Crystal plasticity-based constitutive modelling of irradiated bcc structures

A constitutive crystal plasticity model is proposed and developed for the inelastic deformation of irradiated bcc ferritic/martensitic steels. Defects found in these irradiated materials are used as substructure variables in the model. Insights from lower length- and time-scale simulations are used to frame the kinematic and substructure evolution relations of the governing deformation mechanisms. Models for evolution of mobile and immobile dislocations, as well as interstitial loops (formed due to irradiation), are developed. A rate theory-based approach is used to model the evolution of point defects generated during irradiation. The model is used to simulate the quasi-static tensile and creep response of a martensitic steel over a range of loading histories.     

On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot–Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach–Koehler stress equation, Peach–Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.     

Dislocation glide through non-randomly distributed point obstacles

Abstract

Classical meso-scale models for dislocation–obstacle interactions have, by and large, assumed a random distribution of obstacles on the glide plane. While a good approximation in many situations, this does not represent materials where obstacles are clustered on the glide plane. In this work, we have investigated the statistical problem of a dislocation sampling a set of clustered point obstacles in the glide plane using a modified areal-glide model. The results of these simulations show two clear regimes. For weak obstacles, the spatial distribution does not matter and the critically resolved shear stress is found to be independent of the degree of clustering. In contrast, above a critical obstacle strength determined by the degree of clustering, the critical resolved shear strength becomes constant. It is shown that this behaviour can be explained semi-analytically by considering the probability of interaction between the dislocation line and obstacles at a given level of stress. The consequences for alloys exhibiting solute clustering are discussed.     

Contrast analysis of Shockley partial dislocations in 4H-SiC observed by synchrotron Berg–Barrett X-ray topography

Shockley partial dislocations in 4H-SiC were observed using monochromatic synchrotron X-ray topography with a grazing-incidence Bragg-case geometry, that is, Berg–Barrett topography. The contrast of partial dislocations at the edges of Shockley-type stacking faults is discussed in terms of whether they have C- or Si-core edge components, or screw components. The dissociated state of basal-plane dislocation is discussed on a basis of the stacking sequence for basal-planes in the 4H-SiC crystal structure. It is expected that the results obtained in this study will be useful for characterizing Shockley-type stacking faults in Berg–Barrett topography.     

Dislocation content of geometrically necessary boundaries aligned with slip planes in rolled aluminium

Previous studies have revealed that dislocation structures in metals with medium-to-high stacking fault energy, depend on the grain orientation and therefore on the slip systems. In the present work, the dislocations in eight slip-plane-aligned geometrically necessary boundaries (GNBs) in three grains of near 45° ND rotated cube orientation in lightly rolled pure aluminium are characterized in great detail using transmission electron microscopy. Dislocations with all six Burgers vectors of the ½?1?1?0? type expected for fcc crystals were observed but dislocations from the four slip systems expected active dominate. The dislocations predicted inactive are primarily attributed to dislocation reactions in the boundary. Two main types of dislocation networks in the boundaries were identified: (1) a hexagonal network of the three dislocations in the slip plane with which the boundary was aligned; two of these come from the active slip systems, the third is attributed to dislocation reactions (2) a network of three dislocations from both of the active slip planes; two of these react to form Lomer locks. The results indicate a systematic boundary formation process for the GNBs. Redundant dislocations are not observed in significant densities.     

HRTEM and HAADF-STEM tomography investigation of the heterogeneously formed S (Al2CuMg) precipitates in Al–Cu–Mg alloy

The distribution of variants and three-dimensional (3D) configurations of the heterogeneously formed S (Al₂CuMg) precipitates at dislocations, grain boundaries and the Al₂₀Cu₂Mn₃ dispersoid/Al interfaces were studied in this research. By means of high resolution transmission electron microscopy, we systematically investigated the orientation relationships (ORs) between these heterogeneously formed S precipitates and the Al matrix, and further unraveled that the preferred orientation of S variants at grain boundaries and at dispersoid/Al interfaces are respectively associated with the OR between the precipitate habit plane and the grain boundary plane, and the OR between the precipitate habit plane and the interface plane. The inherent characteristic of the crystal structure of the S phase, i.e. the symmetry of the pentagonal subunit, was considered to be the fundamental factor determining the preference of the variant pair. By using high angle annular dark field scanning transmission electron microscopy tomography, we successively obtained the 3D reconstruction of the S precipitates at these defects. Both the morphology of an individual S precipitate and the overall configuration of the S precipitates nucleated at these defects can be clearly observed without misunderstandings induced by the overlap and projection effects of the conventional two-dimensional methods.     

Electron channelling contrast imaging of dislocations in a conventional SEM

Abstract

Dislocations in shock loaded tantalum single crystals were imaged using both transmission electron microscope (TEM) and electron channelling contrast image (ECCI) in a scanning electron microscope with a conventional backscattered electron detector. The results were compared with backscattered electron intensity profiles across dislocations calculated via the dynamic theory of electron diffraction. A one-to-one correspondence between ECCI and TEM is established. High voltage and low index reflections should be used to obtain the highest dislocation contrast and greatest imaging depth.     

The gauge theory of dislocations: conservation and balance laws

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding J , L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.     

Nucleation of the titanium α and β phases. in situ study of the dislocation role by synchrotron X-ray topography

This “in situ” and real time study is an approach to the role of matrix dislocations in the nucleation of the α or β phases in titanium single crystals. When the dislocations interact, forming tangles, subboundaries…, the residual stresses, present at the transformation temperature, trigger the new phase. If the dislocations are isolated at the transformation temperature they are destabilized by the large crystalline anisotropy resulting from the vibrational entropy dependence with the temperature. These dislocations disappear and do no act as preferential nucleation sites.