Slip In Single Crystals Research Articles

Invertible structured deformations and the geometry of multiple slip in single crystals

Abstract Invertible structured deformations are employed to derive the basic kinematical relations of crystalline plasticity without the use of an intermediate configuration. All of the quantities appearing in these relations have definite geometrical interpretations in terms of either smooth or non-smooth geometrical changes (disarrangements) occuring at macroscopic or sub-macroscopic length scales. For f.c.c. crystals, the kinematical relations are valid for each family of invertible structured deformations. For other single crystals, an appropriate collection of invertible structured deformations is identified and the validity of the kinematical relations is established within this (possibly smaller) collection.

Deformation mechanisms of transition-metal disilicides with the hexagonal C40 structure

Abstract The deformation mechanisms of (0001) 2 10> basal slip in single crystals of five different transition-metal disilicides with the hexagonal C40 structure has been investigated in the temperature range from room temperature to 1500 °C in compression. High resolution transmission electron microscopy of the core structure of 1/3 2 10> dislocations is used to deduce the difference in deformation mechanisms. These five different disilicides are found to be classified into two groups depending on deformation mechanism, which is reflected in the difference in the onset temperature for plastic flow. The low-temperature group, which consists of VSi2, NbSi2 and TaSi2, exhibits the onset temperature for plastic flow around 0.3 T/Tm (Tm: melting temperature) and they deform by a conventional shear mechanism. On the other hand, the high temperature group, which consists of CrSi2 and Mo(Si,Al)2, exhibits the onset temperature around 0.6 T/Tm and they deform by a synchroshear mechanism. Factors affecting the deformation mechanism in these C40 disilicides are discussed in terms of directionality of atomic bonding and the relative stability of the C40 phase with respect to the C11b phase.

Statistical continuum theory for large plastic deformation of polycrystalline materials

This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions are used. A secant modulus-based formulation is used. The statistical analysis is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycrystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations.

Active slip-band separation and the energetics of slip in single crystals

This research supports recent eAorts to provide an energetic approach to the prediction of stress‐strain relations for single crystals undergoing single slip and to give precise formulations of experimentally observed connections between hardening of single crystals and separation of active slip-bands. Non‐classical, structured deformations in the form of twolevel shears permit the formulation of new measures of the active slip-band separation and of the number of lattice cells traversed during slip. A formula is obtained for the Helmholtz free energy per unit volume as a function of the shear without slip, the shear due to slip, and the relative separation of active slip-bands in a single crystal. This formula is the basis for a model, under preparation by the authors, of hardening of single crystals in single slip that is consistent with the Portevin-Le Chatelier eAect and the existence of a critical resolved shear stress. # 2000 Elsevier Science Ltd. All rights reserved.

Yield stress anomalies in single crystals of Ti-54.5 at.% Al II. ½[112](111) slip

Abstract A yield stress anomaly has been observed for ½[112](111) slip in single crystals of γ-Ti-54.5 at.% Al. Weak-beam electron microscopy studies have been carried out to elucidate the origin of this anomaly. At room temperature, screw and 60° dislocations are dissociated in the glide plane, and 30° dislocations are dissociated by glide on intersecting {111} planes, forming weak locks. At high temperatures, ½[112] dislocation loops are elongated along their edge direction, and these edge dislocations are dissociated by climb and glide into sessile configurations consisting of Frank and Shockley partials on different intersecting {111} planes, with a stair-rod dislocation along the line of intersection. There is some evidence for further dissociation of the Frank partial. These strong locks are responsible for the yield stress anomaly. The driving force for the anomaly is the reduction in dislocation energy; the mechanism involves climb, which becomes easier with increasing temperature.

