G. Ravichandran

Deformation behavior of the Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass over a wide range of strain-rates and temperatures

The stress-strain relations for the Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass (Vitreloy 1) over a broad range of temperatures (room temperature to its supercooled liquid region) and strain rates (10−5 to 103 s−1) were established in uniaxial compression using both quasi-static and dynamic Kolsky (split Hopkinson) pressure bar loading systems. Relaxation and jump in strain rate experiments were conducted to further understand the time dependent behavior of Vitreloy 1. The material exhibited superplastic flow above its glass transition temperature (623 K) and strain rates of up to 1 s−1. The viscosity in the homogeneous deformation regime was found to decrease dramatically with increasing strain rate. A fictive stress model was used to describe the basic deformation features of Vitreloy 1 under constant strain-rate loading as well as multiple strain-rate loading at high temperatures.

A micromechanical model for high strain rate behavior of ceramics

A constitutive model applicable to brittle materials such as ceramics subjected to biaxial compressive loading is developed. The model is based on non-interacting sliding microcracks that are uniformly distributed in the material. Tension cracks nucleate and propagate from the tip of the sliding cracks in the direction of maximum applied compression when the stress-intensity factor reaches its critical value. For high strain rate deformation, the rate of crack growth is governed by a universal relation in dynamic fracture. The constitutive model provides strain components for plane deformation which consists of an elastic part and a part due to sliding and growth of the tension cracks. The failure of the material is linked to a critical density of damage and hence a critical length for the tension cracks. The constitutive model is used to study material behavior under uniaxial compressive constant strain rate loading. A critical strain rate beyond which the material would exhibit rate sensitivity is proposed. The model predicts the failure or peak strength to increase with increasing strain rate. For engineering ceramics, the rate sensitivity exponent is found to be a function of the relation between the rate of crack growth and the toughness of the material. The model predictions are compared with the rate-dependent behavior of a hot pressed aluminum nitride tested in uniaxial compression in the strain rate range of 5 × 10^(−6)−2 × 10^3 s^(−1).

Dynamic compressive failure of a glass ceramic under lateral confinement

An experimental technique has been developed for imposing controlled multi-axial loading on cylindrical ceramic specimens. The multi-axial loading is achieved by superposing passive lateral confinement upon axial compression. Descriptions of the experimental technique, as well as experimental results for a machinable glass ceramic, Macor, are presented. The axial compression was applied using a Kolsky (split Hopkinson) pressure bar modified to apply a single loading pulse. Experiments were also conducted under quasi-static conditions using a servo-hydraulic load frame. The specimens were confined laterally using shrink-fit metal sleeves. The confining pressure ranges from 10 to 230 MPa. Under both quasi-static and dynamic loading conditions, the experimental results showed that the failure mode changes from fragmentation by axial splitting without confinement to localized faulting under moderate lateral confinement (10–120 MPa). The process of fault initiation was characterized in detail for specimens under moderate confinement. Based on the experimental results, a compressive failure mechanism was proposed for brittle materials under moderate lateral confinement. The Mohr-Coulomb failure criterion was found to fit the experimental strength data. The failure criterion is shown to be consistent with the analytical results from a micromechanical model for brittle failure. Transition from brittle to ductile behavior was observed under high confinement (230 MPa).

Large strain electrostrictive actuation in barium titanate

Large strain electrostriction in single-crystal ferroelectric materials is investigated. The mode of electrostriction is based on a combined electromechanical loading used to induce cyclic, 90° domain switching. Experiments have been performed on crystals of barium titanate with constant compressive stress and oscillating electric-field input. Induced strains of more than 0.8% have been measured. Strains as large as 5% are predicted for other materials of the same class. The results demonstrate a possible avenue for obtaining large actuation strains in electromechanical devices.

Modeling Constitutive Behavior of Particulate Composites Undergoing Damage

A simple rate-independent phenomenological constitutive model is developed for particulate composites undergoing damage. The constitutive model is motivated by the results of a micromechanical model based on Eshelbys equivalent inclusion analysis and Mori-Tanakas method for an elastic composite undergoing damage either by debonding or cavity formation. The micromechanical model is used to illustrate the behavior of a composite consisting of hard particles reinforcing a soft, nearly incompressible elastic matrix. The composite is assumed to behave linearly elastic in the absence of any damage. The damage accumulation is described by a single scalar internal variable, the maximum volume dilatation attained during the deformation process. Two damage functions govern the degradation of the bulk and the shear moduli in the phenomenological constitutive model. Corresponding computational algorithmic tangent moduli is derived and examples are provided to illustrate the versatility of the proposed model.

