Time - temperature-transformation diagrams

We are now in position to construct the time-temperature-transformation curve for glass formation. A 1 ppm crystallization is just detectable, so we set the transformation threshold to 10 For kt C 1, we can write 

Strain point 3x10 No plastic deformation, approximately equals the Tg 

Annealing point 10 Diffusion fast enough to eliminate internal stresses 

Working point 10 Easily deformed but does not flow 

Source From Callister, W.D., Materials Scierwe and Engineering An Introduction, 7th edn., 2007. 

FIGURE 6.30 Constructing a TTT diagram from F(t) curves at several different temperatures, where the F t) curves are constructed from the G(T) and N(T) curves for the transformation process. The TTT diagram provides the time required to achieve certain amounts of transformation as a function of the temperature of the transformation. TTT curves are also known as C curves, because of their characteristic C-hke shape. The C-like shape is due to the fact that both nucleation and growth (and hence the overall transformation rate) peak at intermediate temperatures. 

The homework provides an opportunity to develop a TTT diagram for a solidification process. The process involves three principal steps  

Calculate F t) at 5-10 different temperatures (using values calculated for iV and G at these 5-10 different temperatures). 

LIQUID-SOLID AND SOLID-SOLID PHASE TRANSFORMATIONS 

Differences between Liquid-Solid and Solid-Solid Phase Transformations 

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Figure 6.4 The time-temperature-transformation diagram of the iron-carbon system, beginning at the composition of austenite...

Characteristics and implementation of the treatments depend on the expected results and on the properties of the material considered a variety of processes are employed. In ferrous alloys, in steels, a eutectoid transformation plays a prominent role, and aspects described by time-temperature-transformation diagrams and martensite formation are of relevant interest. See a short presentation of these points in 5.10.4.5. Titanium alloys are an example of the formation of structures in which two phases may be present in comparable quantities. A few remarks about a and (3 Ti alloys and the relevant heat treatments have been made in 5.6.4.1.1. More generally, for the various metals, the existence of different crystal forms, their transformation temperatures, and the extension of solid-solution ranges with other metals are preliminary points in the definition of convenient heat treatments and of their effects. In the evaluation and planning of the treatments, due consideration must be given to the heating and/or cooling rate and to the diffusion processes (in pure metals and in alloys). 

For a number of applications, particularly those associated with conditions of continuous cooling or heating, equilibrium is clearly never approached and calculations must be modified to take kinetic factors into account. For example, solidification rarely occurs via equilibrium, amorphous phases are formed by a variety of non-equilibrium processing routes and in solid-state transformations in low-alloy steels much work is done to understand time-temperature-transformation diagrams which are non-equilibrium in nature. The next chapter shows how CALPHAD methods can be extended to such cases. 

This section will begin by looking at how thermodynamic and kinetic modelling has been combined to understand time-temperature-transformation diagrams in steels. The woric, for the most part, is semi-empirical in nature, which is forced upon the topic area by difficulties associated with the diffusional transformations, particularly where nucleation aspects have to be considered. The approaches have considered how best to predict the time/temperature conditions for austenite to... 

A discontinuous transformation generally occurs by the concurrent nucleation and growth of the new phase (i.e., by the nucleation of new particles and the growth of previously nucleated ones). In this chapter we present an analysis of the resulting overall rate of transformation. Time-temperature-transformation diagrams, which display the degree of overall transformation as a function of time and temperature, are introduced and interpreted in terms of a nucleation and growth model. 

Wei, J., DeMuse, M. and Hawley, M.C., Kinetics modelling and time-temperature-transformation diagram of microwave and thermal cure of epoxy-resins, Polym. Eng. Sci., 1995, 35, 461. 

Construct a time-temperature-transformation diagram for a thermoset that follows a second order reaction kinetic model described by... 

Figure 3. ATS time-temperature-transformation diagram for isothermal cures in N2.

Gelation, vitrification and phase-separation transitions in curing systems are very well described in the work of GilUiam (1986) via the use of time-temperature-transformation diagrams. 

Fig. 10 Thermodynamic and kinetic basis for solute depletion in the case of a binary alloy consisting of solvent A and solute B. (a) Binary equilibrium phase diagram with complete miscibility in the liquid state, partial miscibility in the solid state given by existence of a terminal solid solution. Cs is the composition along the solvus line. is the overall composition of the alloy, (b) Time-temperature-transformation diagram for precipitation of in an a matrix for the alloy shown in (a) with overall composition,...

Fig. 11 Schematic of time-temperature-transformation diagram for alloy indicated in Fig. 10 indicating regions of both heterogeneous and homogeneous precipitation of the p phase in a a matrix.

Fig. 1.3 A time-temperature-transformation diagram for the Vitreloy 1 glass-forming liquid (a, obtained using electrostatic levitation , obtained using carbon crucibles) (from Busch (2000) courtesy of TMS).

Eno] Enomoto, M., Maruyama, N., Wu, K.M., Tarui, T., Alloying Element Accumulation at Ferrite/Austenite Boundaries Below the Time-Temperature-Transformation Diagram Bay in an Fe-C-Mo Alloy , Mater. Sci. Eng. A, 343, 151-157 (2003) (Calculation, Experimental, Kinetics, Phase Diagram, Phase Relations, 27)... 

Involving the time dependence AFm t) (Equation 1) is close to the thermodynamics of systems with fading memory (Day, 1972) and the TTT type (time-temperature-transformation) diagram, a so-called nose diagram in the spinodal dccompasition theory (Huston et ah, 1966 Cahn, 1968). 

Problem 6.7. Figure 6.42 gives a set of rate of transformation [F(t)] curves for the crystallization of a glass. Using this information, calculate and plot (using a computer program of your choice) a ITT (time-temperature-transformation) diagram for this crystallization that includes curves for 10,50, and 90% transformed with temperature on the vertical axis versus log (time) on the horizontal axis. 

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