Constitutive modeling of aluminum nitride for large strain, high-strain rate, and high-pressure applications

Abstract

This paper presents constitutive modeling of aluminum nitride (AlN) for severe loading conditions that produce large strains, high-strain rates, and high pressures. The Johnson–Holmquist constitutive model (JH-2) for brittle materials is used. Constants are obtained for the model using existing test data that include both laboratory and ballistic experiments. Due to the wide range of experimental data the majority of constants are determined explicitly. The process of determining constants is provided in detail. The model and constants are used to perform computations of many of the experiments including those not used to generate the constants. The computational results are used to validate the model, provide insight into the response of AlN, and to demonstrate that one set of constants can provide reasonable results over a broad range of experimental data.

Introduction

Ceramic materials have been considered for armor applications for over 30 years [1]. Generally, these materials are very strong in compression and weak in tension. They are also very brittle, but can have significant strength after fracture when under compression. Both the intact and fractured materials generally are pressure dependent where the strength increases as the confining pressure increases. They also tend to be lightweight when compared to other materials such as metals. These characteristics make ceramics well suited for armor applications, but also provide a significant design challenge when included in armor systems. Effective armor design can be enhanced, cost can be reduced, and the behavior better understood by the use of computations, if the models and constants adequately represent the material behavior.

Generally, experimental data are required in order to determine constitutive model constants. The most helpful data are those produced in a laboratory environment where measurements of the stresses, strains, strain rates, pressures, etc., are made directly. Unfortunately, due to the high strengths of ceramics, there are currently no available test techniques capable of determining the entire constitutive response. This leads constitutive model developers to use other, less defined experiments, to help determine material constants. Typically, these experiments include plate impact and ballistic experiments that are used to “back out” specific constants. Although not the preferred approach, a process using both laboratory and ballistic experiments can provide a reasonable technique to obtain constitutive model constants.

One material that has been of interest for armor applications in recent years is aluminum nitride (AlN) [2]. There is a wealth of experimental data for AlN available from the literature that includes both laboratory and ballistic tests. Heard and Cline [3] provide some of the earliest work where they report the effect of confining pressure on the strength. More recent work investigating confinement is reported by Chen and Ravichandran [4]. Subhash and Ravichandran [5] present compressive strength for various strain rates. The quasi-static pressure–volume response (i.e. hydrostat), a very important, but rarely available piece of information, has been extensively investigated for AlN. Xia et al. [6] and Ueno et al. [7] report the pressure–volume response from diamond anvil experiments. Dandekar et al. [8] also provide experimental data, including a comprehensive discussion of the equation of state of AlN. Grady [9] presents planar impact experiments and analysis of the shock and release behavior of AlN, and in a subsequent report Grady and Moody [10] present a summary of the shock compression profiles for both the compression and spall response. There is also an abundance of ballistic test results using AlN. Reaugh et al. [11] report the ballistic behavior of AlN for various ceramic thicknesses at impact velocities from 1.3 to 2.6 km/s. Orphal et al. [2] present data for semi-infinite penetration of tungsten rods into AlN targets at impact velocities from 1.5 to 4.5 km/s. Finally, Weber et al. [12] present data for the ballistic response of AlN as a function of confinement and layering.

The objective of this work is to determine constants for AlN using the Johnson–Holmquist constitutive model (JH-2) for brittle materials [13] and to demonstrate the ability of the model to capture the material response for a wide range of experiments. The remainder of this paper presents a description of the JH-2 ceramic model, the process used to determine material model constants for AlN, and a series of computational results using the model and constants.