Deformation of fine-grained alumina by grain boundary sliding accommodated by slip

Creep data from over 40 different polycrystalline alumina materials are reviewed. Most of these studies have attempted to describe the creep data using models based on diffusional creep. In the present paper, however, it is concluded that the dominant deformation mechanism in creep of fine-grained alumina is grain boundary sliding (GBS) accommodated by slip. The slip accommodation process is related to the sequential steps of dislocation glide and climb. When the accommodation process for GBS is that of dislocation climb, the stress exponent is always 2. In this case, the activation energy for creep is either that for oxygen ion diffusion in the lattice or that for oxygen ion diffusion in the grain boundary. When the accommodation process for GBS is that of solute-drag dislocation glide, the stress exponent is 1. For this case, the activation energy is that for solute diffusion at the dislocation site during glide.     

Plastic deformation behaviour of fine-grained materials

A phase mixture model in which a polycrystalline material is regarded as a mixture of a crystalline phase and a grain-boundary phase is presented. The model aims to describe the plastic deformation behaviour of fine-grained materials. The mechanical properties of the crystalline phase are modelled using unified viscoplastic constitutive relations, which take dislocation density evolution and diffusion creep into account. The total strain rate of a crystallite is calculated by summation of the contributions of dislocation, boundary diffusion and lattice diffusion mechanisms. The deformation mechanism for the grain-boundary phase is modelled as a diffusional flow of matter through the grain boundary. Using a simple rule of mixtures, the grain size dependence of the overall plastic deformation behaviour of the material is analysed. Rate effects are also investigated. The results of the calculations are compared with previously published experimental data.     

Kinetics of diffusional creep discussed by energy dissipation and effect of grain-size distribution on the rate equations

The kinetics of diffusional creep of polycrystals is examined using an energy balance method. In the steady state of diffusional creep, work done by an applied stress is considered to be dissipated as heat by sliding of grain boundaries and diffusion of atoms. Describing the sliding and diffusion as Somigliana's dislocations on grain boundaries, the rate equations for Coble creep and Nabarro–Herring creep are derived by using this energy balance. The energy consideration adopted in the present study is simple and enables us to grasp the physics of diffusional creep. Using the energy consideration, we also discuss the effects of grain-size distribution in polycrystals on the rate equations, which have not been treated in previous studies.     

Dependence of strain rate sensitivity upon deformed microstructures in nanocrystalline Cu

The creep behavior of nanocrystalline copper was experimentally characterized with nanoindentation using two sequential regimes, i.e., loading and holding. Significantly enhanced strain rate sensitivity was found within an unusually narrow range of creep rate in the holding regime, which is attributed to the deformed microstructure generated during the loading regime. By quantitatively analyzing the creep rate and rate sensitivity exponent of NC Cu in the holding regime, both the grain boundary sliding (GBS) and dislocation activities are found to be responsible for the observed abnormal behavior, with the contribution of GBS decreasing with increasing grain size and increasing with decreasing loading strain rate. These findings provide a potential way of adjusting the mechanical properties of nanocrystalline metals by pre-straining.     

Colossal anelasticity in polycrystals deforming under conditions of diffusional creep

Since diffusional creep viscosity depends strongly on the grain size, a variability in the grain size in a polycrystal can generate significant internal stresses. Upon unloading, the non-uniform internal stresses recover, leading to anelastic strains. The anelastic strains can be very large, approaching 100 times the elastic strains. We solve the case of bimodal viscosity in closed form to highlight the features of this type of anelasticity. The results are compared to the anelastic behavior of two-phase superplastic alloys. In such alloys the spatial variability in the diffusional viscosity can arise from the variability in the activation energy of grain boundary diffusion, which, because of its Arrhenius nature, can produce a much higher degree of variability than the grain size.     

Creep deformation mechanisms in fine-grained niobium

Creep rates in fine-grained Nb were measured at 600 °C using free-standing Cu/Nb polycrystalline multilayered foils. For specimens with layer thicknesses ranging from 0.5 to 5 μm and Nb grain sizes ranging from 0.43 ± 0.05 to 1.87 ± 0.13 μm, two distinct regimes were observed. At high stresses, the stress dependence, grain size dependence and activation energy for creep are consistent with power-law creep, with an average stress exponent of 3.5. At low stresses, creep rates exhibited a linear dependence on stress and an inverse linear dependence on grain size. A model is presented for a vacancy generation-controlled creep mechanism, whereby deformation rates are controlled by the rate of vacancy generation at or near grain boundaries, not by their diffusion. The proposed model is consistent with experimental observations of stress and grain size dependence, as well as the measured activation energy for creep.     

