Derivation of anisotropic flow curves of ferrite–pearlite pipeline steel via a two-level homogenisation scheme

In order to calculate the effective macroscopic stress–strain curves of a pearlitic–ferritic pipeline steel, a multi-scale approach based on the homogenisation method is presented. Starting from an experimental material characterisation after the cooling process, material models involving microstructural features (e.g. grain size, carbon content) are derived for each phase. Since pearlite is a eutectoid phase mixture, embedded in a ferrite matrix, three length scales are introduced: the nano-scale of a ferrite–cementite bi-lamella of pearlite, the mesoscopic pearlite/ferrite microstructure and the macro-scale of the component. Firstly homogenisation techniques are applied to a bi-lamella Representative Volume Element (RVE) of pearlite. Initial predictions based on the assumption of a hard, elastic cementite phase are further improved by considering its yield behaviour. The present study outlines that cementite is not only anisotropic in elasticity but also in plasticity. Due to uncertainties about the yield behaviour of cementite, a sensitivity analysis has been performed. Secondly pearlite is treated at the micro-scale as an effective phase in an elasto-plastic ferrite matrix. Virtual tensile and shear tests are performed in order to derive the effective flow curves of the pearlite/ferrite microstructures. Comparisons with experimental stress–strain curves in rolling and transverse directions illustrate the accuracy and entitlement of the two-level homogenisation scheme.