Guruswami Ravichandran

A Thermodynamic Internal Variable Model for the Partition of Plastic Work into Heat and Stored Energy in Metals

The energy balance equation for elastoplastic solids includes heat source terms that govern the conversion of some of the plastic work into heat. The remainder contributes to the stored energy of cold work due to the creation of crystal defects. This paper is concerned with the fraction β of the rate of plastic work converted into heating. We examine the status of the common assumption that β is a constant with regard to the thermodynamic foundations of thermoplasticity and experiments. A general internal-variable theory is introduced and restricted to abide by the second law of thermodynamics. Experimentally motivated assumptions reduce this theory to a special model of classical thermoplasticity. The only part of the internal energy not determined from the isothermal response is the stored energy of cold work, a function only of the internal variables. We show that this function can be inferred from stress and temperature data from a single adiabatic straining experiment. Experimental data from dynamic Kolsky-bar tests at various strain rates yield a unique stored energy function. Its knowledge is crucial for the determination of the thermomechanical response in non-isothermal processes. Such a prediction agrees well with results from dynamic tests at different rates. In these experiments, β is found to depend strongly on both strain and strain rate for various engineering materials. The model is successful in predicting this dependence. Requiring β to be constant is thus an approximation of dubious validity.

Study of mechanical deformation in bulk metallic glass through instrumented indentation

Instrumented sharp indentation experiments at the nano- and micro-length scales were carried out in an attempt to quantify the deformation characteristics of Vitreloy 1  bulk metallic glass. The experiments were accompanied by detailed three-dimensional finite element simulations of instrumented indentation to formulate an overall constitutive response. By matching the experimentally observed continuous indentation results with the finite element predictions, a general Mohr-Coulomb type constitutive description was extracted to capture the dependence of multiaxial deformation on both shear stresses and normal stresses. This constitutive response is able to provide accurate predictions of the evolution of shear bands seen in uniaxial compression tests. Constrained deformation of the material around the indenter results in incomplete circular patterns of shear bands whose location, shape and size are also captured well by the numerical simulations. The analysis is also able to predict the extent of material pile-up observed around the indenter. The surface deformation features are also consistent with mechanisms such as localized shear flow, serrated yielding and adiabatic heating, which are observed during macroscopic mechanical tests.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

On the strain and strain rate dependence of the fraction of plastic work converted to heat: an experimental study using high speed infrared detectors and the Kolsky bar☆

The conversion of plastic work to heat at high strain rates gives rise to a significant temperature increase which contributes to thermal softening in the constitutive response of many materials. This investigation systematically examines the rate of conversion of plastic work to heat in metals using a Kolsky (split Hopkinson) pressure bar and a high-speed infrared detector array. Several experiments are performed, and the work rate to heat rate conversion fraction, the relative rate at which plastic work is converted to heat, is reported for 4340 steel, 2024 aluminum and Ti-6A1-4V titanium alloys undergoing high strain and high strain rate deformation. The functional dependence of this quantity upon strain and strain rate is also reported for these metals. This quantity represents the strength of the coupling term between temperature and mechanical fields in thermomechanical problems involving plastic flow. The experimental measurement of this constitutive function is important since it is an integral part of the formulation of coupled thermomechanical field equations, and it plays an important role in failure mode selection — such as the formation of adiabatic shear bands — in metals deforming at high strain rates.

Partition of plastic work into heat and stored energy in metals

This study investigates heat generation in metals during plastic deformation. Experiments were designed to measure the partition of plastic work into heat and stored energy during dynamic deformations under adiabatic conditions. A servohydraulic load frame was used to measure mechanical properties at lower strain rates, 10−3 s−1 to 1 s−1. A Kolsky pressure bar was used to determine mechanical properties at strain rates between 103 s−1 and 104 s−1. For dynamic loading, in situ temperature changes were measured using a high-speed HgCdTe photoconductive detector. An aluminum 2024-T3 alloy and α-titanium were used to determine the dependence of the fraction of plastic work converted to heat on strain and strain rate. The flow stress and β for 2024-T3 aluminum alloy were found to be a function of strain but not strain rate, whereas they were found to be strongly dependent on strain rate for α-titanium.

Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed

The initiation and propagation of shear bands are investigated by subjecting prenotched plates to asymmetric impact loading (dynamic mode-II). The materials studied are C-300 (a maraging steel) and Ti-6Al-4V. A shear band emanates from the notch tip and propagates rapidly in a direction nearly parallel to the direction of impact. When the impact velocity is higher than a critical value, the shear band propagates throughout the specimen. The shear band arrests inside the specimen when the impact velocity is below this critical value. In the latter case and for the C-300 steel, a crack initiates and propagates from the tip of the arrested shear band at an angle to the direction of shear band propagation. Microscopic examinations of the shear band and crack surfaces reveal a ductile mode of shear failure inside the shear band and an opening mode of failure for the crack. The coexistence of shear banding and fracture events in the same specimen signifies a transition in the modes of failure for this material under the conditions described. For Ti-6Al-4V, the only mode of failure observed is shear banding. While the transition is induced by changes in loading conditions, the different behaviors of these two materials suggest it is also related to material properties. The experimental investigation focuses on both the thermal and the mechanical aspects of the propagation of shear bands. Real time temperature histories along lines intersecting and perpendicular to and along the shear band path are recorded by means of a high speed infrared detector system. Experiments show that the peak temperatures inside the propagating shear bands increase with impact velocity. The highest temperature measured is in excess of 1400 °C or approximately 90% of the melting point of the C-300 steel. For Ti-6Al-4V, the peak temperatures are approximately 450 °C. In the mechanical part of the study, high speed photography is used to record the initiation and propagation of shear bands. Recorded images of propagating shear bands at different impact velocities provide histories of the speed of shear band propagation for the C-300 steel. A strong dependence of shear band speed on the impact velocity is found. The highest speed observed for the C-300 steel is approximately 1200 ms−1 or 40% of its shear wave speed.

