

A mean-field model has been developed to simulate curvature-driven grain growth by exploring the evolution of grain size distribution under arbitrary thermal histories. The model was integrated into precipitation module TC-PRISMA, so that the pinning effect of the concurrently precipitated particles on the growing grains can be considered by a modified, location-specific Zener model. The developed model was validated against analytical calculations, and then applied to real alloy systems, fed with assessed grain boundary energy and mobility data. Its capabilities, limitations, and directions to improvements have been discussed.

Phase field model for multiphase alloys under arbitrary thermal history: An application to IN718 super-alloy

Currently, it is still a significant challenge to predict the microstructural evolution of multiphase alloys in complex manufacturing processes such as joining, welding and additive manufacturing due to their complex thermodynamics and thermal history. In this work, we present a phase-field framework, aiming to predict the evolution of precipitate microstructure under arbitrary thermal history. Our model incorporates nucleation, growth and transformation by taking into account interfacial, chemical and elastic energies. In order to quantitatively describe the nucleation of phases, we leverage on experimental time-temperature-transformation data to parameterize the classical nucleation model. For demonstration, we employ super-alloy IN718, where thermodynamic and kinetic data is obtained using CALPHAD method and major precipitate phases, i.e. γ′,γ″ and δ and their variants are considered. The predicted continuous-cooling-transformation diagram is consistent with data existing in literature, thus validating the approach. We further predict the precipitate evolution under rapid thermal cycling to mimic a typical additive manufacturing process.

Citlalmitl: A Laser-based Device for Meteoritical Sample Fabrication with Arbitrary Thermal Histories

Abstract We present Citlalmitl (the word for meteorite in the Nahuatl language), a new experimental device designed and built to simulate high-temperature processes relevant for meteoritics, including chondrule formation and the atmospheric entry of micrometeorites (MMs). The main component of Citlalmitl is a 50 W CO2 laser, used to melt samples that simulate the precursors of meteoritical materials. As examples of the operation of our device, we have irradiated silicate samples controlling the laser duty cycle to reproduce heating profiles predicted by shock-wave simulations. Citlalmitl records the sample temperature during and after irradiation, a unique feature that allows us to directly measure the thermal history of the sample, a key parameter for the characteristics observed in MMs and chondrules. We demonstrate that Citlalmitl can reproduce different heating profiles useful to mimic thermal histories in meteoritical processes.

Model-free isoconversional method applied to polymer crystallization governed by the Hoffman-Lauritzen kinetics

A new method is developed to obtain the kinetic parameters of polymer crystallization from measurements of the transformation rate usually done at (but not restricted to) constant heating or cooling rates. It can be considered a generalization of the Fiedman's isoconversional method to deal with the Hoffman-Lauritzen temperature dependence. Apart from delivering the U* and Kg parameters as a function of the transformed fraction, this method allows to predict the crystallization course for an arbitrary thermal history. It has been applied to the crystallization of PET and PA6 samples, monitored by differential scanning calorimetry (DSC).

A method for the determination and correction of the effect of thermal degradation on the viscoelastic properties of degradable polymers

Small amplitude oscillatory shear is carried out during isothermal degradation of poly(lactic acid) (PLA) in order to determine the evolution of the characteristic relaxation time with degradation time and temperature. After reducing the relaxation time data to a single mastercurve, a 4-parameter function is fitted to the data to allow prediction of the change in relaxation time following an arbitrary thermal history. The method enables separation of the effects of temperature and of degradation on the relaxation time, both of which lead to a horizontal shift of dynamic data along the frequency axis, and hence enable a correction for thermal degradation during rheometry to be carried out. To validate the method, two isothermal frequency sweeps were measured with different temperature histories, producing different mastercurves due to dissimilar in-test thermal degradation. After correcting for thermal degradation using the function and the thermal histories, the two frequency sweeps reduce to the same viscoelastic mastercurve in the undegraded pre-test state.

Prediction of the chemical and thermal shrinkage in a thermoset polymer

A multi-scale model for the response of a bi-material “thermostat”, consisting of a single unidirectional lamina of carbon/epoxy and an uncured layer of neat diglycidyl ether of bisphenol F (DGEBF) with curing agent, diethyltoluenediamine (DETDA), is developed in order to measure thermal strains during a prescribed, but arbitrary thermal history. Molecular modeling simulations provided the elastic modulus, coefficient of thermal expansion, glass transition temperature of DGEBF/DETDA as a function of degree of cure. Cure kinetic properties were determined with differential scanning calorimeter measurements. The model allowed separation of strains due to cure shrinkage and thermal expansion. Combining the molecular modeling predictions, cure kinetic measurements and “thermostat” deflection measurements, the complete polymer shrinkage phenomenon is determined over a prescribed thermal cycle. Furthermore, this work can provide a vehicle to develop cure cycles wherein the difference between instantaneous glass transition temperature and specimen temperature is controlled to provide optimum cure cycles for minimum cure shrinkage.

