^{1}, V. F. Nesterenko

^{1,a)}, D. J. Benson

^{1}, J. Cai

^{2}, K. S. Vecchio

^{3}, F. Jiang

^{3}, J. W. Addiss

^{4}, S. M. Walley

^{4}and W. G. Proud

^{4}

### Abstract

The variation of metallic particle size and sample porosity significantly alters the dynamic mechanical properties of high density granular composite materials processed using a cold isostatically pressed mixture of polytetrafluoroethylene (PTFE), aluminum (Al), and tungsten (W) powders. Quasistatic and dynamic experiments are performed with identical constituent mass fractions with variations in the size of the W particles and pressing conditions. The relatively weak polymer matrix allows the strength and fracture modes of this material to be governed by the granular type behavior of agglomerated metal particles. A higher ultimate compressive strength was observed in relatively high porosity samples with small W particles compared to those with coarse W particles in all experiments. Mesoscale granular force chains of the metallic particles explain this unusual phenomenon as observed in hydrocode simulations of a drop-weight test. Macrocracks forming below the critical failure strain for the matrix and unusual behavior due to a competition between densification and fracture in dynamic tests of porous samples were also observed. Numerical modeling of shock loading of this granular composite material demonstrated that the internal energy, specifically thermal energy, of the soft PTFE matrix can be tailored by the W particle size distribution.

The support for this project provided by the Office of Naval Research Grant No. N00014-06-1-0263 and the Office of Naval Research Multidisciplinary University Research Initiative Award N00014-07-1-0740 (Program Officer Dr. Clifford Bedford) and a U.K. Engineering and Physical Sciences Research Council grant (J. W. Addiss) is highly appreciated.

I. INTRODUCTION

II. EXPERIMENTAL

A. Sample preparation

B. Quasistatic tests

C. Dynamic Hopkinson bar tests

D. Dynamic “soft” drop weight tests

III. NUMERICAL MODELING AND DISCUSSION

A. Numerical modeling of dynamic drop-weight test

B. Numerical modeling of shock wave in granular composite materials

IV. CONCLUSIONS

### Key Topics

- Composite materials
- 31.0
- Stress strain relations
- 24.0
- Powders
- 17.0
- Shear deformation
- 16.0
- Shock waves
- 13.0

## Figures

Fracture detail of various samples after quasistatic testing. (a) Shear crack and (b) axial and shear cracks in the porous PTFE-Al-fine W composite sample. (c) Axial/shear and (d) axial cracks in the porous PTFE-Al-coarse W composite sample. [(e) and (f)] Kinked axial/shear cracks in the dense PTFE-Al-coarse W composite sample. All samples had identical initial dimensions of 10.44 mm diameter and 10 mm height.

Fracture detail of various samples after quasistatic testing. (a) Shear crack and (b) axial and shear cracks in the porous PTFE-Al-fine W composite sample. (c) Axial/shear and (d) axial cracks in the porous PTFE-Al-coarse W composite sample. [(e) and (f)] Kinked axial/shear cracks in the dense PTFE-Al-coarse W composite sample. All samples had identical initial dimensions of 10.44 mm diameter and 10 mm height.

Quasistatic stress-strain curve of PTFE-W-Al composite materials with variation of density and particle size of W. Curve (1) shows the results of the sample with fine W particles and porosity about 14%. Curve (2) shows the results of the sample with large W particles, which was almost fully densified. Curve (3) shows the results of the sample with large W particles CIPed at a lower pressure to induce about 14% porosity.

Quasistatic stress-strain curve of PTFE-W-Al composite materials with variation of density and particle size of W. Curve (1) shows the results of the sample with fine W particles and porosity about 14%. Curve (2) shows the results of the sample with large W particles, which was almost fully densified. Curve (3) shows the results of the sample with large W particles CIPed at a lower pressure to induce about 14% porosity.

Hopkinson bar stress vs strain and strain-rate vs strain curves of a (a) porous PTFE-Al-W composite sample containing fine W particles, (b) porous PTFE-Al-W composite samples containing coarse W particles, (c) dense PTFE-Al-W composite samples containing coarse W particles, and (d) cold isostatically pressed PTFE samples.

