Calculation of the cyclic hardening curves of fatigued FCC monocrystals using a two-phase model

The cyclic hardening curve of fatigued fcc monocrystals shows a maximum of the stress amplitude if the plastic resolved shear strain amplitude γ_ap exceeds the threshold value γ_M for the formation of persistent slip bands (PSBs). Using a simple two-phase model the typical shape of the cyclic hardening curve will be calculated for lower γ_ap values. The calculation takes into account the fact that the PSB formation starts already at a „nucleation stress”︁ amplitude τ_n below the maximum stress amplitude τ_am. Qualitatively the maximum of the cyclic hardening curve follows from the superposition of cyclic hardening of the matrix volume and of volume growth of the „soft”︁ PSB phase between the nucleation cycle number N_n and the saturation cycle number N_s.     

Plateau Behaviour of Fatigued FCC Single Crystals

The mechanical behaviour of fatigued pure nickel monocrystals oriented for single slip was studied in push-pull tests at room temperature. Especially the cyclic hardening curves, the cyclic stress-strain curve and the shape changes of the hysteresis loops were investigated in the range of the plastic resolved shear strain amplitude, γ_ap, between 10^-10 and 10^-2. In this range the cyclic stress-strain curve exhibits a plateau which is related to plastic strain localization in persistent slip bands (PSBs) developing within the residual “matrix” volume. Using a two-phase model the cyclic saturation mechanical behaviour of the PSB and the matrix volumes has been determined. An explanation has been given of the constant plateau stress τ_B of the cyclic stress-strain curve by taking into account the nucleation stress for PSBs depending on the plastic resolved shear strain amplitude of the matrix volume. Further, the propagation rate of PSBs after strain amplitude increase in the plateau range has been calculated by applying the two-phase model.     

Mesoscopic and microscopic aspects of the PSB formation mechanism in fatigued FCC monocrystals

Persistent zones of plastic strain localization (PSBs) can be observed in fatigued fee monocrystals above the “nucleation cycle number” N_n and the “nucleation stress” amplitude τ_n, respectively. They follow after temporary strain localizations existing at N < N_n and being discernible by oscillations of the relative shape of the hysteresis loops (V_H) or by strain bursts. Using a simple rheological model the frequency of internal stresses of mesoscopic wave length (“mesoscopic stresses”) was determined for Ni monocrystals fatigued at four different plastic strain amplitudes up to N_n. A “mesoscopic threshold stress” τ* has been found to be exceeded within the whole volume of the dislocation-dense regions (DRs) at N ≧ N_n. By comparison of τ* with the stress for the operation of Frank-Read sources of the segment lengths l₀ at the border of the DRs, it might be assumed that above N_n and τ_n respectively a mechanism of dislocation sources acts, compensating the high annihilation rate of movable dislocations in the zones of strain localization. In so doing the formation of persistent zones of strain localization becomes possible, in which the “ladder-like” dislocation structure of the final PSBs develops successively.     

A method for the determination of the cyclic stress-strain curve of presistent slip bands in fatigued single crystals

Single crystals of pure nickel oriented for single slip were fatigued at constant total strain amplitude (ε_at) at room temperature. The dependence of the saturation resolved shear stress amplitudes (τ_as) on the saturation plastic resolved shear strain amplitudes (γ_aps) (cyclic stress-strain curve — CSSC) was determined. In the plateau range of the CSSC the volume fraction f of persistent slip bands (PSBs) was found to be linearly related to γ_aps. The reduction of the total strain amplitude after saturation in the plateau range of the CSSC leads to the so-called secondary CSSC with a slope n > 0 in the log-log plot. From the secondary CSSC the ”︁true”︁ cyclic stress-strain curve of the PSB-volume (PSB-CSSC) can be determined. The method is based on the two assumptions that firstly the PSB-groups (or ”︁macrobands”︁) penetrate the whole cross-section of the specimen and secondly the volume fraction of PSBs in the secondary range of the CSSC remains constant.     

