Some observations on the deformation characteristics of bulk polycrystalline zirconium hydrides

The deformation behaviour of bulk polycrystalline zirconium hydrides in the composition range ZrH_1.27 to ZrH_1.66 has been investigated by compressive loading at temperatures between room temperature and 500° C. Single-phase -zirconium hydride is brittle below 100° C. Analyses of slip traces on specimens deformed at temperatures between 100 and 250° C have shown that the glide planes are {111} types. The deformation characteristics of and ( + ) alloys at temperatures between 100 and 500° C are consistent with the hydrogen vacancies in the -phase providing significant lattice friction to the movement of dislocations in the zirconium lattice of the hydride structure. The room temperature fracture stress of ( + ) alloys increases with the volume fraction of the -phase and this can be related to the resistance offered by platelets to the propagation of cleavage cracks in the matrix. In a ( + + ) alloy the resistance to crack propagation at room temperature is further increased by the soft -zirconium phase.     

Plastic deformation of polycrystalline zirconium carbide

The compressive yield strength of arc melted, polycrystalline zirconium carbide has been found to vary from 77 kg mm² at 1200C to 19 kg mm² at 1800C. Yield drops were observed with plastic strain-rates greater than 3×10^–3sec^–1 but not with slower strainrates. Strain-rate change experiments yielded values for the strain-rate sensitivity parameterm which range from 6.5 to 1500C to 3.8 at 1800C, and the productm ^*(T) was found to decrease linearly with increasing temperature. The deformation rate results are consistent with the Kelly-Rowcliffe model in which the diffusion of carbon assists the motion of dislocations.     

Some observations on the deformation characteristics of titanium hydride

Deformation studies have been performed on bulk polycrystalline titanium hydride, of compositions between TiH_1.53 and TiM,_1.99, and at temperatures between –35 and 200° C. The yield stress increased with decreasing temperature and with increasing non-stoichiometric hydrogen vacancy content. The temperature dependence of the yield stress was enhanced with increasing vacancy content. Two-surface analysis of slip lines revealed that the slip plane was {1 1 1}. Strain-rate tests on TiH_1.65 demonstrated a considerable strain-rate dependence of both yield and fracture characteristics. The effects of test temperature, non-stoichiometric defect concentration and strain-rate on the deformation and fracture characteristics are shown to be strongly related to hydrogen ion mobility.     

Hysteresis effects on the high-temperature internal friction of polycrystalline zirconium

Hysteresis effects present on the high temperature internal friction of annealed polycrystalline zirconium are investigated in detail. It is shown that two internal friction maxima are present when the measurements are performed on heating. If a high enough temperature is reached, only one internal friction maxima is observed on cooling. Furthermore, when the temperature is not decreased below a certain value (critical temperature) only the lower temperature peak is present during a subsequent heating cycle. The critical temperature is strongly dependent on the grain size. Finally, both the hysteresis effects and the internal friction maxima are explained by relaxation mechanisms associated with grain boundary sliding and segregation of impurities to the grain boundaries.     

Some observations on the effect of specimen size upon the plastic deformation around deep notches

The purpose of this work was to investigate the effect of specimen thickness on the three-dimensional plastic deformation of notches. Notched bend specimens, made of lead as a model material, were tested. Transverse and longitudinal deformations at the notch root were measured using simple experimental techniques. The results provide a picture of the transition from the plane stress to the plane strain deformation of a notch root, which is discussed and interpreted. The shape which is assumed by the notch under the condition of plane plastic flow is shown to be a consequence of the plastic incompressibility of the material. Further, the formation of cracks at the notch root is discussed.     

X-Ray diffraction study of tensile deformation in a bulk polycrystalline Ag-30 at. % Cd alloy

X-ray diffraction techniques have been used to study plastic deformation in a polycrystalline Ag-30 at.% Cd alloy under tensile load. The positions and shapes of all (hkl) reflections were recorded using a parafocusing arrangement up to a maximum true strain of 0.265. The effects on the peak displacements caused by stacking faults and by macroscopic strains normal to the surface were distinguished. The longitudinal true stress in the surface layer evaluated by least square analysis was smaller than the macroscopic flow stress by an approximately constant amount over the whole range of strain (in accord with previous observations of a stress gradient near a free surface); the apparent rate of work hardening in the surface was equal to that for the specimen as a whole. The stacking fault probability was approximately a linear function of strain and attained a maximum value of 7×10^–3.Fourier analyses were performed on the profiles of (111) — (222) and (200) — (400) pairs of reflections. The effective particle sizes D _e(111) and D _e(100) and the estimated true domain size D decreased approximately inversely with increasing strain, tending to limiting values at high strains of 220, 150 and 300Å respectively. Similarly, the microscopic strains [_L ²_hkl ^*]^1/2 tended to limiting values at high mechanical strains. The twin fault concentration was found to be negligibly small. The particle size and microstrain parameters were compared with values for cold-worked filings of the alloy. A plot of against _L=50Å ²₁₁₁ ^* for the solid specimens and for the filings was linear and yielded a stacking fault energy for Ag-30 at. % Cd of 6.1 ergs/cm².This work was supported by the Office of Naval Research     

