Application of a model for grain boundary sliding to high temperature flow of carrara marble

It has been demonstrated that grain boundary sliding may contribute up to 50 percent of the total strain during experimental, high temperature deformation of Carrara Marble (Schmid, Paterson and Boland, 1980), yet the creep behavior was characterized by a high stress exponent and an apparent thermal dependence related to volume diffusion of carbon in calcite. By adopting the model of Gifkins (1976, 1977) for dislocation accommodated grain boundary sliding, incorporating Nabarro's model of creep by climbing edge dislocations (Weertman, 1975) and using the experimentally determined relationship between stress and subgrain (recrystallized grain) size, a model is developed which fits the high temperature creep data very well. In effect, the model assumes that deformation occurs by a combination of climb of edge dislocations and dislocation accommodated grain boundary sliding. It is shown that the model can be easily and reasonably extended to include creep by climb-controlled dislocation glide.     

Creep in a Cu-14at.%Al solid solution alloy at intermediate temperatures and low stresses

The helicoid spring specimen technique was applied to investigate creep of a Cu-14at.%Al solid solution alloy at homologous temperatures from 0.54 to 0.65 and stresses ranging from 0.2 to 5.0 MPa. At stresses lower than about 1 MPa, Coble-type creep was found to dominate, associated with a threshold stress apparently independent either of grain size or of temperature. At stresses above about 1 MPa, another creep mechanism obviously contributes to the measured creep rate. This mechanism operating in parallel with Coble creep is characterized by the fact that the steady state creep rate is proportional to the second power of stress and inversely proportional to the third power of grain size and is most probably grain boundary diffusion controlled. This mechanism, called the non-viscous mechanism in the present work, is similar to that considered by Gifkins and Kaibyshev et al. to result from the motion of grain boundary dislocations (grain boundary sliding) accomodated by slip of lattice dislocations in thin layers along grain boundaries, although these workers assumed the creep rate to be inversely proportional not to the cube but to the square of the grain size.     

Effects of low- to medium-angle grain boundaries on creep properties of superalloy

The creep properties of Ni-based bicrystal specimens with low- to medium-angle grain boundaries are investigated at 1100°C and 130?MPa with two misorientation angles prepared by double-seed solidification. Experimental results show that the angle of the grain boundary with respect to the stretching direction has a strong effect on creep life. Molecular dynamics simulations show that the effect of the grain boundary on the neighbouring dislocation density is related to the grain boundary angle. A creep constitutive model with the grain boundary angle and the initial damage rate can be adopted to describe the creep damage evolution. The model is then modified according to the molecular dynamics simulation and experimental results to give more accurate predictions of creep life.     

Anisotropy of creep deformation rate in hot-pressed Si3N4 with preferred orientation of the elongated grains

Compressive creep deformation of hot-pressed silicon nitride with two different preorientations of grain was investigated at temperatures in the range of 1300–1400 °C under 30–100 MPa. The stress exponent of the creep rate was determined to be nearly unity of the apparent activation energy of creep rate was found to be about 500 kJ mol^-1. It means the creep deformation is due to diffusion controlled solution/precipitation. Creep rate of specimen with creep loading direction in parallel to the hot-pressing axis was determined to be higher than that in perpendicular to the hot-pressing axis. In addition, microstructural observation revealed that no cavity appeared and grain boundary glass was recrystallized during creep. X-ray diffraction (XRD) analysis confirms that needle-like Si₃N₄ grains were reoriented during creep test. These results indicate that the anisotropy of creep rate results from the disparity in the rate of solution–reprecipitation of grains rather than that in diffusion through the grain boundary, which is dependent on the preferred orientation of the needle-like grains. This revised version was published online in November 2006 with corrections to the Cover Date.     

The role of grain boundary sliding and reinforcement morphology on the creep deformation behaviour of discontinuously reinforced composites

In this study, the role of grain boundary sliding behaviour on the creep deformation characteristics of discontinuously reinforced composites is investigated numerically together with the other influencing parameters: reinforcement aspect ratio, grain size and interfacial behaviour between the reinforcement and the matrix. The results obtained for the composites are compared with results obtained for a polycrystalline matrix material having identical grain size and morphology. The results indicate that, with sliding grain boundaries, the stress enhancement factor for the composites is much higher than the one observed for the matrix material and its value increases with increasing reinforcement aspect ratio, reduction in the matrix grain size and sliding interfacial behaviour between the reinforcement and the matrix. In the composites, the contribution of the grain boundary sliding to overall steady state creep rates occurs in a larger stress range in comparison to the matrix material. Experimentally observed higher creep exponent values or stress dependent creep exponent values for the composites could not be explained solely by the mechanism of grain boundary sliding. However, experimentally observed large scale triple point grain boundary cavitation in the composites could occur due to large grain rotations resulting from grain boundary sliding.     

