Research On Damage Constitutive Relation Of Shape Memory Alloy Materials Under Cyclic Loading

As a smart material,Shape Memory Alloy(SMA)is widely used in various fields.Because it is unavoidably subjected to cyclic loading as a key component of the structure,the damage mechanism of SMA is a problem to be solved urgently.But few scholars consider the attenuation of SMA’s cyclic deformation behavior to be caused by fatigue damage.In order to explore the relationship between SMA fatigue damage behavior and load cycle times,this paper studies the damage mechanism of SMA under stress cycling and temperature cycling through a combination of theory and experiment.The main research contents are as follows:First of all,the Differential Scanning Calorimeter experiment is used to obtain the material’s endothermic curve and the critical phase transformation temperature.Then uniaxial tensile test is performed to obtain the Young’s modulus of martensite and austenite.At the same time,experiments are carried out on rods of different diameters at different temperatures,and the stress-strain relationship curve under uniaxial tensile cycle is obtained.Secondly,this paper fully considers the permanent effects of damage generated in a single cycle on the material and the residual strain accumulation.Therefore,based on Gibbs free energy,the second law of thermodynamics and the basic definition of damage given by mechanics of solid materials,a three-dimensional constitutive model that can simulate the deformation behavior of SMA under cyclic loading is developed.Then,the deduced three-dimensional constitutive model is reduced to one dimension.And the relationship between the damage factor and the number of cycles is derived from the relationship between the attenuation of the Young’s modulus and the number of cycles.The theoretical stress-strain relationship under each number of cycles and one-dimensional stress cyclic loading is given and is compared with the stress cyclic loading experiments of this paper and other scholars to verify the accuracy of the model.A subroutine of SMA constitutive model applied to finite element simulation is developed,and the simulation analysis of the experiment is performed.Finally,the correction parameter is introduced into the one-dimensional constitutive model to simulate SMA materials with different memory effects.And consider the maximum phase change strain attenuation to characterize the degree of damage,so that this model can simulate temperature cycling deformation behavior.Due to the limitation of experimental conditions,the theoretical temperature-strain relationship under temperature cycling load will only be compared with the excellent experiments and theories of other scholars to verify the accuracy of the model.And the subroutine is used to simulate the experiment.This paper presents the thermodynamic damage constitutive model that can simulate cyclic deformation behavior of SMA,which shows a good agreement with the experimental results and can provide a new theoretical method for SMA material fatigue life estimation and damage state judgment in practical applications.