Defect structure in nickel single crystals in dependence on the cyclic deformation prehistory

The development of the dislocation structure in nickel single crystals push-pull fatigued at room temperature is investigated for different deformation types using electrical resistivity measurements and results of TEM observations. The dislocation density in the bundles of the matrix is higher after changing the strain amplitude from region A to region B (CD_AB-type) of the cyclic stress-strain curve (N_dB ≈︁ 1.6 ≈︁ 10¹⁵ m⁻²) than after virginal deformation in region B (VD_B-type) especially at higher strain amplitudes (N_dB ≈︁ 0.75 ≈︁ 10¹⁵ m⁻²). Increasing the strain amplitude within region B (CD_BB-type) does not change N_dB. The farther development of the matrix structure after reaching the v_H-minimum during the VD_B-type of deformation suggests the action of the „formation and dissolution”︁ – mechanism, whereas the CD_BB-type causes the „cord”︁-mechanism of the PSB nucleation.     

Characterization of dislocation structures in copper single crystals using electron channelling contrast technique in SEM

The dislocation structures induced by low‐plastic‐strain‐amplitude cyclic deformation of [111] multiple‐slip‐oriented Cu single crystals were investigated using electron channelling contrast (ECC) technique in scanning electron microscopy (SEM). At a low plastic strain amplitude γ_pl of 8.8 × 10^–5, the saturated dislocation structure is mainly composed of labyrinth‐like vein structure (or irregular labyrinths), and the cyclic hardening behavior at such a low γ_pl is interpreted as being the result of dislocation multiplication by a Frank‐Read mechanism. As γ_pl increases to 4.0 × 10^–4, the unsaturated dislocation structure exhibits two kinds of distinctive configurations, i.e., dislocation walls and misoriented cells. Interestingly, these misoriented dislocation cells are strictly aligned along the primary slip plane (111), constituting a unique persistent slip band (PSB) structure. Here, these cells are thus called PSB cells. In addition, there is a locally distinctive region comprising some cells having a recrystallization‐like feature in the whole structure of PSB cells. The formation of the structure of PSB cells is discussed. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microcracks in fatigued FCC polycrystals by interaction between persistent slip bands and grain boundaries

Persistent slip bands (PSB) are zones of high plastic strain localization in fatigued fee metals. They cannot propagate across the grain boundaries of polycrystalline specimens. Consequently, a local stress field should exist near the end of the PSB, “inducing” new PSBs in the neighbouring grain or initiating cracks within the grain boundary. This interaction between PSBs and grain boundaries will be discussed in the present paper. The observed effects may be divided into few characteristic groups, the occurrence of which depends on the geometrical relations between PSB, grain boundary and specimen axis.     

On the Reasons Leading to an Appearance of Correlated and Anticorrelated Dependences of the Minority Carrier Lifetime on the Dislocation Density in Undoped Semi-Insulating “Stoichiometric” GaAs Crystals

It is shown that in undoped semi-insulating GaAs crystals grown under the stoichiometric conditions both correlated and anticorrelated dependences of the minority carrier lifetime τ on the dislocation density N_d could be observed. The above-pointed effect is connected with a slight excess of Ga atoms (then the correlated dependence τ vs Nd appears) or of As atoms (then the anticorrelated dependence τ vs N_d appears) which inevitably exists even in “stoichiometric” GaAs crystals (i.e. in GaAs crystals of “stoichiometric” composition).     

Dislocation density in heteroepitaxial indium arsenide layers

In As layers have been grown by CVD on (111)B-oriented GaAs substrates. The dislocation density (N_D) distribution through the layer thickness has been studied. N_D is dependent on the mole fraction of AsCl₃ in the gaseous phase and, consequently, on the current carriers concentration. This results in the supposition that the decreasing of N_D in the layers after a “critical” thickness is due to the “pinning” of dislocations at impurity atoms which form stronger bonds with the host In or As atoms than the bond In–As, an effect which is known for bulk GaAs and InP crystals.     

Saturation Dislocation Structures in Cyclically Deformed Nickel Single Crystals of Different Orientations

The major aim of this paper is to describe and characterize qualitatively the saturation dislocation structures in fatigued nickel single crystals with different orientations and to relate them to the mechanical properties. Within the investigated plastic strain amplitude region all measured cyclic stress strain curves exhibit two ranges with a sharp transition. In the first range of the cyclic stress strain curve the dislocation arrangement of the nickel single crystals oriented for single slip is significantly dependent on the plastic strain amplitude, that is the volume of the dislocation-poor regions decreases at increasing amplitude. In the second range ladder-like structures of the persistent slip bands and vein-like structures of the matrix are observed in agreement with the results of copper single crystals. Beside, at great amplitude, but within the second range, there is a steady increase of parquet-like matrix structures. On [001] single crystals the spatial dislocation structure is characterized by condensed and uncondensed {100} dislocation walls. The limited regions with condensed walls are supposed to be regions of high plastic strain amplitude (“mesoscopic” strain localizations). Amplitude changing tests are suitable to obtain results on the stability of the dislocation structures to increasing amplitude and decreasing amplitude, respectively.     