Hopkinson bar stress vs strain and strain-rate vs strain curves of a (a) porous PTFE-Al-W composite sample containing fine W particles, (b) porous PTFE-Al-W composite samples containing coarse W particles, (c) dense PTFE-Al-W composite samples containing coarse W particles, and (d) cold isostatically pressed PTFE samples.

Stress vs time curves obtained in drop weight tests. (a) Curves (1) and (2) correspond to porous samples with coarse W particles. The remarkable difference between the two curves is due to the densification of the sample, shown in curve (2), before fracture. (b) Curve (1) corresponds to the densified sample with coarse W particles. Curve (2) corresponds to the porous sample with fine W particles.

Stress vs time curves obtained in drop weight tests. (a) Curves (1) and (2) correspond to porous samples with coarse W particles. The remarkable difference between the two curves is due to the densification of the sample, shown in curve (2), before fracture. (b) Curve (1) corresponds to the densified sample with coarse W particles. Curve (2) corresponds to the porous sample with fine W particles.

(a) Porous sample (sample 73), engineering strain 0.15 with lower strength containing coarse W particles post drop-weight test corresponding to curve (1) in Fig. 4(a). (b) Porous sample (sample 65), engineering strain 0.26 containing coarse W particles corresponding to curve (2) in Fig. 4(a). (c) Porous sample (sample 64), engineering strain 0.25 with fine W particles corresponding to curve (2) in Fig. 4(b).

(a) Porous sample (sample 73), engineering strain 0.15 with lower strength containing coarse W particles post drop-weight test corresponding to curve (1) in Fig. 4(a). (b) Porous sample (sample 65), engineering strain 0.26 containing coarse W particles corresponding to curve (2) in Fig. 4(a). (c) Porous sample (sample 64), engineering strain 0.25 with fine W particles corresponding to curve (2) in Fig. 4(b).

(a) PTFE-W-Al sample (sample 1) using Al particles and W particles in a PTFE matrix. (b) PTFE-W-Al sample (sample 2) using diameter Al particles and diameter W particles in a PTFE matrix.

(a) PTFE-W-Al sample (sample 1) using Al particles and W particles in a PTFE matrix. (b) PTFE-W-Al sample (sample 2) using diameter Al particles and diameter W particles in a PTFE matrix.

Average engineering stress at the top of the numerical sample plotted against the global strain for a sample using small W particles (sample 1, curve 1) and a sample using large W particles (sample 2, curve 2). Note the stress suddenly increases in curve 1 at 0.13 global strain while the curve 2 coincides with the results for pure CIPed PTFE (curve 3).

Average engineering stress at the top of the numerical sample plotted against the global strain for a sample using small W particles (sample 1, curve 1) and a sample using large W particles (sample 2, curve 2). Note the stress suddenly increases in curve 1 at 0.13 global strain while the curve 2 coincides with the results for pure CIPed PTFE (curve 3).

Stress and strain distribution in sample 1 resulting from a drop-weight calculation with a constant velocity at the top boundary. The color intensity varies from light gray (0 MPa) to dark gray for the von Mises stress and 0 to for the plastic strain. The von Mises true stress distribution (a) and local effective plastic strain (b) at 0.022 global strain. The von Mises true stress distribution (c) and local effective plastic strain (d) at 0.042 global strain. The von Mises true stress distribution (e) and local effective plastic strain (f) at 0.238 global strain.

Stress and strain distribution in sample 1 resulting from a drop-weight calculation with a constant velocity at the top boundary. The color intensity varies from light gray (0 MPa) to dark gray for the von Mises stress and 0 to for the plastic strain. The von Mises true stress distribution (a) and local effective plastic strain (b) at 0.022 global strain. The von Mises true stress distribution (c) and local effective plastic strain (d) at 0.042 global strain. The von Mises true stress distribution (e) and local effective plastic strain (f) at 0.238 global strain.

Stress and strain distribution in sample 2 resulting from a drop-weight calculation with a constant velocity at the top boundary. The color intensity varies from light gray (0 MPa) to dark gray for the von Mises stress and 0 to plastic strain. The von Mises true stress distribution (a) and local effective plastic strain (b) at 0.014 global strain. The von Mises true stress distribution (c) and local effective plastic strain (d) at 0.186 global strain. The von Mises true stress distribution (e) and local effective plastic strain (f) at 0.23 global strain.

