J. N. Johnson

Dynamic fracture and spallation in ductile solids

A mathematical model of ductile hole growth under the application of a mean tensile stress is developed and applied to the problem of spallation in solids. The object is to describe dynamic ductile fracture under a wide range of tensile loading conditions. The mathematical model presented here describes both plate‐impact spallation (as observed by postshot examination and time‐resolved pressure measurements) and explosively produced spallation (as observed by dynamic x‐radiographic techniques) in copper. It is found to be inapplicable to ductile fracture of expanding rings, even in the absence of possible adiabatic shear banding and classical necking instabilities, because of the fact that the mean tensile stress (void growth) and the deviatoric stress (homogeneous plastic shear strain) are not independent. A phenomenological model of void growth under uniaxial stress conditions is developed independently and applied to the numerical finite‐difference solution of fracture in an expanding ring. The initial...

A constitutive model for the dynamic response of brittle materials

A microphysically based material model for the dynamic inelastic response of a brittle material is developed. The progressive loss of strength as well as the post‐failure response of a granular material with friction are included. Crack instability conditions (an inelastic surface in stress space) and inelastic strains are obtained by considering the response of individual microcracks to an applied stress field. The assumptions of material isotropy and an exponential distribution for the crack radius are invoked to provide a tractable formulation. The constitutive model requires a minimal number of physical parameters, is compatible with a previously developed ductile fracture model [J. Appl. Phys. 64, 6699 (1988)] that utilizes inelastic surfaces, and can be formulated as an efficient, robust numerical algorithm for use in three‐dimensional computer codes. The material model is implemented into a Lagrangian computer formulation for the demonstration of material response to dynamic loading conditions. Com...

Shock‐wave initiation of heterogeneous reactive solids

Shock‐wave initiation of solid explosives depends on localized regions of high temperature (hot spots) created by heterogeneous deformation in the vicinity of various defects. Current mathematical models of shock initiation tend to fall into two broad categories: (1) thermodynamic‐state‐dependent reaction‐rate models, and (2) the continuum theory of multiphase mixtures. The level of generality possessed by (1) appears to be insufficient for representation of observed initiation phenomena, while that of (2) may exceed necessary requirements based on present measurement capabilities. As a means of bridging the gap between these two models, we present an internal‐state‐variable theory based on elementary physical principles, relying on specific limiting cases for the determination of functional forms. The appropriate minimum set of internal‐state variables are the mass fraction of hot spots  μ, their degree of reaction  f, and their average creation temperature θ. The overall reaction rate λ, then depends o...

A constitutive model for the non-shock ignition and mechanical response of high explosives

Abstract An understanding of the non-shock ignition properties of energetic particulate composite materials, high explosives such as PBX-9501 is an important part of the safety assessments for conventional handling (transportation, storage, etc.) of weapons systems including assembly operations. This paper develops and demonstrates the use of a numerical constitutive model for PBX-9501 that includes viscoelastic response, statistical fracture mechanics, and an ignition hot-spot mechanism. The intent is that this model can be used in safety analyses involving accidents to prevent undesirable dispersion of Pu. The parameters have been determined that will predict the mechanical response and ignition:non-ignition of a set of experiments that have explored the non-shock properties of this material.

Tensile plasticity and ductile fracture

A mathematical model of tensile plasticity and void growth based on the Gurson flow surface and associated flow law is developed and applied to the problem of ductile fracture under general tensile loading conditions. The flow surface defines the plastic strain components in the tensile region; conditions of fracture are defined in terms of the plastic deformational strain, porosity, and the ratio of mean stress to shear stress, p/τ. This model reduces to the Carroll and Holt [J. Appl. Phys. 43, 759 (1972)] tensile threshold pressure for void growth, and to the Rice and Tracey [J. Mech. Phys. Solids 17, 201 (1969)] expression relating the fractional change in void radius to the incremental plastic deformational strain and p/τ in a triaxial tensile stress field. The model has sufficient generality to represent plastic flow and fracture in notched and smooth tensile bars as well as in uniaxial‐strain spallation tests. One‐ and two‐dimensional finite‐difference calculations demonstrate this capability.

