Spall damage in single crystal tin under shock wave loading: A molecular dynamics simulation

Highlights

• The spall strengths in the molten tin are ~1.5–2.0 GPa lower than that in solid.

• The spall strength drops rapidly when release melting occurs, whereas the downtrend becomes gentle during shock melting.

• The spall strength is affected by the shock pressure and phase state.

Abstract

Using molecular dynamics methods, we investigated the spall damage in single crystal tin under different shock pressures. The results show that release melting and shock melting occur when the shock velocities increase in the metallic tin. The spall strengths in the molten tin are ~1.5–2.0 GPa lower than that in solid. When release melting occurs, the spall strength drops rapidly, whereas the downtrend of the spall strength becomes gentle during shock melting. The results also show that the spall strength is affected by not only the shock pressure and phase state, but also the temperature and strain rate. By visualizing the development of spall damage, we find that it forms a spall layer in the solid. In molten tin, a cavitation region with a large volume is formed. The maximum number of voids increases with an increase in the shock pressure. The growth rate of the void volume fraction slows down after reaching the initial time of void growth at different impact pressures. We elucidated the variation trend of spall strength between solid and molten tin under different shock pressures. The relevant results can provide a reference for future studies on spall damage investigations.

Introduction

When a compressive shock wave in a metal reaches a free surface, spall damage forms owing to the tensile interaction between the incident wave and the reflected rarefaction wave (Antoun et al., 2003; Meyers, 1994; Soulard, 2008). The formation of spall damage is a typical dynamic fracturing process of materials under impact loading. Spall damage has received considerable attention due to its significant influence on material properties. In a ductile metal, spall damage begins to develop upon nucleation of voids. Its evolution is related to the growth and coalescence of voids. If the tensile stress is sufficiently high, the voids begin to nucleate in the material, and the tensile stress decreases when the voids grow and assemble. The maximal tensile stress during the evolution of spall damage is called spall strength. The spall strength is a key material property for estimating the resistance to spall damage in a metal.

Metals remain in a solid state if the shock pressures are sufficiently low. However, metals will melt during the shocking process or release process with the increase in the shock pressure. The solid and molten metals have different spall states and spall strength. If the metal is in a solid state, it forms several spall layers when the spall damage occurs during a shockwave loading. It is generally called a classic spall. When the metal is in a molten state, it forms a cloud of liquid debris with a large area of cavitation. It is called micro-spall (Andriot et al., 1983; Zhiembetov et al., 2002). The spall strength of a metal is significantly lower in the molten state than in the solid state. This has been confirmed in tin, aluminum, and lead using the experimental method reported by Kanel et al., 1996, 2000, 2015.

Metallic tin (Sn) has an extremely low melting point of 507 K. It melts under a very low shock pressure. There are many experimental shock studies on the tin (Chen et al., 2017; Grigsby et al., 2009; La Lone et al., 2013; Rességuier et al., 2007a, 2007b, 2007c; Signor et al., 2010; Sorenson et al., 2002; Werdiger et al., 1999). As reported by the researchers from Las Alamos laboratory in 2004 (Holtkamp et al., 2004), the free surface of tin melts during the release process when the peak pressure increases from ~128 to ~225 kbar. Rességuier et al. (Rességuier et al., 2007a, 2007b, 2007c, 2007b) performed a laser shock experimental investigation on the tin in 2007 and reported that the micro-spall contains three processes. First, high-velocity liquid fragments were ejected from the free surface. Second, the rest of the molten target were separated into bigger fragments and shaped into spheres due to surface tension, moving slower than the high-velocity fragments. Third, these spheres solidified during their flights (Rességuier et al., 2007a, 2007b, 2007c, 2007b) They also reported a critical shock pressure of ~40 GPa for tin when the classic spall in solid tin turned into liquid micro-spall during release melting (Resseguier et al., 2007). In addition to the transformation of tin from solid to liquid form under high shock pressure, Hu et al. also found that a shock-induced phase transition from body-centered tetragonal (bct) to body-centered cubic (bcc) occurred with a shock pressure of ~35 GPa in tin (Hu et al., 2008a, 2008b). A more complicated phase transition under shock loading was observed by Soulard and Durand using molecular dynamics methods (Soulard and Durand, 2020).

Besides the aforementioned difference between the classic spall under moderate shock pressure and micro-spall under high shock pressure, the spall strength was reported to change significantly upon release melting or shock melting with a shock wave loading (Shao et al., 2019). When the temperature reaches the melting point, the spall strength of polycrystalline aluminum decreases to approximately zero (Kanel et al., 1996, 2000). The spall strength of lead and tin was also reduced by an order of magnitude when the metal melted (Kanel et al., 2015). Using experimental methods, we can only deduce the spall strength through acoustic approximation with free surface velocity. Further, it is difficult to obtain the microscopic evolution process of spall damage and the relevant physical properties using experimental methods. In recent years, molecular dynamics (MD) simulations of spall damage have attracted considerable attention. The MD simulation is based on atomic interactions. The direct evolution process of metals under shock wave loadings and detailed information about the change in stress, temperature, and density along with the time or position developing can be obtained using the MD method. It also facilitates obtaining the spall strength by calculating the maximal tensile stress using direct molecular dynamics simulations. Thus, the MD method has been a powerful tool for investigating spall damage in several types of metals (Luo et al., 2009; Shao et al., 2014, 2019; Xiang et al., 2013a, 2013b; Zhou et al., 2019). Nevertheless, surprisingly, very few studies have been carried out on the spall damage in the tin using MD methods. To the best of our knowledge, there is only one report on the spall damage in the tin using the MD method by Liao et al. (2014). They investigated the micro-spall using the non-equilibrium molecular dynamics method, but they did not provide a detailed description of the change in spall strength when the tin changed from solid to molten form. Here, we attempt to provide an integrated description of the developing trend of spall strength from solid state to molten state in the tin using the MD method. Our goal is to elucidate the variation in spall strength between solid and molten tin under different shock pressures and provide a reference for future work on spall damage studies of other metals.

The remainder of this manuscript is organized as follows. The methodology is presented in Section II. The change in spall strength from solid to molten tin is discussed in Section IIIA. In Section IIIB, we discuss the damage development of spall damage and the corresponding evolution of voids. We conclude in section IV.