Hardness Of Single Crystals Research Articles

The concepts of latent hardening and strain hardening in metallic single crystals

Starting from the rate independent theory of the single crystal plasticity (Schmid law), one here tries to both give the most realistic description of the concept of intracrystalline latent hardening—or hardening anisotropy—through the analysis, at the microstructural scale of the dislocation densities, of various and complementary experimental data, and to underline the excessive restriction introduced by the classical assumption of pure strain hardening in the determination of the most general single crystal hardening variation law for the wider range of loading processes. These developments about the microstructural features of single crystal hardening, involving mobile and nonmobile dislocation density evolutions (multiplications) and interactions, are correlated at the macroscopic scale of the slip systems with a strain and load process and orientation hardening law which is shown on few examples to give a better fit with observed behaviour than pure strain hardening. A third part shows that, even starting from a rate dependent assumption for the single crystal plastic flow, the present analysis of latent hardening remains basically unchanged. It shows too that the load process and orientation effect on hardening, which is implicitly present in such approaches although introduced according to specific assumptions on the correlations between slips and dislocation densities, is one of the most significant features in the single crystals hardening evolution during plastic deformation, whatever the theoretical frame is chosen.

Latent hardening in high-density polyethylene

When a parallelopiped specimen is compressed in the x direction (primary deformation) while holding the y dimension unchanged by a vise, the specimen is anisotropically hardened as follows: When the y direction is subsequently compressed while holding the x dimension unchanged the flow stress is higher than the case without the primary deformation. This is similar to the latent hardening in single crystals. On the other hand, if the second compression is in the z direction instead of the y direction, a softening results. Since this second compression reverses the primary deformation, it is similar to the Bauschinger effect. Both effects are reported here together with the results of two successive compressions in two mutually perpendicular directions without any constraints in either compression.

On the strengthening of Magnesium Single Crystals by Cadmium

AbstractSolid solution hardening in single crystals of magnesium containing cadmium (up to 2.4 at.%) has been investigated in the temperature range 77 K to 295 K. A strong temperature dependence of the critical resolved shear stress, τ0, is observed below 230 K, while above this temperature τ0 is temperature independent. At all temperatures τ0 is found to increase linearly with c2/3, where c is the concentration (in atomic fractions) of cadmium as solute. The concentration dependence of τ0 can be explained by the theory of LABUSCH.

High temperature hardness of tungsten carbide

The effect of crystallographic orientation and test temperature on hardness of WC single crystals was investigated along with the hot hardness of poly crystalline tungsten carbide. Also investigated was the effect of carbide grain size and the amount of binder phase on the hot hardness of some cemented tungsten carbides. The hot hardness of single crystal WC on all major crystallographic orientations evaluated decreases very rapidly for increasing temperature, and the single crystal hardness on its hardest orientation is only about half of the polycrystalline material depending on the test temperature. Because of its polycrystalline character, some cobalt bonded cemented tungsten carbides can be harder than single crystal WC over some intermediate temperature range.

Fatigue hardening and nucleation of persistent slip bands in copper

A study of fatigue hardening in single crystals of pure copper shows that, before saturation, stress-strain loops can display workhardening rates of about a third of the elastic shear modulus. These rates exceed tensile workhardening rates by roughly two orders of magnitude. This suggests that there is a large volume fraction of obstacles to plastic flow which are essentially non-deformable and give rise to inclusion stresses of considerable magnitude. The much lower hardening rates in cycles after saturation when persistent slip bands have formed suggest a lower volume fraction of obstacles, as is observed by transmission electron microscopy. A simple composite model involving an inclusion stress, a bowing stress and a passing, stress accounts for the workhardening rates semi-quantitatively in terms of observed dislocation microstructures. Possible implications for polycrystals are considered.

A source model for work hardening of single crystals

The sources, i.e. regions of glide band nucleation in the crystal, are characterized by a locally softened lattice as compared to regions with a perfect lattice. Hence, the depletion of the set of sources during work hardening suggests that the latter can be considered as gradual loss by the crystal of the softening pertaining to the source regions. This model is a realization of A. V. Stepanov's ideas who considered work hardening to be “... disappearance of shear nuclei capable of growth” [21]. It relates the macroscopic plasticity characteristics both with parameters of a non-deformed real crystal (i.e.N(τ)) and with properties of the dislocation ensemble and its internal stress field determiningh (τ, ζ). The model permits of different degrees of accuracy in the description of theτ-e curve, corresponding to a more or less complete account of the contributions due to individual glide bands and their interaction with band sources still unactivated. In its turn, the model can be naturally incorporated in a more general scheme taking into account the time dependence of work hardening as well [8]. Further development of the model would require calculation of dislocation appearance in the surface source regions of the crystals with an account of the lattice imperfection in those regions well before the nucleation of dislocation loops.