On the change of dislocation structure during the postdeformation of cold worked molybdenum single crystals at elevated temperature

Molybdenum single crystals predeformed at low temperature (T₁ ≦ 293 K) exhibit during tensile reloading at T₂ = 493 K pronounced work softening accompanied by stress serrations and localized slip. It is shown that the initial state for the development of coarse slip bands is the formation of narrow obstacle-free slip channels. The change from the homogeneous dislocation structure to the cell structure proceeds in a heterogeneous and discontinuous manner.     

Optical defects in barium—strontium niobate single crystals

The distributions of edge dislocations and residual mechanical stresses in Ba_xSr_1-xNb₂O₆ (BSN) crystals are investigated and the explanation of the nature of the “growth column” is proposed. The “growth column” is a defect zone going through all of the crystal and usually repeating in its cross-section the contour of the seed crystal. The “growth column” boundary is the closed contour with extremely high edge dislocation density. These dislocations are connected with thermal stresses due to seed-melt contact or abrupt crystal widening. Under proper crystal seeding and widening conditions one can obtain the BSN crystals with dislocation densities less than 10 cm⁻² and without the “growth column”. The method of chemico-mechanical polishing of BSN crystals not forming a defect layer on the surface of the crystals have been developed. The high temperature diffusion annealing is shown to eliminate the growth striae in BSN crystals.     

Dislocation arrangements in cyclically deformed polycrystalline molybdenum

The present paper deals with the cyclic stress-strain behaviour of polycrystalline molybdenum at room temperature and the dislocation structures built up within this material during the fatigue process. A cyclic stress-strain curve of molybdenum deformed in a strain-controlled and symmetrical push-pull test is shown. At strain amplitudes e_a < 3 × 10⁻³ arrangements of relatively homogeneously distributed dislocations are observed in the stage of the stabilization of mechanical properties. The characteristics of these dislocation arrangements are similar to those of dislocation structures of unidirectionally deformed molybdenum single crystals. At strain amplitudes e_a > 3 × 10⁻³ dislocation structures are developed with an inhomogeneous dislocation distribution (bundles structures). The dislocation density in the surface layers of fatigued specimens shows larger values than within the material. The cyclic deformation after a change from a small deformation amplitude to a larger one, or vice versa, is connected with characteristic changes of dislocation density.     

HVEM Investigation of the Structure Change during Work Softening of Molybdenum

The change of the dislocation structure of cold worked Mo single and polycrystals during reloading at T₂ ⪆ 350 K has been studied by HVEM. The structure change was found to proceed in three discernible stages: i. formation of obstacle-free zones by local annihilation of existing dislocations, ii. appearence of large scale slip in these zones, iii. blocking of slip zones by the formation of dislocation cell structure.     

Cotton-Mouton Effect in Monodisperse Suspensions of Liquid Crystals

Abstract

The collective Cotton-Mouton (C-M) effect in the system of micron-size liquid-crystal droplets freely suspended in the isotropic liquid is studied experimentally and theoretically. The collective C-M constant in liquid-crystal suspensions is found to be from 10⁴ to 10⁸ times higher than the respective “molecular” C-M constant in the isotropic phase of the same substance. These large values cause the saturation in the C-M effect at relatively low magnetic fields. Using the generalized nth order Langevin's functions L, _n the statistical therory is presented for the collective C-M effect in the monodisperse liquid-crystal suspensions. As a result, the induced birefringence is obtained in the form Δn = 1/2(Δn)∞ (3L ₂ – 1), where (Δn)∞ is the induced birefringence at saturation. The collective C-M constant is C _c = CN _s S _g where N ₈ is the number of molecules in the droplet, S ₈ is the orientational order parameter of the long molecular axes in the droplet, and C is the “molecular” C-M constant. The resultant (measured) C-M constant is C ₈ = C(1 + N ₈ S ₈). The relaxation time τ depends on the rotational (Brownian) diffusion constant D and after removing the field B the orientational order parameter of the optical axes of droplets in the suspension S _s = 1/2(3L ₂ – 1) vanishes exponentially as S _s = exp(?6Dt). Hence, the relaxation time τ = (6D)^?1.

