Volume 6, Issue 4
September 1984, pages 625-835
pp 625-625 September 1984
pp 627-631 September 1984
pp 633-641 September 1984
Shocks and high velocity deformation
The shock Hugoniot curves of a large number of materials up to a few Mbar have been obtained experimentally. Metallurgical examination and physical measurements on metallic and other samples recovered after shock loading up to several 100 kbar indicate the existence of large concentrations of point, line and planar defects. Dislocation mechanisms have been invoked to explain shock wave propagation and the phenomena related to the quick homogenisation of stress and strain behind the shock front. Computer simulation models using molecular dynamics calculations have also been used to understand some aspects of shock wave propagation at an atomistic level. For very strong shocks, the material is expected to melt under shock heating, but the experimental evidence regarding this is inconclusive. A combination of shock temperature measurement and theory may be able to answer this question.
pp 643-643 September 1984
Computer simulation of tensile testing
A brief overview of the molecular dynamics method, with emphasis on the work of Parrinello and Rahman, is presented. Molecular dynamics is a method for studying classical statistical mechanics of well-defined systems through a numerical solution of Newton’s equations. A set ofN particles with coordinatesr_{i} (i=1, …,N) and confined in a cell are allowed to interact through a potential. The bulk is usually simulated by periodically repeating the cell in space. Newton’s equations are then solved numerically and the statistical averages of dynamical properties are calculated as temporal averages over the trajectory of the phase space. This method has already been used to simulate a liquid. Now, based on a Lagrangian formulation, it is possible to study systems under the most general conditions of externally applied stress. Unlike the earlier calculations, in this procedure, shape and size are governed by equations of motion obtained from the Lagrangian. Thus it allows us to study structural transformations which may be brought about by an interplay of external and internal stresses. By applying this technique to a single crystal of Ni, Parrinello and Rahman observe that the stress-strain relations obtained confirm with reported results. Under compressive loading it is found that Ni shows a bifurcation in its stress-strain relation and the system changes from cubic to hexagonal close packing. Such a transformation could perhaps be observed under extreme conditions of shock. Finally the scope of computer simulation is highlighted and the limitations of employing such a method are pointed out.
pp 645-651 September 1984
This paper addresses itself to instabilities observed during tensile testing, and complements the papers of Rodriguez and Ananthakrishna presented at this Meeting. The work of Cagliotiet al on the elastic to plastic transformation is first reviewed. The work of Kubinet al on the serrated (repeated) yielding observed at liquid helium temperatures is then discussed in brief. Finally, our own work relying on electronic simulation is described. We conclude with some brief remarks on a few important questions that merit attention in the future.
pp 653-663 September 1984
This paper attempts an assessment of the current understanding of the phenomenon of “serrated plastic flow”, which manifests itself as serrations, load drops, jerkiness or other discontinuities in the stress-strain curves obtained in constant extension rate tensile tests, and as sudden bursts of strain in constant loading rate tests and in constant load (stress) creep tests (the so called staircase creep). Though one can identify at least seven physical processes that can cause serrations, the discussion here is restricted mainly to serrated yielding in tension tests originating from dynamic strain ageing (dsa). The characteristics of the five types of serrations that have been identified so far and the experimental conditions under which they occur are discussed. The various models of serrated flow that have been put forward are reviewed critically. Some recent results on 316 stainless steel are presented to illustrate the effects of grain size, temperature and strain rate on serrated flow. Manifestations ofdsa other than serrations such as a negative strain rate sensitivity, positive temperature dependence for flow stress and work hardening, and the ductility minimum are also discussed. Finally the various issues to be resolved are enumerated.
