Timothy J. Holmquist

Response of silicon carbide to high velocity impact

This article presents an analysis of the response of silicon carbide to high velocity impact. This includes a wide range of loading conditions that produce large strains, high strain rates, and high pressures. Experimental data from the literature are used to determine constants for the Johnson–Holmquist constitutive model for brittle materials (JH-1). It is possible to directly determine the strength and pressure response of the intact material from test data in the literature. After the ceramic has failed, however, there are not adequate experimental data to directly determine the response of the failed material. Instead, the response is inferred from a comparison of computational results to ballistic penetration test results. After the constants have been obtained for the JH-1 model, a wide range of computational results are compared to experimental data in the literature. Generally, the computational results are in good agreement with the experimental results. Included are computational results that m...

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.

Response of aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures

This article contains a description of a computational constitutive model for brittle materials subjected to large strains, high strain rates, and high pressures. The focus of this model is to determine the response of aluminum nitride under high velocity impact conditions that produce large strains, high strain rates, and high pressures. The strength is expressed as a function of the pressure, strain rate, and accumulated damage; and it allows for strength of both intact and failed material. The pressure is primarily expressed as a function of the volumetric strain, but it also includes the effect of bulking for the failed material. For materials without a phase change this model is an extension of the previous Johnson–Holmquist models for brittle materials. The primary new feature of this model is the capability to include a phase change, and this is required for aluminum nitride. Computations are performed to illustrate the capabilities of the model, to compare computed results to experimental results,...

Characterization and evaluation of silicon carbide for high-velocity- impact

This article presents a characterization and evaluation of silicon carbide for high-velocity impact. This includes a wide range of loading conditions that produce large strains, high strain rates, and high pressures. Experimental data from the literature are used to determine constants for the Johnson–Holmquist–Beissel (JHB) constitutive model for brittle materials. A previous article by the authors presented a characterization of silicon carbide for high-velocity impact using an earlier version of the model (JH-1). The previous work provided good agreement with a broad range of experimental data with the exception of high-velocity penetration data. The current work uses the more recently developed JHB constitutive model, a target geometry that more closely matches the experimental design, and a computational technique that allows for target prestress. These recent developments (primarily the prestress) produce computed results that agree with all the experimental data, including the high-velocity penetra...

A Computational Constitutive Model for Glass Subjected to Large Strains, High Strain Rates and High Pressures

This article presents a computational constitutive model for glass subjected to large strains, high strain rates and high pressures. The model has similarities to a previously developed model for brittle materials by Johnson, Holmquist and Beissel (JHB model), but there are significant differences. This new glass model, presented in Fig. 1, provides a material strength that is dependent on the location and/or condition of the material. Provisions are made for the strength to be dependent on whether it is in the interior, on the surface (different surface finishes can be accommodated), adjacent to failed material, or if it is failed. The intact and failed strengths are also dependent on the pressure and the strain rate. Thermal softening, damage softening, timedependent softening, and the effect of the third invariant are also included. The shear modulus can be constant or variable. The pressure-volume relationship includes permanent densification and bulking. Damage is accumulated based on plastic strain, pressure and strain rate. Significant features of the model are the ability to compute size effects (small scales are stronger than large scales), surface effects (smooth surfaces are stronger than rough surfaces), and high internal tensile strength (as demonstrated by spall plate-impact experiments). Simple (single-element) examples are presented to illustrate the capabilities of the model. Several example computations are presented in Figs. 2-4 to demonstrate the ability to compute more complex, high-velocity-impact conditions. Figure 2 presents computed results for a gold projectile impacting a borosilicate target with a copper buffer attached to the impact surface. The computed results produce interface defeat (no glass penetration) at Vs = 800 m/s and prompt penetration at Vs = 900 m/s. This is consistent with the test results provided by Anderson et al. [1]. Behner et al. [2] performed experiments using no buffer (gold rod impacting bare glass) which produced penetration at much lower impact velocities. For these experiments the penetration velocities were determined using a series of flash x-rays and are presented as a function of impact velocity in the lower protion of Fig. 3. Also shown are the computed penetration velocities for Vs = 900 m/s and Vs = 2400 m/s. The computed results are in good agreement with the experiments. Anderson et al. [3] also performed experiments using a pointed steel projectile impacting thin plates of borosilicate glass at three different scales. The smaller scale targets were stronger than the larger scale targets. Figure 4 demonstrates the capability to compute size effects. Computed results are presented for the 0.50-cal (scale = 1.0) and the 0.22cal (scale = 0.44) projectile for Vs = 300 m/s and Vs = 400 m/s. At 300 m/s the 0.50-cal projectile exits the target at Vr = 22 m/s but the smaller scale 0.22-cal projectile is stopped. As the impact veloicty is increased the computed size effect diminshes as shown at Vs = 400 m/s. The ability for the computations to produce size effects is due to the time-dependent features in the model.