Synchroshear Versus Conventional Shear Mechanisms in Transitionmetal Disilicides with the C40 Structure

AbstractThe deformation behavior of (0001) <1210> basal slip in single crystals of five different transitionmetal disilicides with the C40 structure has been investigated in the temperature range from room temperature to 1500°C in compression. These disilicides are found to be classified into two groups depending on the onset temperature for plastic flow. The low-temperature group, which consists of VSi2, NbSi2 and TaSi2, exhibits the onset temperature for plastic flow around 0.3 T/Tm (melting temperature) and deforms by a conventional shear mechanism. In contrast, the high temperature group, which consists of CrSi2 and Mo(Si,Al)2, exhibits the onset temperature around 0.6T/Tm and deforms by a synchroshear mechanism. Factors affecting the deformation mechanism in these C40 disilicides are discussed in terms of directionality of atomic bonding and the relative stability of the C40 phase with respect to the C11b phase.

Characteristics of Ordinary ½⟨110] Slip in Single Crystals of γ-TiAl

ABSTRACTA study of the occurrence of ordinary slip in single crystals of Ti 54.5 at% Al with various orientations at different temperatures shows that the critical resolved shear stress is approximately the same for ¼⟨110] slip on {111} and {110} planes near the peak of the yield stress anomaly. However the shapes of the glide loops are quite different, suggesting that the order of relative mobilities of screw and edge dislocations is reversed in the two cases. The reason for this and its possible effect on the mechanism responsible for the yield stress anomaly of ½⟨110] {111} slip are discussed. Experiments on the thermal reversibility of the yield stress when either ordinary- or super- dislocation slip systems are operating at both temperatures have shown that the yield stress is reversible for the latter but not reversible in the former case.

Plastic deformation of single crystals of VSi2 and TaSi2 with the C40 structure

Abstract The deformation behavior of (0001)〈1210〉 basal slip in single crystals of VSi2 and TaSi2 with the C40 structure has been investigated in the temperature range from room temperature to 1500 °C in compression. Plastic flow is observed only above 400 and 600 °C for VSi2 and TaSi2, respectively. The critical resolved shear stress (CRSS) for basal slip decreases with increasing temperature but exhibits a moderate peak around 1100 and 1400 °C for VSi2 and TaSi2 respectively. Dislocations with b = 1 3 〈1210〉 gliding on (0001) basal planes both in VSi2 and in TaSi2 are observed to dissociate into two identical partials with b = 1 6 〈1210〉 involving a stacking fault. High-resolution transmission electron microscopy of 1 3 〈1210〉 dislocations indicates that basal slip both in VSi2 and in TaSi2 occurs through a conventional single shearing mechanism, unlike in isostructural CrSi2 and Mo(Si,Al)2 in which basal slip occurs through a synchroshear mechanism.

Characterization of dislocations and their influence on plastic deformation in single crystals

Abstract After providing a rapid summary of some of the main results from a recently constructed theory of structured solids in [1], attention is focussed on the characterization of dislocations and the influence of dislocation density on plastic deformation G p by crystallographic slip in single crystals. The dislocation density is identified in terms of Curl G p and some (but not all) of the results established for the kinematics of crystallographic slip have their counterparts in the traditional developments of crystal plasticity. A two-dimensional crystal undergoing planar motion is used to illustrate predictive capabilities of the theory presented. It may be emphasized that the theory utilized here is applicable to materials of widely varying strengths and hardening characteristics, including ordered intermetallic alloys whose mechanical behavior is primarily governed by the dislocations (through Curl G p ) and not by plastic deformation itself.

Kinking and Cracking Caused by Slip in Single Crystals of Silicon Carbide

α‐SiC single crystals were compressed parallel to the basal plane, (0001), at temperatures between 900° and 1500°C. Plastic deformation by slip on the basal planes which accompanied kinking occurred above 1000°C. At kink boundaries, two kinds of cracks were observed. One was the cracks elongated parallel to the basal plane. This kind of crack was initiated by the tensile stress produced by piled‐up dislocations on the basal planes against a kink boundary. The other was on a kink boundary, and was induced by the stress of dislocations, heterogeneously distributed on the kink boundary. The initiation of cracks produced by dislocations was considered to be a possible cause of fracture in polycrystalline SiC at high temperatures.