On Grain Size Dependence of Minimum Creep Rate

The available experimental results have beensummarized concerning the effect of grain size onminimum creep rate.There are two types of creeprate-grain size relations.One is that there is a criti-cal grain size above which creep rate is independentof grain size,below which creep rate increases withthe decrease of grain size.The other is that there isan intermediate grain size at which creep resistanceis optimum.The first relation usually occurs athigher temperatures(>0.5 T_m),and intermediatestress ranges,while the second relation at interme-diate temperature ranges(0.4-0.5 T_m)and higherstresses.For the two types of creep rate-grain sizerelations,the increase of the creep rates with the de-crease of grain size for small grain sizes is all due tograin boundary sliding.For large grain sizes,a dis-location climb mechanism is dominant in creepdeformation for the first relation,while aHall-Perch grain boundary strengthening effect isbelieved to play an important role by dislocationglide mechanism for the second relation.     

Deformation mechanism maps for micro-grained, ultrafine-grained, and nano-grained materials

There are several deformation mechanisms that depend on grain size and are controlled by grain boundary diffusion. These mechanisms include: Coble creep, superplastic flow (micrograin superplastic flow and high-strain rate superplastic flow), and nanograin deformation. By combining the rate-controlling equations of these mechanisms and by making assumptions regarding triple-junction creep, a deformation map based on grain size was constructed. It is demonstrated that this map can account for the locations of experimental data representing three types of deformation behavior: micrograin superplasticity, high-strain rate superplasticity, and nanograin deformation.     

A steady-state model for diffusion-controlled fracture

Elevated temperature cracking associated with embrittlement from intergranular diffusion of impurities is studied using cohesive zone model for small-scale creep, diffusion and damage. The constitutive equation for the cohesive zone is coupled with stress-assisted diffusion of impurities into the grain boundary. A Kachanov-type damage model is used to describe the effect of impurity concentration on grain boundary strength. Numerical studies reveal the influence of various material parameters and loading conditions on the cracking process.     

A theoretical upper limit to Coble creep strain resulting from concurrent grain growth

The rate of diffusional creep varies with grain size x, either as 1/x ² or 1/x ³, depending on whether lattice or grain boundary diffusion is dominating. Since the rate of grain growth is proportional to 1/x ^p, where p1, the creep and grain growth relationships can be combined to predict the transient creep that results from the two processes operating concurrently. An important result is obtained for grain boundary diffusion creep (Coble creep), where two regimes of behaviour are predicted depending on the value of p. For normal grain growth (p=1) and up to a critical value p=2, the transient gives rise to an upper limit to the grain boundary diffusional creep strain. For p>2, no limiting strain is predicted. The role of the limiting strain is discussed in the context of the various experimental attempts that have been made to verify the Coble mechanism.     

基于EBSD技术的P91钢蠕变过程中小角度晶界演化行为表征

在620℃、145 MPa条件下对给定的P91钢进行高温蠕变持久与间断试验,采用电子背散射衍射(EBSD)技术研究其在蠕变过程中小角度晶界的演化行为。通过引入EBSD图像中的取向差分布来表征小角度晶界处(0.5~5°)的边界位错密度,分析了边界位错密度在蠕变过程中与小角度边界的数量、塑性应变以及内部微观组织演化之间的关系。此外,通过改变EBSD像素点与像素点之间的计算步长,探讨了步长选择对边界位错密度计算结果的影响。结果表明,小角度晶界处的位错密度在蠕变过程中先迅速上升,在最小蠕变率处达到极值后缓慢下降,直到最后基本保持不变;同时,EBSD的计算步长越小,得到的位错密度值越准确。     

