This paper presents experimental data and computational modeling for a well-defined glass material. The experimental data cover a wide range of strains, strain rates, and pressures that are obtained fiom quasi-static compression and tension tests, split Hopkinson pressure bar compression tests, explosively driven flyer plate impact tests, and depth of penetration ballistic tests. The test data are used to obtain constitutive model constants for the improved Johnson-Holmquist (JH-2) brittle material model. The model and constants are then used to perform computations of the various tests. INTRODUCTIONRecently, much effort has been directed at understanding and niodeling brittle materials subjected to impact conditions. Under these conditions brittle materials experience large strains, high strain rates, and high pressures; and under certain conditions may also exhibit bulking or dilatation effects [l]. This paper presents experimental data, for a well-defined glass material, over a wide range of strains, strain rates, and pressures. The data are used to obtain constitutive model constants for the improved Johnson-Holimquist (JH-2) model [2]. The technique used to obtain model constants is discussed and computations of the flyer plate impact and ballistic tests are presented. TEST DATAThe float glass used for all experiments is the same material that was used for the ballistic penetration tests performed previously [3]. The chemical composition and density are presented in Table 1. The results of 16 tests performed on the float glass are summazized in Table 2. Tests 1 through 11 are compression and tension tests at two strain rates. These tests were performed on cylindrical specimens where the z-axis is the axis of symmeny. Tests 1 through 4 are quasi-static uniaxial compression tests. Three flyer plate impact experiments were performed (tests 12, 13, and 14) to determine the Hugoniot Elastic Limit (HEL), the Hugoniot stress state, and the particle velocity-time history wave profiles. The volumetric strain is defined as eV = v/vo-l where v and vo are the compressed volume and initial volume, respectively. The HEL, and Hugoniot states are presented in Table 2 and the wave profiles are presented in Figure I.Ballistic penetration experimental results were reported by Anderson et. al. [3]. Tungsten penetrators impacting float glass targets at two velocities were investigated. The final depths of penetration are provided in Table 2. DETERMINATION OF CONSTANTS FOR THE JH-2 MODELThe JH-2 model is summarized in Figures 2 and 3. The strength of the material is described by a smoothly varying function of the intact strength, fractured. strength, strain rate, and damage. The normalized strength is given bywhere O*i is the normalized intact strength, o*f is the normalized fiactwed strength, and D is the damage (OSD11.0). The normalized equivalent stresseswhere (T is the actual equivalent stress and o~m is the equivalent stress at the HEL. The normalized intact strength is given by o*i = A(P* + T*)N (1 + C*ln&*) where the mat...
CTH is a family of codes developed at Sandia N_onal Laboratories for modelling complex " multi-dimensional, multi-material problems that are characterized by large de/Ormationsand/or strong shocks. A two-s_p, second-order accurateEulerian solution algorithm is used to solve themass, momen-_...._'_ C_[ mm, and energy conservation equations. CTH includes models for material strength, fracture, porous t_ "-_ materials, and high explosive detonation and initiation. [/ft.,' !.,., or rate-dependent models of material strength have been added recently. The formulations _U0 of Johno_3n-Cook,Vise°pla_c Zerilli-Annstrong, and Steinberg-Guina_|-Lundare standard options within CTI-LThese _ _ models rely on the use of an internal state variable (typically the equivalent plastic strain) to account for the histoq dependence of material response. The implementation of internal state variable models will be O _ T [ discussed and several sample calculations will be presented. Comparison with experimental data will be made among the various material strength models. The advancements made in modelling material response have signiticanfly improved the ability of CrH to model complex large-deformation, plasticflow dominated phenomena. The detonation of energetic material under shock loading conditions has been an area of great interest. A recently developed model of reactive burn for high explosives 0-lE) has been added to CTH. This model along with newly developed tabular equations-of-state for the HE reaction by-products has been compared to one-and two-dimensional explosive detonation experiments. These comparisons indicate excellent agreement of CTH predictions with experimental results. The new reactive bum model coupled _cg ___ g _ _ _ _ with the adw,pces in equation-of-state modeling make it possible to predict multi-dimensional bum phe-_. _-_ _ _ 8 _: _ _, _" nomena without modifying the model parameters for different dimensionality. Most current bum models 2. _o _, _ _ _ _., ,, = ct __g"g'_ _ o _ 8 _.__ do not accurately predict both one-dimensional plate acceleration experiments and two-dimensional cylin-_-_"._ _ _. _ _. :" b_" = der expansion experiments simultaneously. Our implementation is significant because it represents the _ _ o _ _ _ _ _ "first time a multi-dimensional model has been used to successfully predict multi-dimensional detonation _ o .., o ,_ _ _ _ z effects without requiringa modification of the model parameters.
, Summary-ALEGRA is a multi-material, arbitrary-Lagrangian-Eulerian (ALE) code for solid dynamics being developed by the Computational Physics Research and Development Department at Sandia +tionat Laboratories. It combines the features of modem Eulerian shock codes, such as CTH, with modem Lagrangian structural analysis codes. With the ALE algorithm, the mesh can be stationary (Eulerian) with the material flowing through the mesh, the mesh can move with the material (Lagrangian) so there is no flow between elements, or the mesh motion can be entirely independent of the material motion (Arbitrary). All three mesh types can coexist in the same problem, and any mesh may change its type during the calculation. In this paper we summarize several key capabilities that have recently been added to the code or are currently being implemented. As a demonstration of the capabilities of ALEGRA, we have applied it to the experimental data taken by Silsby.
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