A. M. Rajendran

Modeling the impact behavior of AD85 ceramic under multiaxial loading

Summary This paper presents an advanced constitutive model to describe the complex behavior of ceramic materials under impact loading conditions. The governing equations utilize a set of microphysically based constitutive relationships to model deformation and damage processes in a ceramic. The total strain is decomposed into elastic, plastic and microcracking components. The model parameters for AD85 ceramic were determined using the data from split Hopkinson bar and bar-on-bar experiments under uniaxial stress state and plate impact experiment under uniaxial strain state. To further validate the generality of the model parameters, modeling of a diagnostic ballistic experiment in which a steel projectile impacted a AD85 ceramic-front-faced thick aluminium plate, was considered. In this experiment, stress histories were measured in the target by embedded manganin and carbon stress gauges. The results from the numerical simulations of the ballistic experiment using a shock-wave propagation based finite element code, successfully matched the measured stress history.

Modeling the shock response of silicon carbide, boron carbide and titanium diboride

An advanced constitutive model is used to describe the shock and high strain rate behaviors of silicon carbide, boron carbide, and titanium diboride under impact loading conditions. The models governing equations utilize a set of microphysically based constitutive relationships to describe the deformation and damage processes of ceramics. The total strain is decomposed into elastic, plastic, and microcracking components. The plastic strain components are calculated using conventional viscoplastic equations. The strain components due to microcracking utilize relationships derived from a penny shaped crack in an infinite elastic solid. The main features of the model include degradation of strength and stiffness under both compressive and tensile loading conditions. When loaded above the Hugoniot elastic limit (HEL), the strength is limited by the strain rate dependent strength equation. However, below the HEL, the strength variation with respect to strain rate and pressure is modeled through microcracking relationships, assuming no plastic flow. The ceramic model parameters were determined using plate impact experimental data.

A void growth-based failure model to describe spallation

A new dynamic failure model to describe void nucleation, growth, and coalescence in ductile metals is reported. The model is based on a pressure‐dependent yield criterion for compressible plastic flow. This three‐dimensional, plasticity‐based continuum damage model is incorporated into a finite difference, wave propagation code. A procedure to determine the failure model parameters is proposed. In this procedure, the model parameters are calibrated based on the ability to match the experimental free‐surface velocity history with code simulations. Model parameters for oxygen‐free high‐conductivity copper have been determined successfully using this procedure.

Impact damage model for ceramic materials

The fracture process in ceramic materials upon impact loading is complex in nature. Most often, the brittle ceramic deforms inelastically due to microcracking under shock (compression) loading. At high‐velocity impact, the shock generated microcracks rapidly open and extend under subsequent tension (due to the release waves from the stress‐free boundaries) leading to complete pulverization of the ceramic materials. The main objective of this paper is to model the damage process in ceramics due to impact loading. A computationally oriented continuum damage‐based constitutive model is considered. Several modifications incorporating strain rate and damage effects on the compressive strength have been introduced into the model. Results are presented in terms of numerical simulations of a plate‐impact test configuration. Effects of the model parameters on the compressive strength and spall strength are described. The proposed damage model has been used successfully to match the measured stress history from a p...

Response of seven crystallographic orientations of sapphire crystals to shock stresses of 16–86 GPa

Shock wave profiles of sapphire (single-crystal Al2O3) with seven crystallographic orientations (c, d, r, n, s, g, and m-cut) were measured with time-resolved VISAR (velocity interferometer for a surface of any reflector) interferometry at shock stresses in the range 16–86 GPa. Shock propagation was in the direction normal to the surface of each cut. The angle between the c-axis of the hexagonal representation of the sapphire crystal structure and the direction of shock propagation varied from 0 for c-cut up to 90° for m-cut in the basal plane. Based on published shock-induced transparencies for three directions of shock propagation, shock-induced optical transparency correlates with the smoothness of the mechanical shock wave profile. The ultimate goal was to find the direction of shock propagation for which shock-compressed sapphire is most transparent as a window material. In the experiments particle velocity histories were recorded at the interface between a sapphire crystal and a LiF window. In most ...

Dynamic pre-strain and inertia effects on the fracture of metals

Abstract A combined experimental and theoretical study is described which examines the influence of strain-rate and dynamic pre-strain on the ductile fracture of thin cylinders. The thin-cylinder configuration is particularly important in this case because it allows inertia terms to be directly incorporated into the theory of plastic instability. A series of quasi-static and dynamic tests is conducted on three materials with differing degrees of strain-rate sensitivity and strain-hardening. The experimental observation that fracture is inhibited at high strain-rates is in accord with the theory when inertia can no longer be considered insignificant. It is also shown that dynamic pre-strain has little or no effect on the flow stress or the strain at fracture in materials which-are essentially strain-rate insensitive, but does reduce the fracture strain in the strain-rate sensitive materials.

