Random Numerical Homogenization Analysis Of Elastoplasticity Of 3D Polycrystalline Metals Under Finite Deformation

On the microscale,nearly all materials show the heterogeneity to some extent.There are some papers published show that the heterogeneity of the material on the microscale has a decisive influence on the macroscopic mechanical properties of materials.So it has always been a hot topic to study the relationship between the mechanical properties on the macroscopic and microscopic scales in the field of materials.In this work,aiming at the ferritic steel DC04,the geometric modeling and material modeling of the polycrystalline microstructure of DC04 steel at finite deformation are firstly established,and the random homogenization mechanics simulation and analysis under different load types which cause the finite deformation of DC04 steel are carried out based on finite element method,crystal plasticity theory and the theory of multiscale homogenization.The main contents of this thesis are as follows:First of all,because the homogenization simulation of polycrystalline metal materials will be implemented with FEAP software which has perfect homogenization module,the software structure and development requirements of FEAP are learnt about and grasped,the secondary development of the user subprogram for crystal elastoplastic model which can characterize cubic lattice system and shear slip deformation mechanism is accomplished based on Fortran language,crystal plasticity theory and standard interface program UMATIn and UMATLn;the accurate and simplified polycrystalline geometry models are then constructed on the basis of Voronoi topology principle,which is programmed with Matlab,Ansys APDL and Python language together.The work in this part is necessary for the following homogenization analysis of polycrystalline metal materials.Secondly,the mechanical simulation test to two kinds of polycrystalline geometric models under uniaxial stretch is carried out,and the advantages and disadvantages of the two polycrystalline geometrical models are compared.The results show that: the results of mechanical properties of polycrystalline materials obtained from two kinds of polycrystalline geometric models are very close,and the simplified polycrystalline geometric model has a higher stability and convergence compared with the accurate model.So the simplified polycrystalline geometry model is chosen for the subsequent homogenization analysis.Moreover,the test to the simplified polycrystalline geometry model is actualized from three aspects including the mesh size,grain average size and grain orientation.The results display that: the mesh size has a small effect on the results,while the average grain size and grain orientation influence the mechanical properties of polycrystalline more greatly,which provides a calculation basis for the determination of the representative volume element in the later homogenization work.At last,the homogenization of multiple microstructure polycrystalline models is tested and the convergence of main components of the homogenized stress tensor is analyzed in order to determine an appropriate RVE,which is based on multi-scale homogenization theory and appropriate stress convergence criterion.Thereafter,considering that some material parameters are stochastic,the loads are converted into the corresponding displacement gradients and then applied to the RVE as the uniform displacement boundary conditions;the effective material parameter set corresponding to the effective material model(Von-mises model or Hill model)is obtained by processing the homogenized stress of every sample computed with the least squares fitting method,and effects of random input material parameters on the numerical characteristics of effective material parameter set are investigated.In the example,the material parameter set is used in the corresponding effective material model,and the obtained mechanical response from the effective material model is compared with the homogenization mechanical response obtained from the RVE,and the results show that: if the effective material model is given,the change of the effective material parameter set is not only related to the selected test load type,but also to the correlation and randomness of microscopic input parameters of materials.