Microstructure-based Thermo-mechanically Coupled Constitutive Models Of Shape Memory Alloys

Shape memory alloys(SMAs)have attracted extensive attention due to their unique superelasticity and shape memory effect,and have been successfully applied as core components in many fields such as aerospace,biomedical and mechanical engineering,etc.Reversible solid-state phase transition which can be induced by temperature or stress is the physical source of excellent properties owned by SMAs.The first-order phase transition property makes the stress induced transformation process accompanied by the temperature change;meanwhile,the temperature change would further affect the correspondent deformation.Thus,the deformation of SMAs shows a strong thermo-mechanically coupled feature.Material microstructures always determine the macroscopic performance of the material.Therefore,it is necessary to theoretically establish a microstructure-based constitutive model to reasonably describe and predict the thermomechanical deformation of SMA devices with different microstructures.Meanwhile,the corresponding constitutive model reflecting the microstructures can provide a theoretical guidance for the optimal design of material microstructures according to the actual demand.In recent years,a series of constitutive models have been established,which can describe the thermo-mechanically coupled deformation of SMAs well.However,the consideration of microstructures is not complete so that the existing work cannot reflect the influence of specific microstructures on the thermo-mechanically coupled deformation,which limits the furhter development of SMAs.Therefore,focusing on several typical microstructures(including the crystalline magnetic spin equilibrium configuration,the bamboo-like oligocrystalline structure,the nanocrystalline grain size,the gradient distribution of grain size and the intermediate rhombohedral R phase)of SMAs,the corresponding thermo-mechanical coupled constitutive models will be established in this dissertation.The main researches and corresponding conclusions are listed as follows:(1)In the framework of crystal plasticity and irreversible thermodynamics,the Helmholtz free energy is redefined by the specific relationship between the heat capacity(including the contribution of crystal vibration,electron and magnetism)and temperature.At the scale of single crystal,a thermo-mechanically coupled model is constructed,which can intrinsically explain the physical essence that the heat effect produced in the process of transformation is originated from the difference of heat capacities in different phases.Based on the statistical physical Ising model and Monte Carlo simulation,the evolution of magnetic heat capacity with temperature caused by the change of crystalline magnetic spin equilibrium configuration in three-dimensional body-center cubic magnetic material is solved,so as to successfully model the anomalous transformation behavior and elascalocric switching effect of Co Cr Al Si single crystalline SMA;(2)On the basis of content(1),the single crystalline thermo-mechanically coupled constitutive model is simplified due to the paramagnetic-ferromagnetic phase transition cannot occur in the conventional SMA and the heat capacity hardly changes in the focused temperature range.In addition,an efficient scale transition rule is proposed for the special bamboo-grained oligocrystalline microwire,which can reasonably predict the two-way shape memory effect and elastocaloric effect of Cu Al Mn bamboo-grained SMA.(3)Aiming at the grain-size dependent deformation of nanocrystalline SMA,the crystal plasticity model derived from the simplified free energy(omitting the change of heat capacity difference with temperature)on the basis of content(2)is regarded as the model of grain interior(GI)phase.Meanwhile,the GB phase is considered as the linear elastic material owing to the non-transformable nature and relatively high yield stress of grain boundary.Furthermore,the thermo-mechanically coupled double inclusion self-consistent homogenization method is developed to obtain the response of polycrystalline aggregate in which the GI phase and GB phase in each grain are taken as the internal and external inclusions,respectively.The grain size dependent thermo-mechanically deformation behaviors of nanocrystalline Ni Ti at different loading rates are reasonably described by the proposed model.(4)In allusion to the R phase induced two-step transformation in Ni Ti SMA,a single crystal plasticity constitutive model is established in the framework of crystal plasticity and irreversible thermodynamics by introducing inelastic deformation mechanisms i.e.,the transformation between austenite and R phase,the transformation between mixed A+R phase and martensite and the reorientation/detwinning of R phase according to special crystalline orientation relationship,and then the single crystal model is extended to polycrystalline version characterizing the overall response by newly developed self-consistent homogenization method.The proposed model successfully predicts the single/two-step transformation and deformation as well as the microstructural evolution of Ni Ti SMA over a wide temperature range.(5)For the deformation of Ni Ti SMA with a axial graded distribution of grain size,adopting the nonlocal-type constitutive model of GI phase and local-type constitutive model of GB phase,a new micromechanics-based method reflecting the interaction of GI and GB phases is proposed in the framework of macroscopic irreversible thermodynamics,i.e.,the grain size dependent scale rule of elastic modulus,the maximum transformation strain and transformation hardening modulus of representative volume element(RVE)are derived.Furthermore,a three-dimensional grain size dependent thermo-mechanically coupled constitutive model is established based on the proposed scale transition rule.The rate dependent deformation behaviors of Ni Ti SMA with uniform and gradient nanocrystalline grain size distributions are successfully described and predicted.