Atomic scale studies of spall behavior in nanocrystalline Cu

The micromechanisms related to ductile failure during dynamic loading of nanocrystalline Cu are investigated in a series of large-scale molecular dynamics simulations. Void nucleation, growth, and coalescence is studied for a nanocrystalline Cu system with an average grain size of 6 nm under conditions of impact of a shock piston with velocities of 250, 500, 750, and 1000 m/s and compared to that observed in single crystal copper. Higher impact velocities result in higher strain rates and higher values of spall strengths for the metal as well as nucleation of larger number of voids in smaller times. For the same impact velocity, the spall strength of the nanocrystalline metal, however, is lower than that for single crystal copper. The results obtained for void nucleation and growth in nanocrystalline Cu for various impact velocities and for single crystal copper [001] suggests two distinct stages of evolution of voids. The first stage (I) corresponds to the fast nucleation of voids followed by the second ...

Statistically stored, geometrically necessary and grain boundary dislocation densities: microstructural representation and modelling

A unified physically based microstructural representation of f.c.c. crystalline materials has been developed and implemented to investigate the microstructural behaviour of f.c.c. crystalline aggregates under inelastic deformations. The proposed framework is based on coupling a multiple-slip crystal plasticity formulation to three distinct dislocation densities, which pertain to statistically stored dislocations (SSDs), geometrically necessary dislocations (GNDs) and grain boundary dislocations. This interrelated dislocation density formulation is then coupled to a specialized finite element framework to study the evolving heterogeneous microstructure and the localized phenomena that can contribute to failure initiation as a function of inelastic crystalline deformation. The GND densities are used to understand where crystallographic, non-crystallographic and cellular microstructures form and the nature of their dislocation composition. The SSD densities are formulated to represent dislocation cell microstructures to obtain predictions related to the inhomogeneous distribution of SSDs. The effects of the lattice misorientations at the grain boundaries (GBs) have been included by accounting for the densities of the misfit dislocations at the GBs that accommodate these misorientations. By directly accounting for the misfit dislocations, the strength of the boundary regions can be more accurately represented to account for phenomena associated with the effects of the GB strength on intergranular deformation heterogeneities, stress localization and the nucleation of failure surfaces at critical regions, such as triple junctions.

EFFECT OF STRAIN RATE AND SIZE ON TENSILE STRENGTH OF CONCRETE

An experimental investigation of the effects of strain rate and size on the tensile strength of concrete was conducted. Concrete specimens of different sizes were tested in the splitting tension configuration at strain rates ranging from 10 to 70 per second. Six different specimen sizes with thicknesses of 0.25 and 0.50 in., and diameters of 0.5, 1.0 and 2.0 in. were tested. A split Hopkinson bar was used to conduct the dynamic tests. Elastic verification tests were performed on specimens instrumented with strain gages at quasi-static and dynamic rates. High speed photography of dynamic tests showed that cracking initiated in the region of maximum tensile stress. The splitting tensile strength of concrete was both size and rate dependent. In this study, the ratio of dynamic to quasi-static strength was about 4.5 at strain rates of 70 per second.

Impact-induced deformation fields in 3D cellular woven composites

Abstract The deformation fields and kinematics of nonporous and porous three-dimensional (3D) woven composite material systems were analyzed and characterized under an incident impact energy of 560 J caused by a 78 g projectile at a velocity of 120 m/s. The analysis quantifies experimental observations of the effects of porosity on the impact resistance and behavior of 3D woven composites. The dynamic nonlinear impact solution was obtained by the finite element method, in which contact between the projectile and the target plate was modeled with gap elements. In the present study, we investigated the spatial and temporal evolution of multi-dimensional elastic fields and potential damage modes in the target plates. A unit cell, representative of the 3D woven composite, was used to obtain estimates of the overall elastic moduli. These estimates were then used with two material models to represent the porous system in the finite element analysis of the target plate. One material model, which had explicit geometrical distributions of 3D voids, was used in the impact region, and the other material model, which was based on a representation of smeared voids, was used in regions removed from the impact zone. The analysis indicates that wave propagation effects at the incident energy applied here are significant, and these effects can lead to projectile penetration at the impact face. Localized shear damage in the 3D woven system precedes penetration in both the nonporous and the porous systems. Experimental observations, which indicate that a porous system can dissipate more energy than the nonporous system before penetration, are found to be mainly attributed to the confinement of local damage fields, which emanate from the boundaries of the embedded voids.