Assessment of timetemperature superposition of linear. The williamslandelferry wlf equation is a model used to describe the. Welcome to mettler toledos webinar on timetemperature superposition using dynamic mechanical analysis dynamic mechanical analysis, or dma, is an excellent characterization tool for determining the frequency dependent behavior of viscoelastic polymeric materials. The initial temperature was set to a uniform value and both the initial temperature and the reference temperature were set to zero to simplify the use of superposition. The elastic moduli of typical amorphous polymers increase with loading rate but decrease when.
Given the software package i am working with, the automatic. Timetemperature superposition has been used for longterm structural durability design with shortterm accelerating tests at elevated. The data taken at various temperatures can be superimposed to a reference temperature of interest to extend the time range of response. Rta theory 09 principle of superposition material balance time duration. Timetemperature superposition avoids the inefficiency of measuring a polymers behavior over long periods of time at a specified temperature by utilizing the fact that at higher temperatures and shorter time the polymer will behave the same. The pressurederivative response can be distorted in latetime data by the effects of superposition in time, except in data acquired from an initial drawdown. The studied epoxy does not degrade chemically via hydrolysis or chain scission. Buildup superposition time in well testing the superposition time function has been used as a tool to analyze transient pressure data measured under the influence of a variable flow rate. Dma 2980 dynamic mechanical analyzer timetemperature superposition basic timetemperature superposition theory the linear viscoelastic properties of polymers are both time and temperature dependent. The superposition of the data substantiated the timetemperature reduction process, which was suggested by herbert leaderman, first put into practice by arthur. Abhijit p deshpande department of chemical engineering iit madras. So, timetemperature superposition tts makes it possible to characterize the viscoelastic properties of materials at various temperatures over an experimentally convenient time or frequency range. Timetemperature superposition and going nuts just got a bollus of new samples that need their viscoelasticity measured. Master curve construction for dma exploiting the tts.
Guide dma 8000 time temperature supposition software background timetemperature superposition tts analysis allows dma data to be applied to data collected within the measuring range of the dma 8000 0. The objective in this study was to check the validity of the timetemperature superposition principle for hotmix asphalt hma with growing damage and viscoplastic strain in the compression state, which is essential for the permanent deformation characterization of. Free highquality documentaries recommended for you. See who you know at symyx technologies, leverage your professional network, and get hired.
Prediction of longterm strength of thermoplastic composites using timetemperature superposition james r. Prediction of polymer properties at short and long observation times is usually performed through timetemperature superposition tts models, which make use of some calculated shift factors. Since the frequency dependence is directly related to time dependence, the relationship is usually referred to as the timetemperature superposition principle tts. This function is usually defined assuming that radial flow equations are valid, however, in practice there are cases that exhibit several flow regimes i. Timetemperature superposition tts allows us to characterize the viscoelastic properties of a material at various temperatures over an experimentally convenient time or frequency range. Timetemperature superposition for asphalt mixtures with. This model relies on the observation that time and temperature. Measure the energy and environmental impact of infrastructure in production and service. The tts principle is the theoretical basis of the master curve technique. A worked example of time temperature superposition data the basics of wlf theory are applied here to actual data. Use the same sized axes for all graphs and use at least two decades on each axis.
The time scale might be limited between several seconds and say 100 hours. Drying time was a good function of temperature and thickness p. Use a different sheet of paper single side only for each temperature. To use it, enter the recommended developing time and temp from the massive dev chart into the relevant fields, along with the actual temperature you want to use. Temperature superposition an overview sciencedirect topics. Explain the timetemperature superposition principle calculate viscoelastic quantities using wlf equation prepare a master curve and predict viscoelastic response at a different time scale for a given temperature. Ever since its discovery and critical study by some of the pioneers of polymer rheology and viscoelasticity leaderman, tobolsky, ferry, plazek et al, timetemperature superposition tts has proved to be a very useful tool to rheologists, enabling us to extend the timefrequency range of experimental data by amalgamating data at different temperatures to produce a single. The data is collected over a time scale range from 10 seconds to 10,000 secs 2 hrs 45 mins and over a temperature range from 83 c to 40 c. Use the wlf equation and timetemperature superposition principle to justify your argument.
It is known as timetemperature superposition, and it relates time to temperature for viscoelastic materials. The timetemperature superposition principle, frequently used to describe the mechanical and electrical relaxation behaviour of polymers, is considered within the more general concept of scaling with translation path parallel to the abscissa. Timetemperature superposition for asphalt concrete at large compressive strains charles w. Determination of timetemperature shift factor inside of the frame of fig. The most general functions leading to scaling with translation path parallel to the horizontal axis are given. The notion of time temperature shift is expressed as follows, with gt, t as shear modulus which depends on time t and temperature t. For amorphous polymers above their t g s, there is a convenient approximation which makes experiments easier. Timetemperature superposition for asphalt concrete at.
