Dislocation Diffusion Research Articles

Secondary particles precipitates in Be-Fe alloys

Mossbauer spectra of monocrystalline Be-Fe alloy (0.85 % Fe) were obtained with the use of resonant detector after isothermal annealing at 600 °C for total duration of 2659 hours, and Mossbauer spectra of coarse-grained Be-Fe alloys (0,09-0,80 % Fe) samples were obtained after annealing at 500-600 °C for different durations. The alloys were prepared from the beryllium of different purity. Spectra of phases were fitted by a convolution equation of the three Lorentz lines. The coherent analysis of the solid solution decomposition process by means of the kinetic law classification and the secondary particles precipitate growth processes based on the diffusion models has been implemented. Nucleation on the numerous dislocation clusters and diffusion growth of the FeBe 11 nano-particles are the dominant processes in the analyzed materials. The phase distribution, the incubation period and the diffusion path were obtained. The dependence between the impurity concentration and Mossbauer parameters of the phases is discussed.

Effect of Si and Mn Interactions on the Spheroidization and Coarsening Behavior of Cementite During Annealing in Severe Cold-Drawn Pearlitic Steel

The effects of Si and Mn interactions on the spheroidization and coarsening behavior of cementite during annealing in severe cold-drawn pearlitic steel were studied. Spheroidization of cementite particles annealed at 873 K (600 °C) in heavily cold-drawn pearlitic steel was obviously retarded by higher Si contents. The coarsening kinetics of cementite particles in heavily cold-drawn and annealed pearlite obeyed a power-law relationship. The values of ECD increase steadily according to a temporal dependence of n S87B (0.21 ± 0.02) for S87B and n S87BM (0.23 ± 0.06) for S87BM. The n values lie between 0.20 and 0.25, indicating that cementite particles coarsening occurs through a combination of dislocation diffusion (n = 0.20) controlled and grain boundary diffusion (n = 0.25) controlled coarsening mechanisms. Higher Si content in S87BM led to more pronounced partitioning of Mn than that in S87B, resulting in more significant suppression of alloying elements and lower coarsening rate constant K on the cementite particles coarsening behavior.

Stress-Rupture Strength of Polycrystalline Oxide Ceramic up to 1600°C

Experimental data are given for stress-rupture strength (time and deformation to failure) determination for densely-sintered oxide ceramic with four-point bending in the range 1400 – 1550°C (somewhat above the brittle-ductile transition temperature) and with loads up to 60 MPa (close to the ultimate strength). It is shown that elementary mechanical deformation over the whole range of specimen ductile behavior is diffusion-viscous flow with different forms, i.e., dislocation and crystal boundary diffusion movement. Data obtained agree with the suggestion that for transition from ceramic brittle to ductile failure occurrence of some critical vacancy concentration within it is necessary. Independent of ceramic crystal size and test conditions the secondary creep rate and time to failure are constant, and deformation to failure is also constant.

Theoretical constraints on the isotope effect for diffusion in minerals

Isotopes of the same element generally diffuse at slightly different rates within a mineral, due to the difference in their masses. The magnitude of the mass dependence of the diffusion coefficient depends on the product of the correlation coefficient f (representing the degree to which the diffusion process deviates from a random walk) and the coupling coefficient K (representing the degree to which the motion of an atom during a single jump is coupled to that of other nearby atoms). Whereas K has been found to vary over a relatively narrow range, f can vary over a wide range from ∼0 to 1.Diffusive isotope effects are expected to be large for trace and minor cations that diffuse slowly relative to the major cations that occupy the same sites and diffuse by the same mechanism. Diffusive isotope effects are also expected to be large for elements that diffuse rapidly by a simple interstitial mechanism. In both of these cases, the correlation coefficient is similar to or equal to unity. Diffusive isotope effects are reduced when the diffusion process is correlated, as for (1) rapid diffusion of trace and minor cations by a vacancy mechanism, with a low migration barrier for the jump to a vacancy; (2) diffusion by an interstitialcy process, or a process involving interstitial–vacancy pairs; (3) diffusion in grain boundaries and dislocations, where both dimensional restrictions and non-uniformity of the structure enhance correlation. The correlation coefficient can be determined from independent experimental data on the jump frequencies involved in the diffusion process, and/or from theoretical calculations of the jump energies. Quantitative estimates of the isotope effect are made for several cations in periclase, olivine, magnetite and rutile.