A Physically Consistent Method for the Prediction of Creep Behavior of Metals

A physically consistent method, which considers the deformation mechanisms, the active and latent hardening in single crystals, and their transient and steady creep, is proposed to predict the creep behavior of polycrystalline materials. This method consists of two steps: first, the material constants of single crystals are determined from the tensile creep data of the polycrystal, and then these constants are used to predict the creep properties of the same polycrystal under required loading conditions. This method simultaneously satisfies the requirements of equilibrium and compatibility over the grain boundaries, and is self-consistent. The proposed method was applied to calculate the creep strains of a 2618-T61 Aluminum alloy under pure shear, combined stress and nonradial loading; the results obtained were in good agreement with the test data.

A simple mathematical theory of finite distortional latent hardening in single crystals

A simple (one-parameter) hardening law is proposed which accounts for the perpetuation of finite single slip, beyond the symmetry line, in the tensile test of f. c. c. crystals and reduces to Taylor’s rule at infinitesimal strain. This new law emerges as the simplest case of a general mathematical theory of finite deformation of elastic-plastic crystals. The fully anisotropic finite-distortional hardening of latent slip systems predicted by the simple theory is in qualitative agreement with experiment.

Laws governing deformation and hardening of single crystals of aging alloys

1. The phenomenon of "early overaging" is not observed in single crystals, i. e., softening of the alloy does not begin until a particle size is reached that is almost an order higher than the "critical" size for polycrystalline material. The phenomenon of early overaging is associated with the structure of the grain boundaries. Softening of single crystals begins when the coherent bond between the particles and the matrix is disrupted. 2. For nickel-base aging alloys hardened with particles of the γ′ type (Ni3Al) one observed an anomalous temperature dependence of the yield strength. The magnitude of the anomaly depends on the properties and the volume percentage of γ′ phase. For alloys with considerable dislocations splitting in the matrix (Ni-Al-Cr alloys, e. g.) the anomalous variation of τc with T at elevated temperatures is combined with a normal variation in the temperature range below room temperature. 3. A means of increasing the ductility of biphase alloys that is new in principle was established—the creation of regular "quasiperiodic macrolattices" from particles of the precipitating phase. The character of the quasiperiodic distribution of particles can be changed by alloying, heat treatment, or application of external loads in the process of aging.

On the computation of plastic stress-strain relations for polycrystalline metals

A computational procedure is presented for computing the macroscopic stress-strain behavior of polycrystalline metals from consideration of slip on the slip systems of a large number of randomly oriented single crystals. This procedure, based on the simplex method of linear programming, is illustrated by applying it to the case of simple tension with no strain-hardening on individual slip systems. The method is shown to be efficient and accurate. Furthermore, the method can be extended to combined stress states and a variety of single-crystal hardening models.

Hardness Anisotropy of Single Crystals of Ice Ih

WE have recently studied the anisotropy in hardness of single crystals of ice of high purity at temperatures down to −12.5° C. The hardness was determined with a Leitz ‘Miniload’ tester fitted with a Knoop diamond indenter. The apparatus was set up in a cold room, together with a thermocouple fixed near the ice specimen under test. Temperatures could be maintained to within 0.2° C.

Anisotropy in the hardness of single crystals

The results of this work, and those published by other researchers who have used Knoop indentation measurements, confirm that the nature of anisotropy in hardness is essentially determined by the crystal structure and the primary slip systems which accommodate dislocation motion during indentation. Materials belonging to the same class of crystal structure and having common slip systems possess similar anisotropic properties. The varying extent of work-hardening or fracture, associated with indentations, does not appear to influence the anisotropy— although twinning on the basal planes of hexagonal closepacked metals may have a significant effect. An analysis of the indentation process is presented which establishes a clear relationship between the ‘effective resolved shear stress’ (t 0 '), in the bulk of the crystal beneath the indenter, and the observed hardness. Directions which correspond to the minimum values of t' e , on specific crystallographic surfaces, are those of maximum hardness and conversely. The analysis is shown to be equally applicable to a wide range of crystalline solids including nonmetallic materials, of various crystal structure, and typical f.c.c., b.c.c. and c.p.h. metals. Finally, anisotropy in hardness can be used to identify active slip systems in those crystals where it is possible for dislocations to move on more than one system.

The influence of diffusion coatings on the fatigue strength of copper

It has been found possible to increase the fatigue strength of copper by selectively alloying a thin layer at the surface. The three alloy systems copper-nickel, copper-silver and copper-zinc were investigated, and the fatigue strength was shown to be independent of the degree of solute penetration and of its mode of distribution, when tested at room temperature in the normal laboratory environment. The greatest increase in fatigue strength was obtained with the copper-zinc surface alloy, for which an increase of 15% was recorded.The increased fatigue strength is thought to be dependent both on the new value of τIII, the threshold stress for stage III hardening in single crystals, and on the relatively greater thermal diffusivity of the foreign atoms introduced; the improvement in fatigue resistance was limited to alloy systems in which the solutes possessed a higher diffusion rate than the copper.

Growth of Single Crystals of Copper

DURING experiments on the effects of alternating deformation on the hardening of single crystals of spectrographically pure copper1, difficulties were experienced in obtaining reproducible hardening behaviour under the same conditions of alternating straining from 2-cm. long specimens taken from opposite ends of longer crystals. A brief discussion of experiments made to investigate this disparity follows.