Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

Effect of Strain Rate on Ductile-to-Brittle Transition Temperature of a Free-Standing Pt-Aluminide Bond Coat

The ductile-to-brittle transition temperature (DBTT) of a free-standing Pt-aluminide (PtAl) bondcoat was determined using the microtensile testing method and the effect of strain rate variation, in the range 10(-5) to 10(-1) s(-1), on the DBTT studied. The DBTT increased appreciably with the increase in strain rate. The activation energy determined for brittle-to-ductile transition, suggested that such transition is most likely associated with vacancy diffusion. Climb of aOE (c) 100 > dislocations observed in analysis of dislocation structure using a transmission electron microscope (TEM) supported the preceding mechanism.

The formation of ultrafine ferrite through static transformation in low carbon steels

A novel approach was used to produce an ultrafine grain structure in low carbon steels with a wide range of hardenability. This included warm deformation of supercooled austenite followed by reheating in the austenite region and cooling (RHA). The ultrafine ferrite structure was independent of steel composition. However, the mechanism of ferrite refinement hanged with the steel quench hardenability. In a relatively low hardenable steel, the ultrafine structure was produced through dynamic strain-induced transformation, whereas the ferrite refinement was formed by static transformation in steels with high quench hardenability. The use of a model Ni–30Fe austenitic alloy revealed that the deformation temperature has a strong effect on the nature of the intragranular defects. There was a transition temperature below which the cell dislocation structure changed to laminar microbands. It appears that the extreme refinement of ferrite is due to the formation of extensive high angle intragranular defects at these low deformation temperatures that then act as sites for static transformation.

Transmission electron microscopy characterization of the bake-hardening behavior of transformation-induced plasticity and dual-phase steels

The effect of prestraining (PS) and bake hardening (BH) on the microstructures and mechanical properties has been studied in transformation-induced plasticity (TRIP) and dual-phase (DP) steels after intercritical annealing. The DP steel showed an increase in the yield strength and the appearance of the upper and lower yield points after a single BH treatment as compared with the as-received condition, whereas the mechanical properties of the TRIP steel remained unchanged. This difference appears to be because of the formation of plastic deformation zones with high dislocation density around the “as-quenched” martensite in the DP steel, which allowed carbon to pin these dislocations, which, in turn, increased the yield strength. It was found for both steels that the BH behavior depends on the dislocation rearrangement in ferrite with the formation of cell, microbands, and shear band structures after PS. The strain-induced transformation of retained austenite to martensite in the TRIP steel contributes to the formation of a complex dislocation structure.

Formation of ultrafine ferrite by dynamic strain-induced transformation

In the current study, the role of dynamic strain induced transformation on ferrite grain refinement was investigated using different thermomechanical processing routes. A Ni-30Fe austenitic model alloy was also employed to study the evolution of the deformation structure under different deformation conditions. It was shown that the extreme refinement of ferrite is more likely due to the formation of extensive high angle intragranular defects in the austenite through deformation. Among the different thermomechanical parameters, the deformation temperature had a significant effect on the intragranular defect characteristics. There was a transition where the cell dislocation structure changed to laminar microband structures with a decrease in the deformation temperature. Moreover, the ultrafine grained structure was also successfully produced through static transformation using warm deformation process; in other words, concurrent deformation and transformation are not necessary for ultrafine ferrite formation.

Plastic flow properties and microstructural evolution in an ultrafine-grained Al-Mg-Si alloy at elevated temperatures

An AA6082 alloy was subjected to eight passes of equal channel angular pressing at 100 °C, resulting in an ultrafine grain size of 0.2 to 0.4 µm. The tensile deformation behavior of the material was studied over the temperature range of 100 °C to 350 °C and strain rate range of 10¯⁴ to 10¯¹ s¯¹. The evolution of microstructure under tensile deformation was investigated by analyzing both the deformation relief on the specimen surface and the dislocation structure. While extensive microshear banding was found at the lower temperatures of 100 °C to 150 °C, deformation at higher temperatures was characterized by cooperative grain boundary sliding and the development of a bimodal microstructure. Dislocation glide was identified as the main deformation mechanism within coarse grains, whereas no dislocation activity was apparent in the ultrafine grains.

