Equilibrium shape of prismatic dislocation loops under uniform stress

The rolling, recrystallization and cooling of AgCl containing 1–5 μm glass spheres generates thermal misfit dislocations. Under stress, prismatic loops elongate in the glide cylinder defined by their line sense and Burgers vector. Using optical microscopy, the shape of dislocation loops under an applied stress of 2.3 MPa is measured. The measurements are corrected for a friction stress of 0.34 MPa and compared with a model which incorporates the orientation dependent line tension (ODLT) of a dislocation. The measured data show considerable scatter; after averaging, good agreement between theory and experiment is obtained.     

Activation volume and density of mobile dislocations in hydrogen-charged iron

In order to monitor the influence of hydrogen on the coupled evolution of dislocation velocity and mobile dislocation density, we applied repeated transients to pure iron under simultaneous hydrogen cathodic charging conditions. The effective activation volume and the thermal stress were determined at different hydrogen concentrations. The effective activation volume decreases immediately with cathodic charging. At high hydrogen concentrations, the activation volume decreases and the thermal stress increases rapidly. The density of mobile dislocations in the hydrogen-charged iron has a lower rate of exhaustion than the hydrogen-free one. The thermal activation energy decreases and the average dislocation velocity increases as a function of hydrogen concentration. Transmission electron microscopy reveals hydrogen-induced tangled dislocations, which indicates a weakening of the repulsive stress field between dislocations.     

Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films

Dislocation dynamics near a free surface and in heteroepitaxial thin films are simulated using an extended version of the nanoscale Phase Field Microelasticity model of dislocations [Acta Mater. 49 (2001) 1847]. The model automatically takes into account the effect of image forces on dislocation motions. In particular, the operations of Frank–Read sources in epitaxial films grown on infinitely thick and relatively thin substrates are investigated. The simulation reveals different misfit dislocation behaviors at the interface. Its implication on the interface susceptibility to crack nucleation is discussed.     

Creep behaviour of a cast TiAl-based alloy for industrial applications

The creep behaviour of a cast TiAl-based alloy with nominal chemical composition Ti–46Al–2W–0.5Si (at.%) was investigated. Constant load tensile creep tests were performed in the temperature range 973–1073 K and at applied stresses ranging from 200 to 390 MPa. The minimum creep rate is found to depend strongly on the applied stress and temperature. The power law stress exponent n is determined to be 7.3 and true activation energy for creep Q is calculated to be 405 kJ/mol. The initial microstructure of the alloy is unstable during creep exposure. The transformation of the α₂(Ti₃Al)-phase to the γ(TiAl)-phase, needle-like B2 particles and fine Ti₅Si₃ precipitates and particle coarsening are observed. Ordinary dislocations in the γ-matrix dominate the deformation microstructures at creep strains lower than 1.5%. The dislocations are elongated in the screw orientation and form local cusps, which are frequently associated with the jogs on the screw segments of dislocations. Fine B2 and Ti₅Si₃ precipitates act as effective obstacles to dislocation motion. The kinetics of the creep deformation within the studied temperature range and applied stresses is proposed to be controlled by non-conservative motion of dislocations.     

小角度非对称倾侧晶界形貌和变形的晶体相场模拟

采用双模晶体相场模型,计算了二维正方相相图,并以正方相为研究对象,在原子尺度上,模拟了小角度非对称倾侧晶界结构及变形过程。结果表明,小角度非对称倾侧晶界由刃型位错和刃型位错组构成;在外加应力作用下,位错先于位错组滑移并进行短程的攀移,最后合并,位错组分离为滑移方向相反的2个刃型位错并最终与其它晶界位错组分离出的异号刃型位错合并,完成晶粒的合并。     

Molecular Dynamics Simulation of the Evolution of Interfacial Dislocation Network and Stress Distribution of a Ni-Based SingleCrystal Superalloy

The evolution of misfit dislocation network at γ/γ' phase interfaces and the stress distribution characteristics of Ni-based single-crystal superalloys under different temperatures of 0,100 and 300 K are studied by molecular dynamics(MD) simulation.It was found that a closed three-dimensional misfit dislocation network appears on the γ/γ' phase interfaces,and the shape of the dislocation network is independent of the lattice mismatch.Under the influence of the temperature,the dislocation network gradually becomes irregular,all[110]dislocations in the y matrix phase emit and partly cut into the γ′ phase with the increase in temperature.The dislocation evolution is related to the local stress field,a peak stress occurs at γ/γ' phase interface,and with the increase in temperature and relaxation times,the stress in the γ phase gradually increases,the number of dislocations in the y phase increases and cuts into γ' phase from the interfaces where dislocation network is damaged.The results provide important information for understanding the temperature dependence of the dislocation evolution and mechanical properties of Ni-based single-crystal superalloys.     