pp 665-676 September 1984
Repeated yield drop phenomena as a cooperative effect
We present a theoretical model of repeated yielding (ry) which reproduces many experimentally observed features, apart from showing how the temporal behaviour of the phenomenon emerges as a consequence of the cooperative behaviour of defects. We first consider the case of step-like creep curves. Our model leads to a coupled set of nonlinear differential equations which admit limit cycle solutions, and thence jumps on the creep curve. Approximate closed form solutions for the limit cycles and the steps on the creep curve are obtained. The model is then extended to the constant strain rate experiment by including the machine equation. The temporal ordering ofry is shown to follow, as well as several other features characteristic ofry. Chaotic flow is also exhibited: the model has a sequence of period-doubling bifurcations with an exponent equal to that of the quadratic map. Finally, we have analysed the fluctuations during the onset ofry using nonlinear Langevin equations. Fluctuations in the periodic (ry) phase are also investigated. We conclude thatry is another example of a dissipative structure.
pp 677-687 September 1984
Mechanisms and empirical equations for deformation and some principles of alloy design
Some aspects of the deformation behaviour of solids at very high, moderately high and low strain rates are discussed. In the very high strain rate region, deformation equations and the physics of the shock front are analysed to propose a route to lower energy dissipation at the shock front. In the moderately high strain rate region, alloy design principles for maximizing the deformation resistance are outlined. In the low strain rate region, an analysis of the physical basis for the power law creep equation is presented. Some physical arguments are presented as a rationale for the high stress exponents and activation energies often observed in particle-strengthened alloys. The additivity of strain rates by various mechanisms is also briefly discussed.
pp 689-698 September 1984
Superplasticity is the phenomenon of extraordinary ductility exhibited by some alloys with extremely fine grain size, when deformed at elevated temperatures and in certain ranges of strain rate. To put the phenomenology on a proper basis, careful mechanical tests are necessary. These are divided into (i) primary creep tests, (ii) steady state deformation tests, and (iii) instability and fracture tests, all of which lead to identification of macroscopic parameters. At the same time, microstructural observations establish those characteristics that are pre-requisites for superplastic behaviour. Among the macroscopic characteristics to be explained by any theory is a proper form of the equation for the strain rate as a function of stress, grain size and temperature. It is commonly observed that the relationship between stress and strain rate at any temperature is a continuous one that has three distinct regions. The second region covers superplastic behaviour, and therefore receives maximum attention. Any satisfactory theory must also arrive at the dependence of the superplastic behaviour on the various microstructural characteristics. Theories presented so far for microstructural characteristics may be divided into two classes: (i) those that attempt to describe the macroscopic behaviour, and (ii) those that give atomic mechanisms for the processes leading to observable parameters. The former sometimes incorporate micromechanisms. The latter are broadly divided into those making use of dislocation creep, diffusional flow, grain boundary deformation and multimechanisms. The theories agree on the correct values of several parameters, but in matters that are of vital importance such as interphase grain boundary sliding or dislocation activity, there is violent disagreement. The various models are outlined bringing out their merits and faults. Work that must be done in the future is indicated.
pp 699-700 September 1984
Grain boundary-dislocation interactions
Our current understanding of the structure of grain boundaries will be described first. The structure of low angle boundaries can be rigorously described in terms of arrays of dislocations. The structure of high angle boundaries continues to defy a complete and rigorous description. A model has been developed based on coincidence site lattices. This model postulates the presence of grain boundary dislocations even at high angles of misorientation to accommodate the deviation from exact coincidence conditions. The Burgers vectors of such grain boundary dislocations can be found by the translation vectors of thedsc lattice. An interesting point is that the Burgers vectors are not lattice translations. Hence the dislocations are confined to the surface of the boundary and cannot move into the grain. Alternative descriptions of the structure of grain boundaries make appeal to the Bernal type of polyhedral voids that occur in metallic glasses. A brief discussion of the strength of this approach will be outlined. Dislocations at grain boundaries can affect both grain boundary migration and sliding. The possible mechanisms for these phenomena will be described. The importance of understanding these mechanisms to explain deformation of metals at high temperatures will be stressed.