A dislocation kinetic model of the dislocation structure formation in a nanocrystalline material under intense shock wave propagation

A dislocation kinetic model of the formation and propagation of plastic shock waves in nanocrystalline materials (with a grain size of 1–100 nm) at pressures ranging from 1 to 50 GPa has been discussed theoretically. The model is based on a nonlinear equation of the reaction-diffusion type for the dislocation density, which includes the processes of multiplication, annihilation, and diffusion of dislocations with a strong absorption of the dislocations by nanograin boundaries. The solution of this equation is obtained in the form of a traveling dislocation density wave propagating with a constant velocity. The dependences of the dislocation density and dislocation front width on the nanograin size and pressure in the wave are determined. A comparison of the obtained dependences with the available results of the experiments and molecular dynamics simulations of shock-deformed nanocrystalline materials demonstrates their good quantitative agreement.

Grain‐size sensitive rheology of orthopyroxene

AbstractThe grain‐size sensitive rheology of orthopyroxene is investigated using data from rheological and microstructural studies. A deformation mechanism map is constructed assuming that orthopyroxene deforms by two independent mechanisms: dislocation creep and diffusion creep. The field boundary between these mechanisms is defined using two approaches. First, experimental data from Lawlis (1998), which show a deviation from non‐linear power law behavior at low stresses, are used to prescribe the location of the field boundary. Second, a new orthopyroxene grain‐size piezometer is used as a microstructural constraint to the field boundary. At constant temperature, both approaches yield sub‐parallel field boundaries, separated in grain size by a factor of only 2–5. Extrapolating to lithospheric conditions, the deformation mechanism transition occurs at a grain size of ~150–500 µm, consistent with observations from nature. As the transition from dislocation to diffusion creep may promote shear localization, grain‐size reduction of orthopyroxene may play a prominent role in plate‐boundary deformation.

High temperature compressive creep of spark plasma sintered zirconium (oxy-)carbide

The effect of stoichiometry (i.e. carbon and oxygen contents) and microstructure (i.e. micro-sized grains) on creep mechanism of zirconium oxycarbide was considered. The synthesis of ZrCxOy powder of controlled stoichiometry and without impurity has been performed via the carboreduction route. Compressive creep experiments were conducted at 1500–1600°C under applied stresses ranging from 60 to 140MPa on fully dense zirconium oxycarbide specimens obtained by spark plasma sintering. The higher oxygen content composition (i.e. ZrC0.79O0.13) reveals low creep resistance in contrary to ZrC0.94O0.05 composition. The analysis of the creep data shows the existence of a linear creep limit (σt). At low stress (i.e. σ≤σt=100MPa, n≈1, m≈1), the creep mechanism seems to be independent of the chemical composition, and is governed by zirconium volume diffusion. At high stress (i.e. σ≥σt=100MPa, n≈3, m≈0), a power law regime of creep appears. However, the nature of the rate-determining step of creep process depends on stoichiometry. The limiting species for volume diffusion are (i) the metal atom for ZrC0.94O0.05; (ii) and the carbon atom for ZrC0.79O0.13 linked to a Rowcliffe dislocation diffusion mechanism.

Gradient ultrafine-grained titanium: Computational study of mechanical and damage behavior

A computational model of ultrafine-grained (UFG) titanium with random and gradient distribution based on Voronoi tessellation and the composite model of nanomaterials is developed. The effect of grain size, non-equilibrium state of the grain boundary phase (characterized by the initial dislocation density and diffusion coefficient) and gradient of grain sizes on the mechanical behavior and damage initiation of the UFG titanium are studied in numerical experiments. Using computational experiments, the authors determined the likely damage criterion (dislocation-based model) and found several effects that can positively influence the mechanical response and strength of UFG titanium (homogeneity of grain sizes, dispersoids/precipitates in grain boundaries and initial dislocation density in grain boundaries). It is shown that the homogeneous structures of UFG titanium ensure higher yield stress and lower likelihood of damage than gradient structures. The availability of dispersoids or precipitates in UFG titanium changes its damage mechanisms and delays the evolution of damage.