Interpretation of viscous deformation of Zr-based bulk metallic glass alloys based on Nabarro-Herring creep model

Superplastic-like viscous deformation of bulk metallic glass alloys around the glass transition temperature (Tg) was analyzed based on the Nabarro-Herring creep model, a classical creep model, where the diffusional motion of atoms or vacancies through the lattice (atomic configuration) is considered. The amorphous matrix of bulk metallic glasses that has a randomly-packed atomic configuration was assumed to behave in a manner similar to the grain boundary in polycrystalline metals so as to approximate the diffusivity of the major constituent element. In spite of rough approximation of the parameters in the Nabarro-Herring creep equation, a reasonable value of the diffusion path (d) could be obtained from the experimentally-obtained metal flow data, including the steady state stress and the strain rate. Due to the absence of vacancy sources such as grain boundaries in homogeneous metallic glasses, the diffusion path, which, in polycrystalline materials, generally is the average distance between vacancy sources such as grain boundaries, was considered in this work as the average distance between tunneling centers in bulk metallic glass alloys. The calculated diffusion path was comparable to the density of tunneling centers around Tg, proposed by M. H. Cohen and G. S. Grest based on free volume theory. The calculated diffusion path showed monotonous decrease with temperature over Tg for Zr-based bulk metallic glass alloys. Based on this analysis, a schematic model for viscous deformation of bulk metallic glass was proposed.     

Constitutive relations for determining the critical conditions for dynamic recrystallization behavior

A series mathematical model has been developed for the prediction of flow stress and microstructure evolution during the hot deformation of metals such as copper or austenitic steels with low stacking fault energies, involving features of both diffusional flow and dislocation motion. As the strain rate increases, multiple peaks on the stress-strain curve decrease. At a high strain rate, the stress rises to a single peak, while dynamic recrystallization causes an oscillatory behavior. At a low strain rate (when there is sufficient time for the recrystallizing grains to grow before they become saturated with high dislocation density with an increase in strain rate), the difference in stored stress between recrystallizing and old grains diminishes, resulting in reduced driving force for grain growth and rendering smaller grains in the alloy. The final average grain size at the steady stage (large strain) increases with a decrease in the strain rate. During large strain deformation, grain size reduction accompanying dislocation creep might be balanced by the grain growth at the border delimiting the ranges of realization (field boundary) of the dislocation-creep and diffusion-creep mechanisms.     

Effects of grain growth on grain-boundary diffusion creep by molecular-dynamics simulation

Molecular-dynamics simulations are used to elucidate the effects of grain growth on grain-boundary diffusion creep and grain-boundary sliding during high-temperature deformation of a nanocrystalline Pd model microstructure. The initial microstructure consists of a 25-grain polycrystal with an average grain size of about 15 nm and a columnar grain shape. Prior to the onset of significant grain growth, the deformation proceeds via the mechanism of Coble creep accompanied by grain-boundary sliding. While grain growth is generally known to decrease the creep rate due to the increase of the average grain size, the results obtained in this study reveal an enhanced creep rate at the onset of the grain growth, when rapid grain-boundary migration occurs. The enhanced creep rate is shown to arise from topological changes during the initial growth phases, which enhance both the stress-induced grain-boundary diffusive fluxes and grain-boundary sliding. Dislocations generated as a result of grain-rotation-induced grain coalescence and grain-boundary decomposition in the vicinity of certain triple junctions also contribute to the deformation.     

Grain size effects during creep of copper

Results for copper single crystals and polycrystals, analysed with data for other metals and alloys, contradict the assumption that dislocation creep processes are grain size independent so the creep rate increases rapidly with decreasing grain diameter only when diffusional mechanisms are dominant at low stresses.     

Viscous Flow of Copper at High Temperatures

Changes in length of copper foils of varying thickness and grain size were measured under such conditions of low stress and high temperature that it is believed that creep was predominately the result of interboundary diffusion of the type recently discussed by Conyers Herring. The surface tension of copper was calculated and results confirmed previous work within the limits of experimental error. Under the assumption of viscous flow, viscosities were calculated as a function of temperature and grain size. Predictions of the Nabarro-Herring theory of surface grain boundary flow were borne out fully and the Herring theory of diffusional viscosity is strongly supported.     

