This report presents the formulation of a crystal elasto-viscoplastic model and the corresponding integration scheme. The model is suitable to represent the isothermal, anisotropic, large deformation of polycrystalline metals. The formulation is an extension of a rigid viscoplastic model to account for elasticity effects, and incorporates a number of changes with respect to a previous formulation [Marin & Dawson, 1998]. This extension is formally derived using the well-known multiplicative decomposition of the deformation gradient into an elastic and plastic components, where the elastic part is additionally decomposed into the elastic stretch V{sup e} and the proper orthogonal R{sup e} tensors. The constitutive equations are written in the intermediate, stress-free configuration obtained by unloading the deformed crystal through the elastic stretch V{sup e-}. The model is framed in a thermodynamic setting, and developed initially for large elastic strains. The crystal equations are then specialized to the case of small elastic strains, an assumption typically valid for metals. The developed integration scheme is implicit and proceeds by separating the spherical and deviatoric crystal responses. An ''approximate'' algorithmic material moduli is also derived for applications in implicit numerical codes. The model equations and their integration procedure have been implemented in both a material point simulator and a commercial finite element code. Both implementations are validated by solving a number of examples involving aggregates of either face centered cubic (FCC) or hexagonal close-packed (HCP) crystals subjected to different loading paths.
Sandia currently lacks a high fidelity method for predicting loads on and subsequent structural response of earth penetrating weapons. This project seeks to test, debug, improve and validate methodologies for modeling earth penetration. Results of this project will allow us to optimize and certify designs for the B61-11, Robust Nuclear Earth Penetrator (RNEP), PEN-X and future nuclear and conventional penetrator systems. Since this is an ASC Advanced Deployment project the primary goal of the work is to test, debug, verify and validate new Sierra (and Nevada) tools. Also, since this project is part of the V&V program within ASC, uncertainty quantification (UQ), optimization using DAKOTA [1] and sensitivity analysis are an integral part of the work. This project evaluates, verifies and validates new constitutive models, penetration methodologies and Sierra/Nevada codes. In FY05 the project focused mostly on PRESTO [2] using the Spherical Cavity Expansion (SCE) [3,4] and PRESTO Lagrangian analysis with a preformed hole (Pen-X) methodologies. Modeling penetration tests using PRESTO with a pilot hole was also attempted to evaluate constitutive models. Future years work would include the Alegra/SHISM [5] and AlegrdEP (Earth Penetration) methodologies when they are ready for validation testing. Constitutive models such as Soil-and-Foam, the Sandia Geomodel [6], and the K&C Concrete model [7] were also tested and evaluated. This report is submitted to satisfy annual documentation requirements for the ASC Advanced Deployment program. This report summarizes FY05 work performed in the Penetration Mechanical Response (ASC-APPS) and Penetration Mechanics (ASC-V&V) projects. A single report is written to document the two projects because of the significant amount of technical overlap.
In this report we present the formulation of the physically-based Evolving Microstructural Model of Inelasticity (EMMI) . The specific version of the model treated here describes the plasticity and isotropic damage of metals as being currently applied to model the ductile failure process in structural components of the W80 program . The formulation of the EMMI constitutive equations is framed in the context of the large deformation kinematics of solids and the thermodynamics of internal state variables . This formulation is focused first on developing the plasticity equations in both the relaxed (unloaded) and current configurations. The equations in the current configuration, expressed in non-dimensional form, are used to devise the identification procedure for the plasticity parameters. The model is then extended to include a porosity-based isotropic damage state variable to describe the progressive deterioration of the strength and mechanical properties of metals induced by deformation . The numerical treatment of these coupled plasticity-damage constitutive equations is explained in detail. A number of examples are solved to validate the numerical implementation of the model.
A numerical screening study of the interaction between a penetrator and a geological target with a preformed hole has been carried out to identify the main parameters affecting the penetration event. The planning of the numerical experiment was based on the orthogonal array OA(18,7,3,2), which allows 18 simulation runs with 7 parameters at 3 levels each. The strength of 2 of the array allows also for two-factor interaction studies. The seven parameters chosen for this study are: penetrator offset, hole diameter, hole taper, vertical and horizontal velocity of the penetrator, angle of attack of the penetrator and target material. The analysis of the simulation results has been based on main effects plots and analysis of variance (ANOVA), and it has been performed using three metrics: the maximum values of the penetration depth, penetrator deceleration and plastic strain in the penetrator case. This screening study shows that target material has a major influence on penetration depth and penetrator deceleration, while penetrator offset has the strongest effect on the maximum plastic strain.