Precipitation behavior in Al-Zn-Mg-Cu alloy after direct quenching

The precipitation behavior in an Al-6.8Zn-1.9Mg-1.0Cu-0.12Zr alloy after direct quenching from solution heat treatment temperature of 470 °C to 205–355 °C was investigated by means of hardness tests, electrical conductivity tests, and transmission electron microscopy. At temperatures below 265 °C, the hardness increased gradually to a peak value and then decreased rapidly with time. At 265 °C, the hardness was almost unchanged within the initial 2000 s and then decreased gradually. At higher temperatures, the hardness decreased slowly with time. The electrical conductivity started to increase after a certain period of time and then tended to maintain a constant value at all temperatures. Microstructure examination indicated heterogeneous precipitation of the η phase at grain boundaries and inside grains during holding at 205 °C and 325 °C. Based on the electrical conductivity data, the precipitation kinetics could be described quite well by the Johnson-Mehl-Avrami-Komolgorov relationship with a n value varying between 0.78 and 1.33. The activation energy was estimated to be about 44.9 kJ/mol, which is close to that expected for a dislocation diffusion mechanism. Time-temperature-transformation diagrams were constructed and the nose temperature ranged from 295 °C to 325 °C.

Reply to comment by P. Olivier on “Preorogenic exhumation of the North Pyrenean Agly Massif (Eastern Pyrenees, France)”

We make this reply to Philippe Oliver's comments on the deformation of the Mesozoic cover of the northern Agly massif.

Modeling of the Plastic Deformation of Polycrystalline Materials in Micro and Nano Level Using Finite Element Method

Recent experiments on polycrystalline materials show that nanocrystalline materials have a strong dependency to the strain rate and grain size in contrast to the microcrystalline materials. In this study, mechanical properties of polycrystalline materials in micro and nanolevel were studied and a unified notation for them was presented. To completely understand the rate-dependent stress-strain behavior and size-dependency of polycrystalline materials, a dislocation density based model was presented that can predict the experimentally observed stress-strain relations for these materials. In nanocrystalline materials, crystalline and grain-boundary were considered as two separate phases. The mechanical properties of the crystalline phase were modeled using viscoplastic constitutive equations, which take dislocation density evolution and diffusion creep into account, while an elasto-viscoplastic model based on diffusion mechanism was used for the grain boundary phase. For microcrystalline materials, the surface-to-volume ratio of the grain boundaries is low enough to ignore its contribution to the plastic deformation. Therefore, the grain boundary phase was not considered in microcrystalline materials and the mechanical properties of the crystalline phase were modeled using an appropriate dislocation density based constitutive equation. Finally, the constitutive equations for polycrystalline materials were implemented into a finite-element code and the results obtained from the proposed constitutive equations were compared with the experimental data for polycrystalline copper and good agreement was observed.

Tensile creep behavior of heat-treated TC11 titanium alloy at 450–550 °C

The effect of heat treatment on the tensile creep behavior of duplex titanium alloy Ti–6.3Al–1.6Zr–3.4Mo–0.3Si (TC11) at 500°C, 300MPa, as well as the tensile creep of heat-treated TC11-2 alloys over the temperature range 450–550°C at stress range 300–450MPa have been investigated in detail, by means of curve measurements and microstructure observation. At 500°C and 300MPa, the TC11 alloys with duplex microstructure exhibited less creep deformation and strain rates than basket-weave microstructure, and heat treatment at condition of 970°C/1h/AC+530°C/6h/AC has the best creep performance. TEM analysis indicates that the creep in duplex structure alloy is controlled by dislocation climb (Metal-type or Class II alloy creep), and changes to a jogged-screw creep model in basket-weave structure. For heat-treated TC11-2 alloy, the corrected activation energies between 65kJ/mol and 188kJ/mol, and stress exponents in the range 1–3.8 were obtained. At 450°C, small apparent stress exponent (equal ∼1) as well as low activation energies suggested that the creep is controlled by double mechanisms of Harper–Dorn dislocation creep and diffusion type creep. At 500°C and 550°C, the higher stress exponents and apparent activation energies indicated that creep is controlled by climb of dislocation. The second phases, mainly (Ti,Zr)5Si3, inhomogeneously precipitated from both primary α grain and α/β lath interface, which has limited effects on hindering the movement of dislocations during creep.