Micromechanics of spall and damage in tantalum

The authors conducted a series of plate impact experiments using an 80-mm launcher to study dynamic void initiation, linkup, and spall in tantalum. The tests ranged in peak shock pressures so that the effect of peak pressure on the transition from void initiation, incipient spall, and full spall could be studied. Wave profiles were measured using a velocity interferometry system (VISAR), and targets were recovered using {open_quotes}soft{close_quotes} recovery techniques. The authors utilized scanning electron microscopy, metallographic cross-sections, and plateau etching techniques to obtain quantitative information concerning damage evolution in tantalum under spall conditions. The data (wave profiles and micrographs) are analyzed in terms of a new theory and model of dynamic damage cluster growth.

Rate-dependent ductile failure model

A rate‐dependent constitutive model for the dynamic deformation of ductile materials is developed. The model introduces a physical length scale into the equations governing the progressive failure of materials due to void growth. Consequently, mesh sensitivity or localization problems inherent to rate‐independent models are precluded. The model is implemented into an explicit, finite‐difference computer code. The insensitivity of the model to changes in the mesh size is demonstrated. Comparisons are provided between numerical simulations and data for uniaxial impact experiments. Excellent agreement is established between the final porosity levels and the width of the damage zone. Also, excellent agreement is provided for the stress histories, including the peak stress values and the spall signal.

Effect of pulse duration and strain rate on incipient spall fracture in copper

Data are presented on real time (VISAR) measurements of the spall fracture of copper for various pulse durations and tensile strain rates at the spall plane. The impactors consist of Teflon, Y-cut quartz, and a tungsten heavy alloy. VISAR data are compared with finite-difference calculations employing a rate-dependent void-growth model. The data and comparisons show little dependence of the onset of void growth on either pulse duration or tensile strain rate. Also, it is shown that hydrodynamics (wave propagation properties) involving the transmission of the spall signal from the spall plane to the free surface (plane of the VISAR measurement) can mask slight differences in the void-growth or fracture response. In addition, new results are presented for the elastic description of planar wave propagation in Y-cut quartz; expressions are given for the six independent stress components to second order in infinitesimal Lagrangian strains. A discussion with regard to additional use of Y-cut quartz in impact experiments is presented.

Quasielastic release in shock‐compressed solids

Shock‐ and release‐wave measurements are reported for 6061‐T6 aluminum [J. R. Asay and L. C. Chhabildas, in Shock Waves and High‐Strain‐Rate Phenomena in Metals, edited by M. A. Meyers and L. E. Murr (Plenum, New York, 1981), pp. 417–431], oxygen‐free‐electronic copper, and a Si‐bronze alloy. Significant departure from ideal elastic‐plastic response is observed in all three materials. Experimentally determined release‐wave profiles show evidence for the onset of reverse plastic flow immediately upon release from the shocked state. This phenomenon is analyzed in terms of internal stresses acting on straight dislocation pileups and pinned dislocation loops created by the shock‐compression process. Following shock compression and prior to release, the internal stresses are opposed by the applied shear stress; that is, they exactly balance each other and no plastic flow occurs. As the applied stress is reduced in the unloading wave, reverse plastic flow occurs immediately due to internal reverse stresses acti...

The effect of void growth on Taylor cylinder impact experiments

Taylor cylinder impact experiments have provided useful information concerning the dynamic response of materials. In an effort to obtain data at elevated strain rates, Taylor experiments have been conducted at high velocities. Sections of the recovered specimens reveal a region of porosity located near the base of the cylinders. Computational simulations have been performed to explore the effect of porosity growth on the experimentally observable parameters for Taylor impact tests. The constitutive model used to simulate the growth of voids is based on the Gurson yield surface. A robust and efficient numerical algorithm was developed and implemented into an explicit, two‐dimensional, finite‐element computer code. The calculations provided good qualitative comparison with experimental data.