Research On 3D Lattice-spring Model For Brittle Material Fracture Problem

Brittle materials generally have some defects,which are prone to form cracks with high speed when subjected to strong loads such as impact,earthquake and explosion.At present,the research on crack propagation in brittle materials mainly focuses on quasi-static crack propagation.The mechanism of crack growth under shock wave tension is still controversial.The models used to simulate crack growth are mainly two-dimensional models,while the structures used in engineering are mostly three-dimensional structures.Therefore,it is of great significance to establish a three-dimensional lattice-spring model to simulate the propagation and bifurcation of cracks in brittle materials under impact tension.(1)In this paper,a hexahedral base mesh,which is shared by finite element method and lattice-spring method,is established.The general stiffness matrix of the finite element is mapped to the stiffness coefficients of normal and tangential springs in the lattice-spring model by the parameter mapping method proposed by Gusev.The nodes in the finite element are lattice points(particles)in the lattice-spring model.(2)The parameters of the two brittle materials are input into the model,and the elastic modulus of the compact samples is verified by the quasi-static tension and compression,with an error of about 0.01%.The longitudinal and shear waves are verified by the impact and jitter of the piston on the samples,respectively,with an error of less than 1.5%.A model of semi-infinite pre-crack and ellipsoid hole is established.Uniaxial tension and far-field triaxial compression loads are applied respectively.Stress concentration phenomena are verified by extracting stress contours around the crack tip and ellipsoid hole.Therefore,the model established in this paper can accurately represent the mechanical properties of brittle materials.(3)A model of semi-infinite pre-crack and ellipsoid hole is established.Uniaxial tension and far-field triaxial compression loads are applied respectively.Stress concentration phenomena are verified by extracting stress contours around the crack tip and ellipsoid hole.Therefore,the model established in this paper can accurately represent the mechanical properties of brittle materials.(4)During the crack propagation process,the stress concentration region at the crack tip changes,and the butterfly wing shape appears before the cracking.After the cracking,it exhibits a swept wing shape.After the crack starts,the crack tip velocity instantaneously jumps and then continues to increase,corresponding to the expansion of a single crack.Subsequent slight reductions then increase to the maximum velocity of crack propagation,corresponding to the fracture phase before the bifurcation;then the crack propagation velocity undergoes significant oscillations,corresponding to the bifurcation phase of the crack.The relationship between crack morphology,maximum tensile stress and crack propagation velocity during crack propagation was investigated by applying different loads.