Superplastic HSLA Steels: Microstructure and Failure

Certain materials can show superplasticity when traction tested at temperatures higher than 50% of their melting point and with low strain rates (\( \dot{\varepsilon } \) 100%) without localized necking and mainly intergranular fractures. This behavior requires that the starting grain size is small (<10 μm) so the flow of matter can be non-homogeneous (sliding and rotating of the grain boundaries, accommodated by diffusion). This work presents the superplastic characteristic of shipbuilding steel deformed at 800 °C and a strain rate slower than 10−3 s−1. The fine grain size (5 μm) is obtained when using Nb as a microalloying element and manufactured by controlled rolling processes (three stages). After the superplastic deformation, the steel presents mixed fractures: by decohesion of the hard (pearlite and carbides) and ductile (ferrite) phases and by intergranular sliding of ferrite/ferrite and ferrite/pearlite, just as it happens in stage III of the creep behavior. This is confirmed through the Ashby–Verrall model, according to which the dislocation creep (power-law creep) and diffusion creep (linear-viscous creep) occur simultaneously.

A Creep Model for Solder Alloys

Demand for long-term reliability of electronic packaging has lead to a large number of studies on viscoplastic behavior of solder alloys. Various creep models for solder alloys have been proposed. They range from purely empirical to mechanism based models where dislocation motion and diffusion processes are taken into account. In this study, most commonly used creep models are compared with the test data and implemented in ABAQUS to compare their performance in cycling loading. Finally, a new creep model is proposed that combines best features of many models. It is also shown that, while two creep models may describe the same material stress–strain rate curves equally well, they may yield very different results when utilized for cycling loading. One interesting observation of this study is that the stress exponent, n., also depends on the grain size.

Mechanisms of grain boundary softening and strain-rate sensitivity in deformation of ultrafine-grained metals at high temperatures

Two-dimensional dislocation dynamics and diffusion kinetics simulations are employed to study the different mechanisms of plastic deformation of ultrafine-grained (UFG) metals at different temperatures. Besides conventional plastic deformation by dislocation glide within the grains, we also consider grain boundary (GB)-mediated deformation and recovery mechanisms based on the absorption of dislocations into GBs. The material is modeled as an elastic continuum that contains a defect microstructure consisting of a pre-existing dislocation population, dislocation sources and GBs. The mechanical response of the material to an external load is calculated with this model over a wide range of temperatures. We find that at low homologous temperatures, the model material behaves in agreement with the classical Hall–Petch law. At high homologous temperatures, however, a pronounced GB softening and, moreover, a high strain-rate sensitivity of the model material is found. Qualitatively, these numerical results agree well with experimental results known from the literature. Thus, we conclude that dynamic recovery processes at GBs and GB diffusion are the rate-limiting processes during plastic deformation of UFG metals.

Clarification of high density electronic excitation effects on the microstructural evolution in UO 2

In order to understand the properties of ion tracks and the microstructural evolution under accumulation of ion tracks in UO 2, 100 MeV Zr 10+ and 210 MeV Xe 14+ ions irradiation examinations have been done at a tandem accelerator facility of JAEA-Tokai, and it has been observed the microstructure by means of a transmission electron microscope (TEM) and a scanning electron microscope (SEM) in CRIEPI. Comparison of the diameter of ion tracks between UO 2 and CeO 2 under irradiation with 100 MeV Zr 10+ and 210 MeV Xe 14+ ions at room temperature clarify that the sensitivity on high density electronic excitation of UO 2 is much less than that of CeO 2. By the cross-sectional observation of UO 2 under irradiation with 210 MeV Xe 14+ ions at 300 °C, elliptical changes of fabricated pores that exist till ∼6 μm depth and the formation of dislocations have been observed in the ion fluence over 5 × 10 14 ions/cm 2. The drastic changes of surface morphology and inner structure in UO 2 indicate that the overlapping of ion tracks will cause the point defects, enhance the diffusion of point defects and dislocations, and form the sub-grains at relatively low temperature.