Creep and stress relaxation in free-standing thin metal films controlled by coupled surface and grain boundary diffusion

An analytical solution is presented that interprets the effects of grain size, surface and grain boundary diffusivities, surface and grain boundary free energies, as well as grain boundary grooving on the creep rate in free-standing polycrystalline thin metal films. The Coble creep in the film plane is also taken into account; this has a significant effect on the creep rate of the film. The effects of diffusion ratio and free energy ratio between surface and grain boundary on film agglomeration are illustrated as well. A closed-form expression for stress relaxation in films under constrained strain conditions is derived from this solution. An exponential decay in stress is found as a function of the film microstructure. Results predicted by the solution are shown to be in agreement with the experiments.     

The high temperature tensile and compressive deformation characteristics of magnesia doped alumina

The mechanical characteristics of alumina have not yet been characterized completely in tension due in part to strain hardening accompanying grain growth and premature cavitation failure. Tensile tests were conducted on fine grained magnesia doped alumina over a range of strain rates, grain sizes and temperatures to evaluate the stress exponent, inverse grain size exponent and activation energy. Constant stress compression creep tests were also carried out under a similar range of experimental conditions. Extensive microstructural characterization after deformation indicated that there was considerable grain growth during deformation; however, the grains retained their initially equiaxed structure after significant deformation. Although a standard plot of strain rate versus stress indicated a stress exponent of ∼2, a complete analysis including the compensation of data for concurrent grain growth revealed that true stress exponent was ∼1, consistent with diffusion creep. It is argued that grain rearrangement processes accompanying grain growth will tend to mask the development of an elongated grain structure predicted by diffusion creep processes. In contrast to several ceramics with a significant amount of glassy phase, there is no significant difference between the elevated temperature tensile and compressive behavior of alumina.     

Internal stress plasticity due to chemical stresses

Internal stress plasticity occurs when a small external stress biases internal mismatch strains produced by, e.g., phase transformation or thermal expansion mismatch. At small applied stresses, this deformation mechanism is characterized by a deformation rate which is proportional to the applied stress and is higher than for conventional creep mechanisms. In this work, we demonstrate the operation of internal stress plasticity due to internal chemical stresses produced by chemical composition gradients. We subject specimens of β-phase Ti-6Al-4V to cyclic charging/discharging with hydrogen (by cyclic exposure of specimens to gaseous H₂), under a small external tensile stress. As expected for internal stress plasticity, the average strain rate during chemical cycles at 1030°C is larger than for creep at constant composition (hydrogen-free or -saturated), and a linear stress dependence is observed at small applied stresses. Additionally, we present an analytical model which couples elastic and creep deformation with a transient diffusion problem, wherein the diffusant species induces swelling of the host lattice. Without the use of any adjustable parameters, the model accurately predicts both the observed strain evolution during hydrogen cycling of Ti-6Al-4V and the measured stress dependence of the deformation.     

Reappraisal of grain boundary diffusion creep equations for nanocrystalline materials

Grain boundary diffusion creep equations developed previously for nanocrystalline materials were reappraised in order to elicit further understanding of plastic deformation of these materials in relation to grain boundary diffusion. From a mechanistic viewpoint, the strain rate is inversely proportional to the second power of the grain size when the grain size is refined to the same order of the grain boundary thickness. The presence of the threshold stress appears to be inherent, as a relatively large volume fraction of the grain boundary region is associated with irregularities.     

Atomistic simulations of diffusional creep in a nanocrystalline body-centered cubic material

Molecular dynamics (MD) simulations are used to study diffusion-accommodated creep deformation in nanocrystalline molybdenum, a body-centered cubic metal. In our simulations, the microstructures are subjected to constant-stress loading at levels below the dislocation nucleation threshold and at high temperatures (i.e., T > 0.75T_melt), thereby ensuring that the overall deformation is indeed attributable to atomic self-diffusion. The initial microstructures were designed to consist of hexagonally shaped columnar grains bounded by high-energy asymmetric tilt grain boundaries (GBs). Remarkably the creep rates, which exhibit a double-exponential dependence on temperature and a double power-law dependence on grain size, indicate that both GB diffusion in the form of Coble creep and lattice diffusion in the form of Nabarro–Herring creep contribute to the overall deformation. For the first time in an MD simulation, we observe the formation and emission of vacancies from high-angle GBs into the grain interiors, thus enabling bulk diffusion.     