Creep in pure and two phase nickel-doped alumina

Creep in pure and two phase nickel-doped alumina has been investigated in the stress range 0.70 to 4.57 kgf mm^–2 (1000 to 6500 psi), and temperature range 1450 to 1800° C, for grain sizes from 15 to 45 m (pure alumina) and 15 to 30 um, (nickel-doped alumina). The effect of stress, grain size and temperature on the creep rate suggests that diffusion controlled grain-boundary sliding is the predominant creep mechanism at low stresses and small grain sizes. However, the stress exponents show that some non-viscous boundary sliding occurs even at the lowest stresses investigated. This mechanism is confirmed by metallographic evidence, which shows considerable boundary corrugation in the deformed aluminas. At higher stresses and larger grain sizes the localized propagation of microcracks leads to high stress exponents in the creep rate equation. The nickel dopant, which introduces an evenly distributed spinel second phase into the alumina matrix, increases the creep rate and enhances boundary sliding and localized crack propagation. The weakening effect of the second phase increases with grain size, and tertiary creep occurs at strains of 0.5% and below in large grained material.     

Stress relaxation of thin film due to coupled surface and grain boundary diffusion

A numerical scheme, based on an energy statement, is developed to simulate thin film morphology evolution and stress relaxation due to concurrent surface diffusion and grain boundary diffusion. Different from previously published works, this paper also explores the effects of mobility ratio of the two processes and the dihedral angle at the surface-grain boundary triple junction. The range of mobility ratio, in which the stress relaxation process is limited by either surface diffusion or grain boundary diffusion, is determined. It is found that, when the stress relaxation is limited by the rate of surface diffusion, the dihedral angle at the surface-grain boundary junction plays a significant role. A scheme of using both experimental and numerical results to determine grain boundary diffusivity is also presented. As an example, we obtain the activation energy and diffusivity for grain boundary diffusion in Cu thin film.     

On the initiation of wedge-type cracks at grain-boundary triple junctions during high-temperature creep

The typical grain boundary cracks are often formed at the grain-boundary triple junction as a result of blocking of grain-boundary sliding. However, a theoretical discussion has not fully been made on the nucleation of grain corner cracks at high temperatures where diffusional recovery occurs. In this study, a continuum mechanics model which incorporated the recovery effect by diffusion of atoms has been developed to explain the initiation of wedge-type cracking during high-temperature creep. A good agreement was found between the result of calculation based on this model and experimental results in austenite steels. It was considered that there is a critical creep rate for wedge-type cracking. The model was also applied to the prediction of the rupture life in creep.     

Creep of polycrystalline alumina,pure and doped with transition metal impurities

Grain size effects were used to evaluate the relative contributions of aluminium lattice and oxygen grain boundary diffusion to the high temperature (1350 to 1550° C) steady state creep of polycrystalline alumina, pure and doped with transition metal impurities (Cr, Fe). Divalent iron in solid solution was found to enhance both aluminium lattice and oxygen grain-boundary diffusion. Large concentrations of divalent iron led to viscous Coble creep which was rate-limited entirely by oxygen grain-boundary diffusion. Nabarro-Herring creep which was rate-limited by aluminium lattice diffusion was observed in pure and chromium-doped material. Chromium additions had no effect on diffusional creep rates but significantly depressed non-viscous creep modes of deformation. Creep deformation maps were constructed at various iron dopant concentrations to illustrate the relative contributions of aluminium grain boundary, aluminium lattice, and oxygen grain-boundary diffusion to the diffusional creep of polycrystalline alumina.     

A constitutive model of nanocrystalline metals based on competing grain boundary and grain interior deformation mechanisms

In this work, a viscoplastic constitutive model for nanocrystalline metals is presented. The model is based on competing grain boundary and grain interior deformation mechanisms. In particular, inelastic deformations caused by grain boundary diffusion, grain boundary sliding and dislocation activities are considered. Effects of pressure on the grain boundary diffusion and sliding mechanisms are taken into account. Furthermore, the influence of grain size distribution on macroscopic response is studied. The model is shown to capture the fundamental mechanical characteristics of nanocrystalline metals. These include grain size dependence of the strength, i.e., both the traditional and the inverse Hall–Petch effects, the tension–compression asymmetry and the enhanced rate sensitivity.     