Recommendations for calculating the characteristics of thermal creep of mixed uranium–plutonium oxide fuel when analyzing fuel-element serviceability

Recommendations for calculating the characteristics of thermal creep of mixed uranium‐plutonium oxide fuel when analyzing the serviceability of fuel elements are developed on the basis of a physical model of deformation. The deformation processes in the model include diffusion and diffusion-controlled motion of dislocations. It is shown on the basis of an analysis of the thermodynamics of point defects in ionic crystals that the diffusion of ions in the cationic sublattice is controlled by the vacancy and displacement mechanisms and the coefficient of diffusion depends on the temperature and the oxygen coefficient. The model takes account of the effect of temperature, stress, fuel density, plutonium content, grain size, and oxygen coefficient on the creep rate. The application of physical ideas to obtain computational relations made it possible to improve by more than a factor of 10 the agreement between the calculations and the experimental data as compared with the previously used empirical relations to describe the characteristics of creep. The use of mixed uranium‐plutonium oxide fuel in the fuel elements in power reactors is a necessary condition for adopting a closed fuel cycle and expanding the raw materials resources of nuclear power. Adding to the knowledge base on the properties of mixed fuel is a necessary and important problem for designing fuel elements to be used in power reactors. Recommendations for calculating the characteristics of thermal creep of uranium dioxide are presented in [1]. The objective of the present work is to obtain relations for calculating the characteristics of thermal creep of mixed uranium‐plutonium oxide fuel. Analysis of the experimental data on the thermal creep of mixed fuel has shown that the creep rate is a linear function of the stress for σ≤ 30‐40 MPa. A power law with exponent 4‐5 is observed at high stress levels. The creep rate at low stress is inversely proportional to the squared grain size. Therefore, just as in uranium dioxide [1], the creep rate ξ can be represented in the following form with accuracy to verification coefficients in a wide range of stresses:

Recommendations for calculating the thermal creep properties of uranium dioxide when analyzing fuel-element serviceability

Recommendations for calculating the thermal creep properties of uranium dioxide for fuel element serviceability analysis programs are developed on the basis of a physical model. The deformation processes in the model include diffusion and diffusion-controlled motion of dislocations. It is shown on the basis of the analysis of the thermodynamics of point defects in ionic crystals that the diffusion of ions is controlled by a vacancy mechanism and that the diffusion coefficient depends on the temperature and oxygen coefficient. The model includes the influence of temperature, stress, fuel density, grain size, and oxygen ratio on the creep rate. The relations obtained in the this work have made it possible to improve by approximately a factor of 10 the agreement between the calculations and experimental data as compared with the empirical relation used previously to describe the characteristics of creep.

Evidence for low viscosity garnet-rich layers in the upper mantle

Abstract The rheological properties of upper mantle rocks play an important role in controlling the dynamics of the lithosphere and mantle convection. Experimental studies and microstructures in naturally deformed mantle rocks usually imply that olivine controls the upper mantle rheology. Here we show for the first time evidence from the geometry of folded compositional layers in mantle rocks from Western Norway that garnet-rich rocks can have lower solid-state viscosities than olivine-rich rocks. Modeling of melt-free and dry rheology of garnet and olivine confirms that the reversed viscosity contrast between garnet-rich and olivine-rich layers for this folding event can be achieved over a relatively wide range of temperatures at low stress conditions when the fine-grained garnet deforms by diffusion creep while the coarse-grained olivine deforms by dislocation creep and/or diffusion creep. In general, modeling of the fold viscosity contrast shows that in the stable subcontinental lithospheric mantle or convecting mantle such a reversed viscosity contrast can be formed due to diffusion creep processes in fine-grained garnets in a dry mantle environment or at conditions where the garnet-pyroxene layer is partially molten, i.e. close to solidus–liquidus conditions in the upper mantle. Alternatively in cold plate tectonic settings, e.g. in subduction zones, some water-weakening is a feasible mechanism to create the reversed viscosity contrast between garnet and olivine.

Microstructure-based multiscale modeling of elevated temperature deformation in aluminum alloys

Abstract A multiscale model for predicting elevated temperature deformation in Al–Mg alloys is presented. Constitutive models are generated from a theoretical methodology and used to investigate the effects of grain size on formability. Flow data are computed with a polycrystalline, microstructure-based model which accounts for grain boundary sliding, stress-induced diffusion, and dislocation creep. Favorable agreement is found between the computed flow data and elevated temperature tensile measurements. A creep constitutive model is then fit to the computed flow data and used in finite-element simulations of two simple gas pressure forming processes, where favorable results are observed. These results are fully consistent with gas pressure forming experiments, and suggest a greater role for constitutive models, derived largely from theoretical methodologies, in the design of Al alloys with enhanced elevated temperature formability. The methodology detailed herein provides a framework for incorporation of results from atomistic-scale models of dislocation creep and diffusion.