Dynamically propagating shear bands in impact-loaded prenotched plates-II. Numerical simulations

Abstract The experimental observations of dynamic failure in the form of propagating shear bands and of the transition in failure mode presented in Part I of this investigation is analyzed. Finite element simulations are carried out for the initiation and propagation of shear-dominated failure in prenotched plates subjected to asymmetric impact loading. Coupled thermomechanical simulations are carried out under the assumption of plane strain. The simulations take into account finite deformations, inertia, heat conduction, thermal softening, strain hardening and strain-rate hardening. The propagation of shear bands is assumed to be governed by a critical plastic strain criterion. The results demonstrate a strong dependence of band propagation speed on impact velocity, in accordance with experimental observations. The calculations reveal an active plastic zone in front of the tip of the propagating shear bands. The size of this zone and the level of the shear stresses inside it do not change significantly with the impact velocity or the speed of shear band propagation. Shear stresses are uniform inside this zone except near the band tip where higher rates of strain prevail. The shear band behind the propagating tip exhibits highly localized deformations and intense heating. Temperature rises are relatively small in the active plastic zone compared with those inside the well-developed shear band behind the propagating tip. The calculations also show shear band speeds and temperature rises that are in good agreement with experimental observations. Computed temperature fields confirm the experimental observation that dissipation continues behind the propagating shear band tip. In addition, the numerical results capture the arrest of the shear band. The arrested shear band is first subjected to reverse shear. Subsequently, the arrested band is subjected to mixed-mode loading which eventually leads to tensile failure at an angle about 30 ° to the band.

Laser-induced shock compression of monocrystalline copper: characterization and analysis

Controlled laser experiments were used to generate ultra-short shock pulses of approximately 5 ns duration in monocrystalline copper specimens with [001] orientation. Transmission electron microscopy revealed features consistent with previous observations of shock-compressed copper, albeit at pulse durations in the µs regime. At pressures of 12 and 20 GPa, the structure consists primarily of dislocation cells; at 40 GPa, twinning and stacking-fault bundles are the principal defect structures; and at a pressure of 55–60 GPa, the structure shows micro-twinning and the effects of thermal recovery (elongated sub-grains). The results suggest that the defect structure is generated at the shock front; the substructures observed are similar to the ones at much larger durations. The dislocation generation is discussed, providing a constitutive description of plastic deformation. It is proposed that thermally activated loop nucleation at the front is the mechanism for dislocation generation. A calculational method for dislocation densities is proposed, based on nucleation of loops at the shock front and their extension due to the residual shear stresses behind the front. Calculated dislocation densities compare favorably with experimentally observed results. It is proposed that simultaneous diffraction by Laue and Bragg of different lattice planes at the shock front can give the strain state and the associated stress level at the front. This enables the calculation of the plastic flow resistance at the imposed strain rate. An estimated strength of 435 MPa is obtained, for a strain rate of 1.3 × 10 7 s 1 . The threshold stress for deformation twinning in shock compression is calculated from the constitutive equations for slip, twinning, and the Swegle–Grady relationship. The calculated threshold pressure for the [001] orientation is 16.3 GPa.  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Quantifying cellular traction forces in three dimensions

Cells engage in mechanical force exchange with their extracellular environment through tension generated by the cytoskeleton. A method combining laser scanning confocal microscopy (LSCM) and digital volume correlation (DVC) enables tracking and quantification of cell-mediated deformation of the extracellular matrix in all three spatial dimensions. Time-lapse confocal imaging of migrating 3T3 fibroblasts on fibronectin (FN)-modified polyacrylamide gels of varying thickness reveals significant in-plane (x, y) and normal (z) displacements, and illustrates the extent to which cells, even in nominally two-dimensional (2-D) environments, explore their surroundings in all three dimensions. The magnitudes of the measured displacements are independent of the elastic moduli of the gels. Analysis of the normal displacement profiles suggests that normal forces play important roles even in 2-D cell migration.

Three-Dimensional Traction Force Microscopy: A New Tool for Quantifying Cell-Matrix Interactions

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.

Pressure-dependent flow behavior of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass

An experimental study of the inelastic deformation of bulk metallic glass Zr_(41.2)Ti_(13.8)Cu_(12.5)Ni_(10)Be_(22.5) under multiaxial compression using a confining sleeve technique is presented. In contrast to the catastrophic shear failure (brittle) in uniaxial compression, the metallic glass exhibited large inelastic deformation of more than 10% under confinement, demonstrating the nature of ductile deformation under constrained conditions in spite of the long-range disordered characteristic of the material. It was found that the metallic glass followed a pressure (p) dependent Tresca criterion τ = τ0 + βp, and the coefficient of the pressure dependence β was 0.17. Multiple parallel shear bands oriented at 45° to the loading direction were observed on the surfaces of the deformed specimens and were responsible for the overall inelastic deformation.