Characterization of the bake-hardening behavior of transformation induced plasticity and dual-phase steels using advanced analytical techniques

The bake-hardening (BH) behavior of TRansformation Induced Plasticity (TRIP) and Dual-Phase (DP) steels after intercritical annealing (IA) has been studied using transmission electron microscopy, X-ray diffraction and three dimensional atom probe tomography. It was found for the DP steel that carbon can segregate to dislocations in the ferrite plastic deformation zones where there is a high dislocation density around the "asquenched" martensite. The carbon pinning of these dislocations, in turn, increases the yield strength after aging. It was shown that bake-hardening also leads to rearrangement of carbon in the martensite leading to the formation of rod-like low temperature carbides in the DP steel. Segregation of carbon to microtwins in retained austenite of the TRIP steel was also evident. These factors, in combination with the dislocation rearrangement in ferrite through the formation of cells and microbands in the TRIP steel after pre-straining, lead to the different bake-hardening responses of the two steels.

Substructure and texture development in austenite through thermomechanical processing

The data collection was performed using EBSD and TEM techniques. The objective was to characterise the substructure and crystallographic texture development during dynamic and post-dynamic deformation. The work reveals the role of the initial dislocation structure and texture on the softening characteristics in austenite and how these evolve during softening. It is also shown that the differences in the deformation dislocation structures between the dynamically recrystallized and deformed regions play a major role in determining the extent of recovery. An enhanced static recovery can be seen during post dynamic softening.

The formation of ultrafine ferrite through static transformation in low carbon steels

A novel approach was used to produce an ultrafine grain structure in low carbon steels with a wide range of hardenability. This included warm deformation of supercooled austenite followed by reheating in the austenite region and cooling (RHA). The ultrafine ferrite structure was independent of steel composition. However, the mechanism of ferrite refinement changed with the steel quench hardenability. In a relatively low hardenable steel, the ultrafine structure was produced through dynamic strain induced transformation, whereas the ferrite refinement was formed by static transformation in steels with high quench hardenability. The use of a model Ni-30Fe austenitic alloy revealed that the deformation temperature has a strong effect on the nature of the intragranular defects. There was a transition temperature below which the cell dislocation structure changed to laminar microbands. It appears that the extreme refinement of ferrite is due to the formation of extensive high angle intragranular defects at these low deformation temperature that then act as sites for static transformation. © 2008 World Scientific Publishing Company.

Effects of grain size and microstructure on threshold values and near threshold crack growth in powder-formed Ni-base superalloy

Threshold stress intensity values, ranging from ∼6 to 16 MN m −3/2 can be obtained in powder-formed Nimonic AP1 by changing the microstructure. The threshold and low crack growth rate behaviour at room temperature of a number of widely differing API microstructures, with both ‘necklace’ and fully recrystallized grain structures of various sizes and uniform and bimodal γ′-distributions, have been investigated. The results indicate that grain size is an important microstructural parameter which can control threshold behaviour, with the value of threshold stress intensity increasing with increasing grain size, but that the γ′-distribution is also important. In this Ni-base alloy, as in many others, near threshold fatigue crack growth occurs in a crystallographic manner along {111} planes. This is due to the development of a dislocation structure involving persistent slip bands on {111} planes in the plastic zone, caused by the presence of ordered shearable precipitates in the microstructure. However, as the stress intensity range is increased, a striated growth mode takes over. The results presented show that this transition from faceted to striated growth is associated with a sudden increase in crack propagation rate and occurs when the size of the reverse plastic zone at the crack tip becomes equal to the grain size, independent of any other microstructural variables.

INFLUENCE OF THE 90-DEGREES PARTIAL DISLOCATION CORE STRUCTURE IN SILICON ON ENERGY-LEVELS

An LCAO-scheme taking into account 10 atomic orbitals (s-, p-, and d-type) is used to calculate the electronic structure of the reconstructed 90-degrees partial dislocation in Si. Two different valence force fields producing deviating results are used for modelling the core structure. Geometrical data published by another group is also used. The aim is to explore the influence of geometry on energy levels. We find that the band structure depends sensitively on bond angles. Using data determined by the Tersoff potential we obtain two bands of which the upper one penetrates deeply into the indirect band gap while the geometry minimizing the simple Keating potential leaves the gap completely clear of dislocation states. Thus, from a theoretical point of view, the chief difficulty in calculating the electronic structure of the reconstructed 90-degrees partial is the lack of accurate structural information.