Interval Homogenization Analysis Of Metal Polycrystalline Materials Under Finite Deformation

From the viewpoint of micromechanics,most of metal materials in engineering belong to heterogeneous materials,and it is not easy to obtain the deterministic values of material parameters,which greatly affects the accuracy of results when analyzing the mechanical properties of metal materials.In this work,aiming at the representative DC04 steel,the interval analysis method is combined with the crystal plasticity theory and the multi-scale homogenization based on the finite element method,the numerical homogenization model and the material model for the microstructure taken from DC04 steel are presented respectively when considering the interval uncertainty of material parameters,and the interval homogenization analyses are addressed when different loads are applied to the microstructure;The effective/macroscopic mechanical properties are then obtained and characterized as interval form as well since the input parameters are interval,and a relatively reliable model for interval homogenization analysis of metal polycrystalline materials is obtained.The main contents and key work of this work are as follows:First,the software FEAP is chosen for the homogenization analysis,a polycrystalline microstructure model is constructed based on the principle of Voronoi algorithm by combining Matlab with Abaqus.At the same time,the material constitutive model mainly composed of slip deformation is written as a subroutine of the FEAP user model with Fortran language.The corresponding interface programs UMATIn and UMATLn are programmed,by which the second compilation of FEAP is finished and the required crystal elastoplastic material model is constructed as well.In addition,by constructing a single crystal model and changing the relevant parameters of the material model,and the validity of the material model is verified by the variations of the mechanical responses of the single crystal model.Secondly,based on the convergence rule of the mechanical responses of the microstructures,the size of the representative volume element(RVE)used for homogenization analysis is determined,and the model of interval homogenization analysis of the polycrystalline metal under finite deformation is established based on the homogenization analysis and interval optimization algorithm.The establishment of the RVE model is accomplished by constructing multiple sets of microstructure models with the same geometric dimensions but different amounts of grains,and the convergence of uniform response stress of the microstructures under different loadings of uniaxial tension is then computed,finally,the model meeting certain convergence rule is chosen as the appropriate RVE of the metal material.The interval averaging algorithm is programmed based on the basic particle swarm algorithm(PSO),in which PSO algorithm is improved as an interval algorithm capable of operating multi-objective optimization based on Pareto domination.Then,the computation of the effective plastic parameters of the homogenization model is embed into the interval optimization program,and the interval homogenization algorithm program is finished at last.Finally,based on the work above,the forming process of polycrystalline metal materials is simulated by different loads applied to RVE,and the interval homogenization analysis of polycrystalline materials under finite deformation when the simple shear load and three-way shear load acting on RVE.The interval range of every effective parameter of the macroscopic material model(Von-Mises model and Hill model)is obtained,and the variations of the interval effective responses with different loads and their interval variation are obtained.Moreover,after substituting the effective material parameters computed from the interval homogenization into the corresponding macroscopic material model and then analyzing the results,the errors of the homogeneous response between the macroscopic material model and RVE under the corresponding conditions is obtained,which verifies the effectiveness of the interval homogenization model of polycrystalline metal and material effective parameters constructed on the multi-scale interval homogenization method.