Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ～±10^?4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L¹ optimisation method. A lower bound estimate for the noise on the GND density determination is ～±10¹² m^?2 for a 200-nm step size, and near the indent densities as high as 10¹⁵ m^?2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ～±10¹⁴m^?2 for the GND density.     

Precipitate assemblies formed on dislocation loops in aluminium-silver-copper alloys

The precipitation microstructure of the γ′ (AlAg₂) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-90at.Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ′ phase formed assemblies with a two-dimensional, open arrangement of precipitates. Each such assembly contained two variants of the γ′ phase alternately arranged to form a faceted elliptical unit. The θ′ (Al₂Cu) phase formed on these assemblies after further ageing. Each assembly was formed via repeated precipitation of the γ′ phase on dissociated segments of a single dislocation loop. This faceted elliptical assembly has not been previously reported for the γ′ precipitate. The difference between the precipitation behaviour of the γ′ phase in Al-Ag and Al-Ag-Cu alloys was attributed to copper modifying the as-quenched defect structure of the matrix. The formation of faceted elliptical γ′ phase assemblies clarifies earlier observations on the precipitate number density and mechanical properties of aluminium-silver-copper alloys.     

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks under loads at infinity was investigated. General solutions of complex potentials to this problem were derived by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the shear modulus and the distance between the two cracks, but it decreases with the increase of dislocation azimuth and the distance between the dislocation and the cruciform crack tip. The critical loads at infinity for dislocation emission increase with the increment of the emission angle, the distance the two cracks and the vertical length of the cruciform crack.     

Determination of the activation energy by stochastic analyses of molecular dynamics simulations of dislocation processes

An investigation is reported of the probability and the probability density of thermal activation of stress-driven dislocation processes, as simulated using molecular dynamics (MD). Stochastic analyses of the survival probability are found to lead to simple relationships between the loading history and the distribution of the interaction time and strength. It is shown that the determination of the activation energy associated to a thermally activated event can be achieved by a reduction of the stochastic process to a process obeying the Poisson's distribution, preserving the activation probability at the survival time. The method is applied to the kink-pair mechanism for screw dislocations in iron. Predictions are compared with experimental results and with other methods reported in the literature, which allows the difference in the approximations and in the assumptions considered in these models to be underlined.     

Microstructure evolution during severe plastic deformation

Radiotracer diffusion studies of severely deformed, ultra-fine grained materials have revealed the presence of ultra-fast transport paths, which include “non-equilibrium” grain boundaries and free volume. Under some experimental conditions, percolating porosity is produced even in pure copper. Micro-cracks may form in metals, if the local maximum shear stress exceeds the shear yield stress. However, their growth and propagation is postponed till late in the deformation process owing to the ductility of metals, the hydrostatic component of the stress system and/or dynamic recovery/recrystallization. In other words, crack growth and propagation is present only when the scope for further deformation is highly restricted. Using this approach, the load required for equal channel angular pressing, the change in the slope of the Hall–Petch plot with decreasing grain size and the theoretical limit for the smallest grain size attainable in a metal in a severe plastic deformation process are predicted and validated by experimental results. Experimentally successful prevention of percolated crack formation by the superposition of a hydrostatic pressure is also accounted for using this model.     

Continuum model for dislocation dynamics in a slip plane

In this paper, we present a continuum model for dislocation dynamics in a slip plane, which accurately incorporates both the long-range interaction and the local line tension effect of dislocations. Unlike the continuum models in the literature using dislocation densities, we use the disregistry across the slip plane to represent the continuous distribution of dislocations in the slip plane, which has the advantage of including the orientation dependence of dislocations in a very simple way. The continuum dislocation dynamics model is validated by linear instability analysis of a uniform dislocation array to small perturbations and comparisons of the results with those of the discrete dislocation dynamics model. Numerical examples for the evolution of distributions of dislocations and plastic slips in a slip plane are presented.     

Dislocation emission from a crack under mixed mode loading studied by molecular statics

The dislocation emission surface in (k _I,?k _II,?k _III) space is calculated by means of atomistic simulations for the {111}?110? crack in Al. For each relevant combination of loading mode, the precise nature of the dislocations and of the emission process are determined. When appropriate, the analytic formulas proposed by Rice are used by calculating the unstable stacking energy including the effect of the mixed mode loading. Quantitative agreement with the full atomistic calculation is found in the case where dislocations glide in the crack plane. This clearly identifies when and how ab initio data can be introduced in the calculation.     

Analysis of slip activity and heterogeneous deformation in tension and tension-creep of Ti–5Al–2.5Sn (wt %) using in-situ SEM experiments

The deformation behavior of a Ti–5Al–2.5Sn (wt %) near-α alloy was investigated during in-situ deformation inside a scanning electron microscope. Tensile experiments were performed at 296?K and 728?K (≈0.4?T _m), while tensile-creep experiments were performed at 728?K and 763?K. Active deformation systems were identified using electron backscattered diffraction-based slip trace analysis. Both basal and prismatic slip systems were active during the tensile experiments. Basal slip was observed for grains clustered around high Schmid factor orientations, while prismatic slip exhibited less dependence on the crystallographic orientation. The tension-creep experiments revealed less slip but more development of grain boundary ledges than in the higher strain rate tensile experiments. Some of the grain boundary ledges evolved into grain boundary cracks, and grain boundaries oriented nearly perpendicular to the tensile axis formed ledges earlier in the deformation process. Grain boundaries with high misorientations also tended to form ledges earlier than those with lower misorientations. Most of the grain boundary cracks formed in association with grains displaying hard orientations, where the c-axis was nearly perpendicular to the tensile direction. For the tension-creep experiments, pronounced basal slip was observed in the lower-stress creep regime and the activity of prismatic slip increased with increasing creep stress and temperature.     

Ordinary dislocation configurations in high Nb-containing TiAl alloy deformed at high temperatures

Abstract

High Nb-containing TiAl (Nb–TiAl) alloys possess mechanical properties at elevated temperatures superior to conventional TiAl alloys. However, the strengthening mechanisms induced by Nb addition have been discussed controversial for a long time. In the present study, the dislocation structures in a polycrystalline high Nb–TiAl alloy after tensile tests at 700 and 900 °C were investigated by transmission electron microscope (TEM) observation. The results show that abundant double cross slip of ordinary dislocations is activated in the samples deformed at 700 °C. The dislocations are pinned at the jogs and numerous dipoles are observed. Debris can be commonly observed in the vicinity of screw dislocations. Trace analysis shows that the cross-slip plane is (1?1?0)γ at 700 °C but (1?1?1)γ octahedral plane at 900 °C. Three-dimensional (3D) dislocation structures, caused by cross-slip and annihilation of ordinary dislocations, were observed along the screw orientation. The dipoles and debris produced by high-temperature cross slip can be important for the strengthening of high Nb–TiAl alloys.