Porter & Easterling, chapter 5

Transcription

1 Porter & Easterling, chapter 5 Question 1 At a fixed composition, a certain binary metal alloy can take either of three different phases, indicated by the letters, β en. The three phases consist of three different crystalline structures. The free energies G for each phase as a function of temperature T are given in the graph below. The temperatures at which G is equal for two phases are denoted by T β 0 en T 0. The interfacial energies can be considered independent of temperature. G β a. What is the stable phase in each of the three following temperature ranges: (1) T < T 0, (2) T 0 < T < T 0 β, (3) T > T 0 β? b. A metal production company wants to produce this metal in its -phase. What is a time/temperature-path that can be applied to form the material in the -phase? c. The crystalline structures of the three phases are such that coherent interfaces can form between and, but only incoherent interfaces can form between and β and between β and. Discuss the consequences of these types of interfaces for the possible formation of the -phase in the time/temperature path of b. d. Assume that the metal is indeed produced in the -phase. What transformations can take place during a subsequent heat treatment at T < T 0? Likewise, what would happen at T 0 < T < T 0 β or at T > T 0 β? e. The addition of 1% of a third element affects the G-line for the β-phase, shifting it to higher values, whereas the - and -line remain practically unaffected. Will this addition make the production of -phase material easier or more difficult? Explain why. ANSWERS a. (1) T < T 0 : the β-phase; (2) T 0 < T < T 0 β : the β-phase; (3) T > T 0 β : the -phase. T

2 b. Producing the -phase by heating at a high temperature, and subsequently annealing at T < T 0, the only temperature range in which could form from or β. c. The interfacial energy of /-interfaces will be lower than that of /β-interfaces, which favours -nucleation. d. Assume that the metal is indeed produced in the -phase. What transformations can take place during a subsequent heat treatment At T < T 0 only the formation of β is possible. At T 0 < T < T 0 β both and β can form, and the same holds for T > T 0 β. e. The addition of 1% of a third element affects the G-line for the β-phase, shifting it to higher values, whereas the - and -line remain practically unaffected. Will this addition make the production of -phase material easier or more difficult? Explain why. It will make the production of the -phase more likely, since it can only be formed in a temperature range in which the β-phase is the stable phase. The increase in G β makes the -phase less instable with respect to the β-phase. Question 2 This question concerns the process of phase transformations in metals. For a phase transformation to occur, both nucleation and growth should take place. Sketch the dependence of the nucleation rate as a function of temperature for a phase transformation from a phase β to a phase, with β being stable for temperatures above the transition temperature T 0, and being the stable phase below T 0. Explain the reasons behind this dependence. ANSWER At temperatures just below the transition temperature T 0 the driving force for transformation is quite low, and consequently the activation energy for nucleation is very

3 high. This high activation energy results in a low nucleation rate. At low temperatures the atomic mobility is reduced substantially. This leads to a low nucleation at low temperatures. In the intermediate range both the driving force and the atomic mobility are considerable, and the nucleation rate reaches a maximum. Question 3 This question concerns the microstructures of steel and aluminium. a) The main forms in which the B phase in steel can be present are ferrite, bainite and martensite. Relate the carbon distribution in the material in each of these three cases to the conditions in which the phase is produced. b) Precipitation reactions in aluminium alloys can result in the presence of metastable phases, of which the classical examples are the θ - and θ -phases in Al-u alloys. Explain why these phases form more readily than the equilibrium θ- phase. ANSWER a) In the formation of ferrite the carbon has a sufficient diffusivity (related to the time available during the transformation) to redistribute over distances on the order of micrometers to form carbides, for instance in the plate-like shape that is found in pearlite. In the bainite formation, taking place faster and at lower temperatures, carbon can redistribute over distances typically less than a micrometer, which leads to finely distributed carbon particles. In martensite, carbon redistribution is not possible, and the carbon remains homogeneously distributed in the martensite phase, as it previously was in the austenite. b) The activation energy for nucleation does not only depend on the driving force for the transformation, but also on the interface energies involved. Since θ and θ can form coherent interfaces with the aluminium matrix, the interface energy is lower than for θ, which can result in a lower activation energy.

4 Question 2 G (J/mol) x 0 Atom fraction arbon x a) onstruct in the figure above the lines that determine the equilibrium compositions of carbon in the ferrite ( x,eq ) and austenite ( x,eq ) phases in this diagram at temperature T 2. Write down these symbols at the appropriate position along the composition axis x. Explain why this construction gives the equilibrium compositions in both phases. b) onstruct in the same figure the lines that indicate the driving force G V for nucleation for the overall composition x 0 at temperature T 2. Write down in Fig. 1 the symbol G V for the driving force for nucleation at the appropriate position. c) Explain with the help of the figure why the average carbon concentration in the remaining austenite and the average driving force for nucleation change as the ferrite fraction increases during the isothermal austenite to ferrite transformation. d) Explain in which carbon-content range the formation of massive ferrite can take place at temperature T 2.

5 ANSWERS a) & b): G G V m µ = µ n m x,eq x x 0 x,eq arbon concentration a) In case that the tangent to both ferrite and austenite Gibbs free energy curves are the same, i.e. line m, the chemical potentials of the carbon atoms in the ferrite and the austenite are the same, which corresponds to the equilibrium situation. b) Indicated in the figure. c) As the isothermal austenite to ferrite transformation proceeds, the carbon concentration in the remaining austenite increases, because the equilibrium solubility of carbon in ferrite is much smaller than the overall carbon concentration of the alloy, i.e. x,eq <<x 0. As the carbon concentration of the remaining austenite x increases, i.e. x >x 0, the tangent to the austenite Gibbs free energy curve becomes smaller and therefore the driving force for nucleation G V becomes smaller.

6 d) Massive ferrite can form in the carbon composition region where the Gibbs free energy curve of the austenite is higher that the Gibbs free energy curve of the ferrite, i.e. 0 < x < m m x, with x the carbon composition at which the Gibbs free energy curves of the austenite and ferrite phases cross at T 2.