Lee Davison

Shock compression of solids

Abstract This review contains a brief, comprehensive, critical assessment of the status of investigations concerning the response of solids to shock compression. Mechanical, metallurgical, electrical, optical and other phenomena occurring in substances subjected to shock pressures covering the range from about 0.1 to 6000 GPa are considered. Emphasis is placed on physical interpretation of observations peculiar to the shock environment and on the relationships among observations in the various areas of investigation.

Theory of spall damage accumulation in ductile metals

Abstract S pall damage is a type of fracture produced when large tensile stresses are developed in material bodies as a result of the interaction of stress waves. The damage develops independently at various points in the body because of the short duration of stress application, but interacts in a complicated way with the stress wave. A theory of these phenomena is presented for the case where the basic response of the material is viscoplastic, and where the damage takes the form of a distribution of small rounded voids. This theory is specialized to the case of rectilinear motion and an example problem solved numerically.

Thermomechanical constitution of spalling elastic bodies

In this article we develop a theory of spallation of a brittle thermoelastic body, and of the interaction between propagating waves and accumulated damage. This theory is applied to the prediction of the effect of spall damage on the elastic stiffness and thermal conductivity of the material.

Spall fracture in aluminum monocrystals: a dislocation‐dynamics approach

High‐purity monocrystalline aluminum disks of three crystallographic orientations were subjected to carefully controlled planar impact producing low levels of spall damage. This damage was observed by optical and scanning electron microscopy of sections through the recovered disks, and was found to consist of voids of essentially octahedral form having {111} planes as faces. To describe the growth of these voids we propose a kinematical model based on the motion of edge dislocations. Dynamical equations describing the rate of growth of an individual void are obtained by applying established concepts of dislocation mechanics to the kinematical model. Finally, the dynamical void growth model is combined with an empirically established nucleation model to yield equations for calculating the total volume growth rate in a spalling sample. Extension of these results to other ductile fracture phenomena is suggested.

Continuum Measures of Spall Damage

Following the introduction of the concept of continuous spall damage as a replacement for the customary discrete description, existing spall criteria are generalized to continuous measures of damage and are classified according to their dependence on the history of the continuum field variables. A compound‐damage‐accumulation theory is proposed in which the rate of damage accumulation depends on the existing damage, in addition to the applied stress. Several examples of the application of the new theory to the correlation of existing data are given.

Shock‐Wave Structure in Porous Solids

In this paper several variations of a simple theory of dynamic compaction of porous solids are presented and discussed. This theory elaborates the conventional theory of shock propagation in such a way that the shock structures observed to propagate in these materials can be described. Steady‐wave profiles are calculated for several compaction models, and the inference of constitutive equations from experimental data is discussed. It is shown that the theory can be made to reproduce steady‐wave profiles observed in the usual plate‐impact experiments exactly.

Perturbation theory of nonlinear elastic wave propagation

Abstract In this article a perturbation method is given for obtaining uniformly valid approximations to the solution of problems of plane wave propagation in finite elasticity theory. Examples are given showing its application to problems of longitudinal and shear wave propagation, including an explicit numerical example concerning the propagation of a shear wave in a polyurethane foam rubber.

Analysis of capsules for recovery of shock‐Compressed matter

There many circumstances in which it is desirable to recover matter that has been subjected to compression by a strong shock wave. In most cases this necessitates designing an encapsulation device that ensures that the material is processed by the shock in the most uniform way possible and is protected from the aftereffects of the explosion or impact producing the shock. For scientific purposes, it is necessary that the conditions to which the material has been subjected be known. Calculation is necessary for both designing sample recovery capsules and inferring the conditions to which the sample material has been subjected. Means for performing these calculations are discussed, along with their strengths and limitations, and some results for a particular configuration of interest are presented.

Electrical responses of nonlinear piezoelectric materials to plane waves of uniaxial strain

In this paper we consider propagation of finite‐amplitude plane waves of uniaxial strain in piezoelectric disks exhibiting fully coupled nonlinear response. In particular, we derive explicit expressions for determination of the electric current in external circuits consisting of resistors, inductors, or capacitors connecting the electrodes on the faces of a disk. The formulation of a specific‐boundary initial‐value problem is discussed and a discussion of how the fully coupled electromechanical problem may be solved numerically is given.

Kinematics of finite elastoplastic deformation

Abstract A model in which plastic deformation occurs as a result of crystallographic slip is used to derive a formula for decomposing a deformation gradient into parts attributable to elastic and plastic deformation processes. The dislocation kinematics are those in long use, for example by Rice (1971, J. Mech. Phys. Solids 19 , 433) and by Hill and Havner (1982, J. Mech. Phys. Solids 30 , 5). The analysis presented here differs from that given by these authors in that it concerns total deformation (and its elastic and plastic parts) rather than incremental deformation. The decomposition obtained is inherent in the physics of the deformation process, arising naturally when the spatial discreteness of the active slip planes is taken into account. Expressions for the decomposition components are obtained by means of volumetric averaging of contributions of elastic deformation and slip to the total deformation. The decomposition captures the effects of isoclinic orientation central to Mandels (1973, Int. J. Solids Struct. 9 , 725) theory, but without introduction of the intermediate configuration that arises when the deformation is assumed to be expressible as though the plastic and elastic deformations occurred sequentially. Because no intermediate configuration arises, the established objectivity principle applies without modification and the concept of elastic embedding that is essential to proper selection of temporal rates is implemented quite naturally. Although the new decomposition is motivated by dislocation-mechanical considerations, the result is a continuum-mechanical expression that can be used in other contexts in which the sites of inelastic deformation are spatially separated in the material.