Bradford E. Clements

Pressure-induced phase change in poly(tetrafluoroethylene) at modest impact velocities

Although poly(tetrafluoroethylene) (PTFE) is an unusually ductile polymer, it undergoes an abrupt ductile-brittle transition at modest impact velocities. No previous explanation for this behavior has been found after an extensive literature search. In this paper, we examine the role of a pressure-induced phase transition in PTFE in the dynamic failure of Taylor cylinder samples. There is a known phase transition in PTFE with a marked decrease in volume and compressibility that occurs at 0.5–0.65GPa at 21°C, with the transition pressure inversely related to temperature. Varying the temperature of the samples in the experiment revealed that the phase transition is probably involved in sample failure because the ductile/brittle transition velocity increased for decreasing temperature, despite the material fracture toughness decreasing. Additionally, Taylor tests were carried out on samples of poly(chlorotrifluoroethylene) PCTFE to investigate the behavior of a similar material to PTFE but without a pressure-...

Dynamic mechanical behavior of filled polymers. I. Theoretical developments

A constitutive theory is developed for modeling the mechanical response of dynamically loaded filled-polymer composites. The basis for this work is Mori and Tanaka’s effective medium theory. Expressions derived by Weng and co-workers are used for the elastic stiffness tensor of the composite. The filler is a low volume concentration of randomly positioned elastic ellipsoidal particles. Random and aligned orientations of the ellipsoids are considered. The viscoelastic stress–strain behavior of the polymer matrix is modeled using the Boltzmann superposition principle with a Prony series representation for the stress relaxation functions. We argue that for rubbery polymers it is reasonable to express the composite stress relaxation functions as series expansions about the ratio of the polymer shear relaxation function to its bulk modulus. The smallness of this ratio allows accurate results to be obtained when truncating the expansion at first order. Inverse Laplace transformations required by the theory can ...

Dynamic mechanical behavior of filled polymers. II. Applications

A filled-polymer composite theory, based on effective medium theory, has been developed that allows the dynamic mechanical behavior to be modeled. The stress–strain behavior of the composite is derived using Schapery’s nonequilibrium thermodynamic basis for generalizing Boltzmann’s superposition principle, in conjunction with a Prony series representation for the stress relaxation moduli. Schapery’s theory allows nonlinear viscoelastic effects to be included into the mechanical response. The coefficients of the Prony series are functions of the filler’s bulk modulus, concentration, and shape. The theory is applicable to rubbery polymers and is shown to be accurate for filler concentrations up to approximately 30%. Higher concentrations can be modeled by introducing a phenomenological filler–filler correlation parameter. Effects due to heating and varying strain rate are easily accounted for in this approach. To demonstrate the utility and validity of the theory we compare its predictions to several dynami...

WAVE PROPAGATION IN LAMINATES : A STUDY OF THE NONHOMOGENIZED DYNAMIC METHOD OF CELLS

Abstract The nonhomogenized dynamic method of cells (NHDMOC) method uses a truncated expansion for the particle displacement field; the expansion parameter is the local cell position vector. We derive and numerically solve the NHDMOC equations for the first-, second-, and third-order expansions, appropriate for modeling a plate-impact experiment. All materials are linear elastic. The performance of the NHDMOC is tested at each order for its ability to resolve the shock wave front as it propagates through a homogeneous target. The same performance is again tested for a shock propagating through a bilaminate target. We find for both cases that the displacement field expansion converges rapidly: given the same cell widths, the first-order theory gives only a qualitative description of the propagating stress wave; the second-order theory performs much better; and the third-order theory gives small refinements over the second-order theory. In the third-order theory the stress is nearly always continuous across material boundaries, whereas in first-order, one commonly encounters substantial stress discontinuities. The first-order theory requires a considerable finer computational grid to achieve the same satisfactory representation of the wave profile as the third-order theory. Thus very little computational time is saved by using it. The numerical (unphysical) oscillations inherent in these calculations are largely reduced in the third-order theory, again indicating the rapid convergence of the displacement series.

