Finite Element Simulations Of The High Velocity Expansion And Fragmentation Of Ductile Metallic Rings

Expanding ring test is an effective experimental method for investigating the mechanics properties of materials during 1-D dynamic tensile loading. It's of great significance both on the academic research and engineering applications of the fragmentation of material under tensile loading. In this paper, through the finite element numerical simulation experiments of the fragment of ductile metal expansion rings, we analysis the mechanics properties ,fracture characteristics and distribution of fragments of ductile metallic materials during 1-D dynamic tensile loading. Further, we explored the mechanics properties and fragmentation characteristics of ductile metallic materials under 2-D axial tension loading on the base of the expansion spherical shell model.In this paper, we establish the finite element model of ductile metal expansion ring by ABAQUS. The Johnson-Cook failure model incorporating a cohesive fracture instability criterion and temperature softening effect was used to describe the fracture and the separation progress of the material. We obtain the corresponding constitutive parameters of OFHC by fitting the curve. Fracture energy criterion is used to judge if the elements is failure. ABAQUS/Explicit code with element erosion function was used in the numerical simulations. Mesh dependency test is used to determine the mesh technology, element type, shape, size of finite element discrete model. To obtain the statistical properties of the fragments, we meshed a ring with different control points, obtaining different meshes in an identical ring. Multiple simulations were conducted with a same initial velocity on these rings; each created a group of fragment samples. Different simulations were conducted with different initial velocity to analyse the impact of strain rate on tensile properties and fracture characteristics of expanding ring.We establish the finite element model of ductile metal expansion spherical shell by ABAQUS to analyse the 2-D homogeneous tensile properties and fracture characteristics of ductile metal. The same finite element analysis techniques, constitutive model and material parameters of expansion ring are used. Through the simulations experiments with different initial velocity ,we analyse the impact of strain rate on tensile properties, fracture characteristics and fragment number of expanding ring expansion spherical shell. In this paper,the main conclusions:(1) By analyzing the whole process of the expanding ring and expansion spherical shell radically expanding and fragmenting. The whole process include: start, homogeneous elastic deformation, uniform plastic expansion, non-uniform plastic (necking) expansion, fracture initiation, complete fragmentation, free flight..(2) By analyzing fracture characteristics of the expanding ring and expansion spherical shell, ductile metallic materials have shown multiple injuries and multiple fragmentation of the phenomenon under one-dimensional and two-dimensional uniform tension impact loads. Damage and fracture (fragmentation) occurred in the sequence. Multiple neck occurred in expansion rings. Multiple micro-cracks occurred in expansion spherical shell. At the same time non-uniform plastic deformation obviously occurred in different regions with the uneven temperature distribution.(3) Strain rate obviously influences the mechanical properties and fracture characteristics of the expanding ring and expansion spherical shell. Fracture expansion velocity, fracture regional temperature and fragments number rise as strain rate increasing. Fracture regional have shown non-smooth state. But the expanding ring and expansion spherical shell under different strain rates showed different mechanical properties and fracture characteristics. The fracture radius and fracture strain of expanding ring increased with the initial expansion velocity. The fracture radius of expansion spherical shell didn't increased with the initial expansion, but just fluctuated in the vicinity of a value.(4) The fragment size calculated by Grady-Kipp theoretical formula of ductile material is less than simulations with the fragments number being higher the numerical simulation. The results calculated by fracture strain rate and radius is more consistent with simulation results than initial. Theoretical estimates result of fragments number are higher than simulation 3~6. The change trend of theoretical and simulation are synchronous with the increasing of initial expansion velocity. The reason is the randomness of plastic flow, plastic unloading wave propagation, fracture non-arbitrary choice and the order of the fracture.(5) )By analyzing the average fragments sizes, we found the statistical characteristic of fragments can be described by the Weibull distribution function. The average size of fragments and fragment size distribution width decreased as the strain rate increasing. The cumulative distributions of the normalized fragment sizes at different initial expansion velocities can be modeled as a Rayleigh distribution. The minimum normalized fragment size is 0.37, the maximum normalized size 2.1. We discover that the cumulative distribution of the fragments presents a step-like nature. This feature weakens with the increase of the initial strain rate.