Diffusionally accommodated interfacial sliding in metal-silicon systems

The kinetics and mechanism of diffusionally accommodated interfacial sliding (interfacial creep) under far-field shear and normal stresses was studied, based on diffusion-bonded Al-Si-Al sandwich specimens. A previously developed interfacial creep law [Funn and Dutta, Acta Mater 1999; 47: 149], which proposed that interfaces may slide via interface-diffusion controlled diffusional creep, was experimentally validated by carrying out a systematic parametric study. In agreement with the model, the Si-Al interfaces slid via diffusional creep (n = 1) under the influence of an effective shear stress, which depends on the far-field shear and normal stresses, as well as the interfacial topography. Compressive stresses acting normal to the interface lowered the effective shear stress, resulting in a threshold effect, thus reducing the sliding rate. The rate of sliding was controlled by diffusional mass transport through a thin amorphous, O-rich interfacial layer, under the influence of local interfacial stress gradients, which arose due to the topological features of the interface. Instances of interfacial sliding in the absence of interfacial de-cohesion, which have been noted in composites, thin-film systems, etc., may be explained by the present mechanism, which also offers an alternative rationalization of threshold behavior during diffusional flow (besides interface-reaction control).     

AZ31B镁合金板材中晶界滑移的晶体塑性仿真

建立一种耦合滑移、动态再结晶以及晶界滑移的晶体塑性模型以仿真镁合金的高温变形行为及织构演化.首先,通过实验测量单轴拉伸、压缩后的织构以及显微组织演化,研究AZ31B镁合金在300°C的变形机制.结果发现,动态再结晶在应变小于0.2时起到细化晶粒的作用,之后晶界滑移在变形过程中起显著作用.此外,建立晶界滑移模型来评估由晶...     

The effect of grain boundary character distribution on the high temperature deformation behavior of Ni–16Cr–9Fe alloys

The objective of this work was to test the Thaveeprungsriporn model for the dependence of creep rate on the coincident site lattice (CSL) fraction. The model attributed the large reduction in creep rate in alloys with a high population of CSL boundaries to the greater difficulty of extrinsic grain boundary dislocation (EGBD) absorption at coincident site lattice boundaries (CSLBs) vs. high angle boundaries (HABs). Ease of EGBD absorption was assessed by measuring the annihilation rates of EGBDs in both CSL-related and HABs following an anneal at 360 °C. Results showed that EGBDs are annihilated at HABs at a rate that is on average three times that at CSLBs, implying a grain boundary diffusion coefficient in CSLBs that is 12 times lower than that in HABs. The expectation that a reduction in EGBD absorption would lead to greater matrix hardening was investigated using nano-hardness measurements. Results showed that the hardness in the vicinity of CSLBs is greater than that near HABs, and the grain-averaged hardness increases with the fraction of contiguous CSLBs. Further, strain hardening is greater in CSL-enhanced samples than in reference, solution annealed samples. These results taken together substantiate the hypothesis that CSLBs impede dislocation absorption into the grain boundary, thereby increasing lattice hardening and internal stress in the sample, resulting in a reduced creep rate.     

Molecular dynamics study of diffusional creep in nanocrystalline UO2

We present the results of molecular dynamics (MD) simulations to study high-temperature deformation of nanocrystalline UO₂. In qualitative agreement with experimental observations, the oxygen sublattice undergoes a structural transition at a temperature of about 2200 K (i.e. well below the melting point of 3450 K of our model system), whereas the uranium sublattice remains unchanged all the way up to melting. At temperatures well above this structural transition, columnar nanocrystalline model microstructures with a uniform grain size and grain shape were subjected to constant-stress loading at levels low enough to avoid microcracking and dislocation nucleation from the grain boundaries (GBs). Our simulations reveal that in the absence of grain growth, the material deforms via GB diffusion creep (also known as Coble creep). Analysis of the underlying self-diffusion behavior in undeformed nanocrystalline UO₂ reveals that, on our MD timescale, the uranium ions diffuse only via the GBs, whereas the much faster moving oxygen ions diffuse through both the lattice and the GBs. As expected for the Coble-creep mechanism, the creep activation energy agrees well with that for GB diffusion of the slowest-moving species, i.e. the uranium ions.