An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation

This paper presents an explicit 2D Lagrangian algorithm to automatically convert distorted elements into meshless particles during dynamic deformation. It also provides the contact and sliding algorithms to link the particles to the finite elements. For this approach the initial grid is composed entirely of finite elements and the response is computed with finite elements until portions of the grid become highly strained. When finite elements on the boundaries reach a user-specified plastic strain they are converted to particles and linked to the adjacent finite element grid. This approach allows for the use of accurate and efficient finite elements in the lower distortion regions, and for the use of meshless particles in the higher distortion regions. Example computations are presented to demonstrate the accuracy and utility of this approach.

Mechanics of dwell and post-dwell penetration

Abstract Abstract This article presents test data, analysis and computed results for gold rods impacting silicon carbide targets. This work focuses on the dwell phenomenon, but also investigates the penetration response. Experiments are presented for several target configurations including targets that use a small diameter copper buffer, targets that use a large diameter copper buffer, and targets that use no buffer. The dwell-penetration transition velocity for a silicon carbide target with no buffer is 822±46 m s−1 and increases to 1538±12 m s−1 when a buffer is used. The results demonstrate the significant effect a buffer has on interface defeat and that silicon carbide can resist extremely large surface stresses (∼24 GPa) without the use of any confinement or prestress. A significant finding is the non-linear ‘erratic’ penetration velocity that occurs when dwell is not maintained. Computations are also presented that reproduce the effect of using a buffer including the effect of buffer separation. Of particular interest is the non-linear penetration velocity produced in the computed results.

The failed strength of ceramics subjected to high-velocity impact

This article addresses the response of failed ceramics. Under high-velocity impact, ceramics transition from a solid intact material to a fragmented and granular material. This process is often referred to as “damage and failure” and is a complex phenomenon. Because ceramics are very strong in compression, it is difficult to perform laboratory experiments that produce conditions similar to those produced during projectile impact, where the ceramic transitions from an intact material to a granular (failed) material. This limitation generally requires the damage and failed strength to be inferred from computed results that provide good agreement with ballistic penetration experiments. Previous work by the authors [J. Appl. Phys. 97, 093502 (2005)] has suggested a relatively low failed strength for silicon carbide (∼200 MPa) that is generally lower than other published data (although the data vary significantly). Work presented here provides additional evidence for a low failed strength for silicon carbide (...

Conversion of Finite Elements into Meshless Particles for Penetration Computations Involving Ceramic Targets

This paper presents a new computational algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. It also presents computed results for projectiles impacting ceramic targets. The new computational algorithm, together with an appropriate ceramic model, provides computed results that are in good agreement with test data. Included are problems involving dwell and penetration. This computational approach is especially well‐suited for brittle materials such as ceramics, because the conversion from elements into particles generally occurs after the material has failed. The result is that the particles represent only failed material, which does not produce any tensile stresses. For some particle algorithms it is possible to introduce tensile instabilities, but this is not a concern if the particles represent only failed material.

The response of layered aluminum nitride targets subjected to hypervelocity impact

Abstract This work presents both experimental and computational ballistic results of layered Aluminum Nitride (AlN) targets. An L/D = 6 tungsten penetrator is used to impact AlN targets at a nominal impact velocity of 2100m/s. The primary objective of this work is to determine the ballistic performance of layered ceramic targets to hypervelocity impact. Various layering configurations are investigated including separating the AlN ceramic layers by thin, low impedance, polymethyl methacrylate (PMMA). PMMA thicknesses of 1 mm, 0.5 mm and 0 mm are used. The number of AlN ceramic layers is also investigated. Target configurations of two, four, six, and twelve layers are considered. All targets consist of 76.2 mm of AlN. The experiments show that target resistance decreases when PMMA is added. Target resistance is also reduced when more layers are used. A secondary objective of this work is to evaluate the ballistic effect of reducing the lateral dimension of the ceramic tile (reduction in self-confinement). The experiments show reduced target resistance when the lateral tile size is decreased. Computations of selected experiments are presented to provide insight into the behavior of the AlN targets. The computations capture the effect of layering, PMMA separation and lateral tile size and provide insight into the behavior of the ceramic when used in these types of configurations.