Free Path Of Mobile Dislocations Research Articles

Impact of coherent and incoherent twin boundaries on the microhardness of annealed nanocrystalline Ni–W alloys

The microstructural evolution of nanocrystalline Ni–W alloys with annealing temperature and more specifically grain boundary (GB) character is investigated through several techniques and correlated with the hardening behaviour. It is shown that two distinct regions can be identified in relation to the annealing temperature and the microstructural evolution. At temperatures below 550 °C (Regime I), a small increase in grain size is observed and is accompanied by a significant hardening and an increase in the fraction of Σ3 incoherent twin boundaries. At temperatures above 550 °C (Regime II), the thermal stability is overcome and important grain growth occurs with a decrease in both the volumic fraction of GBs and the microhardness. It is suggested that the microhardness evolution during heat treatment is influenced by two opposing processes: an increase in the fraction of incoherent twin boundaries (hardening effect) and grain growth (softening effect). Both aspects are directly associated with the mean free path of mobile dislocations.

Correlation between dislocation organization and slip bands: TEM and AFM investigations in hydrogen-containing nickel and nickel–chromium

Various forms of the plastic deformation in single crystals are studied in pure and hydrogen-containing nickel and nickel alloys oriented for single slip [135] and strained in the stage III regime (shear strain, γ=0.8). The heterogeneity of deformation is investigated at two distinct scales: slip bands and dislocation structures, using atomic force microscopy (AFM) and transmission electronic microscopy (TEM). Size and distribution of slip band thicknesses and geometrically necessary boundary (GNB) spacing are comparable. GNB structures both screen the long-range stress fields and decrease the mean free path of mobile dislocations, whereas equiaxed cells only impede dislocation motion through their role as obstacles. Consequently, GNB formation localizes deformation in specific slip bands. Additionally, the observed similarity between GNB spacing and equiaxed cell size suggests a correlation between these microstructural features. The impact of solid solution atoms on the inter-wall spacing is established for chromium and hydrogen. Both decrease the GNB spacing because of a decrease of the cross-slip probability and stacking fault energy, combined to a shielding effect for the later. The effect of GNB spacing on strain hardening is discussed in terms of the length scale associated with GNBs and the effect of solute content.

Combination between Voce formalism and improved Kocks–Mecking approach to model small strains of flow curves at high temperatures

Tensile test curves of an austenitic stainless steel (AISI 316L) are described through the Voce equation in combination with the kinetic approach to strain hardening analysis proposed by Kocks and Mecking (KM) at temperatures ranging from 700 to 1000°C with strain rates between 10−2 and 10−5s−1. The KM approach to strain hardening analysis is used to find the Voce parameters (saturation stress σV, relaxation strain εC, back-extrapolated flow stress to zero strain σo) from the strain hardening rate dσ/dε vs. the flow stress σ. The obtained Voce equations can well describe the flow curves only at large strains in Stage III of strain hardening, while a significant discrepancy occurs at small strains. In order to reduce this discrepancy an improved KM approach is here proposed. The original KM approach assumes that in Stage III of strain hardening the mean free path of mobile dislocations Λ is defined as β/ρ with β constant and ρ the total dislocation density. Λ, and in turn β, are linked to the dislocation cell-pattern typical of Stage III. The proposed improvement of the KM approach consists of assuming that β is not constant at small strains, where dislocations are not organised in cell-pattern, but homogeneously distributed in the material. Based on TEM observations reporting dislocation distributions at small and at high strains, it is proposed that β varies from an initial value at small strains to achieve at high strains the equilibrium value predicted by the original KM approach in Stage III of strain hardening. This assumption provides very good modelling flow curves also at small strains.

Micro–macro investigations about the fatigue behavior of pre-hardened 304L steel

In this work, the effect of cyclic pre-hardening (CPH) and monotonic pre-hardening (MPH), on the Cyclic Stress–Strain Curve (CSSC) and fatigue are considered. New tension-compression tests on two types of 304L alloys used in nuclear power plants are carried out under the following conditions: (i) strain or stress control near endurance limit; (ii) zero or positive mean stress; (iii) virgin, CPH or MPH specimens. Macroscopic results show a detrimental effect of pre-hardening in strain control and a beneficial one in stress control. Some macroscopic considerations are given to explain this result and the effects of an applied mean stress which differ under stress and strain control. Relations between macroscopic results and microstructures at failure are investigated using SEM and TEM. SEM is used for analysis of fatigue striation space.TEM analyses suggest that cyclic pre-hardening mainly promotes wavy slip during subsequent fatigue testing, while monotonous pre-loading favors planar slip. For CPH case it seems that primary cells which are preserved and refined for the most part during fatigue testing, constitute the hard stable structure. After MPH and subsequent fatigue testing, a hard structure is constituted by embedding of three kinds of microstructures, small twins, small cells, crossing twin systems. The formation of a hard structure creates an important internal stress. Observation shows that in pre-hardened specimens, softening arrays as veins and PSBs are frequent under strain control and rather scarce under stress control. It can be so deduced that the increase of fatigue life by pre-hardening in stress control is related to reduced mean free path of mobile dislocations due to internal stress.The obtained results may help to understand some aspects about linear versus non linear fatigue damage accumulation.