pp 701-701 September 1984
Instabilities in first order phase transitions
Majority of the metallurgical phase transformations are first-order transitions which occur by the nucleation and growth process near equilibrium conditions. In recent years, homogeneous transformation has been reported in some of these cases at conditions significantly away from those of equilibrium. In this paper some of these transformations will be discussed. In the first part of the presentation the thermodynamic and the mechanistic distinctions between first and higher order phase transformations will be discussed and a comparison made between homogeneous and heterogeneous modes of phase transformations and those of deformation. Based on Landau’s free energyvs generalised order parameter plots, an instability temperature is defined for first order phase transformations below which the transformation can occur by a continuous amplification of a concentration or a strain fluctuation. In the second part experimental evidence in support of the continuous mode of transformations in two ordering reactions are presented. These are: (i) a transition from the short range to the long range chemical order in Ni_{4}Mo (D1a structure) and (ii) a hybrid displacive-replacive ordering in Zr_{2}Al (B8_{2} structure). In order to make the continuous mode operative in these first order transformations (which is possible at a high “supercooling”), radiation in the former and rapid quenching in the latter were employed. In the last part, the martensitic transformation and the shape memory effect is described in terms of Landau’s plots and the mechanical and thermodynamical consequences of the model are discussed.
pp 703-716 September 1984
Deformation and martensitic transformation
The influence of applied stresses and imposed plastic deformation on the martensitic transformation of a parent phase is described. Changes in mechanical properties such as flow stress, work hardening rate, fracture toughness, etc brought about by strain-induced martensitic transformation are briefly examined. In the absence of appreciable dislocation glide, atomic displacements associated with glissile boundaries are highly ordered and reversible modes of (plastic or nonlinear pseudoelastic) deformation. Such processes lead to large strains and are encountered in deformation twinning, martensitic transformations and in the reorientation of martensite units. The reversibility leads to phenomena such as elastic twinning, thermoelastic martensites, superelasticity, shape memory and two-way shape memory effects, and rubber-like behaviour. These are discussed using a unified approach based on thermoelastic equilibrium. The shape memory effect suggests several potential applications of the martensitic transformations in non-ferrous alloys in which the effect is most commonly observed. Recent developments in this area are reviewed with special reference to the prerequisites for the effect and the influence of metallurgical processing on the extent of shape recovery.
pp 717-732 September 1984
Strength and electronic structure
The main attribute of a solid is its resistance to deformation, or its ‘strength’. We discuss first the interpretation of the strength parameter. The current situation with regard to the central problem of providing a microscopic description of the strength parameter is briefly reviewed. Electrons in metals provide the cohesion, so that an understanding of the role played by electronic structure in the strength attribute should lead to practical hints for building stronger materials. The useful ‘aircraft alloy’ (Ti + Al + V) illustrates one such important relationship,viz., that the addition of a nond-character metal to ad-electron host strengthens the latter. Again, metals are distinguished from non-metals by the Fermi surface they possess, and it is interesting to examine any possible relationship between the anisotropy of the Fermi surface with the observed anisotropy in hardness (or yield strength). Next, we turn to cleavage, and point out that the assumption that it is the exact opposite of cohesion faces objections. Cohesion is an average property, whereas cleavage is a crack-tip phenomenon. Finally, among the processes familiar to the metallurgist wherein a metal is hardened, electron-moderated mechanisms have been identified in at least two cases, and we conclude with a brief account of these.
pp 733-753 September 1984
This paper surveys the present-day description of ferroelasticity in terms of the notion of symmetry descent. Based on the work of earlier authors, a symmetry classification of phase transitions is presented. A general classification of twinning in crystals is also attempted on the basis of this scheme. Most kinds of twinning fall into two broad categories: nonferroelastic and ferroelastic. The shape-memory effect associated with martensitic transitions is discussed briefly. The interesting possibilities of this effect in the case of ferroelectric ferroelastics, for which the electric field provides an additional control parameter, are also mentioned.
pp 755-772 September 1984
Effects of mechanical deformation: Exoemission
An introduction to some of the physical effects (e.g. exoemission, acoustic emission and mechanoluminescence) associated with the mechanical deformation of solids is presented. Greater emphasis has been given to exoelectron emissions. Experimental information and plausible mechanisms for exoemission have been described briefly. In particular, exoelectron emission from metals and oxide-coated metals has been discussed at some length, with the hope of generating a common interest among physicists and metallurgists.
