[Paper Review] Non-isentropic layers in matter behind shock and ramp compression waves

K. V. Khishchenko, Alexander E. Mayer|arXiv (Cornell University)|Jul 31, 2014

High-pressure geophysics and materials30 references3 citations

TL;DR

This study investigates non-isentropic layers—regions of elevated or reduced entropy with corresponding temperature deviations—formed near interfaces during shock and ramp loading of metals. Using a dislocation plasticity-based model and numerical simulations, it demonstrates that high-entropy layers form under impact and ramp loading, while low-entropy layers emerge under ramp loading or at interfaces between materials of differing impedance, affecting surface phenomena like melting and pyrometric measurements.

ABSTRACT

According to the ideal fluid dynamics approach, the temperature and entropy values of a medium undergo a jump increase in the shock front as well as on contact interface between different materials after the shock wave propagation, but remain constant behind the shock front out of the contact interface. In the real condensed matter, the shock fronts and transition regions near the interfaces have finite thicknesses; therefore, the temperature field is disturbed around the interfaces. In this work, such disturbances are numerically analyzed for the problems of formation of the steady shock wave at impact and ramp loading of metals, reflection of the steady shock wave from a free surface, and the shock wave passing through the interface between two different materials. Theoretical analysis and computations show that the non-isentropic layers (the high-entropy ones with the increased temperature and the low-entropy ones with the decreased temperature) arise near the interfaces in the above problems of shock and ramp loading. The impact produces the high-entropy layer; while the ramp loading can result in the both high- and low-entropy layers. At the shock wave passing through the interface, the high-entropy layer is formed in the lower-impedance material and the low-entropy in the higher-impedance one. These high- and low-entropy layers should be taken into account in simulations of shock-wave processes in thin targets or in other cases where surface effects are important. For example, melting can take place in the high-entropy layer on the interface between colliding plates at shock intensities lower than the bulk melting threshold; also the temperature perturbations near the studied surface can affect the result of pyrometric measurements. A mathematical model with accounting for the dislocation plasticity is described here as well as the appropriate numerical scheme is proposed.

Motivation & Objective

• To analyze temperature and entropy disturbances near interfaces in real condensed matter under shock and ramp loading, beyond ideal fluid dynamics assumptions.
• To investigate the formation of non-isentropic layers—regions of increased or decreased entropy—due to finite shock front thickness and material interface effects.
• To develop a mathematical model incorporating dislocation plasticity to accurately simulate these thermal and entropic anomalies in shock-wave processes.
• To assess the implications of these layers for surface phenomena such as melting and pyrometric measurements in thin targets or interface-dominated systems.

Proposed method

• Numerical analysis of steady shock wave formation under impact and ramp loading in metals using a dislocation plasticity-based model.
• Simulation of shock wave reflection from a free surface and transmission across a bi-material interface to study interface-induced entropy variations.
• Application of a finite-difference numerical scheme to solve the governing equations with entropy and temperature evolution accounted for in the transition zones.
• Incorporation of dislocation plasticity into the thermomechanical model to capture non-equilibrium effects near interfaces.
• Use of computational modeling to resolve finite-thickness shock fronts and transition regions where entropy and temperature deviate from isentropic behavior.
• Analysis of entropy and temperature profiles in the vicinity of interfaces to identify high- and low-entropy layers under different loading conditions.

Experimental results

Research questions

• RQ1 What types of non-isentropic layers (high- or low-entropy) form near interfaces during shock and ramp loading of metals?
• RQ2 How does the loading type—impact versus ramp—affect the formation of high- and low-entropy layers?
• RQ3 What role does material impedance contrast play in determining the location and nature of entropy anomalies at bi-material interfaces?
• RQ4 To what extent do these non-isentropic layers influence surface phenomena such as melting or pyrometric measurements?
• RQ5 How can dislocation plasticity be effectively modeled to capture entropy and temperature deviations in shock-compressed materials?

Key findings

• High-entropy layers form near interfaces under impact loading due to increased temperature and entropy in the compressed region.
• Ramp loading can generate both high- and low-entropy layers, depending on the material properties and loading history.
• At a bi-material interface, a high-entropy layer develops in the lower-impedance material, while a low-entropy layer forms in the higher-impedance material during shock transmission.
• These non-isentropic layers can lead to melting at shock intensities below the bulk melting threshold, particularly in thin targets.
• Temperature perturbations near interfaces can significantly affect pyrometric measurements, introducing errors if not accounted for.
• The proposed dislocation plasticity model and numerical scheme successfully capture the non-isentropic behavior in shock-compressed materials with realistic thermomechanical evolution.