Brad Clements

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

Taylor impact tests and simulations of plastic bonded explosives

Taylor impact tests were conducted on plastic bonded explosives PBX 9501 and PBXN-9 for impact velocities between 80 and 214 m/s. High-speed photography was used to image the impact event at a rate of one frame for every 25 μs. For early times, PBXN-9 showed large-deformation mushrooming of the explosive cylinders, followed by fragmentation by an amount proportional to the impact speed, was observed at all velocities. PBX 9501 appeared to be more brittle than PBXN-9, the latter demonstrated a more viscoelastic response. The post-shot fragments were collected and particle size distributions were obtained. The constitutive model ViscoSCRAM was then used to model the Taylor experiments using the finite element code ABAQUS. Prior to the Taylor simulations, ViscoSCRAM was parameterized for the two explosives using uniaxial stress-strain data. Simulating Taylor impact tests validates the model in situations undergoing extreme damage and fragmentation.

Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids.

We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function Z(t) and diffusion coefficient D. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for Z(t) and D agree remarkably well with molecular dynamics simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.

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.]

Investigation of the Observed Anisotropic Fracture in Steels

A theory has been developed to model the fracture of 1080 steels. In the process of hot rolling, high aspect ratio MnS inclusions condense in 1080 steels. The inclusions align along the rolling direction. Even though the volume concentration of these inclusions is low, fractography has shown that they have a substantial effect on the fracture characteristics of the steel. We use the Method of Cells (MOC) to model this system with a (2×2×2) representative volume element to model micro‐structural effects. One of the eight MOC cells contains an elongated MnS inclusion while the remaining seven cells contain pure 1080 steel. The steel is modeled using the von Mises plasticity model. Weak interfacial bonding between the MnS and 1080 steel is assumed. We compare MOC with TEPLA to study the void growth characteristics of the MOC theory. Finally, we implement the MOC theory in the finite‐element code EPIC, carry out 3‐dimensional plate impact experiments, and compare our results with the plate impact experiments ...

Dynamically driven phase transformations in damaged composite materials

A model developed for composite materials undergoing dynamicaly driven phase transitions in its constituents has been extended to allow for complex material micro‐structure and evolution of damage. In this work, damage is described by interfacial debonding and micro‐crack growth. We have applied the analysis to silicon carbide‐titanium (SiC‐Ti) unidirectional metal matrix composites. In these composites, Ti can undergo a low pressure and temperature solid‐solid phase transition. With these extensions we have carried out simulations to study the complex interplay between loading rates, micro‐structure, damage, and the thermo‐mechanical response of the system as it undergoes a solid‐solid phase transitions.

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.

Low‐Pressure Equation of State of Polymers

Low‐pressure equations of state (EOS) are constructed for two representative polymers: polycarbonate and polytetrafluorethylene. Our method, which is based on well‐known semi‐empirical EOS procedures, relies on having heat capacity data at zero pressure, specific volume data as a function of temperature and pressure, and phase diagram information. The resulting equations of state incorporate the glass transition observed for polycarbonate and the solid‐solid phase transformations observed in polytetrafluoroethylene.

Observation of single transits in supercooled monatomic liquids.

A transit is the motion of a system from one many-particle potential energy valley to another. We report the observation of transits in molecular dynamics calculations of supercooled liquid argon and sodium. Each transit is a correlated simultaneous shift in the equilibrium positions of a small local group of particles, as revealed in the fluctuating graphs of the particle coordinates versus time. To the best of our knowledge, this is the first reported direct observation of transit motion in a monatomic liquid in thermal equilibrium. We found transits involving 2-11 particles, having mean shift in equilibrium position on the order of 0.4R(1) in argon and 0.25R(1) in sodium, where R1 is the nearest neighbor distance. The time it takes for a transit to occur is approximately one mean vibrational period, confirming that transits are fast.