^{1,2}, Q. An

^{3}, B. Li

^{1}, H. A. Wu

^{1}, W. A. Goddard III

^{3}and S. N. Luo

^{2,4,a)}

### Abstract

Using large-scale molecular dynamics simulations, we investigate shock response of a model Cu nanofoam with cylindrical voids and a high initial porosity (50% theoretical density), including elastic and plastic deformation, Hugoniot states, shock-induced melting, partial or complete void collapse, nanojetting, and hotspot formation. The elastic-plastic and overtaking shocks are observed at different shock strengths. The simulated Hugoniot states can be described with a modified, power-law (pressure–porosity) model, and agree with shock experiments on Cu powders, as well as the compacted Hugoniot predicted with the Grüneisen equation of state. Shock-induced melting shows no clear signs of bulk premelting or superheating. Voids collapse via plastic flow nucleated from voids, and the exact processes are shock strength dependent. With increasing shock strengths, void collapse transits from the “geometrical” mode (collapse of a void is dominated by crystallography and void geometry and can be different from that of one another) to “hydrodynamic” mode (collapse of a void is similar to one another); the collapse may be achieved predominantly by flow along the {111} slip planes, by way of alternating compression and tension zones, by means of transverse flows, via forward and transverse flows, or through forward nanojetting. The internal jetting induces pronounced shock front roughening, leading to internal hotspot formation and sizable high speed jets on atomically flat free surfaces.

This work was supported in part by National Science Foundation of China (11172289) and by the Fundamental Research Funds for the Central Universities of China.

I. INTRODUCTION

II. METHODOLOGY

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

##### B82B1/00

## Figures

Partial configuration of a Cu nanofoam created from a [100] single crystal. Shock loading is along the *x*-axis or [100].

Partial configuration of a Cu nanofoam created from a [100] single crystal. Shock loading is along the *x*-axis or [100].

The *x* – *t* diagram of for , showing different regimes: unshocked, elastic precursor, plastic wave, and elastic release.

The *x* – *t* diagram of for , showing different regimes: unshocked, elastic precursor, plastic wave, and elastic release.

The shock velocity–particle velocity ( ) plot for elastic and plastic shocks. HEL: Hugoniot elastic limit. (2.5 km s^{−1}) and *C* _{0} (0.16 km s^{−1}) are the intercepts of the straight lines with the vertical axis.

The shock velocity–particle velocity ( ) plot for elastic and plastic shocks. HEL: Hugoniot elastic limit. (2.5 km s^{−1}) and *C* _{0} (0.16 km s^{−1}) are the intercepts of the straight lines with the vertical axis.

The stress ( )–specific volume (*V*) curves obtained from MD simulations, fit to MD results, experiments on porous and full density Cu, ^{ 6,31 } and predicted compacted Hugoniot.

The stress ( )–specific volume (*V*) curves obtained from MD simulations, fit to MD results, experiments on porous and full density Cu, ^{ 6,31 } and predicted compacted Hugoniot.

(a) The shock pressure–temperature (*P–T*) plot for different (circles), along with the equilibrium melting curve (solid curve). ^{ 32 } The dashed curves are guide to the eye. (b) MSDs obtained from the absorbing wall simulations. The numbers in (a) and (b) denote in km s^{−1}.

(a) The shock pressure–temperature (*P–T*) plot for different (circles), along with the equilibrium melting curve (solid curve). ^{ 32 } The dashed curves are guide to the eye. (b) MSDs obtained from the absorbing wall simulations. The numbers in (a) and (b) denote in km s^{−1}.

Atomic configurations (projected onto the *xy*-plane) for (a) and *t* = 100 ps; (b) and *t* = 50 ps; (c) and *t* = 37 ps. Color-coding is based on . Shock direction: left right.

Atomic configurations (projected onto the *xy*-plane) for (a) and *t* = 100 ps; (b) and *t* = 50 ps; (c) and *t* = 37 ps. Color-coding is based on . Shock direction: left right.

Atomic configurations (projected onto the *xy*-plane) for and *t* = 14 ps; (b) and *t* = 9 ps, showing forward or transverse flows (arrows). Color-coding is based on *u _{x} * in km s

^{– 1}. Shock direction: left right.

Atomic configurations (projected onto the *xy*-plane) for and *t* = 14 ps; (b) and *t* = 9 ps, showing forward or transverse flows (arrows). Color-coding is based on *u _{x} * in km s

^{– 1}. Shock direction: left right.

The *x* – *t* diagram of a 1-nm thick slice cut along the void diameter in the shock direction (*AOB* in Fig. 1 ) obtained from the 2D binning analysis for , showing internal jetting (circled region), free surface jetting and atomization. Color-coding is based on *u _{x} *. Shock direction: left right.

The *x* – *t* diagram of a 1-nm thick slice cut along the void diameter in the shock direction (*AOB* in Fig. 1 ) obtained from the 2D binning analysis for , showing internal jetting (circled region), free surface jetting and atomization. Color-coding is based on *u _{x} *. Shock direction: left right.

2D stress ( , and in GPa) maps on the *xy*-plane for and *t* = 50 ps [cf. Fig. 6(b) ]. Shock direction: left right.

2D stress ( , and in GPa) maps on the *xy*-plane for and *t* = 50 ps [cf. Fig. 6(b) ]. Shock direction: left right.

2D temperature maps on the *xy*-plane for different shock strengths, showing hotspot formation due to internal jetting. Temperature is in K. Color is saturated above a chosen temperature. Shock direction: left right.

2D temperature maps on the *xy*-plane for different shock strengths, showing hotspot formation due to internal jetting. Temperature is in K. Color is saturated above a chosen temperature. Shock direction: left right.

Atomic configurations (projected onto the *xy*-plane) showing nanojets at free surfaces for (a) and (b) . Atoms are color-coded with *u _{x} * in km s

^{−1}. Shock direction: left right.

Atomic configurations (projected onto the *xy*-plane) showing nanojets at free surfaces for (a) and (b) . Atoms are color-coded with *u _{x} * in km s

^{−1}. Shock direction: left right.

Jet velocity (a) and jet height (b) for different . The numbers denote in km s^{−1}. The curves for are shifted by −50 ps.

Jet velocity (a) and jet height (b) for different . The numbers denote in km s^{−1}. The curves for are shifted by −50 ps.

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