Stochastic Model for Volume Relaxation in Glass Forming Materials: Local Specific Volume Model

A stochastic model for structural relaxation in glassy materials is developed, where the rate of relaxation in a mesoscopic domain depends upon the state in that meso-domain. Because the meso-domains have nanometer dimensions, fluctuations are included. The model predicts the volume relaxation for arbitrary thermal histories at ambient pressure in the glass transition region, where the local rate of relaxation is given by a single relaxation time that depends on the local density and temperature. Using a single set of parameters, the stochastic model accurately predicts the entire Kovacs poly(vinyl acetate) volume relaxation data set. The meso-domain size was determined to be 2.8 nm, consistent with NMR and other measurements. This model indicates that the origin of the wide relaxation spectra observed experimentally is a single Debye process that experiences significant fluctuations in its state. The stochastic model also naturally predicts the small amount of thermorheological complexity that is observe...

Unified approach for determining the enthalpic fictive temperature of glasses with arbitrary thermal history

We propose a unified routine to determine the enthalpic fictive temperature of a glass with arbitrary thermal history under isobaric conditions. The technique is validated both experimentally and numerically using a novel approach for modeling of glass relaxation behavior. The technique is applicable to glasses of any thermal history, as proved through a series of numerical simulations where the enthalpic fictive temperature is precisely known within the model. Also, we demonstrate that the enthalpic fictive temperature of a glass can be determined at any calorimetric scan rate in excellent agreement with modeled values.

OS15-3-1 Estimation Corresponding to Temperature Change of Creep Behavior on Glass Fiber Reinforced-Polycarbonate

Thermoplastic resin was practically used without post cure treatment and physical aging treatment which is called "molded material". For such materials, it is known that creep behavior and physical aging occur simultaneously. And the effect of physical aging has the time and temperature dependency. The effect was occurred on the materials after molded, and the effect saved on the materials as the thermal history. This history has big influence on mechanical properties, especially creep properties. Therefore, it is necessary to understand the progress of the physical aging. In this report, the creep deformation of polycarbonate (PC) was researched to grasp the effect of physical aging on creep behavior. Two types of materials were prepared. One was "molded material", and another was pre-physical aged material. It was confirmed that the effect had the time and temperature dependency, and it had been able to apply the time-pre-aging time superposition principle and time-pre-aging temperature superposition principle of physical aging on creep behavior. The estimation corresponding to temperature change of creep deformation became possible using this superposition principle. The estimation result of the creep deformation of glass fiber reinforced polycarbonate (GFRPC) with temperature change during a creep test had the tendency similar to the experimental data. Therefore, it should be able to estimate the creep behavior with arbitrary thermal history since the materials reached to the saturated state of physical aging.

Arbitrary Thermal History Control of Wafer in Photo Resist Processing Using Integrated Heating and Cooling Plate

For photo resist processing in semiconductor manufacturing, the precise temperature control of wafer has been demanded to realize a more fine device in recent years. However, it is difficult to achieve the precise temperature control by a current wafer heating and cooling system, because the system cannot control the temperature of transient state including wafer movement from the nature of the system. An integrated heating and cooling plate was developed to overcome above problem. On the other hand, it is difficult to achieve the precise temperature control of the plate because of its mutual intervention and unstable non-steady heat conduction. For that reason, we propose the control system based on thermal model with finite element in this paper, which is the state feedback control with scheduled gain to the process progress. Moreover, we propose the in-process estimation of wafer temperature based on system identification. Experimental results illustrate the effectiveness of the proposed method and the arbitrary thermal history control of wafer.

Microstructural predictions including arbitrary thermal histories, reaustenization and carbon segregation effects

A microstructural prediction algorithm for hypoeutectoid steels is presented that accounts for carbon segregation effects and permits arbitrary thermal histories and austenite decomposition during reheating. Two austenization models are included: an instantaneous austenite formation and homo-genization model; and a transient, heterogeneous austenite formation algorithm. The transient heterogeneous model predicts slightly slower formation rates than measured but compares favourably with experimental results. The two models provide upper and lower bounds for the austenization time. Predicted grain size, martensite fraction and hardness distributions are compared with measurements taken from a weld heat-affected zone (HAZ). Predictions are in good agreement with experimental results.

Microstructural Predictions Including Arbitrary Thermal Histories, Reaustenization and Carbon Segregation Effects

Microstructural Predictions Including Arbitrary Thermal Histories, Reaustenization and Carbon Segregation Effects

Microstructural Predictions Including Arbitrary Thermal Histories, Reaustenization and Carbon Segregation Effects