A calculation of the bulk modulus of polycrystalline materials

It is shown that the bulk modulus of a polycrystalline material, composed of cubic single crystals, is the same as that of the constituent single crystal. The bulk modulus of the aggregate is independent of the distribution of the individual single crystals. The same results apply also to other polycrystalline systems, whose constituent single crystals undergo a pure uniform contraction when subjected to hydrostatic pressure.     

Low-temperature deformation behaviour of polycrystalline copper

Low-temperature plastic flow in copper was investigated by studying its tensile and creep deformation characteristics. The dependence of the flow stress on temperature and strain rate was used to evaluate the thermal activation energy while the activation area was derived from the change-in-stress creep experiments. A value of 0.6 eV was obtained for the total obstacle energy both in electrolytic and commerical copper. The activation areas in copper of three selected purities fell in the range 1200 to 100 b². A forest intersection mechanism seems to control the temperature dependent part of the flow stress. The increase in the athermal component of the flow stress with impurity content in copper is attributed to a change in the dislocation density. The investigation also revealed that thermal activation of some attractive junctions also takes place during low-temperature creep. The model of attractive junction formation on a stress decrement during creep, yields a value of 45±10 ergs cm⁻² for the stacking fault energy in copper.     

Some observations on the bowl phenomenon

Previous studies suggest that performance of a series system may be enhanced if those station(s) having smallest mean operation time requirement(s) and/or smallest variability are placed in the middle of the line. There has been considerable confusion relative to whether this ‘bowl phenomenon’ has to do with the placement of means, variances, or some combination of the two. The results of the current study show that the phenomenon observed is not related to an imbalance in means. Rather, it is associated with an imbalance in absolute variability. Furthermore, it is suggested that the bowl effect vanishes altogether in cases where a minimal level of in-process buffer stock is provided.     

On the Taylor principles for plastic deformation of polycrystalline metals

Grain orientation evolutions and texture formation based on the Taylor principles offer important references to reveal crystallographic mechanisms of deformation behaviors. Strain equilibrium between grains is achieved in Taylor theory, however, stress equilibrium has not yet been reached perfectly even in many modifications of the theory though the textures predicted become very close to those of experimental observations. A reaction stress model is proposed, in which mechanical interactions between grains are considered in details and grain deformation is conducted by penetrating and non-penetrating slips. The new model offers both of the stress and strain equilibria and predicts the same textures indicated by Taylor theory. The rolling texture simulated comes very close to the experimental observations if the relaxation effect of the non-penetrating slips on the up-limits of reaction stresses is included. The reaction stress principles open theoretically a new field of vision to consider deformation behaviors of polycrystalline materials, whereas the Taylor principles become unnecessary both theoretically and practically. Detailed engineering conditions have to be included in simulations if the deformation textures of industrial products should be predicted.     

Some observations on the stochastic averaging method

Formulas required for the application of Stratonovich's stochastic averaging method are rederived using a mathematical procedure more appealing to engineers. By so doing the physical implications are made clear, allowing certain variations and relaxation of some restrictions. In particular, the time-averaging portion of the original method is removed so that it becomes applicable to non-stationary excitations as well as cases where deterministic time-varying properties must be preserved. A less restrictive general condition is proposed for this modified stochastic averaging method, and heuristic arguments are given for further relaxation of the condition in stability analyses. Application of this modified method is illustrated by a simple example.     

Some observations on the tearing of ductile materials

A relationship between tearing force and tensile properties is deduced by analogy with notched tensile failure and proves to be quite accurate in predicting the tearing forces of a wide range of materials. It is found that the elasticity modulus is a significant factor in the relationship and its role is investigated. A model of the tearing process is presented which seems to be a more accurate representation of the physical situation for many materials than those previously suggested. A simple analysis of the model leads to the relationship which is found to be experimentally reliable.     

Soft X-ray emission spectroscopy as a tool for studying hydriding behaviors and equilibrium properties of zirconium,zirconium alloys and their hydrides

L-emission spectra from zirconium, zirconium-based alloys and their hydrides are recorded, and empirical measures for the electron densities of d symmetry at the zirconium sites are derived. Hydrogen in these samples are covalently bound to zirconium, and the energetic features of the Zr 4d - H 1s bondings govern the stabilities of the hydrides. The positive relationship between the cell dimensions of an alloy and the stability of its hydride is well understood in terms of the d - H 1s bondings together with the d-d interactions in the starting alloy.