Study On The Dynamics Of Martensitic Transformation In CuAlNi Based On Multi-scale Constitutive Relations

Represented by the ternary alloy Cu Al Ni,shape memory alloys have a wide range of applications in engineering fields such as aerospace profiles,precision medical instruments,industrial robots,civil engineerings,municipal constructions and transportations.The fundamental mechanism of shape memory effects is the martensitic transformation.But the complex microstructures of multi-levels and the extremely fast formation speed during the transformation process bring great challenges for its mechanism studies,and thus hinder the further applications of shape memory alloys.Due to the rich microstructures of multi-scale in the transition between parent phase and product phase,forming a constitutive relation of multi-scale for the martensitic transformation to explore its fundamental mechanism would enhance the understanding of shape memory alloys and contribute to the related engineering applications.Based on the techniques of multi-scale analysis,this thesis constructs a complete set of cross-scale consitutive model for the dynamics of the martensitic transformation of the ternary alloy Cu Al Ni based on first-principles calculations,molecular dynamics simulations,thermodynamical analysis and macroscopic phase field simulations.First the configuration free energies and the developments of twinned lattice structures obtained by first-principles based structural optimizations are combined with the characteristics of atomic deformations from molecular dynamics simulations of the transformation dynamics.Then with the thermodynamic modeling and the data fitting,a series of chemical potential functionals are proposed to construct the phase field model of the macroscopic martensitic transformation.Following this scheme,the thesis contains three different kinds of simulations.In Chapter 2,the relationship between martensitic configurations and lattice free energies in the transformation process is obtained with first-principles based configuration optimizations.Through first-principles based density functional theory,structural optimizations of different inhomogeneous DO₃ lattice models are carried out.Evolutions of twinned martensitic configurations and corresponding lattice free energy variations are then obtained.The analysis of localized lattice models with different atomic occupations has revealed that the influence of the material composition on the transformation intiation is caused by the microscale competition of localized lattices due to their deformation and free energy differences in the early stage of the transformation.In Chapter 3,a second nearest neighbor modified-embedded-atom-method（2NN MEAM）for the atomic simulation of the Cu Al Ni martensitic transformation is constructed.Based on it,a comprehensive molecular dynamics simulations of both temperature induced and stress induced martensitic transformation processes of Cu Al Ni are conducted.Typical twinning microstructures and transformation hysteresis loops are obtained.Effects of temperature rate,strain rate,stress rate and material composition on the transformation at microscale are then analyzed.The obtained variation details of martensitic microstructures along with the driving factor have provided the base for the nano-micro scale analysis of the transformation dynamics.In Chapter 4,the macroscopic asymmetric chemical potential functionals of the martensitic transformation are established based on the data of previous chapters to carry out phase field simulations of the macroscopic transformation dynamics with different chemical potentials.The influence of different potential functionals on simulation results are revealed with example analyses.First,the connection between configuration free energies and driving factors is bridged with the microscopic deformation data from previous chapters,and is used to establish the asymmetric chemical potential functionals of macroscale with thermodynamical modeling and data fitting processes.Then an order parameter based phase field model of the macroscopic martensitic transformation is established considering the effects of non-linearity,finite deformation,strong elastic anisotropy and multi-variants,as well as the corresponding parallel program for finite element simulations.A systematic finite element simulations are then carried out for different chemical potentials.Developments of geometric and mechanical parameters are obtained.Through comparison,we summarize the influences of different chemical potentials on the transformation dynamics and the corresponding phase distributions.Chapter 5 analyzes the interaction between the elastic field and the dynamics of the transformation in the results of multi-examples phase field simulations from above chapter.The coupling mode of the elastic field and the transformation dynamics is unveiled.Through the observation and the analysis which are mainly focused on the evolutions of microstructures and elastic fields represented by the elastic constant and the elastic energy in a multi-fields coupled way,the coupling phenomenon of the interface migration and the elastic field evolution in the transformation process is found.The evolution of the extremely high elastic energy regions and the boundaries formed by the gradient of the elastic energy are connected with the deformation of the transformation interfaces with special formations.Evidences of the asymmetric differentiation of twinning variants are also found in the process.Therefore,through first-principles based optimizations,molecular dynamics simulations,and macroscopic phase field simulations,a multi-scale method for studying the dynamics of the Cu Al Ni martensitic transformation is successfully constructed in this thesis.Following results are obtained in the process:the second nearest neighbor multi-body potential suitable for molecular dynamics simulations of the Cu Al Ni martensitic transformation,the macroscopic asymmetric chemical potential functionals of finite temperatures for the macroscopic simulation,and a phase field model and corresponding parallel finite element program for the macroscopic martensitic transformation considering nonlinearity,elastic anisotropy,finite deformation effect,inequality constraints,multiple order parameters and other effects.Also,through the simulations of the transformation dynamics at different scales,three important information about the transformation mechanism are given as follows:the microscopic mechanism for the influence of material composition on the initiation of the martensitic transformation,the effects caused by symmetry changes of the chemical potential functional on simulation results,and the interaction mechanism of the elastic energy and the microstructure development in the transformation.This multi-scale method for the study of the martentisitic transformation can be used for other materials or transformation types.Among it,the second nearest neighbor modified-embedded-atom-method constructed in this thesis has provided the base for the in-depth microscopic research of the martensitic transformation of the ternary alloy Cu Al Ni.The proposed asymmetric chemical potential functionals have granted a feasible choice for the introduction of the temperature as an additional control parameter into the macroscopic simulation.The obtained information of the transformation mechanism have provides new perspectives for the mechanism research on the material composition,chemical potential functionals,and elastic fields which affect the transformation dynamics in different ways.