pp 773-774 September 1984
Relevance of liquid state to solid state properties
H R Krishna Murthy T V Ramakrishnan
We outline in this talk the beginning of a new programme to study physical properties of crystalline solids. It is based on considering the latter, a broken symmetry phase, in terms of the higher symmetry liquid phase. The solid is a calculable perturbation on the fluid. This is exactly opposite to the standard approach which relates mechanical properties to the behaviour of defects (mainly dislocations) etc., in an otherwise perfect crystalline solid. However, most other broken symmetry phases (e.g. ferromagnets) are discussed starting from a symmetric Hamiltonian or a free energy functional, and earlier work by one of the authors shows that the liquid-solid transition is well described, qualitatively and quantitatively, by this approach. On the other hand, defect theories of melting have a long record of nonsuccess. In the first part of the talk, the density wave theory of freezing will be outlined, and it will be shown how properties such as Debye Waller factor, entropy change of freezing etc. can be calculated with no or one free parameter. The problem of calculating shear elastic constants and dislocation core structures as well as energies in terms only of observable liquid state properties will be set up, and results presented. The method will be contrasted with zero temperature ‘atomistic’ models which obscure the essential dependence on structure and flounder in a mass of detail. The concluding part will describe further proposed applications, some suggestive experimental results extant in the literature, and some speculations.
pp 775-798 September 1984
Elastic continuum theories of lattice defects: a review
The presently available elastic continuum theories of lattice defects are reviewed. After introducing a few elementary concepts and the basic equations of elasticity the Eshelby’s theory of misfitting inclusions and inhomogeneities is outlined. Kovács’ result that any lattice defect can be described by a surface distribution of elastic dipoles is described. The generalization of the isotropic continuum approach to anisotropic models and to Eringen’s isotropic but non-local model is discussed. Kröner’s theroy (where a defect is viewed as a lack of strain compatibility in the medium) and the elastic field equations (formulated in a way analogous to Maxwell’s field equations of magnetostatics) are described. The concept of the dislocation density tensor is introduced and the utility of higher-order dislocation density correlation tensors is discussed. The beautiful theory of the affine differential geometry of stationary lattice defects developed by Kondo and Kröner is outlined. Kosevich’s attempt to include dynamics in the elastic field equations is described. Wadati’s quantum field theory of extended objects is mentioned qualitatively. Some potential areas of research are identified.
pp 799-804 September 1984
Fracture of particulate composites
A thermodynamic analysis of the process of fracture in elastically deformable composites is formulated. The critical dimensions leading either to particle fracture or to matrix-particle decohesion are identified. Fracture in plastically deformable composites is discussed in the light of the experimental evidence regarding void or cavity nucleation. Models of void growth under the application of stress and the role of void growth in causing failure are described in brief.
pp 805-806 September 1984
Experimental study of fluctuations in materials
Mechanical behaviour is decided by the structure and kinetics of defects in materials. External forces play an important role in determining the growth, decay and motion of defects. In addition there is an inherent fluctuation in the various microscopic characteristics of the system as the latter acts as a ‘heat bath’. A disturbance that is set up in the system is affected by these fluctuations. The response of the system to external forces can be related to the behaviour of the system due to intrinsic fluctuations in the absence of impressed forces. This is the basis of relation between study of fluctuations in the system and various relaxation phenomena observed. It is proposed to discuss certain features of this subject in relation to various material properties.
pp 807-815 September 1984
Elementary concepts in chaos and turbulence
The phenomenology of aperiodic or chaotic behaviour is described with reference to simple theoretical models and experiments. A brief description is given of the current understanding of how irregular dynamical motions can arise.
pp 817-822 September 1984
An elementary introduction to the concept of fractals is given. Some examples of fractals drawn from nature are briefly discussed. It is suggested that fractal geometry may be useful in characterizing the grain size and shape distributions in polycrystalline solids.
pp 823-825 September 1984
pp 827-835 September 1984
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