Study Of Impact Fragmentation Of The Single Brittle Sphere

Fragmentation of brittle solids is widely found in all fields of human life and production,such as the rockfill production,mineral separation,powder industry,glass fragmentation and so on.From time scale,the damage of brittle solid can be divided into two classes:continuous and instantaneous fragmentation.These brittle granular geomaterials fragmented continuously under quasi-static compression conditions,whose mechanical response and failure mechanism have been extensively studied.A lot of interesting phenomena such shear band,jamming transition,and force chain have been reported and discussed.However,there are still great gaps in the deformation characteristics and failure mechanism of instantaneous fragmentation under dynamic loads such as impact and explosion.The impact fragmentation of solids is a rapid transition process from a continuous medium to a highly discretized system.Major scientific problems in many fields,such as meteorite impact,earthquake,and missile penetration,are closely related to granular dynamics.Brittle solid particles are the basic units in geomaterials.Therefore,the physical and mechanical behaviors and particle breakage characteristics of solid brittle spheres under impact loading are systematically studied by single brittle sphere impact fragmentation.To avoid the initial shape effect,the single sphere is adopted as the breakable projectile bodies.Based on the Finite and Discrete Element Method,a sphere FDEM model is established by using a random tetrahedral mesh and a non-thickness cohesive interface element,and the crack is simulated by cohesive zone model,and a two-parameter Weibull model is used to characterize the spatial distribution of the strength parameters of materials.By choosing the appropriate the fracture process zone（FPZ）length,calculation step and mesh size,the FDEM sphere model can simulate the impact fragmentation characteristics of real brittle solids,such as damage-fragmentation phase transition and fragment fractal distribution.In this thesis,the influence of two important material properties,namely the fracture mechanism and material disorder,on impact fragmentation response of brittle solid spheres are discussed.The specific work includes the following two aspects:1.In order to investigate the effect of different fracture mechanisms on impact fragmentation of brittle solid,three groups of numerical impact tests were designed by changing the strength threshold of interface elements.The failure mechanisms correspond to purely shear-dominated,tension-dominated and mixed fracture mode,respectively.A series of impact simulations in a certain velocity range are carried out under the different fracture mode.The results show that one can identify a threshold velocity that separates two velocity regimes.Particles experience fracture and damage without major splitting if the impact velocity is below such critical velocity,while thorough fragmentation and comminution occur when such threshold is exceeded.This shows the obvious damage-fragmentation transition in the impact events of brittle solid.The mass distribution of the fragments under the three fracture modes is characterized with the power law distribution,and the power-law exponent have the relationship ofτ_tension>τ_shear>τ_mixed.The power-law exponent in three modes increases with the impact velocity,and converges to a uniform value,indicating that the power-law exponent is dependent on the impact velocity,but it has a universal law after exceeding the critical velocity.Different fracture mechanisms affect the transition and failure modes of impact fragmentation.In the mixed mode,the critical impact velocity in the pure shear-dominated,tension-dominated and mixed mode is 15 m/s,20 m/s,80 m/s,respectively.The steepest slope of the fragment mass curve in tension-dominated mode means the sharpest phase transition.The crack network is statistically analyzed,combined with the crack network structure and the impact stress field analysis of the non-breakable sphere.In tension-dominated mode,the crack network is characterized with meridional plane crack and the secondary oblique crack,and the sphere fragmented into the wedge-shaped fragments.In shear-dominated mode,a 30-45°fine cone formed while producing a large number of diffusion cracks.In the mixed mode,a highly fragmented zone is formed near the contact zone,and the conical fragments are formed at the upper part under the splitting of meridional plane crack and a small amount of secondary crack.Based on the computational geometry technique,the Domokos shape factor,sphericity and convexity are used to characterize the shape of the fragments,which exhibits a high degree of variability.The Domokos shape factor of the fragments in the purely shear-dominated mode is the smallest,but the sphericity and convexity are larger than those in the tension-dominated mode,indicating that the shear fracture mechanism tends to produce isotropic,relatively smooth and convex fragments;while the tension fracture mechanism is more likely to slender,angular and concave fragment.2.In order to investigate the influence of material disorder on impact fragmentation,Weibull distribution was used to model the parameter variability of brittle materials,in which Weibull modulus characterize the disorder degree of meso-parameters.Four sets of impact numerical tests with Weibull modulus of 1,2,5,and 10 were designed.The simulation results show that the higher disorder solid impact indicates greater critical impact velocity.The four failure modes under critical impact velocities are also obviously different.The main failure modes are characterized with penetrating cracks in low disorder spheres,while the non-penetrating branch cracks in high disorder spheres.It can conclude that material disorder has a great influence on the impact fragmentation mode and critical characteristics of brittle solids.The damage response in brittle spheres with different disorder degree is different under the same impact velocity.From the analysis of crack structure,the meridional crack and secondary crack are the main cracks in low disorder spheres,the crack structure is of good integrity and smooth.Two main characteristic cracks still exist in high disorder spheres,but non-penetrating cracks and micro-cracks in fragments increase significantly.Quantitative analysis of debris morphology under critical impact velocity is carried out by flatness and sphericity.The probability distribution of two fragment shape indices in the four groups of disorder spheres is basically the same.The higher disorder spheres present lower the concentration degree of flatness,and the sphericity distribution changes from symmetrical distribution to left-sided distribution,with lower peak value and larger distribution range.This indicates that the higher disorder spheres produce fragments of higher morphological variability.The disorder essentially influences the impact fracture mechanism of brittle materials.The stress state analysis of cohesive interface elements close to failure shows that tension is the dominant fracture mechanism under low disorder degree,and the proportion of shear fracture mechanism increases with the disorder degree.According to the phase diagram proposed by Shekhawat,the main fracture phase in low disorder brittle solid is nucleation and percolation in high disorder degree.More generally,avalanche is the main failure phase and three-phase coexists in medium disorder solid fragmentation events.