Directional dependence of c-plane slip in single crystals of mercuric iodide

An experimental study of plastic deformation in thin single crystals of mercuric iodide (Hgl2) subjected to (0 0 1) [1 0 0] and (0 0 1) [1 1 0] shear loadings has established a directional dependence to the phenomenon of (0 0 1) orc-plane slip in Hgl2. The average stressess c for the “onset of yielding” were 12.6 psi (86.9 kPa) for (0 0 1) [1 0 0] shear and 16.5 psi (113.8 kPa) for (0 0 1) [1 1 0] shear; the average values of the deformation parameters 0, interpreted as a “bulk yield stress”, were 24.7 psi (170.3 kPa) for (0 0 1) [1 0 0] shear and 37.7 psi (259.9 kPa) for (0 0 1) [1 1 0] shear. These values are in agreement with the theoretical relationss c(θ)=s c(0)/cosθ ands 0(θ)=s 0(0)/cosθ, whereθ is the smallest angle between 〈1 0 0〉 crystallographic axis and the direction of shear stress applied in the (0 0 1) plane.

Effects of interstitial content and grain size on the strength of titanium at low temperatures

Abstract The effects of interstitial solute content (0.1 to 1.0 at.% Oeq) and grain size (1–23 μ) on the deformation kinetics and strain hardening in titanium were investigated over the temperature range of 4.2 to 650°K and compared with previous results on single and polycrystals. The flow stress is given by τ ≈ τ ∗ (T,⋗g, C i ) + 0.5 μb{ρ(γ, d, C i )} 1 2 where T is the temperature, ⋗g the strain rate, Ci the interstitial solute content, μ the shear modulus, b the Burgers vector, ρ the dislocation density, γ the shear strain and d the grain size. Good agreement occurred between polycrystalline results, those for prism slip in single crystals and dislocation velocity measurements when a Taylor factor of 5 was used. τ ∗ is proportional to √Ci, the proportionality constant increasing with decreasing temperature and being 0.05 μ, at 4.2°K. The deformation kinetics obey an Arrhenius-type rate equation with a Gibbs free energy of activation ΔG at τ ∗ = 0 and 0°K equal to ~1.5 eV (~0.21 μ0b3). It is concluded that the rate-controlling mechanism is the thermally activated overcoming of interstitial solute atoms by dislocations moving on the first-order prism planes. The effects of grain size and interstitial content on strain hardening are principally through their influence on the dislocation density.

The effect of carbon content on the beginning of slip in single crystals of Fe-3·2 wt%Si alloy

Specimens with 18 ppm and 100 ppm carbon of different orientations were deformed by compression (έ∼1·1×10−4 s−1) at the temperatures 150 °K, 195 °K, 293 °K, 393 °K and 483 °K. The measuredΨ(χ) andτ(χ) curves are presented. The changes of the curves caused by increased carbon content are discussed from the point of view of the low temperature induced cross-slip. Deviations from the Schmid law of critical resolved shear stress are found for both carbon contents. The dependence of the CRSS on temperature for specimens of standard purity has a slightly different course for orientationχ=−30° than for orientationsχ=0° andχ=+30°. These deviations are discussed in terms of the influence of normal stress on the slip. The course ofΔτ (difference between the CRSS in the MRSS plane for specimens with 100 ppm and 18 ppm of carbon) onχ is discussed using different models of lattice hardening due to interstitial impurities. These models can also be applied to the explanation of deviations ofτ(χ) curves from the Schmid law.

The effects of temperature and strain rate on the strength of beryllium sheet

The stress-strain behavior and the deformation dynamics of compression rolled and hot upset beryllium sheet prepared from SR powder were investigated in tension over the range 25° to 355°C. The true stress-true strain curves were approximated by the relationσ =σ(0) +he1/2. Both σ(0) andh decreased with temperature. σ(0) was higher at all temperatures for the compression rolled sheet, whereash was the same for the two materials. The difference in σ(0) was in the athermal component of the stress. The effects of temperature and strain rate on the flow-stress of the polycrystalline sheet agreed with those for prism slip in single crystals. Thermal activation analysis of the deformation dynamics yielded values of 123 to 158 b3 for the activation volume, 1.5×107 sec−1 for the preexponential factor and 1.8 ev (0.18 μb3) for the activation energy,Ho.

