Crystal Plasticity Constitutive Model With Size Effect Of Ultrafine Grained Materials And Its Finite Element Implementation

The theory of crystal plasticity is more close to the nature of material physical deformation, and the relation between dislocation slip and plastic deformation is established, which provides a theoretical support for the study of crystal plasticity behavior under grain scale. The crystal structure, texture characteristics, grain size and other factors all have significant influence on the mechanical behavior of crystal. In order to analysis internal deformation and grain size effect of ultrafine grained materials on mesoscopic level, this paper introduces the Hall-Petch relation based on crystal cyclic plasticity constitutive, which aims to establish the relationship between ultrafine grained microstructure variation and macro mechanical response, and to investigate the effect of grain size. The development of CPFEM software is researched; the mechanical behavior and mesoscopic heterogeneity are analyzed of FCC metal (Ultra-Fine Grained Copper). The main contents and innovation are as follows:1. Under the direction of crystal plasticity theory, according to the dislocation slip mechanism of FCC metals, the Hall-Petch effect was introduced within the framework of Gerard crystal cyclic plasticity constitutive, a crystal cyclic plasticity constitutive model for ultrafine grained materials was established with comprehensive reflection of isotropic hardening, kinematic hardening and grain size effect. Effect on slip deformation was attributed to coupling of isotropic hardening, kinematic hardening and grain size effect. The isotropic hardening, which introduced cyclic softening term, was described on basis of Hutchinson, and the relationship between the back stress and shear strain rate was established with the Armstrong-Frederick model. The numerical simulation results agree well with the experimental data, It is proved that the developed crystal plasticity constitutive model was effective.2. In this paper, effective integration of crystal plasticity constitutive model and finite element is another key problem that needs to be solved.In terms of finite element microstructure modeling, using Voronoi diagram and numbering rule of mesh generation in ABAQUS/CAE modeling, to avoid complexity of unit information extraction process with previous polycrystal plasticity finite element modeling, taking combination of MATLAB and FORTRAN language programming method, according to the Miller indices, the orientation of finite element model is given, generating input file to establish polycrystal represent unit. The results show that the model can reflect the differences in the crystal structure and grain orientation, and taking into account the computational costs. In the numerical solution of the constitutive model, the established crystal plasticity constitutive model was discretized, and stress integration algorithm was deduced through Newton-Raphson iterative method. Based on this work, UMAT was written by FORTRAN to implement into ABAQUS/CAE.3. Parameters determination of the crystal plasticity constitutive model is also a key problem to be solved in this paper. The ultrafine grained copper (T2) as the research object, experimental data was fitting and material parameters were identified under uniaxial tensile and cyclic loading conditions respectively. Compared with the experimental results, monotonic tension simulation show that the error was about 0.5% and the maximum error was only 1.7%. Strain cycling conditions results were compared with the experimental results, which show that the overall error was small, the difference mainly reflected in the initial stage of plastic flow, hardening rate of simulation data was higher, and the deviation of tensile stage was larger than compression phase. The error of simulation was relatively small in later stages. In summary, this crystal plasticity constitutive model can better describe the uniaxial tensile and cyclic strain deformation behavior of ultrafine grained copper (T2).4. Finally, using the built model, the mechanical behaviors of ultrafine grained copper (T2) were analyzed deeply, including nonuniform internal deformation of polycrystal, grain size effect, cyclic characteristics under different strain magnitude. In crystal deformation inhomogeneity, uniaxial tensile deformation results showed that the uneven distribution of stress and strain was existed in the whole loading process, and with the increase of deformation, the uneven degree improved gradually, stress concentration was found in the grain boundary; in the effect of grain size, uniaxial tensile results bases on variable of grain size showed that the proposed constitutive model effectively describes the size effect of ultrafine grained copper (T2); in terms of cycle characteristics, the results showed that the mechanical properties of ultrafine grained copper under cyclic loading were:(1) The change of energy dissipation and strain amplitude were in the direct ratio. (2) Cyclic softening degree decrease with the number of cycle’s increase gradually until the cycle curve tends to be stable. (3) The change of strain amplitude affects the softening capacity, the larger the strain amplitude, the greater the amount of softening. (4) Bauschinger effect was not prominent.