Phase Field modeling of sigma phase transformation in duplex stainless steels : Using FiPy-Finite Volume PDE solver

Abstract: Duplex Stainless Steels (DSS) are used extensively in various industrial applications where the properties of both austenite and ferrite steels are required. Higher mechanical strength and superior corrosion resistance are the advantages of DSS. One of the main drawbacks for Duplex steels is precipitation of sigma phase and other intermetallic phases adversely affecting the mechanical strength and the corrosion behavior of the steels. The precipitation of these secondary phases and the associated brittleness can be due to improper heat treatment. The instability in the microstructure of Duplex stainless steels can be studied by understanding the phase transformations especially the ones involving sigma phase. To reduce the time and effort to be put in for experimental work, computational simulations are used to get an initial understanding on the phase transformations. The present thesis work is on the phase transformations involving sigma phase for Fe-Cr system and Fe-Cr-Ni system using theoretical approach in 1D and 2D geometries. A phase field model is implemented for the microstructural evolution in DSS in combination with thermodynamic data collected from the Thermo-Calc software. The Wheeler Boettinger McFadden (WBM) model is used for Gibbs energy interpolation of the system. FiPy- Finite volume PDE solver written in python is used to simulate the phase transformation conditions first in Fe-Cr system for ferrite-austenite and ferrite-sigma phase transformations. It is then repeated for Fe-Cr-Ni ternary system. In the present study a model was developed for deriving Gibbs energy expression for sigma phase based on the common tangent condition. This model can be used to describe composition constrained phases and stoichiometric phases using the WBM model in phase field modeling. Cogswell’s theory of using phase order variable instead of an interpolating polynomial in the expression for Gibbs energy of whole system is also tried.