Stress and strain distribution in sample 2 resulting from a drop-weight calculation with a constant velocity at the top boundary. The color intensity varies from light gray (0 MPa) to dark gray for the von Mises stress and 0 to plastic strain. The von Mises true stress distribution (a) and local effective plastic strain (b) at 0.014 global strain. The von Mises true stress distribution (c) and local effective plastic strain (d) at 0.186 global strain. The von Mises true stress distribution (e) and local effective plastic strain (f) at 0.23 global strain.

Different types of metallic particle agglomerate distributions within the soft PTFE matrix (not to scale). (a) Groups of metallic particles coalesce but do not interact immediately upon loading. The interaction of these groups does not contribute to the effective elastic modulus, but may contribute to the critical failure stress as these groups interact with one another during compression testing. (b) The metallic particle force chains are highlighted by a darker color for distinction.

Different types of metallic particle agglomerate distributions within the soft PTFE matrix (not to scale). (a) Groups of metallic particles coalesce but do not interact immediately upon loading. The interaction of these groups does not contribute to the effective elastic modulus, but may contribute to the critical failure stress as these groups interact with one another during compression testing. (b) The metallic particle force chains are highlighted by a darker color for distinction.

Material configuration composite samples that will be impacted from the top boundary at an impact velocity . (a) The sample with small W particles (diameter of ). The subfigure on the left shows a more detailed view of the microstructure. (b) The sample with large W particles (diameter of ). The subfigure on the right shows a more detailed view of the microstructure. The Al particles have a diameter in both configurations.

Material configuration composite samples that will be impacted from the top boundary at an impact velocity . (a) The sample with small W particles (diameter of ). The subfigure on the left shows a more detailed view of the microstructure. (b) The sample with large W particles (diameter of ). The subfigure on the right shows a more detailed view of the microstructure. The Al particles have a diameter in both configurations.

(a) Fraction of internal energies in each material during the propagation of shock wave for the numerical sample with small W particles. (b) Fraction of internal energies in each material during the propagation of a shock wave the numerical sample with large W particles.

(a) Fraction of internal energies in each material during the propagation of shock wave for the numerical sample with small W particles. (b) Fraction of internal energies in each material during the propagation of a shock wave the numerical sample with large W particles.

Temperature distribution in the shocked composite numerical samples at a constant impact velocity of from the top boundary. The temperature scale ranges from 300 K (light gray) to (black) for parts (a) and (b). (a) The numerical sample with small W particles at 41.5 ns after impact. (b) The numerical sample with large W particles at 38.3 ns after impact. (c) Velocity profile (averaged in the horizontal direction) of the material starting from the bottom of the numerical samples shown in parts (a) and (b). Curve (1) corresponds to the numerical sample with small W particles. Curve (2) corresponds to the numerical sample with large W particles.

Temperature distribution in the shocked composite numerical samples at a constant impact velocity of from the top boundary. The temperature scale ranges from 300 K (light gray) to (black) for parts (a) and (b). (a) The numerical sample with small W particles at 41.5 ns after impact. (b) The numerical sample with large W particles at 38.3 ns after impact. (c) Velocity profile (averaged in the horizontal direction) of the material starting from the bottom of the numerical samples shown in parts (a) and (b). Curve (1) corresponds to the numerical sample with small W particles. Curve (2) corresponds to the numerical sample with large W particles.

## Tables

Properties of various composite materials.

Properties of various composite materials.

Quasistatic test results at a strain rate of for the composite materials.

Quasistatic test results at a strain rate of for the composite materials.

Hopkinson bar test results at an average strain rate of for each composite material.

Hopkinson bar test results at an average strain rate of for each composite material.

Drop-weight tests results at an average strain rate of for each composite material.

Drop-weight tests results at an average strain rate of for each composite material.

Density and volume fraction of material components in tapped powders

Density and volume fraction of material components in tapped powders

The mass ratio and the increase of thermal energy with respect to total internal energy increase of composite in samples with large and small W particles.

The mass ratio and the increase of thermal energy with respect to total internal energy increase of composite in samples with large and small W particles.

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