Spallation caused by the diffusion and agglomeration of vacancies in ductile metals

Highlights

• The spalling temperature, a new concept, is proposed first.

• The dependence of the damage and the void growth velocity is obtained.

• A characteristic stress at the void boundary is discovered first.

• The temperature near the growing void is high, possibly causing the metal to melt.

Abstract

In this paper, the spallation process for the ductile metals under plane shock loading is discussed in theory. By employing the phase transition theory and non-equilibrium theory, the spallation process may be understood as a result of the diffusion and agglomeration of the generated vacancies. Through the detailed theoretical analysis, the following important points are concluded: (1) the spalling temperature, a new concept, is proposed first and the appearance of spallation critical behavior is proved; (2) the quantitative grain size, tensile strain rate and temperature dependence of both the damage evolution rate and the void growth velocity is obtained; (3) the existence of a characteristic size for the voids and a characteristic stress at the void boundary is discovered first, and their magnitude depend on the vacancy excitation energy and the average volume of one vacancy; (4) the temperature of metal near the growing void is found to be high, possibly causing the metal to melt, and it decreases quickly with the distance away from the void; (5) the area of the plastic zone, surrounding one formed spherical void, is clarified; (6) the viewpoint is put forward that the void growth may arise from the agglomeration of vacancies rather than the emission of dislocations when the shocking temperature approaches spalling temperature. Most of the above theoretical results are novel and obtained first.

Introduction

Due to the wide spectrum of issues ranging across defense and industrial applications, material behaviors at high pressure, high strain and high strain-rate physical processes, e.g. spallation process, is interesting in science. For the ductile metal in the spallation process, typically possessing the above extreme physical conditions, the dynamic damage occurs and is experimentally found to exist in the form of voids of different sizes in the spallation planes (Qi et al., 2011, Belak, 2004, Pei, 2013). In the spallation process, the dynamic behaviors, such as the nucleation rate of void, void growth velocity, coalescence of voids, damage evolution rate and so on, are paramount importance and have been investigated persistently in experiments and theoretically in the last four decades (Qi et al., 2011, Belak, 2004, Pei, 2013, Seaman et al., 1976, Gurson, 1977, Johnson and Addessio, 1988, Curran et al., 1987, Strachan et al., 2001, Reina et al., 2011). However, up to date, owing to the lacking of effective in situ dynamic characterizations, it is still difficult to investigate the dynamic behaviors in the spallation process in experiments. Also, due to the obstacle brought by the cross-scale dynamic features of the spallation phenomena in the space and time, it is challenging to describe the spallation phenomena in theory. Because of the difficulties and challenges in both the experiments and theory, the spallation phenomena have not been understood well and the effective theoretical description is still an open problem.

In this paper, the spallation process for the ductile metal under the plane shock loading is systematically discussed in theory. By means of the phase transition theory, non-equilibrium transport theory and the subsequent theoretical analysis, the conclusions are obtained: the spalling temperature, a new concept, is proposed first and the spallation critical behavior is proved to exist; the quantitative grain size, tensile strain rate and temperature dependence of both the damage evolution rate and the void growth velocity is obtained, i.e., a larger grain size, tensile strain rate and higher temperature will cause a larger damage evolution rate and void growth velocity; the existence of a characteristic size for the voids and a characteristic stress at the void boundary is discovered first, and their magnitude depend on the vacancy excitation energy and the average volume of one vacancy; the temperature for the metal adjacent to the growing void is found to be so high that it is possible to melt the metal, but it decreases quickly with the distance away from the void; the area of the plastic zone surrounding one formed spherical void is clarified; against the widely accepted viewpoint that the void growth is induced by the emission of dislocations (Belak, 2004), the distinctive viewpoint is put forward that when the shocking temperature approaches spalling temperature the void growth may arise from the agglomeration of vacancies rather than the emission of dislocations.