Multiscale analysis of heat treatments in steels: Theory and practice

•Description of the differential formulation of the transient multiscale model as well as its numerical equations, practical implementation, validation and multiscale application.•Application of a rigorous and consistent multiscale tool called Asymptotic Expansion Homogenization.•Application of the transient multiscale model to model heat treatments is original. No publication was found with this approach.

Multiphase steels offer impressive mechanical properties. However, their characterisation still represents a challenge. In a quenching process, phenomena such as undesirable strains or residual stresses are inevitable and can be the cause for non-admissible final parts. Microstructural phase transformations generally magnify the problem. The non-existence of efficient non-destructive experimental procedures capable of measuring them leads to the need of numerical tools capable of quantifying these undesirable effects.In this work, a numerical multiscale transient model, that uses the Asymptotic Expansion Homogenisation (AEH) methodology combined with Finite Element Method (FEM), is proposed for the analysis of heat treatments in steels. The implementation of the AEH method is carried out using the commercial program Abaqus, considering an uncoupled and transient problem with implicit time integration. Within the homogenisation method, the existence of two distinct scales is assumed, defining a micro- and a macroscale. In the smaller scale, the evolution of a steel periodic microstructure is analysed in detail and an equivalent homogeneous material model is established for macroscopic use. Moreover, it is presented in this work that AEH is a rigorous and effective homogenisation method that allows the modelling of the thermomechanical and transient thermal behaviour in periodic materials, particularly in heat treatments.