Materials Science Forum Vols. 539-543

Abstract: A tracking procedure for the high-resolution X-ray computed tomography (CT) has been developed in order to measure 3-D local strain within a deforming material in high-density. A dispersion-strengthened copper alloy model sample with alumina particles, which contains micropores, was visualized by the synchrotron radiation CT. The pores observed in reconstructed CT volumes were used as tracking markers. The developed tracking method using a set of matching parameters, which classifies matched, pended and rejected markers, exhibited high ratio of success tracking. Furthermore, the ratio was improved by applying the spring model method, which is one of the particle image velocity (PIV) methods utilized in the field of the fluid mechanics, to the pended markers. The method based on the image analysis of CT imaging volumes provides us 3-D high-density strain mapping.

Abstract: The phase transformations and the microstructure developments in Fe-Cu base alloys during isothermal aging are simulated based on the phase-field method. Since the chemical free energy used in this simulation is obtained from the thermodynamic database of phase diagrams, the calculated microstructure changes are directly related to the phase diagram of the real alloy system. Firstly the phase decomposition and the microstructure changes in the Fe-Cu binary alloy system are demonstrated as the simple example of the phase-field modeling, i.e., the phase decomposition in bcc phase where the Cu-rich phase forms, the structural phase transformation from bcc to fcc phase in the Cu-rich nano-particle, and the shape change of fcc-Cu precipitates from sphere to rod. Secondly, the phase decomposition in bcc phase of the multi-component alloys such as the Fe-Cu-X (X=Mn,Ni) ternary system and the Fe-Cu-Mn-Ni quaternary alloy is simulated. At the early stage of aging, the Cu-rich zone with bcc structure begins to nucleate, and the component X (=Mn, Ni) is partitioned to the Cu-rich phase. When the Cu composition in the precipitate reaches equilibrium, the component X inside the precipitates moves toward to the interface region between the precipitate and matrix. Finally, there appears the shell structure that the Cu precipitates surrounded by the thin layer with high concentration of component X.

Abstract: The thermodynamic assessment of the Al-Ir binary system, one of the key sub-systems of the Ir-based alloys, was performed using the CALPHAD technique. The AlIr(B2) phase was described using the two sublattice model with the formula (Al,Ir)0.5(Ir,Va)0.5, while other intermetallic phases were treated as stoichiometric compounds. The calculated data of the phases in the Al-Ir system can be used to accurately reproduce experimental data, such as phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases.

Abstract: Our recently proposed calculating method reliably predicts the nucleation free energy barrier of the homogeneous and coherent precipitations. Helmholtz free energy change is clearly defined and calculated by the purely enthalpic and entropic contributions between the initial state of the isolated solute atoms scattering around the matrix and the final state of the cluster of size n traveling around the matrix. The enthalpic term is calculated by the reliable first principles method and the entropic term is estimated by the ideal solution model. The vibrational free energy is also included by the quasi-harmonic approximation. The model calculation was performed on bcc Cu precipitations in the Fe-Cu system. The predicted values of the critical number of 12 atoms and the critical free energy barrier of 0.6eV show good agreement with the experimentally estimated ones for the annealing temperature of 773K and the initial concentration of 1.4at%Cu.

Abstract: One common point amongst extant theories of abnormal grain growth (AGG) is that they treat this phenomenon in terms of the relative grain size, or grain radius, of the abnormal grains. Topological and metrical quantities of abnormal grains, such as the number of their faces, or their grain boundary curvature, are taken into account only indirectly through the grain size itself. This paper, by contrast, treats AGG in terms of concepts, that include both the boundary curvature and the number of faces of the abnormal grain. Two cases are examined: 1) AGG, in which the matrix grains are fully pinned, so normal grain growth cannot occur; 2) AGG in which the matrix grains are free to evolve, so that normal grain growth ensues simultaneously in the matrix.

Abstract: Thermodynamic assessment of the Al-Cr system has been carried out by incorporating first-principles calculations into the CALPHAD approach. A regular solution approximation was adopted to describe the Gibbs energy of the solution phases. The several phases appearing in the composition range between about 30 and 42 at.%Cr were treated as a single homogeneous γ-phase, based on recent experimental results, and the Gibbs energy of the γ-phase was represented using the four-sublattice model with the formula (Al,Cr)8(Al,Cr)8(Cr)12(Al)24. The calculated results enable the reproduction of experimental results on both the phase equilibria and thermochemical properties. In addition, a B2 ordered bcc phase, which was suggested to form as an equilibrium phase in a previous X-ray diffraction study, is not likely to form in either the stable state or metastable state based on our first-principles calculations.

Abstract: A thermodynamic analysis of the Fe−M−P (M = Nb, Ti) ternary system has been performed by combining first-principles calculations with the CALPHAD approach. Because of the lack of experimental information available, thermodynamic properties of orthorhombic anti-PbCl2-type FeMP were evaluated using the Full Potential Linearized Augmented Plane Wave method, and the estimated values were introduced into a CALPHAD-type thermodynamic analysis. Applying this procedure, the phase diagrams of the Fe−M−P ternary phase diagrams whose contents are uncertain so far were calculated with a high degree of probability. Phase diagrams for high-purity ferritic stainless steels obtained following the same procedure are also presented.

Abstract: Modeling of Glass transition is attempted based on the Cluster Variation Method. Free energy functional of an L10 ordered phase is employed to describe the first order nature of the transition. Free energy contour surface calculated as a function of temperature and an order parameter which simulates an amount of defects provides a generalized stability diagram in which the ideal glass transition temperature is identified as a critical point. Transition kinetics is investigated by Path Probability Method which is the kinetics version of the CVM to time domain. Continuous cooling behavior is calculated by explicitly incorporating the temperature dependent viscosity term based on VFT (Vogel-Fulcher-Tamman) formula. The glass transition is realized as the freezing of the order parameter due to the enhanced viscosity. The extension of the present theoretical scheme to non-Bravais lattice is attempted by Continuous Cluster Variation Method.

Abstract: Precipitates are the key ingredient for the strength of heat treatable alloys. To optimize the mechanical properties of alloys it is important to know the response of precipitates to thermomechanical treatments. In the past, application of computer models to describe the evolution of precipitates in the course of these processes has proven difficult due to the complexity of the problem. In this work, a new model based on a mean-field representation of precipitates in a multicomponent matrix is applied to heat treatments of steels. Example simulations are presented for a 9- 12% Cr ferritic/martensitic heat resistant steel for power plant application and a complex tool steel with both carbides and intermetallic phases using the software MatCalc. The predictions of the model are verified on experimental results and the potential application to industrial heat treatment simulation is discussed.