Controlling shockwave dynamics using architecture in periodic porous materials

Additive manufacturing (AM) is an attractive approach for the design and fabrication of structures capable of achieving controlled mechanical response of the underlying deformation mechanisms. While there are numerous examples illustrating how the quasi-static mechanical responses of polymer foams have been tailored by additive manufacturing, there is limited understanding of the response of these materials under shockwave compression. Dynamic compression experiments coupled with time-resolved X-ray imaging were performed to obtain insights into the in situ evolution of shockwave coupling to porous, periodic polymer foams. We further demonstrate shock wave modulation or “spatially graded-flow” in shock-driven experiments via the spatial control of layer symmetries afforded by additive manufacturing techniques at the micron scale.

A model for heterogeneous materials including phase transformations

A model is developed for particulate composites, which includes phase transformations in one or all of the constituents. The model is an extension of the method of cells formalism. Representative simulations for a single-phase, brittle particulate (SiC) embedded in a ductile material (Ti), which undergoes a solid–solid phase transformation, are provided. Also, simulations for a tungsten heavy alloy (WHA) are included. In the WHA analyses a particulate composite, composed of tungsten particles embedded in a tungsten–iron–nickel alloy matrix, is modeled. A solid–liquid phase transformation of the matrix material is included in the WHA numerical calculations. The example problems also demonstrate two approaches for generating free energies for the material constituents. Simulations for volumetric compression, uniaxial strain, biaxial strain, and pure shear are used to demonstrate the versatility of the model.

Wave propagation in an epoxy-graphite laminate

The third-order, nonhomogenized, dynamic method of cells is used to calculate the particle velocity for a shock wave experiment involving an epoxy–graphite laminate. Constitutive relations suitable for the various materials are used. This includes linear and nonlinear elasticity and, when appropriate, viscoelasticity. It is found to be beneficial to incorporate artificial viscosity into the analysis. Artificial viscosity successfully removes the unphysical high-frequency ringing in the numerical solutions of the theory, while leaving the physical oscillations, characteristic of wave propagation in a periodic laminate, largely undiminished. It also allows the viscoelastic relaxed moduli to be closer to their unrelaxed counterparts than in a previous calculation, thus making them more acceptable. The results agree well with the corresponding plate-impact experiment, and are compared to the second-order theory of Clements, Johnson, and Hixson [Phys. Rev. E, 54, 6876 (1996)].

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.

Moderate Velocity Ball Impact of a Mock High-Explosive

Modeling of thermal and mechanical events in high-explosive materials is complicated by the composite nature of the material, which experiences viscoelastic and plastic deformations and sustains damage in the form of microcracks that can dominate its overall behavior. A mechanical event of interest is projectile interaction with the material, which leads to extreme local deformation and adiabatic heating, which can potentially lead to adverse outcomes in an energetic material. Simulations of such an event predicted large local temperature rises near the path of a spherical projectile, but these were experimentally unconfirmed and hence potentially non-physical. This work concerns the experimental verification of local temperatures both at the surface and in the wake of a spherical projectile penetrating a mock (unreactive) high-explosive at ~700 m/s. Fast response thermocouples were embedded radially in a mid-plane of a cylindrical target, which was bonded around the thermocouples with epoxy and recorded by an oscilloscope through a low-pass filter with a bandwidth of 500 Hz. A peak temperature rise of 70 K was measured both at the equator of the projectile and in its wake, in good agreement with the temperature predicted in the minimally distorted elements at those locations by a finite element model in ABAQUS employing the ViscoSCRAM constitutive model. Further work is needed to elucidate the extreme temperature rises in material undergoing crushing or fragmentation, which is difficult to predict with meshed finite element methods due to element distortion, and also challenging to quantify experimentally.

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.