Peter P. Gillis

Dynamical Dislocation Theory of Crystal Plasticity. I. The Yield Stress

The derivation is outlined of a general relation connecting the macroscopic plastic strain rate with the configuration and velocity distribution of dislocations in a monocrystal with a single active glide system. This can be simplified for particular cases, the most simple being the case of parallel straight dislocation lines.A new form of the dynamical theory of plasticity is applied to detailed calculations and compared with previous work. The major modification is the use of the equation v=v* exp[−D/τ] to express the quasi‐viscous behavior of dislocation velocities. Here, v=dislocation velocity, v*= terminal velocity, D=characteristic drag stress, and τ=resolved shear stress. Also, a physical relation between dislocation density and plastic strain is derived.The nonlinear differential equation that results from combining the strain‐rate equation with an equation that describes the loading machine is integrated. Approximate analytic solutions, and numerical calculations, are given for the upper yield st...

On the equation of motion of the undeformed section of a Taylor impact specimen

In this paper a one‐dimensional analysis is presented that leads to the appropriate equation of motion for the undeformed portion of a plastic, rigid rod after impact with a rigid anvil. This equation is used as a basis for deducing material properties of the rod material from post‐test measurements.

Cellulose: Refutation of a Folded-Chain Structure

Calculations of modulus of elasticity for extended-and folded-chain configurations have been compared with the experimental observations of mechanical properties of native cellulosic fibers. A recent folded-chain proposal is incompatible with the experimental evidence.

Stress dependences of dislocation velocities

Abstract Motion of a dislocation through a crystal is treated as comprising jumps past relatively disperse obstacles and viscous glide through the clear lattice between obstacles. Well-known expressions for dislocation velocity dependence upon stress for these two types of motion are combined in series to obtain an expression for overall velocity. This expression is investigated in terms of three parameters: stress, drag ratio and limiting velocity ratio. It is shown that under some circumstances no relationship exists between average velocity and parameters determinable from ultrasonic attenuation. Furthermore, this treatment qualitatively reconciles some apparently anomalous dislocation velocity observations with a fairly simple theory of dislocation motion.

Some fundamental aspects of the theory of acoustic emission

Abstract A dislocation process that seems likely to be of importance in the generation of acoustic emissions is described. A simple mathematical theory, which describes this process, is developed so that order of magnitude estimates can be made. These estimates indicate that acoustic emission events may be associated with only a small fraction of the total plastic strain. Hence, it may be difficult to correlate acoustic emission with parameters related to total strain.

A generalized quadratic flow law for sheet metals

A planar quadratic flow law is proposed for anisotropic sheet materials. This law is similar to the anisotropic strength criterion of Tsai and Wu. It has six experimentally determinable coefficients as compared to four in Hill’s flow law and, thus, allows more experimental information to be accommodated. However, the resulting strain increment vector, while unique, is not necessarily normal to the flow surface.

Continuum descriptions of dislocations under stress reversals

A general continuum theory of dislocation motion is used to investigate the response of crystalline solids to cyclic straining in uniaxial tension and compression. For macroscopically homogeneous deformation under uniaxial stress a simple one‐dimensional equation suffices to relate the plastic strain rate to dislocation flux. The material is characterized by evolutionary equations for multiplication of dislocations and for immobilization of moving dislocations. Some simple example materials are considered and it is shown by numerical calculation that these exhibit respectively a Bauschinger effect, isotropic hardening, and isotropic softening when subjected to a program of alternating strains at a constant rate.

On the penetration of semi-infinite targets by long rods

Abstract T he one-dimensional eroding-rod penetration theory proposed by A. T ate ( J. Mech. Phys. Solids 15 , 387, 1967; 17 , 141, 1969) is modified in two ways. In the equation of motion of the rigid end of the rod, a proper accounting is made of mass transfer into the plastic region. Also, the mushroom strain at the deforming end of the rod is incorporated into the analysis. It is shown that this latter factor has a very substantial effect on calculated penetrations.

Calculating the elastic constants of graphite

Abstract The elastic constants of crystalline graphite are calculated from a fairly simple model. The bending and stretching force constants of the carbon-carbon bonds, along with the crystal geometry, determine the elastic compliances. The key ingredient to the success of the calculation is the selection of suitable bending and stretching force constants for the in-plane and out-of-plane bonds.

Estimation of flow stress under high rate plastic deformation

Abstract The impact of a cylindrical specimen against a rigid anvil was analysed in 1948 by G. I. Taylor. In 1987, Jones, Gillis and Foster proposed a modification to Taylors analysis. This modification included a new equation of motion for the undeformed section of the specimen and relaxed one of the assumptions of Taylors original work. While Jones and co-authors were able to show the existence of an exact solution, the utility of the analysis was severely limited by its complexity. The present paper introduces and approximation into this model which produces a simple algebraic formula to estimate its exact solution. Results of 92 tests of copper, aluminum and steel specimens are reported and used to evaluate this new approximation to the Jones, Gillis and Foster analysis.