Publisher Summary The fundamental assumption of all theories of plasticity—that of time independence of the equations of state—makes simultaneous description of the plastic and rheologic properties of a material impossible. I t is well-known that in many practical problems, the actual behaviour of a material is governed by plastic as well as by rheologic effects. It can even be said that for many important structural materials, rheologic effects are more pronounced after the plastic state has been reached. Every material shows more or less pronounced viscous properties. In some problems, the influence of viscous properties of the material may be negligible, while in others, it may be essential. Both sciences—plasticity and rheology—are concerned with the description of important mechanical properties of structural materials. Each of them has created its own methods of investigation and has developed within the framework of certain assumptions which, unfortunately, cannot always be satisfied in reality. The results of rheology are confined to cases where plastic strain is of no decisive importance.

Fundamental Problems in Viscoplasticity

After a brief historical introduction, recent achievements in the theory of plasticity are surveyed with emphasis on applications in mechanical engineering.Kinematic models are presented that indicate the complexities of mechanical behaviour in the plastic range. The fundamental theorems of limit analysis are discussed, and their application to two- and three-dimensional problems is illustrated by examples. Shakedown analysis and limit design are defined. Problems involving large plastic deformations are discussed with special reference to metal forming processes. Applications of the theory of plasticity to impact testing and blast damage are reviewed. Recent changes in the theory of structural stability in the plastic range are mentioned. Throughout the lecture, impending developments of the theory of plasticity are indicated.

The Theory of Plasticity: A Survey of Recent Achievements

The paper is concerned with the structure of multiaxial stress-strain relations in timedependent metal plasticity, as for transient creep and rate sensitive yielding. First. a general kinematical relation is developed between the macroscopic inelastic strain tensor and microstructural slip displacements, as modeled either by continuum shearing on crystallographic planes of individual grains or by the motion of discrete dislocation lines. It is assumed that at any given slipped state, the rate of slipping on a particular system is governed by the resolved shear stress on that system (or by the local \"forces\" on dislocation lines). 'This leads to the primary result of the paper: Components of the macroscopic inelastic strain rate tensor are deriz!able, at each instant in the course of deformation, from a potential function of stress, General features of the flow potential surfaces in stress space are discussed, and some specific functional forms are examined, Linear viscoelasticity and tirre-independent plasticity are developed as limiting cases of the flow potential formulatic!, and the appropriateness of a potential function for stationary creep is discussed,

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On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals

The dislocation dynamics of Gilman and Johnston are applied to the problem of elastic—plastic flow in Armco iron at very high strain rates. The dislocation velocity is assumed to follow the law v=v∞ exp(−τ0/τ); experimental data support this form of dependence and are used to determine the value of τ0. This value is in reasonable agreement with other measurements taken from Luders band front velocities. A second quantity which can be evaluated is the initial density of dislocation lines, N0, which is found to be 2.0×108 cm−2.

Dislocation Dynamics and Dynamic Yielding

In this paper a new anisotropic model for time-dependent behaviour of soft soils is presented. The formulation is based on a previously developed isotropic creep model, assuming rotated Modified Cam Clay ellipses as contours of volumetric creep strain rates. A rotational hardening law is adopted to account for changes in anisotropy due to viscous strains. Although this will introduce some new soil parameters, they do not need calibration as they can be expressed as functions of basic soil parameters through simple analytical expressions. To start with, the one-dimensional response of the model is discussed, making it possible to explore how the model is capable of capturing key features of viscous soft soil behaviour. Subsequently, the three-dimensional generalisation of the model is presented, followed by comparison with experimental data, showing good agreement in both triaxial undrained compression and extension. In the authors' opinion, the simple formulation of the model makes it attractive for use in engineering practice.

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Anisotropic creep model for soft soils

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L. E. Malvern

Papers

Plastic wave propagation in a bar of material exhibiting a strain rate effect