The collective C-M effect and its saturation can be used as methods for the analysis of the presence and change of the orientational order within colloidal grains and the derivation of several parameters characterizing the aggregation, self-organization, and morphogenesis processes in multicomponent complex systems.     

Lang method applied to investigation of Al single crystal initial structure and of its effect on the eventual development of plastic strain

The land method was used to study the structure of Al single crystals (99.9997% pure) grown from the melt, the thermal stability and the character of changes in different subgrain structures during work hardening. The method has proved to permit observation of slip development both in the early strain region (where occurs “levelling” of the structure of the bulk under strain), and during concert dislocation movement in specific slip planes up to large strains at 4.2°K.     

Effect of buffer layers on the dislocation structure of heteroepitaxial systems

Transmission electron microscopy (TEM) as well as X-ray topography (XRT) and X-ray diffractometry have been used for investigation of the structure of the LPE heteroepitaxial system In_0.05Ga_0.95As-In_yGa_1−yAs_1−xP_x-GaAs(111) A. A critical value of the lattice misfit has been shown to exist at the metallurgical boundary ((Δa/a)* ≈ 10⁻³) which results in the change of the film nucleation and growth mechanism as well as the change of misfit dislocations (MDs) generation mechanism. With (Δa/a)₀ > (Δa/a)* the nucleation and growth mechanism is mixed: island growth at the first stages of growth and layer-by-layer growth at large thicknesses. MDs are created in an “island film” developing a non-ordered dislocation network. The density of threading dislocations (N_d) is ∼ 10⁸ cm⁻². With (Δa/a)₀ < (Δa/a)* there is layer-by-layer mechanism of film's nucleation and growth from the very first stages of crystallization. MDs are injected into continuous layer along the inclined slip planes {111}, thus forming a regular three-dimensional grid of MDs. N_d is less than 10⁶ cm⁻² in the case. A model of dislocation structure formation in heterolayers has been proposed. Within the frame of this model the two critical values of phosphorus concentration in the quaternary melt have been quantitatively determined. These are corresponding to the change of MD generation mechanism. The expected values of N_d for (Δa/a)₀ > (Δa/a)* and (Δa/a)₀ < (Δa/a)* have been theoretically determined.     

Dislocation Structure and Strain Localisation in Nickel Single Crystals Cyclically Deformed at 77 K

An experimentally based investigation is presented of the dislocation structure and of glide effects occurring in single slip oriented nickel crystals cyclically deformed at 77 K until saturation of the stress amplitude. Special attention is paid to a comparison of slip and structure phenomena observed in fatigue tests at 77 K and those found after cycling at room temperature (RT) and elevated temperatures. At strain amplitudes within the plateau region of the cyclic stress‐strain curve, where at higher temperatures in the crystal two structure types co‐exist, at 77 K nearly the entire specimen volume is occupied by one structure “phase”, a dislocation‐“condensed” wall configuration. On different scale levels the main characteristics of this extended wall structure were found to be independent of the imposed amplitude, and they turned out to fit in the temperature dependence of the structure features of the ladder‐like wall phase characterising the zones of intense slip (persistent slip bands) at RT and elevated temperatures. At 77 K the strain is localised in narrow slip bands (SBs) in the same way as at higher temperatures, although there is no indication of a “two‐phase” structure. From the experimental findings it is concluded that WINTERs “two‐phase” model remains valid, when averaging the plastic strain values over all SBs and over a sufficient number of cycles.     

Etch- and Transmission Electron Microscope Investigations of Microdefects in (001) LEC-GaP Substrates

The etch pattern of (001) and (110) LEC-GaP doped with sulphur (N_DN_A in the range from 3–7 × 10¹⁷ cm⁻³) do not only show dislocation etch pits but fine pits, so-called “saucer pits” (S-pits). The distribution of S-pits, their etching behaviour and transmission electron microscope observations of etched samples indicated a clear correlation between S-pits and microdefects (fauted-, prismatic dislocation loops and precipitates).