Schaeffler-Type Phase Diagram of Ti-Based Alloys
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NTRODUCTION
SINCE Ti transforms from cph-a (T < 1155 K) to bcc-b (1155 K < T < 1943 K), commercial Ti alloys are classified into three categories, namely, a and near-a, a+b, and b alloys, depending on the content of alloying element, respectively,[1–5] where the alloying elements can be classified as a stabilizer or b stabilizer which increases or decreases the a/b transformation temperature. This situation is very similar to the ferrite forming or austenite forming element in steels. Commercial stainless steels are classified into ferrite, ferrite-austenite duplex, and austenite types. The Schaeffler diagram,[6] as shown in Figure 1, is well known to be utilized for the alloy design of stainless steels, where Cr and Ni equivalents are introduced. The coefficient of Cr or Ni equivalents shows the degree of relative stability of alloying elements compared with Cr or Ni, which are empirically estimated. A similar situation of phase stability of Ti-based alloys has been proposed by using Al and Mo equivalents, which are typical a and b forming elements, respectively,[1–5,7] as shown in Figure 2. Other approaches to alloy stability of Ti alloys have been reported, such as electron-atom ratio,[8] multiple linear regression analysis for b transus temperatures,[9] the DV-Xa cluster method using parameters of metal d-orbital level (Md) and the bond order between atoms (Bo),[10] and an artificial neural networks model.[11]
K. ISHIDA is with the Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan. Contact e-mail: [email protected] Manuscript submitted March 8, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS A
This paper presents a thermodynamic definition of Al and Mo equivalents denoted as Aleq and Moeq, respectively, and these parameters 40 alloying elements are evaluated from the previous and present thermodynamic assessments.
II.
THERMODYNAMIC DEFINITION OF Aleq AND Moeq
When we consider the equilibrium between a and b solution in the Ti–X binary system, the following parameter, which represents the relative stability by alloying element, can be defined[12–16]: ¼ RT ln xaX =xbX ; Dla!b X
½1
where xaX and xbX are the equilibrium compositions of a!b a and b phase at T (K), respectively. DlX means the difference in partial molar Gibbs energy of alloying component X between the a and b phases in a dilute solution. The systematic variation of the above parameter in Ti alloys with the Periodic Table was reported by Worner.[13] Dla!b X can be expressed by the regular solution model[14–16]: a!b ¼ DGX þ DLa!b Dla!b X X ;
½2
is the Gibbs energy difference between a where DGa!b X and b crystal modification of pure component X, and is the difference in regular solution parameters DLa!b X between the a and b phases. When the interaction parameters are not available, can be evaluated by the distribution coefficient Dla!b X xaX =xbX in Eq. [1] and the allotropic phase boundary
between the two phase xoX in dilute solution[15,16] as shown in Figure 3. xoX 1 Dla!b DGa!b
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