Slip in single crystals of niobium-molybdenum alloys deformed in compression

The slip geometry and morphology, and the hardening behaviour in compression of single crystals of Nb-Mo alloys with up to 50 at. % Mo has been investigated in the range 77–475°K; a few tensile experiments are also reported. Detailed results have been obtained for Nb-5 at. % Mo and Nb-16 at. % Mo. The orientation dependence of the operative slip plane [the ψ(χ) curve] is changed by temperature or alloying mainly for orientations in the left half of the stereographic triangle, i.e. near [001], and this behaviour cannot be fully explained by current theories. The change in the morphology of the slip bands with temperature and molybdenum content appears to depend largely on the stress level, and is interpreted in terms of the ability of screw dislocations to cross-slip. Some results indicate that the yield point drop is connected with the beginning of cross-slip. From measurements of work hardening rates, it is concluded that the effect of adding solute atoms is to increase the yield stress, increase θ I and decrease On. The increase in θ I is discussed in terms of our present knowledge of dislocation structure in deformed crystals. La géométrie et la morphologie du glissement, ainsi que le comportement au durcissement au cours d'essais de compression effectués sur des monocristaux d'alliage Nb—Mo ayant une concentration de Mo allant jusqu'à 50%at., ont été étudiés entre 77°K et 475°K. Les auteurs présentent également quelques expériences de traction. Des résultats détaillés ont été obtenus pour Nb-5 %at. Mo et Nb-16 %at. Mo. La relation entre l'orientation et le plan de glissement effectif [la courbe ψ(χ)] varie avec la température ou la concentration de l'alliant, principalement pour les orientations correspondant à la moitié gauche du triangle stéréographique, e.a.d. voisines de [001], et ce comportement ne peut pas être interprété entièrement à l'aide des théories courantes. La variation de la morphologie des bandes de glissement avec la température et la concentration en molybdène semble dépendre dans une large mesure du niveau de contrainte, et est interprétée par l'aptitude des dislocations vis à effectuer un glissement dévié. Certains résultats montrent que la chute de la limite élastique correspond au commencement du glissement dévié. D'après les mesures des taux de consolidation, les auteurs concluent que l'addition d'atomes dissous augmente la limite élastique, augmente également θ I et diminue θ II . L'augmentation de θ I est discutée dans le cadre des connaissances actuelles de la structure des dislocations dans les cristaux déformés. Die Gleitgeometrie, Morphologie und das Verfestigungsverhalten bei der Druckverformung von Nb-Mo-Einkristallen mit Mo-Gehalten bis zu 50 At. % wurden im Temperaturbereich zwischen 77° und 475°K untersucht; auch Über einige Zugversuche wird berichtet. Ausführliche Messungen wurden an Nb-5 At. % Mo und Nb-16 At.%Mo durchgeführt. Die Orientierungsabhängigkeit der aktiven Gleitebene [ψ(χ)-Kurve] wird hauptsächlich bei Orientierungen in der linken Hälfte des Orientierungsdreiecks, d.h. bei [001], durch Temperaturänderungen und Änderungen der Legierungszusammensetzung beeinfluβt; dieses Verhalten kann durch die vorhandenen Theorien nicht vollständig erklärt werden. Änderungen der Morphologie der Gleitbänder mit der Temperatur und dem Molybdängehalt scheinen hauptsächlich von der Spannung abzuhängen und werden anhand der Fähigkeit der Schraubenverset-zungen zur Quergleitung interpretiert. Einige Ergebnisse deuten darauf hin, daβ der Streckgrenzenabfall mit beginnender Quergleitung zusammenhängt. Aus Messungen der Verfestigungsgeschwindigkeiten wird geschlossen, daβ die Zugabe von Fremdatomen die Flieβspannung erhöht, θ I erhöht und θ II erniedrigt. Die Zunahme von θ I wird anhand der gegenwärtigen Kenntnisse über die Versetzungsstruktur in verformten Kristallen diskutiert.

