Ares J. Rosakis

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.

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

In 1993, a new beryllium bearing bulk metallic glass with the nominal composition of Zr_(41.25)Ti_(13.75)Cu_(12.5)Ni_(10)Be_(22.5) was discovered at Caltech. This metallic glass can be cast as cylindrical rods as large as 16 mm in diameter, which permitted specimens to be fabricated with geometries suitable for dynamic testing. For the first time, the dynamic compressive yield behavior of a metallic glass was characterized at strain rates of 10^2 to 10^4/s by using the split Hopkinson pressure bar. A high-speed infrared thermal detector was also used to determine if adiabatic heating occurred during dynamic deformation of the metallic glass. From these tests it appears that the yield stress of the metallic glass is insensitive to strain rate and no adiabatic heating occurs before yielding.

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.

How fast is rupture during an earthquake? New insights from the 1999 Turkey Earthquakes

We report that during the two devastating 1999 earthquakes in Turkey, rupture propagated over a large part of the nearly 200km long fault zone at supershear speed approaching 5km/s. We present observations and modeling which confirm the original inference of supershear rupture during the Izmit earthquake and we show that supershear rupture also occurred during the Duzce earthquake. We show that the rupture velocity measured—about √2 times the shear wave velocity—is the value predicted by theoretical studies in fracture dynamics. We look for clues to explain these observations.

On crack-tip stress state: An experimental evaluation of three-dimensional effects

Abstract The extent of the region of three-dimensionality of the crack-tip stress field is investigated using reflected and transmitted caustics. The range of the applicability of two-dimensional near tip solutions is thus established experimentally. The experiments are performed using Plexiglass and high-strength 4340-steel compact tension specimens. A wide spectrum of thicknesses is investigated. At each thickness, measurements are performed at a variety of distances r from the crack tip, ranging from r/h = 0 to r/h = 2, where h is the specimen thickness. The results indicate that plane-stress conditions prevail at distances from the crack tip greater than half the specimen thickness, while no significant plane-strain region is detected. The experimental results are also compared to the crack-tip boundary-layer solution of Yang and Freund[1], and the numerical results of Levy, Marcal and Rice[2]. Their solutions are consistent with the results of this work and approach the plane stress field at r/h = 0.5. In addition, and unlike what might be commonly expected, the analytical solution[1] exhibits no plane-strain behavior very near the crack tip. This behavior is in good agreement with the results of both the transmission and the reflection experiments.

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.

Fracture toughness determination for a beryllium-bearing bulk metallic glass

A class of beryllium-bearing bulk metallic glass alloys has recently been developed at the California Institute of Technology. These alloys can be fabricated in the form of large ingots with minimum dimensions on the order of centimeters, which allows valid mechanical tests to be performed on these materials. Such tests were not formerly possible given the small dimensions of earlier metallic glass specimens. Some basic physical and mechanical properties have been measured on specific beryllium-bearing bulk metallic glass with a nominal composition of Zr{sub 41.25}Ti{sub 13.75}Cu{sub 12.5}Ni{sub 10}Be{sub 2.5}, by the authors and some of their co-workers. The purpose of this paper is to report on the first ever direct measurement of the fracture toughness of any bulk metallic glass system.

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.

Intersonic shear cracks and fault ruptures

Recent experimental observations of intersonic shear rupture events that occur in a variety of material systems have rekindled interest in the intersonic failure phenomenon. Since the early 1990s, engineers and scientists working in all length scales, from the atomistic, the structural, all the way up to the scale of the earths deformation processes, have undertaken joint efforts to study this unexplored area of fracture mechanics. The analysis in the present article emphasizes the cooperative and complementary manner in which experimental observations and analytical and numerical developments have proceeded. The article first reviews early contributions to the theoretical literature of dynamic subsonic and intersonic fracture and highlights the significant differences between tensile and shear cracks. The article then uses direct laboratory observations as a framework for discussing the physics of intersonic shear rupture occurring in constitutively homogeneous (isotropic and anisotropic) as well as in inhomogeneous systems, all containing preferable crack paths or faults. Experiments, models, and field evidence at a variety of length scales (from the atomistic, the continuum, and up to the scale of geological ruptures) are used to discuss processes such as (1) shock wave formation, (2) large-scale frictional contact and sliding at the rupture faces, and (3) maximum attainable rupture speeds and rupture speed stability. Particular emphasis is given to geophysical field evidence and to the exploration of the possibility of intersonic fault rupture during shallow crustal earthquake events.