Quenching & Partitioning (Q&P) steels owe their good strength-ductility combinations to the martensite/austenite (α’/γ) mechanical interactions and to the formation of mechanically-induced martensite (α′_mech) through the transformation-induced plasticity (TRIP) effect. An essential role is played by carbon, whose distribution among the phases can be modified through the Q&P route. This study presents a methodology to systematically and quantitatively examine the influence of the α’/γ mechanical interactions on the overall work hardening of the steel with respect to the role of carbon in the martensite. The methodology rests on the generation of a 3D micro-mechanical model that allows to derive, by crystal plasticity simulations, the overall response of a mechanically-stable α’/γ virtual microstructure. In combination with theoretical knowledge on hardening, the comparison between the experimental and simulated mechanical responses enables the quantification of the influence of the martensite carbon content and distribution on the overall TRIP strengthening contribution of the steel. The approach is applied to two low carbon Q&P-processed α’/γ microstructures of similar initial volume fractions of austenite and α′_mech formation kinetics with strain, but one containing a Nb-microaddition and displaying improved strength-ductility values. It is shown that the martensite strength and work hardening ability might additionally enhance or partially counteract the strengthening contribution from the austenite-to-α′_mech transformation during uniaxial loading. The results of this study highlight that the processing-dependent properties of the carbon-depleted martensite should be considered in the optimization of Q&P processed steels.

Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single-phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of two-dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.