Over many decades, significant efforts have been made to improve the strength-elongation product of advanced high strength steels (AHSSs) by creating tailored multi-phase microstructures. Successive solid-state phase transformations for steels with a well selected chemical composition turned out to be the key instrument in the realisation of such microstructures. In this contribution, we first provide a brief review of the desired microstructures for Transformation-induced plasticity (TRIP), Carbide-free Bainitic (CFB), Quenching & Partitioning (Q&P) and Medium Manganese steels followed by comprehensive discussions on the phase transformations to be used in their creation. The implications for the steel composition to be selected are addressed too. As the presence of the right amount and type of metastable retained austenite (RA) is of crucial importance for the mechanical performance of these AHSSs, special attention is paid to the important role of successive solid-state phase transformations in creating the desired fraction and composition of RA by suitable element partitioning (in particular C and Mn). This critical partitioning not only takes place during final cooling (austenite decomposition) but also during the back transformation (austenite reversion) during reheating. This review aims to be more than just descriptive of the various findings, but to present them from a coherent thermodynamic / thermo-kinetic perspective, such that it provides the academic and industrial community with a rather complete conceptual and theoretical framework to accelerate the further development of this important class of steels. The detailed stepwise treatment makes the review relevant not only for experts but also metallurgists entering the field.

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Let (A, A, μ) and (B, B, ν) be probability spaces, let F be a sub-σ-algebra of the product σ-algebra A× B, let X be a Banach space and let 1 < p, q< ∞. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to F defines a bounded linear operator from L p (μ; L q (ν; X)) onto LFp(μ;Lq(ν;X)), the closed subspace in L p (μ; L q (ν; X)) of all functions having a strongly F-measurable representative. @en

Extending results of Pardoux–Peng and Hu–Peng, we prove well-posedness results for backward stochastic evolution equations in UMD Banach spaces.

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