PSI - Issue 13

Xin Yu et al. / Procedia Structural Integrity 13 (2018) 1037–1042 X. Yu, X. Huang and M. Zheng/ Structural Integrity Procedia 00 (2018) 000 – 000

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detonation waves in solid media or generated by a high-speed oblique collision may reflect by the rigid wall or interaction border accompanied with high pressure or other special mechanical behavior. Therefore, relevant research is of great significance to defense application and the relevant research area. The shock reflection in the gas was firstly discovered and recorded in Mach's experiment. He recorded two different structures of reflection, the regular reflection and Mach reflection. After that Von Neumann proposed Double Shock Theory and Triple Shock Theory to explain regular reflection and Mach reflection. On the base of Von Neumann's theory, the flow parameters in each region near the reflection point could be derived. Since the constraints of the boundary conditions in the solution of the shock reflection are streamline rotation angles and the pressure, the shock polar is thought to be an effective and useful tool in this field. For example, regular reflection could be obtained at the intersection point of the reflection shock-polar and the longitudinal axis. Then the intersection points of the Mach-polar and the reflected shock-polar is the solution of the Mach reflection. Usually, the supersonic flow around the wedge in the gas will produce stationary shock reflection structure, but the moving shock along the wedge surface may transport to a quasi steady reflection structure. The type of quasi steady reflection is more abundant than that of regular one, such as double Mach Reflection and so on. Yet the systematic investigation about the oblique shock reflection in solid rarely appears in published literatures. An important reason is that the equation of state(shorted as EOS as following) of solid under high pressure is more complex than that of liquid, and the forms of EOS could be extracted in various ways for the absence of accurate solution. For example, the EOS based on the vN particle velocity, the EOS of the Grüneisen and the EOS of stiffed gas could be seen in recent studies. Dawei Chen and his cooperators studied the oblique shock reflection with EOS of stiffed gas in condensed matter and Brown and Ravichandran studied the interface shock refraction of solid with EOS of the Grüneisen. Whereas, most of these research lacks the contrast between the results obtained with different forms of EOS. It is interesting to reveal the effect of difference and to suggest the application in relevant area. Based on the theoretical analysis of shock-polar, the aim of this work is to compare the oblique shock reflection in solid with different EOS, and to discuss the effect of the different EOS on the pressure accuracy after the reflection. 2. Theoretical Method

2.1. Equation of state

A typical Mach reflection structure is presented in Figure 1. The incident shock(OI) and Mach stem(OT) is thought to be the principle shock, and the reflected shock (OR) is thought to be a second shock. When different EOS is employed to investigate the relationship between the first shock and the second shock, different results could be obtained.

Fig. 1. Schematic diagram of a Mach reflection.

Experimental studies indicate that the vN particle velocity of shock is linear and the speed of sound 0 c and  in formula (1) is general parameters of material: 0 D c u  = + (1)