Elasto Visco-Plastic Model of Steel Solidification with Local Damage and Failure

A Nonlinear elastic visco-plastic thermo-mechanical steel microstructure model is coupled with a Gurson-Tvergaard-Needleman (GTN) model to predict local damage and failure in the columnar solidification zone of a steel casting. The new model operates on two scales a unit cell grain model of micro-scale in the columnar zone as well as a macro-model tensile specimen to map observations with experiments. The model aims to investigate inter-granular embrittlement at intermediate temperatures during solidification processes. This embrittlement occurs due to pro-eutectoid ferrite film formation and precipitation of inclusions at the prioraustenite grain boundaries. This behavior of the unit cell is then mapped onto macro-model tensile specimens to measure reduction in ductility. The effect of ferrite film and temperature are studied by calculating the micro-strains, macro-strains and void fractions at which cracks begin to form during the continuous casting process. INTRODUCTION: Steel is an important engineering material which is subject to defects and embrittlement at elevated temperatures. Although thermo-mechanical analysis using computational models has been applied as a powerful tool to predict stress and deformation during steel processing, little previous work has been done to predict steel ductility. PROCEDURES, RESULTS AND DISCUSSION: The model developed in this work to predict steel ductility has two different scales – a micro-scale grain model capturing the microstructural behavior and a macro-model capturing necking behavior during a tensile test [Cardoso 1995]. The grain model represents the columnar microstructure as a honeycomb of regular hexagons, as shown in Fig.1. The unit cell modeled includes three grain boundaries intersecting at the triple point and parts of the three regular hexagonal grains, which gives a rectangular shape to the unit cell. The preliminary isothermal model presented here solves the standard mechanical equilibrium equations, with total strain decomposed into elastic and inelastic (plastic) components [Koric 2006]. The dimensions of the grain model are based upon grain size measurements from experiments and equating the area of the grain to that of a circular grain of the same diameter as the grain size measurement. To account for the effect of ferrite films formation, the grain boundary region is assumed to be composed entirely of pro-eutectoid alpha ferrite while the grain matrix region consists of prior austenite and alpha-ferrite. The phase fractions are obtained from the Fe-C phase diagram at the temperature of interest. The temperature dependent mechanical constitutive model for the austenite is based on the formulations by Kozlowski [Kozlowski 1992], while the mechanical model of alpha ferrite is based on the power law formulation [Zhu 1993] An experiment based strain rate is used as input to both these models to get the plastic behavior relationship of the two phases as shown in Fig 2. The behavior of the ferrite film is the same as