Basal slip in Mg3Cd

Abstract Abstract The critical resolved shear stress (C.R.S.S.) for basal slip in single crystals of Mg3Cd has been determined as a function of temperature between 77°K and 500°K. From 77°K to 293°K the crystals were tested in either the ordered or the disordered condition depending upon the prior heat treatment. From 293°K to 500°K the state of order was that in equilibrium at the testing temperature, varying from complete order at the lower temperatures to complete disorder at the higher temperatures. The strain–rate sensitivity of the C.R.S.S. was determined using stress-relaxation tests. The C.R.S.S. of the disordered material between 150°K and 293°K is ascribed to short-range order hardening; the greater C.R.S.S. of the ordered material in the same temperature range is attributed to the immobilization of the screw components of superlattice dislocations by cross-slip onto prism planes. Above 293°K the form of the C.R.S.S. versus temperature curve is attributed to a form of Sumino hardening.

Orientation and Temperature Dependences of Slip in Single Crystals of Iron Alloys

Orientation and Temperature Dependences of Slip in Single Crystals of Iron Alloys

Slip in Single Crystals of Ice

AbstractRectangular specimens of ice (c. 5 cm × 2 cm × 0.5 cm) were cut from large single crystals (c, 10 cm × 5 cm2) grown from pure water by a modified Bridgman technique. When these specimens were deformed under controlled conditions, slip lines which were predominantly parallel to the basal plane became visible. In some cases short. perpendicular segments were also seen which can be interpreted as evidence for cross-slip in ice. Measurements of slip-band spacings were made on silvered “formvar” replicas of some deformed crystals. These measurements showed that “coarse” slip occurred when the resolved shear stress on the basal plane. σ, was greater than about 0.2 bars, and that the average thickness of the slip lamellae, d (cm) was approximately given by Wakahama’s relationship. (σ−0.2) d = 0.45 × 10−3. At lower stresses “fine” slip occurred, and the relationship between the average thickness of the lamellae and the resolved shear stress was more adequately described by Taylor’s formula, σd = 7.2 × 10−5. It is. however, possible that both coarse and fine slip occurred at higher stresses, but that the fine slip was then below the limit of resolution.

Slip in Single Crystals of Ice

AbstractRectangular specimens of ice (c.5 cm × 2 cm × 0.5 cm) were cut from large single crystals (c, 10 cm × 5 cm2) grown from pure water by a modified Bridgman technique. When these specimens were deformed under controlled conditions, slip lines which were predominantly parallel to the basal plane became visible. In some cases short. perpendicular segments were also seen which can be interpreted as evidence for cross-slip in ice. Measurements of slip-band spacings were made on silvered “formvar” replicas of some deformed crystals. These measurements showed that “coarse” slip occurred when the resolved shear stress on the basal plane.σ, was greater than about 0.2 bars, and that the average thickness of the slip lamellae,d(cm) was approximately given by Wakahama’s relationship. (σ−0.2)d= 0.45 × 10−3. At lower stresses “fine” slip occurred, and the relationship between the average thickness of the lamellae and the resolved shear stress was more adequately described by Taylor’s formula,σd= 7.2 × 10−5. It is. however, possible that both coarse and fine slip occurred at higher stresses, but that the fine slip was then below the limit of resolution.

Damage due to electric spark discharge machining of zinc

Electric spark discharge machining has been observed to produce severe damage in the form of kinking and slip in single crystals of high-purity zinc. A mechanism by which conditions of plastic anisotropy, relatively high machining temperatures and loading from spark discharge machining interact to produce this damage is proposed. A method for preventing the damage is explained.