A microstructural prediction algorithm for hypoeutectoid steels is presented that accounts for carbon segregation effects and permits arbitrary thermal histories and austenite decomposition during reheating. Two austenization models are included: an instantaneous austenite formation and homogenization model; and a transient, heterogeneous austenite formation algorithm. The transient heterogeneous model predicts slightly slower formation rates than measured but compares favourably with experimental results. The two models provide upper and lower bounds for the austenization time. Predicted grain size, martensite fraction and hardness distributions are compared with measurements taken from a weld heat-affected zone (HAZ). Predictions are in good agreement with experimental results. Copyright © 1996 Canadian Institute of Mining and Metallurgy. Published by Elsevier Science Ltd. Résumé On présente un algorithme de prédiction de la microstructure des aciers hypoeutectoïdes qui tient compte des effets de la ségrégation du carbone et permet les histoires thermiques arbitraires et la décomposition de l'austénite lors du réchauffage. Deux modèles d'austénization sont inclus: un modèle de formation instantanée d'austénite et d'homogénization; et un algorithme de formation transitoire hétérogène d'austénite. Le modèle transitoire hétérogène prédit des taux de formation légèrement plus lents que ceux mesurés mais se compare favorablement avec l'expérience. Les deux modèles fournissent les limites supérieure et inferieure du temps d'austénization. La taille de grain prédite, la fraction de martensite et les distributions de dureté sont comparées avec les mesures prises dans la zone affectée thermiquement (ZAT) d'une soudure. Les prédictions agréent avec l'expérience.

Structural Relaxation of Glass-Forming Polymers Based on an Equation for Configurational Entropy. 1. DSC Experiments on Polycarbonate

A phenomenological model for the process of structural relaxation in glass-forming materials is discussed. The model is based on an expression for the evolution of the configurational entropy of the material when subjected to an arbitrary thermal history and contains four fitting parameters. The prediction of the model is presented in terms of heat capacity c p (T) curves, which are compared with the experimental DSC heating scans. Experimental results on polycarbonate with a broad series of thermal histories are presented, and the routine employed to fit the parameters of the model is described. The procedure permits the determination of material parameters (independent of thermal history) of the polymer : a curve of calorimetric equilibrium relaxation times as a function of temperature and a value for the width parameter of the Kohlrausch-Williams-Watts relaxation function. The possibility that the limit states of the structural relaxation process do not coincide with the states obtained from the extrapolation of the experimentally determined liquidus curve is also discussed.

Global rates of devolatilization for various coal types

This modeling study reports global rate expressions for transient weight loss and yields of tar and gas for coals across the rank spectrum. A novel kinetic analysis demonstrates that the Distributed Activation Energy Model (DAEM) reliability correlates transient weight loss at various heating rates, and makes reasonably accurate extrapolations for pulverized coal (p.c.) firing conditions. This performance motivates solutions of the DAEM for arbitrary thermal histories, including approximate closed-form solutions for transient weight loss along linear temperature ramps and exponential temperature histories. Our analysis also rigorously defines the rate constants in single first order reactions that give the same devolatilization rate as the DAEM at every instant in any thermal history. For devolatilization during heatup at constant rates, frequency factors increase by a factor of 6 for every order-of-magnitude increase in heating rate, while activation energies remain constant. Throughout convective heating, however, both rate parameters decrease continuously, so that straight lines on Arrhenius diagrams do not represent rate constants for coal devolatilization. Rate variations for different coal ranks are modest by comparison. For ranks from lignite to high-volatile bituminous, rates decrease by up to a factor of 3. Low volatility coals are much more resistant to thermal decomposition; they devolatilize at rates up to 5 times slower than all other lower ranks. Correlations for different coal types from FLASH2, a more detailed devolatilization model, describe separate gas and tar evolution rates, and replace hypothetical ultimate yield parameters by accurate predictions for ultimate tar and gas yields.

Transient Brake Temperatures Found by use of Analytical Solutions for Finite Hollow Cylinders

A linear analytical model for calculating transient axisymmetric temperature distributions in finite hollow cylinders is established and adapted for practical use. A homogeneous isotropic material with temperature-independent thermal properties is assumed. Among possible applications are brake discs, brake drums and block braked railway wheels. The thermal power from braking is applied as prescribed heat influxes over parts of the lateral and radial surfaces of the cylinder. Bessel series solutions to the heat conduction equation are found where Newton's law for heat transfer is used in the boundary conditions. In addition to convection prescribed surface temperatures and insulated surfaces are also studied. Arbitrary thermal loading histories are treated by use of Duhamel's principle where step loadings are superposed. Convergence and limitations of the method and required computer times are discussed. Calculated numerical results for some typical braking operations are compared with those of other studies.

Time, temperature, and linear viscoelasticity

AbstractLinear viscoelastic bodies satisfy the Boltzmann superposition principle which permits the calculation of the effect of arbitrary stress or strain history in terms of creep or stress relaxation parameters, respectively. In such calculations, the temperature is not considered as an independent variable; rather, the temperature must be constant, and the stress relaxation and creep parameters used are for the given temperature. By assuming the validity of the time‐temperature superposition principle, it is shown how an arbitrary thermal history may be included. By employing spring‐dashpot model methods, Boltzmann's principle is generalized, leading to the concepts of equivalent stress σ(t) and equivalent time w(t), the latter concept having also been introduced for creep and stress relaxation by Hopkins. These quantities are defined by where t = time, p = density, T = temperature, and a[T(t), T(0)] is the time‐temperature shift factor between temperatures T(0) and T(t). In terms of the equivalent stress and equivalent time, Boltzmann's principle for shear remains the same as for the isothermal case with stress relaxation or creep parameters at the initial temperature, T(0). In the case of tensile experiments, the observed strain must be corrected for thermal expansion.