An experimental technique for imposing dynamic multiaxial-compression with mechanical confinement

A new experimental technique for imposing controlled lateral confinement on specimens subjected to dynamic uniaxial compression has been developed. A description of the experimental technique and experimental results on a ceramic are presented. The axial compression is applied by a split Hopkinson pressure bar modified to subject the specimen to a single loading pulse during the experiment. The specimen is confined laterally by a shrink-fit metal sleeve. The results show that the failure occurs by fragmentation due to axial splitting under uniaxial stress condition, whereas failure occurs by localized deformation on faults under moderate lateral confinement. The compressive failure strength of the ceramic increases with increasing confinement pressure.

Fundamental structure of steady plastic shock waves in metals

The propagation of steady plane shock waves in metallic materials is considered. Following the constitutive framework adopted by R. J. Clifton [Shock Waves and the Mechanical Properties of Solids, edited by J. J. Burke and V. Weiss (Syracuse University Press, Syracuse, N.Y., 1971), p. 73] for analyzing elastic–plastic transient waves, an analytical solution of the steady state propagation of plastic shocks is proposed. The problem is formulated in a Lagrangian setting appropriate for large deformations. The material response is characterized by a quasistatic tensile (compression) test (providing the isothermal strain hardening law). In addition the elastic response is determined up to second order elastic constants by ultrasonic measurements. Based on this simple information, it is shown that the shock kinetics can be quite well described for moderate shocks in aluminum with stress amplitude up to 10 GPa. Under the later assumption, the elastic response is assumed to be isentropic, and thermomechanical coupling is neglected. The model material considered here is aluminum, but the analysis is general and can be applied to any viscoplastic material subjected to moderate amplitude shocks. Comparisons with experimental data are made for the shock velocity, the particle velocity and the shock structure. The shock structure is obtained by quadrature of a first order differential equation, which provides analytical results under certain simplifying assumptions. The effects of material parameters and loading conditions on the shock kinetics and shock structure are discussed. The shock width is characterized by assuming an overstress formulation for the viscoplastic response. The effects on the shock structure of strain rate sensitivity are analyzed and the rationale for the J. W. Swegle and D. E. Grady [J. Appl. Phys. 58, 692 (1985)] universal scaling law for homogeneous materials is explored. Finally, the ability to deduce information on the viscoplastic response of materials subjected to very high strain rates from shock wave experiments is discussed.

Dynamic pore collapse in viscoplastic materials

Dynamic pore collapse in porous materials is studied by analyzing the finite deformation of an elastic/viscoplastic spherical shell under impulsive pressure loading. Effects of dynamic loading rate, pore size, initial porosity, strain‐rate sensitivity, strain hardening, thermal softening, and mass density of the matrix material on the pore collapse process are examined and results are compared with those from quasistatic analyses of both rate‐independent and rate‐dependent matrix materials. Dynamic (inertia) effects are found to be significant or even dominant in certain shock wave consolidation conditions. An approximate method is proposed to incorporate dynamic effects into quasistatic pore‐collapse relations of viscoplastic matrix materials. Implications of results of current study are discussed in terms of understanding the processes of shock wave consolidation of powders.

Canonical aspects of adiabatic shear bands

It is demonstrated that, for relatively mild conditions on the thermal-viscous flow law, the structure of all adiabatic shear bands is the same within scalings that depend only on simple material properties. This fact in turn suggests that measurements made in the neighborhood of a band, together with the known canonical structure, may provide a window into material response under extreme conditions that are not accessible by ordinary laboratory means.

Constitutive Modeling of Textured Body Centered Cubic (BCC) Polycrystals

A new latent hardening model for body-centered-cubic (bcc) single crystals motivated by the inapplicability of the Schmid law (Critical Resolved Shear Stress Criterion) is presented. This model is based on the asymmetry of shearing resistance of the {112} slip planes depending on the shearing direction in the sense of ‘twin’ and ‘anti-twin’. For the interpretation of deformation of polycrystalline aggregates depending upon initial texture, a constitutive law for bcc single crystals is developed. This law is based on a rigorous constitutive theory for crystallographic slip that accounts for the effects of strain hardening, rate-sensitivity and thermal softening. The deformation response of textured polycrystal is investigated by means of a Taylor type averaging scheme and an established numerical procedure. Results for textured tungsten polycrystals at low and high strain rates for two different textures [001] and [011] are presented and compared with experimental results. The predictions compare well with experimental observations for the [001] texture. In the [011] texture, due to the reduced symmetry of deformation, lateral tensile stresses develop even under uniaxial compression. These lateral tensile stresses are responsible for observed lack of ductility and transgranular failure in the [011] texture.