A plasticity-induced internal length mean field model based on statistical analyses of EBSD and nanoindentation data

Abstract

A new plasticity-induced internal length mean field model (ILMF) is developed, based on statistical analyses of geometrically necessary dislocation (GND) densities and total dislocation densities estimated from EBSD and nanoindentation data, respectively. It is applied to a single phase ferritic Al-killed steel, which plastically deforms with the occurrence of heterogeneous intra-granular fields. During tensile tests up to 18 % of overall plastic strain, the deformation maps of GND densities due to intra-granular plastic strain gradients are obtained together with nano-hardness maps. The Nye tensor (or dislocation density tensor) is calculated from the 2D EBSD orientations to estimate the intragranular GND density, while a mechanistic model is used to estimate the intragranular total dislocation density from nano-hardness measurements. These data are quantified as a function of the distance to grain boundaries (GBs) to study the development of such plastic strain gradients in the vicinity of GBs. The novel methodology lies in extracting the evolution law of a single plasticity-induced internal length, denoted $\lambda$, from the statistical analysis of GND and total dislocation densities spatial distribution. Hence, it is introduced as an evolving variable in an elastoviscoplastic self-consistent model (EVPSC) for a two-phase composite as a new internal mean field (ILMF) approach. Both experimentally quantified microstructural internal lengths defined by the mean grain size and the evolving layer $\lambda$, are considered to more realistically describe the macroscopic and phase response in terms of stress, GND density evolution and total dislocation density in each phase. An experiment/model comparison is also discussed regarding GND density evolution with plastic deformation.