Temperature-time/frequency analysis

Dynamic mechanical analysis measures changes in mechanical behavior, such as modulus and damping as a function of temperature, time, frequency, stress, or combinations of these parameters. The technique also measures the modulus (stiffness) and damping (energy dissipation) properties of materials as they are deformed under periodic stress. Such measurements provide quantitative and qualitative information about the performance of materials. The technique can be used to evaluate reinforced and unreinforced polymers, elastomers, viscous thermoset liquids, composite coating and adhesives, and materials that exhibit time, frequency, and temperature effects or mechanical properties because of their viscoelastic behavior. 

The frequency and temperature dependences of e" and tan 8 resemble the behavior of in many respects. These quantities are also small for nonpolar polymers, increase with increasing polarity, and manifest peaks at certain combinations of temperature and frequency. The detailed analysis of the frequency and temperature dependences of , " and tan 8 requires the consideration of relaxation times. Many useful general functional forms have been developed empirically and fitted to experimental data [7-13], On the other hand, the a priori prediction of , e" and tan 8 as functions of the temperature and frequency prior to running any experiments is not possible at this time. 

Dynamic Mechanical Analysis (DMA) is a technique in which the elastic and viscous response of a sample under oscillating load, are monitored against temperature, time or frequency. This technique became well known by the impressive amount of information about the structure of polymers obtained with the torsion pendulum apparatus. The torsion pendulum DMA apparatus is a so-called resonant system i.e. the measuring frequency is not constant. The modern DMA systems are nearly always fixed frequency systems operating at frequencies between about 0.01 and 100 Hz. and in a temperature region ranging from about -150°C to 300°C. A survey of the DMA technique and the available commercial equipment was given by Wunderlich [1]. 

Both sensors were heated to their operational temperature of 700°C by the Pt-heater. A temperature modulation frequency of 0.156 Hz was applied to the modulation heater. The thermopower was determined by a continuous regression analysis over two periods. Due to this low modulation frequency, the sensor response time is limited to 12.8 seconds. 

Thermoelectrometry or thermoelectrical analysis (TEA) is the generic title for a group of techniques involving the measurement of electrical properties of a sample as a function of temperature. The electrical properties commonly measured in TEA are conductance, capacitance, and dielectric properties. The most prominent technique in TEA is dielectric thermal analysis (BETA), which involves measurements of both the capacitance and the conductance of the sample as functions of time, temperature, and frequency. The former is the ability of the sample to store charge whilst the latter is a measure of its ability to transfer charge. Eour parameters are associated with BETA the permittivity, the loss factor, the dissipation factor, and the ionic conductivity. These parameters provide information related to molecular motion within the sample and as for most TA... 

The sequences of events that may lead to vessel failure and their frequencies are determined from probabilistic risk assessment (PRA) analyses. The pressure, temperature and heat transfer coefficient time histories at the vessel inner surface are determined from thermal hydraulic analyses for the events identified by the PRA analyses. These time histories are used together with probabilistic fracture mechanics (PFM) analysis to calculate the conditional probability of RPV failure. Discussion of the methodology used to perform the PRA analyses and define the transient events and associated frequencies, and the thermal hydraulic analyses used to define the event pressure and temperature time histories are outside the scope of this chapter. Consequently, the remainder of this chapter focuses on the PFM evaluation assumptions and procedures. 

An example of the analyses that were performed and used to define the PTS licensing criteria is presented here. This example uses a vessel fabricated from rolled plate connected with axial welds to form two cylindrical shell courses. Circumferential welds connect the two shell courses. The vessel conditions used in this example are specified in Table 12.2. The pressure and temperature time histories at the vessel inner surface for the postulated transient are shown in Figs 12.2 and 12.3, respectively. The heat transfer coefficient used in the analysis was 2825W/mV°C (500 BTU/(hr-ft -°F)). Table 12.3 presents the frequency distribution for the postulated event. This event is representative of an event that is a significant contributor to TWCF. 

A dielectric analyzer (DEA) measures the capacitive and conductive properties of materials as a function of temperature, time, and frequency under a controlled atmosphere. It provides high-sensitivity studies of the chemistry, rheology, and molecular mobility of materials. It can offer considerably improved sensitivity to low-energy transitions over what is available from DSC or TMA. A key feature of DEA is its flexibility for analysis of liquids, paste, and powder samples. 

DMA provides material scientists and engineers with the information necessary to predict the performance of a material over a wide range of conditions. Test variables include temperature, time, stress, strain, and deformation frequency. Because of the rapid growth in the use of engineering plastics and the need to monitor their performance and consistency, dynamic thermal analysis has become the fastest growing thermal analysis technique. 

In this chapter, we briefly review some of our recent studies on structure and dynamics of normal and supercritical water based on first principles simulations. The work reviewed here was based on the methods of ab initio molecular dynamics for trajectory generation and time series analysis for frequency calculations. We consider normal water at room temperature and also supercritical water at three different densities ranging from 1.0 to 0.35 g cm at a temperature of 673 K. More details of the work reviewed here can be found in [16,17]. The next section of this chapter contains a brief account of the ab initio simulations and time series analysis. The results of the hydrogen-bonded structures and their relations to the vibrational frequencies and also the dynamics of the hydrogen bond and vibrational frequency fluctuations in normal and supercritical water are discussed in Section 14.4. This chapter is concluded in Section 14.5. 

DMTA Dynamic Thermo-Mechanical Analysis measures the mechanical properties of materials under stress as a function of time, temperature, and frequency. DETA Dynamic Electrical Thermal Analysis measures the electrical properties of materials as a function of time, temperature, and frequency. 

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