Eric Mas

A VISCOELASTIC MODEL FOR PBX BINDERS

Abstract. Stress-strain measurements done at different rates and temperatures along with measurementsof the rate- and temperature-dependent dynamic storage modulus have allowed us to construct a generalizedMaxwell model for the linear viscoelastic response of plasticized estane. A theoretical analysis ispresented to include effects of impurites.INTRODUCTIONComplete knowledge of the thermo-mechanicalbehavior of the constituents of PBX-9501 is requiredfor any micromechanics method to be a useful toolfor modeling its behavior. The primary constituentsof PBX 9501 are the explosive cyclotetramethylene-tetranitramine (HMX) crystals and the inertplasticized estane binder matrix. Estane 5703 is apolyester polyurethane elastomer manufactured bythe B.F. Goodrich Company with a density of 1.19gm/cm 3 . The polymeric binder shows dramaticsensitivity to changes in strain rates andtemperatures. For example, a change in thetemperature from -50 C to 50 C will have anassociated change in the shear modulus of five ordersof magnitude. Obviously, a successful theory forPBX 9501 must account for this behavior. Becauseof recent experimental effort, much high-qualitystress-strain data has become available for theplasticised binder. A primary goal was to use thisdata to formulate a generalized Maxwell model(GMM) thermo-mechanical constitutive law for thebinder. While a GMM constitutive law hasimmediate applications for PBX 9501, ourtheoretical analysis used to obtain the constitutivelaw has interest to the general community involvedwith plastic bonded high explosives.The aforementioned stress-strain data was measuredby the LANLs Material Structure/Property Group(MST-8) and was obtained by several differentexperimental methods. An Intron 5567 testingmachine was used for measuring uniaxial stress-strain data for rates in the range of 1

Finite Element Method Calculations on Statistically Consistent Microstructures of PBX 9501

We have used data from image analysis to guide us in creating a finite element mesh of PBX 9501. Information about the binder concentration at different length scales taken from micrographs allows us to create a mesh that naturally incorporates inhomogeneities of the microstructure in a manner that is statistically consistent with the observed microstructure. We then apply constitutive models that are consistent with the different binder concentrations and run finite element simulations. We will present our technique for incorporating the image analysis information into the mesh, our mechanical models, and results of the simulations.

Dynamic Response of PBX‐9501 through the β‐δ Phase Transition

The Gibbs free energies of the β and δ phases of HMX are constructed from zero pressure heat capacity data, specific volume measurements, numerical simulations, and diamond anvil experiments. The free energies provide input into a dynamic phase transition model developed for heterogeneous materials that undergo dynamically driven phase transitions. This model, which uses the method of cells analysis to treat the HMX‐polymer binder composite, is used to study dynamically loaded PBX‐9501 as it transforms from the beta to the delta phase.

Applying Micro‐Mechanics to Finite Element Simulations of Split Hopkinson Pressure Bar Experiments on High Explosives

We have developed a constitutive theory based on the Method of Cells and a modified Mori‐Tanaka (MT) effective medium theory to model high explosives. MT effective medium theory allows us to model the smaller explosive grains in the viscoelastic matrix while the Method of Cells partitions the representative volume element into a single subcell designating a large grain, and the remaining subcells for the small grain‐binder mixture. The model is then implemented into the finite‐element code EPIC. Split Hopkinson Pressure Bar (SHPB) experiments are simulated. We compare the predicted incident, transmitted and reflected strains with SHPB experimental values. [Research supported by the USDOE under contract W‐7405‐ENG‐36.]

Modeling Aspects of the Dynamic Response of Heterogeneous Materials

In engineering applications, simulations involving heterogeneous materials where it is necessary to capture the local response coming from the heterogeneities is very difficult. The use of homogenization techniques can reduce the size of the problem but will miss the local effects. Homogenization can also be difficult if the constituents obey different constitutive laws. Additional complications arise if inelastic deformation occurs. In such cases a two-scale approach is preferred and this work addresses these issues in the context of a two-scale Finite Element Method (FEM). Examples of using two-scale FEM approaches are presented.

A TWO‐SCALE FEM FORMULATION FOR HETEROGENEOUS MATERIALS

This article proposes a two‐scale finite element approach for the dynamic response of heterogeneous materials. While common two‐scale Finite Element Method (FEM) formulations consider the Representative Volume Element (RVE) much smaller than the finite element mesh, the present paper extends the formulation for the cases when RVE becomes comparable with the finite element in the mesh. The new two‐scale equations and their FEM implementation, are presented together with an example.

Two‐Scale FEM in the Dynamic Response of a Heterogeneous Material

It is common in the numerical simulation of the dynamic response of a heterogeneous material to use the average material properties, which usually are obtained through a homogenization technique. This approach would lead to an average response of the composite. However, if ones interested in the local response of the material then a localization technique needs to be used. This paper addresses the localization problem in the dynamic response of such material, using a two‐scale FEM approach. The basic equations for coupling between the first (or coarse) scale to the second (or fine scale) are presented. Numerical examples are included.