Intrinsic Effects due to the Reduction of Thickness on the Mechanical Behavior of Nickel Polycrystals

Uniaxial tensile tests were performed on high-purity nickel polycrystals with thicknesses (t) ranging from 12.5 to 3200 μm. The grain size (d) of each sample was set to a value close to 100 μm in order to avoid grain size effects. Experimental results highlight the intrinsic effect of the thickness on the mechanical properties of nickel. For plastic strains higher than 0.01, a strong softening of the flow stress is clearly observed when the t/d ratio decreases from four to one. This critical range is independent of the plastic strain. Transmission electron microscopy (TEM) investigations of dislocation structures were carried out in core and surface regions of samples plastically strained in the second hardening stage. It is shown that the mean dislocation cell diameter obtains values two or three times higher near free surfaces than in core areas for specimens with t/d ratios lying at a range of 1 to 4. This observation can be interpreted in terms of an increase in the mean free path of mobile dislocations in the second hardening stage. The transition between polycrystal and single-crystal behavior for nickel with constant grain size and various thicknesses is, therefore, an intrinsic effect related to progressively stronger surface softening effects.

Correlations between disorientations in neighbouring dislocation boundaries

During plastic deformation, dislocation structures develop with regions of different orientations separated by dislocation boundaries. Experimental investigations by means of electron back-scattering diffraction or rocking curves from X-ray diffraction give some evidence for the existence of correlations between the disorientations in neighbouring boundaries. Based on a straightforward statistical model an occurrence of anti-correlations between disorientation angles is predicted which can be traced to the limited free path of mobile dislocations carrying the plastic deformation.

Extension of a constitutive model describing the inelastic behaviour of a precipitation hardened alloy

The one intemal variable model by Kocks, Mecking and Estrin has been applied for the description of the hot tensile and creep behaviour under constant loading conditions of Alloy 800H, a carbide precipitation strengthened high temperature alloy. The model was extended by incorporating an expression for a mean free path of mobile dislocations which depends on the kinetics of the precipitation and ripening process of the secondary carbides. Microscopy and mechanical data for three different heats of Alloy 800H at 900°C were evaluated to enable comparison between calculations using the extended model and experimental data. Difficulties were caused by the complex precipitation behaviour of the alloy in which both larger carbides of type M23C6 and smaller ones of type M(C,N) are formed in the investigated range of temperature. Although the microstructural data available is not sufficient for a reliable quantitative description of the evolution with time of the average carbide spacing a qualitative agreement between calculations and mechanical data gives a preliminary verification of the developed extended model.

Solution hardening in aluminium-magnesium alloys: A nuclear magnetic resonance and transmission electron microscopic study

Pulsed nuclear magnetic resonance techniques as well as transmission electron microscopy have been applied to study dislocation motion in aluminium magnesium alloys (0.2–1.6 at.% Mg). The spin lattice relaxation rate in the rotating frame of 27A1 has been been measured at 77 K as a function of strain at constant plastic strain rate ϵ. For finite strain rates, the movement of dislocations induces an additional relaxation rate arising from time fluctuations in the nuclear quadrupole interactions. From the motion-induced part of the relaxation rate the mean free path of mobile dislocations can be calculated. The NMR experiments are combined with transmission electron microscopic investigations to reveal the static structure of defects in the samples. The NMR measurements clearly indicate that fluctuations in the quadrupolar field caused by moving dislocations in AlMg are different compared to those in ultra pure Al. From the NMR data it could be concluded that moving dislocations advance over a number of solute atoms (order of 7) as described by Mott-Nabarro's model. On the other hand, Mott-Nabarro's model does not predict the effective solute spacing as a function of the concentration of solute atoms in accordance with NMR experiments.