Time temperature superposition is a procedure that has become important in the field of polymers to observe the dependence upon temperature on the change of viscosity of a polymeric melt. Weiss system, as long as the refractive indices of the two polymers are suitably different. Timetemperature superposition principle and scaling. The master curve of e versus the reduced time t was constructed by shifting e at various constant temperatures along the log scale of t and the log scale of e. The theoretical basis builds on decades of development in the technical literature. Timetemperature superposition to determine the stress. Syed ali ashter, in thermoforming of single and multilayer laminates, 2014. A worked example of time temperature superposition data. Improved miscibility of two polymers may be accomplished by promoting specific intermolecular interactions, and, in this regard, ionomers offer a. The master curves allow the dynamic behavior of materials to be determined at frequencies outside of practical measurement ranges. The underlying basis for timetemperature superpositioning is the demonstrated equivalency between time or frequency and temperature. This is the basic principle of timetemperature superposition 17, obeyed by polymers in a variety of guises, in the solidstates and meltstates, in viscoelastic processes of both pure and.
Dma 2980 dynamic mechanical analyzer ta instruments. Time temperature superposition principle application. When considering a material for an application, many times we want to know how the viscoelastic properties will change over a long period of time. Time dependant responses and superposition electronics. The horizontal timetemperature shift factor atot and the vertical temperature shift factor btot at a reference temperature t0 plotted in fig. Reeder langley research center, hampton, virginia national aeronautics and space administration langley research center hampton, virginia 236812199 august 2002. Isothermal viscoelastic properties of pmma and ldpe over. A mathematical computation that accounts for the flowrate history in analytical models generated to match with pressuretransient test data. Note that the system has an initial rate of temperature increase in the first unit of time that is rapid compared to the rate of temperature increase at later times.
Tsai department of aeronautics and astronautics, stanford university durand 381, stanford, california, 94305, usa summary. Polymer software optional tts timetemperature superposition to create master curves spectra mwd molecular weight distribution interfacial rheometry optional automatic data quality evaluation selection of predefined measurement and analysis elements in haake rheowin data evaluation using lissajous plots 11. A methodology for predicting cable degradation under ambient nuclear power plant aging conditions, author gillen, k t and clough, r l, abstractnote timetemperature superposition is an empirical approach that has been used in polymers for more than 30 years to make thermal aging. A sequence of measurements of e r t is performed at different temperatures at a fixed initial strain. Simultaneous timetemperaturethickness superposition. At its core, the reduced time approach requires high. For example, if a polymer is subjected to a constant load, the elastic. The evidence of a superposition capability is an alternative manifestation of the well known timetemperature equivalence principle but the existence of a unique intrinsic response in the normalized stressstrain plane extends the validity of the principle to the field of nonlinear viscoelastic behaviors. Master curve obtained via tts of separate e r curves at various temperatures. Akin to timetemperature superposition tts, this reduced time approach is essentially timeentropy superposition tss. This calculator takes a standard developing time and adjusts it for temperature. In particular, time temperature superposition is used to obtain an extended range of time or frequency. Important questions relating to the techniques needed to obtain smooth master curves will be discussed, as will the validity the resulting curves and the corresponding stressrupture lifetime.
This technique is known as the timetemperature superposition principle and will be applied to kevlar 49 yarns. Ihs markit reservoir engineering solutions 2,726 views. In this work, a timetemperatureplasticization superposition principle ttpsp is described and used for predicting the longterm creep behavior of an epoxy compound. Timetemperature superposition and going nuts rheo thing. For linearviscoelastic data, plot both g and g as a function of frequency on each graph. Analysts must be aware of this limitation in diagnosing reservoir features. The measuring is hardly the problem its when i have to do the timetemperature superpositon that i start getting blurryeyed. The time temperature superposition principle is a concept in polymer physics and in the physics of glassforming liquids. It has been demonstrated that viscoelastic data collected at one temperature can be superimposed upon data obtained at a different temperature simply by shifting one of the curves along the time or frequency axis 1. Automated shift for timetemperature superposition sangwook sihn and stephen w.636 1457 429 975 1078 1139 1471 548 1030 146 866 1139 335 378 398 1395 587 465 298 279 1140 19 1052 29 1347 332 519 1089 655 512 1325 1043 343 329 89 503 423 861 1160 222 466