Grain boundary sliding revisited: Developments in sliding over four decades

It is now recognized that grain boundary sliding (GBS) is often an important mode of deformation in polycrystalline materials. This paper reviews the developments in GBS over the last four decades including the procedures available for estimating the strain contributed by sliding to the total strain, ξ, and the division into Rachinger GBS in conventional creep and Lifshitz GBS in diffusion creep. It is shown that Rachinger GBS occurs under two distinct conditions in conventional creep depending upon whether the grain size, d, is larger or smaller than the equilibrium subgrain size, λ. A unified model is presented leading to separate rate equations for Rachinger GBS in power-law creep and superplasticity. It is demonstrated that these two equations are in excellent agreement with experimental observations. There are additional recent predictions, not fully resolved at the present time, concerning the role of GBS in nanostructured materials.     

Microstructure evolution and deformation features of AZ31 Mg-alloy during creep

By means of the measurement of the creep curve and the observation of SEM and transmission electron microscope (TEM), an investigation has been made into the microstructure evolution and deformation features of AZ31 Mg-alloy during high temperature creep. Results show that the deformation features of the alloy in the primary stage of creep are that significant amount of dislocation slips are activated on basal and non-basal planes, then these ones are concentrated into the dislocation cells or walls as creep goes on. At the same time, twinning occurs as an additional deformation mechanism in the role of the compatibility stress. During steady state creep, the dislocation cells are transformed into the subgrains, then, the protrusion and coalition of the sub-boundaries results in the occurrence of dynamic recovery (DRV). After the dynamic recrystallization (DRX), the multiple slips in the grain interiors are considered to be the main deformed mechanism in the later stage of the steady state creep. An obvious feature of creep entering the tertiary stage is that the cracks appear on the locations of the triple junction. As creep continues, the cracks are viscous expanded along the grain boundaries; this is taken for being the fracture mechanism of the alloy crept to failure. The multiple slips in the grain interiors and the cracks expanded viscous along the grain boundary occur in whole of specimens, that, together with the twins and dynamic recrystallization, is responsible for the rapid increase of the strain rate in the later stage during creep.     

Kinetics and Nanostructure Dependence of High Temperature-Low Stress Creep of Al and Al-0.3%Fe

The novel nanostructure of Al and Al-Fe were prepared by ball milling alumina with elemental Fe.The kinetics and nanostructure dependence of high temperature low stress Newtonian creep of Al and Al-0.3%Fe have been investigated and compared with the predications of the Nabarro-Herring(N-H) theory of directional diffusion.A simple theory based on the climb controlled generation of dislocations from a fixed density of sources is developed to explain the observed behavior.The dislocation density increases and subgrains form during the creep.Also,the presence of precipitates of FeAl 3 reduces the creep rate of Al by absolute faster of 100 at the same stress and temperature,in spite of the fact that the grain size in the Al-0.3%Fe alloy is smaller by a factor of about 100 nm.The reduction of grain size to the nanometer scale improves their mechanical properties.Electron diffraction methods combined with transmission electron microscopy(TEM) and scanning electron microscopy(SEM) studies are a convenient and powerful technique for the characterization of the phases and grain structure of the resulting materials.     

Effects of phosphorus on creep behaviour of nickel and Ni–20Cr and on creep and strength of Nimonic 80A

Abstract

The influence of P on the creep behaviour of Ni, Ni–20Cr (wt-%), and Nimonic 80A was investigated by carrying out creep tests under various loads and at different temperatures. After creep fracture the samples were investigated using optical, scanning electron, and transmission electron microscopy. The grain boundary segregation was examined using Auger electron spectroscopy (AES). It was found that P segregates to the grain boundaries in all the materials investigated. The creep rate of Ni–20Cr and Nimonic 80A is decreased by the addition of P. Grain boundary segregation of P and its influence on strength was also investigated using AES for specimens aged between 600 and 700°C after fracture by a tensile test inside an ultrahigh vacuum chamber. Maxima of tensile strength are observed to be time dependent as a result of carbide precipitation, which is affected by the P segregation.

MST/1679     

Self-consistent Constitutive Modeling of the Creep Damage Behaviour of Nickel-base Directionally Solidified Superalloys with Different Grain Orientations

A self consistent creep damage constitutive model is developed for nickel-base directionally solidified superalloys. Grain degradation and grain boundary voiding are considered. The model parameters are determined from the creep test data of single crystal and directionally solidified superalloy with a special grain orientation. The numerical analysis shows that the model creep damage behaviours of nickel-base directionally solidified superalloys with difFerent grain orientations are in good agreement with the experimental data.