Langer–Schwartz–Kampmann–Wagner precipitation simulations: assessment of models and materials design application for Cu precipitation in PH stainless steels

Abstract

Quantitative modelling of precipitation kinetics can play an important role in a computational material design framework where, for example, optimization of alloying can become more efficient if it is computationally driven. Precipitation hardening (PH) stainless steels is one example where precipitation strengthening is vital to achieve optimum properties. The Langer–Schwartz–Kampmann–Wagner (LSKW) approach for modelling of precipitation has shown good results for different alloy systems, but the specific models and assumptions applied are critical. In the present work, we thus apply two state-of-the-art LSKW tools to evaluate the different treatments of nucleation and growth. The precipitation modelling is assessed with respect to experimental results for Cu precipitation in PH stainless steels. The LSKW modelling is able to predict the precipitation during ageing in good quantitative agreement with experimental results if the nucleation model allows for nucleation of precipitates with a composition far from the equilibrium and if a composition-dependent interfacial energy is considered. The modelling can also accurately predict trends with respect to alloy composition and ageing temperature found in the experimental data. For materials design purposes, it is though proposed that the modelling is calibrated by measurements of precipitate composition and fraction in key experiments prior to application. Graphic abstract

Laves phase formation in Fe-based alloys from strengthening particle to self-healing agent: a review

“…Similarly, MatCalc considers the activation energy within the modeling so that it maximizes the nucleation rate. In either case, the software obtains the minimum value for the activation energy, which is a combination of the driving force and the interfacial energy [77].…”

“…where n s is the number of atoms per unit of area, z s is the number of atoms bonded through the interphase, z 1 is the coordination number of the atoms in the matrix, N A is Avogadro's number and DE s is the solution enthalpy in multi-component system. The approximation for the interfacial energy in MatCalc (equation ( 29)) is similar to the one implemented in TC-Prisma but differs from an additional factor as a function of the precipitate size (a r ( )), which increases from 0 to 1 as the radius of the nucleus increases and a function / f T T c ( )that represents the influence of the diffuse interface [77].…”

On the role of transmission electron microscopy for precipitation analysis in metallic materials

“…This study on precipitate-matrix interface composition via analytical TEM on FIB lamella samples unveils the kinetics of cementite precipitation and suggests the necessity of improving precipitation modeling to enable predictive modeling of, for example, cementite precipitation kinetics and other cases of precipitation where it has been shown that the deviation from local equilibrium occur. [20,219] It should be noted here that the analytical TEM in Ref. [103] was performed with a conventional TEM on carefully prepared site-specific FIB samples.…”

“…In fact, advanced methods allowing for three-dimensional (3D) and in situ characterization are becoming more important today due to the advancement of the modeling. For instance, precipitation modeling by the Langer-Schwartz-Kampmann-Wagner (LSKW) approach [17][18][19][20] needs 3D experimental information of particle size distribution and property modeling is nowadays capable of treating the full 3D microstructure. [21] Specifically for precipitation, high-resolution techniques capable of resolving nanoscale precipitates with proper statistics are needed.…”

Optimization of Interfacial Energy for Langer-Schwartz Based Precipitation Simulations

“…Models based on Langer-Schwartz (LS) theory can utilize CALPHAD assessments, and account for concurrent nucleation, growth, and coarsening. A major limitation of both phase field and LS is selection of input parameters surrounding nucleation, specifically interfacial energy [4].…”