Study On Equivalent Thermal-mechanical Properties Of Mo/ZrC Graded Materials Based On Asymptotic Homogenization Method

Mo/ZrC functionally graded material is an advanced composite material with the characteristics of high temperature resistance,wear resistance and thermal shock resistance,which is widely used in modern aerospace industry.The two-phase material components of Mo/ZrC functionally graded materials present a continuous gradual distribution,which makes the materials show multi-scale characteristics of micro-heterogeneity and macro-heterogeneity.Therefore,it is of great significance to study the relationship between its structure and properties for its application.In this paper,Mo/ZrC functionally graded materials are taken as the research object,and the equivalent thermal and mechanical properties of those materials under thermal-mechanical coupling are studied from both analytical and numerical aspects under the framework of asymptotic homogenization method.The main research contents are as follows:(1)The theory of equivalent thermal performance prediction of composite materials is deducedBased on the structural dynamical equation and heat conduction equation,the displacement and temperature parameters are basically gradually expanded,and the stress and heat flux density are derived gradually.On this basis,the prediction theory of equivalent thermal and mechanical properties of composites considering thermal-mechanical coupling is deduced,and the theoretical formulas of equivalent elastic tensor,equivalent thermal expansion tensor and equivalent thermal conduction tensor of composites are given.(2)An analytical method for predicting the equivalent properties of Mo/ZrC functionally graded materials considering local effects and multi-field coupling effects is proposedThe theoretical formulas of equivalent thermal and mechanical performance considering thermal-mechanical coupling effect established in this paper need to be integrated in micro-local area,but the complex microstructure makes integration very difficult.In order to solve the local area equivalent formulas analytically,the Mo/ZrC functionally graded materials are assumed to be a multi-layer composite material with a layered rectangular structure,and then the generalized periodic boundary conditions are introduced.Based on this boundary condition,the local function is solved,and the analytical solution for predicting the equivalent thermal and mechanical properties of Mo/ZrC functionally graded materials is obtained,The correctness of the analytical method is verified from many aspects.(3)The numerical calculation method of the asymptotic homogenization method for functionally graded materials is obtainedThe microscopic model of Mo/ZrC composites was built by using the three-dimensional Gaussian random field method and threshold segmentation algorithm.Based on the two-phase heterogeneous microscopic model,the influences of equidistant discrete points,correlation length and Gaussian complexity on the morphology of the microscopic model were explored.Taking the model as a unit cell for numerical calculation of the equivalent properties of Mo/ZrC composites,the numerical solution of the equivalent thermal properties of Mo/ZrC composites was obtained by finite element method.Finally,the influence of the cluster and complexity of the micro-model on the calculation of the equivalent properties was discussed.The results show that when the correlation length is 2.0 and the Gaussian complexity is 30,the maximum error between the equivalent properties of Mo/ZrC composites calculated by numerical gradual homogenization method and analytical method is less than 5%.(4)The numerical calculation method of the asymptotic homogenization method for functionally graded materials is obtainedBased on Gaussian random field method,a three-dimensional heterogeneous two-phase microscopic model is established,which is regarded as a unit cell for numerical calculation of equivalent performance of Mo/ZrC functionally graded materials.Combined with finite element method,the characteristic displacement is solved.By substituting the characteristic displacement into the equivalent thermal and mechanical performance prediction formulas,the numerical solution of equivalent thermal and mechanical performance of Mo/ZrC functionally graded materials is obtained.At the same time,this paper discusses the influence of the particle size,clusters and complexity of the microscopic model on the equivalent performance calculation.The results show that the equivalent performance of Mo/ZrC functionally graded materials calculated by the numerical progressive homogenization method is the closest to that calculated by the analytical method when the correlation length is2.0 and the Gaussian complexity is 30,and the maximum error is less than 5%.(4)The relationship between the structure and thermal and mechanical properties of Mo/ZrC functionally graded materials is exploredThe composition volume ratio and gradient change form of Mo/ZrC functionally graded materials have a crucial influence on the structure and properties of the materials.In this paper,a model with two-parameter power law distribution of volume fraction is selected,and a gradient structure model is built based on the modeling method of two-phase heterogeneous gradient microscopic model,which reveals the distribution characteristics of material components.Finally,the relationship between different gradient structures and thermal and mechanical properties of Mo/ZrC functionally graded materials and the change law are studied by the analytical method of equivalent thermal and mechanical properties prediction.The results show that the composition ratio and gradient index of Mo/ZrC functionally graded materials have important influence on the properties.The increase of material composition ratio will lead to the overall difference of material properties.The increase of gradient index of the material leads to more obvious local differences in material properties.