Martensite evolution in a NiTi shape memory alloy when thermal cycling under an applied load

The microstructural evolution of a near equiatomic NiTi shape memory alloy has been studied by in situ synchrotron diffraction, whilst being thermally cycled under an applied load. The martensite texture was found to be cyclically dynamic and an elongation of the sample was observed with each thermal cycle. The martensite formed when cooling under load exhibited progressive variant selection, in an attempt to accommodate the applied stress, accompanied by strain relaxation of the material. The characteristic transformation temperatures were found to decrease with cycling, possibly as a result of the generation and accumulation of dislocations. The magnitude of elongation, variant selection, lattice relaxation and damage accumulation were found to increase as a function of applied stress and their rate decrease with cycle number.     

Strain energy release maximization model for recrystallization textures

In 1995, the author advanced a model for the evolution of recrystallization texture. In the model the absolute maximum internal stress direction due to dislocations generated during deformation or fabrication in the fabricated material is aligned with the minimum Young’s modulus direction in recrystallized grains, whereby the energy release during recrystallization can be maximized. This comes from the fact that material concerned does not change macroscopically its shape and volume during recrystallization, and so the recrystallization is a displacement controlled process. This strain energy release maximization model originates from the presumption that the stored energy due to dislocations is the major driving force for the recrystallization. The absolute maximum internal stress direction may be obtained from the operating slip systems, which are related to the deformation mode and texture. If one slip system is activated, the absolute maximum normal stress direction is parallel to the slip direction, or the Burgers vector direction. If more than one slip system is activated, the absolute maximum normal stress direction can be determined by the vector sum of related slip directions, taking their contribution to slip into account. This paper discusses recrystallization textures of plastically deformed and electrodeposited metals, based on the model. A brief comment was made also on the growth textures of axisymmetrically deformed copper and silver and electrodeposited silver and Fe-Ni alloy. This article is based on a presentation made in the symposium “ ’99 International Symposium on Textures of Materials”, held at Sunchun National University, Sunchun, April 21~22, 1999 under the auspices of The Korean Institute of Metals and Materials and The Research and Development Center for Automobile’s Parts and Materials.     

Work-hardening/softening behaviour of b.c.c. polycrystals during changing strain paths: I. An integrated model based on substructure and texture evolution,and its prediction of the stress–strain behaviour of an IF steel during two-stage strain paths

For many years polycrystalline deformation models have been used as a physical approach to predict the anisotropic mechanical behaviour of materials during deformation, e.g. the r-values and yield loci. The crystallographic texture was then considered to be the main contributor to the overall anisotropy. However, recent studies have shown that the intragranular microstructural features influence strongly the anisotropic behaviour of b.c.c. polycrystals, as revealed by strain-path change tests (e.g. cross effect, Bauschinger effect). This paper addresses a method of incorporating dislocation ensembles in the crystal plasticity constitutive framework, while accounting for their evolution during changing strain paths. Kinetic equations are formulated for the evolution of spatially inhomogeneous distributions of dislocations represented by three dislocation densities. This microstructural model is incorporated into a full-constraints Taylor model. The resulting model achieves for each crystallite a coupled calculation of slip activity and dislocation structure evolution, as a function of the crystallite orientation. Texture evolution and macroscopic flow stress are obtained as well. It is shown that this intragranular–microstructure based Taylor model is capable of predicting quantitatively the complex features displayed by stress–strain curves during various two-stage strain paths.     

Discrete dislocation plasticity modeling of short cracks in single crystals

The mode-I crack growth behavior of geometrically similar edge-cracked single crystal specimens of varying size subject to both monotonic and cyclic axial loading is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The fracture properties are specified through an irreversible cohesive relation. Under monotonic loading conditions, with the applied stress below the yield strength of the uncracked specimen, the initiation of crack growth is found to be governed by the mode-I stress intensity factor, calculated from the applied stress, with the value of K_init decreasing slightly with crack size due to the reduction in shielding associated with dislocations near a free surface. Under cyclic loading, the fatigue threshold is ΔK-governed for sufficiently long cracks. Below a critical crack size the value of ΔK_I at the fatigue threshold is found to decrease substantially with crack size and progressive cyclic crack growth occurs even when K_max is less than that required for the initiation of crack crack growth in an elastic solid. The reduction in the fatigue threshold with crack size is associated with a progressive increase in internal stress under cyclic loading. However, for sufficiently small cracks, the dislocation structure generated is sparse and the internal stresses and plastic dissipation associated with this structure alone are not sufficient to drive fatigue crack growth.     

