Numerical Simulation Of Mechanical Properties Of Particle Reinforced Metal Matrix Composites

Particle reinforced metal matrix composites(PRMMCs)are widely used in industry,aerospace and other fields due to their excellent mechanical properties.Because of the complex microstructure of PRMMCs,there are some limitations in the experimental and mesomechanical methods to study its mechanical properties.The finite element method has more advantages because it can solve the numerical solution of the representative volume element model which is close to the actual microstructure.Aiming at the zirconia toughened alumina particle reinforced iron matrix composite(ZTA_p/Fe45)prepared by vacuum pressureless sintering,the parametric modeling algorithm of the high volume fraction geometric model,the influence of matrix defects,non-ideal interface and microstructure characteristics on the mechanical properties,and the fracture mechanism are explored and studied in this paper.The following results were obtained.(1)Based on the general finite element software ABAQUS,this paper uses Python language as a tool to realize parametric modeling of various cell models and random distribution models,and encapsulates the program as a plug-in of ABAQUS,which is convenient for operation and user-friendly,so as to facilitate the distribution and expansion of the software.For spherical particles,the perturbation algorithm can be used to construct the RVE with volume fraction up to 80 vol%.The statistical analysis of the distribution of particles by Voronoi diagram and the first and second closest distances shows that the distribution of particles is relatively uniform and the distribution of particles is better.In order to achieve the high volume fraction of irregular particles,a rigid particle space compression method is developed,which can realize the rapid construction of 3D RVEs of irregular particles with volume fraction up to 50vol%.The algorithm does not rely on computational geometry,but uses the interaction force between particles to avoid particle intersection.Therefore,it has the characteristics of relatively easy programming,high efficiency,large volume fraction(maximum 80 vol%of the two-dimensional model of spherical particles),and can adapt to a wide range of particle morphology.It can be applied to the construction of particle models with spherical,ellipsoidal and irregular shapes.(2)Based on the modeling algorithm developed in this paper,three-dimensional RVE models of ZTA_p/Fe45 composite with volume fraction range of 10～50vol%are constructed.The effective elastic properties of ZTA_p/Fe45 composite are calculated by the finite element method,and compared with the micromechanical solution.The mesh sensitivity analysis shows that the results of effective elastic properties are less sensitive to the mesh size,and the appropriate mesh density can be selected by comparing the stress nephogram of the calculation results.In order to ensure the statistical characteristics of the RVEs and reduce the errors caused by the randomness of particle distribution,the number of particles in the RVEs should not be less than 30.The calculation results of effective elastic properties show that the reinforcement effect of irregular particles on effective elastic properties is better than that of spherical particles;the increase of particle volume fraction makes the elastic modulus and shear modulus increase;the finite element results are well consistent with the mesomechanic results,which shows that the models in this paper are more accurate.(3)Based on the crack band model and cohesive zone model,the effect of micro void in matrix and interface mechanical properties on mechanical properties of ZTA_p/Fe45composite with 20vol%volume fraction were analyzed by two-step homogenization method.The results show that the micro void of matrix has a great influence on the mechanical properties of the matrix material and ZTA_p/Fe45 composite.The young’s modulus of the ZTA_p/Fe45 composite decreases linearly with the increase of micro void;the tensile strength of the material decreases nonlinearly with the increase of porosity.The increase of interface modulus makes the young’s modulus of ZTA_p/Fe45composite increase significantly,but with the increase of interface modulus to 0.5times of that of particle material,the increase of composite modulus gradually slows down.With the increase of the interface modulus,the tensile strength of the composite decreases gradually.Before the interface strength is less than 0.5 times of the particle strength,the tensile strength of ZTA_p/Fe45 composite increases gradually with the increase of the interface strength,but when the interface strength is greater than 0.5times of the particle strength,the strength of the composite tends to be stable,about302MPa.The change of interface strength makes the damage mechanism of ZTA_p/Fe45 composite change.When the interface strength is 0.5 times lower than the particle strength,the damage of composite is mainly in matrix and interface.When the interface strength increases to 0.5 times,the damage is mainly in matrix and particle.The interface strength can only improve the overall strength of composite to a certain extent,when the interface strength is close to the particle strength,the strengthening began to weaken.Therefore,the porosity of matrix should be strictly controlled to improve the density of matrix.When the interface elastic modulus and strength are about 0.5 times of the particle related properties,it is more advantageous to improve the elastic modulus and strength of ZTA_p/Fe45 composite.(4)Based on the two-dimensional RVE,the influence of mesostructure characteristics such as particle morphology,volume fraction and particle size on the mechanical properties of ZTA_p/Fe45 composite was analyzed.In the case of lower volume fraction(less than 30vol%),the crack of ZTA_p/Fe45 composite is mainly located in the matrix material,so the strength is mainly determined by the strength of the matrix;in the case of higher volume fraction(more than or equal to 40vol%),the crack of ZTA_p/Fe45 composite is mainly composed of interface crack,so the strength is mainly determined by the interface strength.In the case of non ideal interface,the difference of interface length per unit area is caused by the difference of volume fraction,which makes the leading factor to determine the tensile strength of ZTA_p/Fe45composite change.The strength calculated by the equal axial particle model is higher,and the increase of the aspect ratio is accompanied by the decrease of the composite strength.The strength of the ellipsoid particle model is higher than that of the irregular particle model under the same aspect ratio.The closer the aspect ratio of the reinforced particles is to 1,the higher the strength of the composite is,so the equiaxed particles should be selected as far as possible in the actual preparation.When the volume fraction is the same and the interface property is the same,the particle size is not enough to affect the elastic property of the composite for the particles of millimeter grade(0.5-2mm).The smaller the particle size is,the smaller the tensile strength of ZTA_p/Fe45 composite is,and the larger the tensile strength of the large particle composite is.(5)Based on the improvement of FEM-DEM method,the mesh model of high-order FEM-DEM method is realized,and the fracture mechanism of ZTA_p/Fe45 composite is analyzed.The results of element size sensitivity analysis show that the elastic modulus values calculated by the first-order and second-order models tend to be stable with the increase of mesh division,and the order of solid element has little influence on the calculation results of elastic modulus.The meso stress field analysis shows that the second-order solid element coupling double zero thickness cohesive element model can reduce the sensitivity of stress distribution to element size,and the continuity of stress nephogram is better than that of the first-order solid element coupling single zero thickness cohesive element model,the stress transition is smooth,the zigzag area of the first-order model is avoided.The serrated area of the first-order model and the integral multiple of the element area of the plastic area at the crack tip are avoided,and the size sensitivity problem that the first-order model needs to be solved by a very fine mesh is solved.The particle shape has a great influence on the crack growth of particle reinforced metal matrix composite.The crack of composite first occurs at the interface perpendicular to the stress direction,and then the matrix cracks after the interface crack grows to the stress concentration of matrix.The crack of composite is composed of the interface and matrix crack.