A New Crystal Plasticity Model for Steels Exhibiting Transformation Induced Plasticity with Application to Quenched and Partitioned Steel
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Date
2021-05-28
Authors
Connolly, Daniel
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Publisher
University of Waterloo
Abstract
This thesis outlines the development of a constitutive model and the modelling techniques required to accurately model steels that exhibit transformation induced plasticity over a wide range of strain-rates and temperatures. A novel thermodynamically consistent rate-dependent crystal plasticity formulation incorporating stress-induced transformation is first developed from the existing models in the literature. In this baseline model, plastic slip and martensitic transformation are governed by thermodynamically derived driving forces that account for various physical mechanism (e.g. temperature, crystal orientation, stress, and martensite surface energy). Thermodynamic arguments are used to derive a physics driven temperature evolution law. Both plastic slip and transformation kinetics are described by power law type rate-dependent evolution. Homogenization of retained austenite (RA) and transformed martensite is considered implicitly using the plastic slip kinetics law. The constitutive model is implemented into a thermo-mechanical Crystal Plasticity (CP) Finite Element Method (FEM) formulation to study the bulk material properties of QP1180 steel. The initial material microstructure is characterized using Electron Backscatter Diffraction (EBSD) and Scanning Electron Microscope (SEM) data. A new method for incorporating thermal boundary conditions in CPFEM models is proposed. The constitutive model is calibrated using experimental stress-strain and martensite evolution measurements characterized using in-situ High Energy X-Ray Diffraction (HEXRD) uniaxial tension experiments. Numerical experiments are conducted to study the effect of thermal and mechanical boundary conditions. Results are presented for a range of temperatures, strain-rates and thermal boundary conditions.
Building on the the initial framework, a generalized constitutive model is proposed that avoids several limiting assumptions of the baseline model. Thermodynamic arguments are again used to derive plastic slip and transformation driving forces that account for various physical mechanisms, as well as a constitutive law governing temperature evolution. Homogenization of RA and transformed martensite is considered explicitly using a modified Taylor homogenization law to determine strain partitioning while accounting for transformation. The mechanical thermo-elasto-viscoplastic behaviour is explicitly and separately modelled in RA and transformed martensite. The model is calibrated and validated for a QP3Mn alloy over a large range of temperatures (-10C to 70C) and strain-rates (5e-4 1/s to 200 1/s). The fully calibrated model is compared to a model recalibrated without strain-rate dependent transformation, demonstrating that capturing strain-rate dependent transformation may be necessary even for materials where no direct experimental strain-rate dependence. The calibrated model is used to conduct plane strain and equibiaxial tension simulations, showing that increasing triaxiality results in increased transformation.
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Keywords
Transformation Induced Plasticity, Thermo-mechanical Modelling, Crystal Plasticity, Strain-rate Dependence, Temperature Dependence, Phase Transformation, Quenched and Partitioned Steel