Simulations of stress-induced twinning and de-twinning: A phase field model

Twinning in certain metals or under certain conditions is a major plastic deformation mode. Here we present a phase field model to describe twin formation and evolution in a polycrystalline fcc metal under loading and unloading. The model assumes that twin nucleation, growth and de-twinning is a process of partial dislocation nucleation and slip on successive habit planes. Stacking fault energies, energy pathways (γ surfaces), critical shear stresses for the formation of stacking faults and dislocation core energies are used to construct the thermodynamic model. The simulation results demonstrate that the model is able to predict the nucleation of twins and partial dislocations, as well as the morphology of the twin nuclei, and to reasonably describe twin growth and interaction. The twin microstructures at grain boundaries are in agreement with experimental observation. It was found that de-twinning occurs during unloading in the simulations, however, a strong dependence of twin structure evolution on loading history was observed.     

Micromechanics-based strain hardening model in consideration of dislocation-precipitate interactions

A micromechanics-based model to predict yield strength and plastic work hardening is proposed. To simplify the problem, additional strengthening by dislocation-dislocation interaction is assumed to be related only to the resistance to the motion of dislocations by uniformly distributed precipitates. The interaction between the mobile dislocations and precipitate particles is facilitated in a physically based approach. The main parameters of the proposed model are the size and strength of the precipitate under different aging conditions and microstructural parameters along with the stress state around the idealized precipitate. For verification purposes, the proposed hardening model was calibrated with previously published data and applied to the prediction of the yield stress and flow curve for precipitated alloys under different aging conditions. In particular, the existence of a transient region in the hardening rate from positive to negative could be reproduced well.     

Effect of climb on dislocation mechanisms and creep rates in γ′-strengthened Ni base superalloy single crystals: A discrete dislocation dynamics study

Creep of single-crystal superalloys is governed by dislocation glide, climb, reactions and annihilation. Discrete three-dimensional (3D) dislocation dynamics (DDD) simulations are used to study the evolution of the dislocation substructure in a γ/γ′ microstructure of a single-crystal superalloy for different climb rates and loading conditions. A hybrid mobility law for glide and climb is used to map the interactions of dislocations with γ′ cubes. The focus is on the early stages of creep, where dislocation plasticity is confined to narrow γ channels. With enhancing climb mobility, the creep strain increases, even if the applied resolved shear stress is below the critical stress required for squeezing dislocations into the γ channels. The simulated creep microstructure consists of long dislocations and a network near the corners of the γ′ precipitate in the low-stress regime. In the high-stress regime, dislocations squeeze into the γ channels, where they deposit dislocation segments at the γ/γ′ interfaces. These observations are in good agreement with experimentally observed dislocation structures that form during high-temperature and low-stress creep.     

Improvement of the creep resistance of FeCo–2V alloy arising from a small addition of Cr

This work presents our recent findings that a small addition (0.5 at. %) of Cr to FeCo–2V alloy leads to a great improvement in creep resistance. High resolution electron microscopy was applied to study microstructural evolution of the Cr added alloy during the creep process performed at 600 °C under 200 MPa. At an initial step of the creep, there appear plate-like precipitates with bcc/fcc structure as well as some rod-like ones with hcp structure. A coherent relationship is identified between the precipitates and bcc FeCo matrix. With prolonging the creep, the rod-like hcp precipitates are revealed to remain in the bcc matrix, showing a good stability under the creep condition and in turn resulting in piling-up of dislocations to a great extent around the precipitates. In addition, the Cr added alloy is shown to have a large stress exponent of 8.4, indicating a strong interaction between dislocations and the hcp precipitates.     

Correlation Between the Microstructural Defects and Residual Stress in a Single Crystal Nickel-Based Superalloy During Different Creep Stages

The present work attempts to reveal the correlation between the microstructural defects and residual stress in the single crystal nickel-based superalloy, both of which play the significant role on properties and performance. Neutron diffraction was employed to investigate the microstructural defects and residual stresses in a single crystal (SC) nickel-based superalloy, which was subjected to creeping under 220 MPa and 1000 °C for different times. The measured superlattice and fundamental lattice reflections confirm that the mismatch and tetragonal distortions with c/a?>?1 exist in the SC superalloy. At the initially unstrained state, there exists the angular distortion between γ and γ’ phases with small triaxial compressive stresses, ensuring the structural stability of the superalloy. After creeping, the tetragonal distortion for the γ phase is larger than that for the γ’ phase. With increasing the creeping time, the mismatch between γ and γ’ phases increases to the maximum, then decreases gradually and finally remains unchanged. The macroscopic residual stress shows a similar behavior with the mismatch, indicating the correlation between them. Based on the model of shear and dislocations, the evolution of microstructural defects and residual stress are reasonably explained. The effect of shear is dominant at the primary creep stage, which greatly enlarges the mismatch and the residual stress. The dislocations weaken the effect of shear for the further creep stage, resulting in the decrease of the mismatch and relaxation of the residual stress. Those findings add some helpful understanding into the microstructure-performance relationship in the SC nickel-based superalloy, which might provide the insight to materials design and applications.     

