The Effects Of The Local Constraints Patterns On The Fragmentation Of A Single Grain

Particle breakage is widely found in all aspects of human life and production,such as chemical industry,pharmaceutical industry,food industry,civil engineering and so on.The research of particle breakage is of great significance for the effective application of materials and engineering.At present,scholars at home and abroad mainly consider the properties of particle material,particle size and particle shape in the study of the related factors of single particle breakage.In fact,the particle composition,volume fraction and coordination number around each particle are different because the particles are mostly in the heterogeneous structure.The difference in the confinement state and degree provided by the surrounding environment makes the stress distribution in the particles complex and changeable,which will have a great influence on the particle breakage,However,it is complex and changeable that the particle is constrained by its surrounding particles.It is difficult to quantify the multiple package effect of single particles by numerical method.So far,there are few studies on the constraint mode in particle breakage.However,particles are constrained by their surrounding particles,which are complex and changeable.How to quantify the multiple wrapping effect of single particle is difficult in the research.In order to simulate the heterogeneous structure of particles,the mesh topology based on Voronoi diagram was applied in the thesis.And plenty of numerical simulations of two dimensional particle crushing was carried out using the combined finite-discrete element method?FDEM?.A method of singular value decomposition?SVD?for statistical analysis is proposed by means of multidisciplinary research.By means of singular value decomposition,the distribution of stress and the development of cracks are analyzed.What's more,the relationship between particle local constraint mode and particle crushing threshold is discussed.To study the effect of different test conditions and material parameters on the mechanism of particle breakage,two typical constrained conditions are selected for numerical experiments.The advantages of triangular mesh generation based on Voronoi graphics are obvious compared with conventional mesh generation method from the aspects of grid topology and crack propagation pattern.7 groups of numerical experiments under different grid sizes are designed to find the best mesh size that can meet the computation accuracy and cost.The effects of loading rate on the failure process,breaking strength,calculation length and failure mode of the samples are analyzed through 7 groups of numerical experiments at different loading rates.By changing the values of meso parameters and optimizing the parameters,an effective reference for the selection of numerical experiments can be provided.In order to investigate the effect of the local constraint mode on the crushing form and the crushing strength of the single particles,95 different constraint modes are designed by adjusting the contact angle under 4 coordination numbers.Singular value decomposition and particle breakage numerical simulation for different constraint modes are carried out.The process of crushing can be divided into two stages.During the first stage,stress concentration occurs at every constraint area of particles.Because the direction of the loading axis represents the leading direction of the forces around the particles,the stress concentration area in the confinement area near the axis of loading is rapidly expanded to form a crack,and then develops into a penetrating main crack.During the second stage,small cracks appeare at various lateral restraints and gradually develope into secondary cracks with different shapes,among which most fractures extend from the constraint part to the end of the main crack.In addition,in the case of more concentrated constraints,marginal cracks are easily produced between adjacent constraints,and the some of the secondary cracks may occur simultaneously with main fractures.Main cracks consistent with the direction of the main axis satisfie the tensile failure.After the main fracture is produced,most secondary fractures originate from shear failure dominated by shear stress.With the help of SVD decomposition,the correlation values of singular values and singular values of different constraint modes are obtained,and the relationship between the corresponding singular values and particle crushing thresholds under different constraints is analyzed.Through a large number of experiments,it is found that under the condition of the same number of coordinates,the higher the average singular value?P₁+P₂?/2 or the lower the degree of partial state?p₁,p₂?,the higher the crushing threshold is.Under the condition of different coordination numbers,the relative deviation value of singular values?p₁-p₂?/?p₁ + P₂?is used to describe the constraint modes under all coordination numbers.And with the increase of the value,the crushing thresholds of particles generally showed a downward trend.