Dislocation dynamics in doped NaCl single crystals determined by pulsed NMR between RT and 300°C

Abstract The mean free path of mobile dislocations is measured by determination of the spin-lattice relaxation rate of deforming NaCl single crystals as a function of temperature and of the concentration of Ca++ impurities. The latter may influence the magnitude of the mean free path but this depends to a large extent on the point defect configuration. The degree of association and the mobility of the point defects is studied by measuring the spin-lattice relaxation rate without deforming the samples. On the other hand the distribution of dislocations varies also with temperature and this affects the mobility of dislocations too. The work-hardening rate of the crystals is compared with the mean free path as a function of temperature and it is shown that both quantities have extremes under the influence of competitive mechanisms such as an enhanced thermal activation of dislocations at obstacles, an increasing mobility of point defects, and increasing number of intersections of mobile dislocations with dislocation dipoles.

The relationship between flow stress and dislocation behaviour in [111] aluminium single crystals

Abstract Slip bands and the corresponding dislocation structures in [111] aluminium single crystals at various strains have been simultaneously studied in detail by high-voltage electron microscopy to investigate the mean free path of mobile dislocations. The length of the slip bands is determined by the cell size at every strain and decreases with increasing strain as a function of the inverse of strain. It has been also clarified by the in situ deformation technique that the mean free path of mobile dislocations is precisely determined by the cell size. Each mobile dislocation is retarded by the forest dislocations in each cell wall, so that the flow stress necessary for the dislocation motion is determined by the forest cutting process of the dislocations. On the basis of the dislocation behaviour, the relationship between flow stress and cell size has been quantitatively clarified.

The mean free path of mobile dislocations in doped NaCl single crystals measured by N.M.R. between room temperature and 300°C

Abstract The mean free path of mobile dislocations has been measured by determining the spin–lattice relaxation rate of deforming NaCl single crystals as a function of temperature and of the concentration of Ca2+ impurities. The latter may influence the magnitude of the mean free path, but this depends to a large extent on the point-defect configuration. The degree of association and the mobility of the point defects has been studied by measuring the spin–lattice relaxation rate without deforming the samples. On the other hand, the distribution of dislocations also varies with temperature, and this affects the mobility of dislocations too. The work-hardening rate of the crystals is compared with the mean free path as a function of temperature, and it is shown that both quantities have extremes under the influence of competitive mechanisms such as an enhanced thermal activation of dislocations at obstacles, an increasing mobility of point defects and an increasing number of intersections of mobile dislocations with dislocation dipoles.

Nuclear Spin Relaxation Investigations on the Influence of Impurities and Temperature on the Mean Free Path of Mobile Dislocations in Nacl

ABSTRACTDislocation motion in alkali halide single crystals is strongly impeded by the presence of impurities, apart from obstacles built by the forest dislocations. The mean free path L of stepwise moving dislocations is measured by determination of the spin-lattice relaxation rate 1/T1ρ as a function of the strain rate έ, varying the content of impurities and the temperature. The latter influences the distribution of the point defects and the activation rate of dislocations before obstacles, while the former merely shorten L, thereby raising 1/T1ρ.

In situ deformation of the [111] aluminum single crystals observed by high voltage electron microscopy

Successive stages of cell formation have been investigated in the [111] aluminium single crystals by in situ deformation in a 3 MV ultra-high voltage electron microscope at 2 MV. Dislocation tangles which include many small dislocation loops are formed homogeneously all over the specimen at the early stage of deformation and all of them develop into cell wall. Mobile dislocations stop exactly at cell walls so that the mean free path of mobile dislocations is determined by the cell size. Flow stresses show a good linear relationship against the inverse of the cell size. Furthermore, shear stresses of both [111] single crystals and polycrystals with various grain sizes obey the same linear relationship against the inverse of cell size. The similarity between flow stresses of the [111] single crystals and polycrystals is discussed on the basis of the results.

The effect of grain size and deformation sub-structure on mechanical properties of polycrystalline aluminum

The effect of grain size on the apparent yield and flow stresses is investigated in polycrystalline aluminum of various grain sizes in the temperature range from 77 to 473°K. The apparent yield stress can always be correlated with the grain size by the Hall-Petch relation. In low temperature deformation at 77–293°K. however, the flow stresses can not be expressed by a simple linearrelation, but are subdivided into two groups characterized by different linear functions of the inverse square root of the grain size. Transition between these two groups always occurs at about 80 μ in grain size. On the other hand, these flow stresses can be expressed by a single linear function of the inverse of the cell size determined by the amount of deformation. Even in high temperature deformation at 373–473°K, deviation from the Hall-Petch relation when only the grain is considered becomes prominent when the strain exceeds about 15 per cent. Furthermore, when the specimens include subgrains in their interior, neither the apparent yield nor the flow stresses satisfy the Hall-Petch relation even when both grain sizes and subgrain sizes are considered. However, in this case, the flow stresses at 20 per cent strain are a linear function of the inverse of the cell size. These results are discussed from a view point of the mean free path of mobile dislocations.