Anomalous plastic flow of cerium near the isomorphic phase transformations under high hydrostatic pressure

Compression tests have been carried out on cerium specimens at room temperature (0.27T_m) under high hydrostatic pressures up to 1.2 GPa. A strong increase of the yield strength was observed for both isomorphic γ and α phases at pressures approaching the γ↔α isomorphic phase transformations. That increase was in good agreement with the theory of dislocations when the dependence of elastic properties and a lattice parameter of cerium on pressure was applied to calculate the effect of pressure on the yield stress controlled by the edge dislocations. An anomalous strong decrease of the yield stress was observed in both γ and α phases in the vicinity of both γ↔α phase transformations. That phenomenon was explained as an effect of pressure induced new phase atoms through spreading the cores of edge dislocations. A complete disappearance of work hardening in both γ and α phases was also observed in the wide range of pressures. The influence of hydrostatic pressure on the energy of grain boundaries of both phases was considered to be responsible for that property. The ratio of the grain boundary energy to the Peierls energy is suggested to be a criterion of the work hardening ability of f.c.c. polycrystals.     

Characterization of creep properties and creep textures in pure aluminum processed by equal-channel angular pressing

High-purity aluminum was processed by equal-channel angular pressing (ECAP) and then tested under creep conditions at 473 K. The results show conventional power-law creep with a stress exponent of n = 5 which is consistent with an intragranular dislocation process involving the glide and climb of dislocations. It is demonstrated that diffusion creep is not important in these tests because the ultrafine grains produced by ECAP are not stable at this temperature. Texture measurements were undertaken using the high-pressure preferred orientation neutron time-of-flight diffractometer and they reveal significant differences in the evolution of texture during creep in pressed and unpressed specimens. These experimental measurements of texture are in excellent agreement with theoretical textures predicted using a visco-plastic self-consistent model that limits deformation to plastic slip. The calculations provide additional confirmation that creep occurs through an intragranular dislocation process.     

Dissociated dislocations in confined plasticity

The influence of the dissociation of dislocations when plasticity is localized in small volumes is illustrated for the case of γ/γ′ superalloys. Dissociated dislocations constrained to move through channels present three different types of behavior. Dislocation dynamic simulations in a face-centered cubic crystal show these three types of behavior and give the conditions under which a dissociated dislocation can move through a channel bordered by impenetrable obstacles. We show that a partial dislocation needs a lower stress for its motion than a perfect one in a significant domain of stress orientations. The consequences of the uncorrelated motion of one of the partials, leading to the formation of large stacking faults, are also examined.     

Low-angle grain boundary migration in the presence of extrinsic dislocations

We investigated the migration of a symmetric tilt, low-angle grain boundary (LAGB) under applied shear stress in the presence of extrinsic dislocations. The results demonstrate that there is a threshold stress for the LAGB to depin from extrinsic dislocations. Below the threshold stress, the LAGB remains immobile at zero dislocation climb mobility, while for finite climb mobilities, it migrates at a velocity that is directly proportional to the applied stress, with a proportionality factor that is a function of misorientation, dislocation climb mobility and extrinsic dislocation density. We derive analytical expressions for the LAGB mobility and threshold stress for depinning from extrinsic dislocations. The analytical prediction of the LAGB mobility is in excellent agreement with the simulation as well as experimental results. We discuss the implications of these results for understanding the migration of general grain boundaries.     

Dislocation evolution in epitaxial multilayers and graded composition buffers

This paper presents models to describe the dislocation dynamics of strain relaxation in an epitaxial uniform layer, epitaxial multilayers and graded composition buffers. A set of new evolution equations for nucleation rate and annihilation rate of threading dislocations is developed. The dislocation interactions are incorporated into the kinetics process by introducing a resistance term, which depends only on plastic strain. Both threading dislocation nucleation and threading dislocation annihilation are characterized. The new evolution equations combined with other evolution equations for the plastic strain rate, the mean velocity and the dislocation density rate of the threading dislocations are tested on Ge_xSi_1−x/Si(100) heterostructures, including epitaxial multilayers and graded composition buffers. It is shown that the evolution equations successfully predict a wide range of experimental results of strain relaxation and threading dislocation evolution in the materials system. Meanwhile, the simulation results clearly signify that the threading dislocation annihilation plays a vital role in the reduction of threading dislocation density.