Diffusive relaxation of stress concentrations at grain boundary cavities in elevated temperature creep

This work deals with certain aspects of elevated temperatures creep cavitation of grain boundaries under cyclic and rapidly applied loading. The response of partially damaged materials (where damage is represented as crack-like cavities on the grain boundaries) following load alterations at temperatures in the vicinity of 0.5 T_m or higher is analyzed. The interaction between grain boundary diffusion and elastic deformation is important in alleviating local stress concentrations under these conditions. The stress levels considered are assumed to be low enough that plastic deformation is significant. Diffusive processes contribute to high temperature creep rupture by material redistribution from the void surfaces to the grain boundaries, and any non-uniform matter accommodation along the grain boundaries is accomplished by elastic deformation under the conditions assumed. The same material redistribution mechanism dominates in the stress relaxation process. The analysis of the stress and displacement fields is based on consideration of the coupled elasticity-diffusion boundary value problem, which leads to an integral equation. On the basis of the solution obtained, the detailed analysis of the process under cyclic, step and ramp loadings is given. For suddenly applied loading the results demonstrate that the elastic stress concentration is effectively relaxed by diffusion after t = 0.05τ where $\text{τ ≈}\text{L}{}^3\text{DE}$, L is half of the distance between adjacent tips of neighboring cracks along the grain boundary, E is Young's modulus, and D is diffusion parameter relating volumetric flux along the grain boundary to the stress gradient. By t = 0.25τ the stress distribution becomes essentially identical to that calculated for rigid grains, i.e. diffusion has become the dominant process and elastic deformability of the adjoining grains is then irrelevant.     

On the relation between creep cavitation and grain boundary orientation

• 1.1. The influence of grain boundary inclination on the creep cavity nucleation rate and the cavity growth rate has been studied using SEM and a stereo microscopy technique in a CuSb alloy.
• 2.2. Both the cavity growth rate and the cavity nucleation rate were found to be higher on transvers boundaries.
• 3.3. A possible explanation for the higher nucleation rate on boundaries by stochastic grain boundary sliding has been proposed.

     

Analysis of creep crack growth by grain boundary cavitation

Intergranular creep crack growth in metals at high temperatures is analysed by assuming that the crack advances when cavities coalesce on grain boundary facets approximately normal to the maximum principal tensile stress. The analyses are based on a material model that describes the nucleation and growth of grain boundary cavities, accounting for diffusive growth as well as growth by dislocation creep of the surrouding grains, and also incorporating the effect of grain boundary sliding. Plane strain center cracked panels are analysed by a numerical method that fully accounts for the development of damage in every point of the specimen, and the solutions are compared with crack growth rates predicted by a simple model based on the singular stress fields around the tip of a sharp crack. The development of crack growth rates and the general crack growth patterns predicted by this material model are determined for a range of material parameters, including cases where failure occurs at small strains as well as cases where failure occurs at large strains.

---

Résumé On analyse la croissance d'une fissure de fluage intergranulaire dans les métaux à hautes températures en supposant que la fissure progresse lorsque s'effectue une coalescence de cavités sur les faces des frontières de grains, dans une direction sensiblement normale par rapport à la tension principale maximum. L'analyse est basée sur un modèle de matériau qui décrit la nucléation et la croissance des cavités aux frontières des grains. tenant compte à la fois d'une croissance diffusive et d'une croissance associée au fluage des grains voisins, et incorporant les effets de glissement des frontières de grain. On analyse des panneaux à fissure centrale en état plan de déformation à l'aide d'une méthode numérique qui tient compte au développement de l'endommagement en chaque point de l'éprouvette. On compare les solutions avec les vitesses de propagation de fissure dérivées d'un modèle simple basé sur les champs de contraintes singulières règnant autour de l'extrémité d'une fissure aiguë. Le développement des vitesses de croissance d'une fissure, et l'aspect général de la propagation d'une fissure prédits par ce modèle ont été établis pour une large gamme de paramètres de matériau, et en considérant aussi bien les cas où se produit une rupture sous de faibles déformations, que les cas où de grandes déformations sont requises.

     

Dissolution kinetics of nanoscale liquid Pb/Bi inclusions at a grain boundary in aluminum

In situ transmission electron microscopy is used to study dissolution of liquid single-phase Pb/Bi inclusions attached to a grain boundary in an alloy of Al_99.29Pb_0.65Bi_0.06 at temperatures of 343, 370, and 389 °C, respectively. The initial size of the inclusions was smaller than 60 nm. Dissolution of the inclusions was observed until their complete disappearance. Digitized video recordings of the process of dissolution were used to obtain the dependence of the inclusion size with time. The kinetics of the dissolution of the grain boundary inclusions can be described with a model where it is assumed that grain-boundary diffusion of Pb and Bi is the controlling mechanism. The high value (2.3 eV) of the apparent activation enthalpy of dissolution indicates that the process is likely governed by the large negative enthalpies of solubility of Pb and Bi in Al.

---

Surface and interior measurements of grain boundary sliding during creep

Measurements of grain boundary sliding have been made on polycrystalline specimens of Magnox AL80, a magnesium-0.78 wt% aluminium alloy, at successive strains during creep at 200° C under a stress of 2800 psi. Three independent methods were used to determine the strain due to sliding ( _gb) at the surface and two to determine _gbin the interior of the specimens. The one direct method of measuring _gbin the interior used oxide markers introduced by extruding a composite billet. The values of _gbobtained from the offsets in these interior markers were found to agree with those given by the three sets of measurements made on the surface, but not with those from the indirect method for the interior which relies on the measurement of grain strain via grain shape changes.     

The interplay between osteoblast functions and the degree of nanoscale roughness induced by grain boundary grooving of nanograined materials

From the perspective of osseointegration, nanograined/ultrafine-grained (NG/UFG) metals provide surfaces that are different from conventional coarse-grained (CG) polycrystalline metals because of the high fraction of grain boundaries. We describe here the interplay between the cellular response and grain boundary grooving as a potential approach to enhance osteoblast functions and facilitate the biomechanical interlocking and anchorage. This is accomplished by making a relative comparison of osteoblast response of NG/UFG grains electrochemically grooved to different depths to induce different degree of nanoscale roughness with planar NG/UFG surfaces, under identical biological environment. Electrochemically grooved NG/UFG structures indicated significant attachment and proliferation, and consequently enhanced modulation of cellular response that was significantly different from planar (non-grooved) NG/UFG substrate. Consistent with cell attachment and proliferation, immunofluorescence microscopy and computational analysis indicated stronger vinculin signals associated with actin stress fibers in the outer regions of the cells and cellular extensions on electrochemically-grooved NG/UFG substrates. These observations are indicative of accelerated response of cell-substrate interaction and activity. The behavior is attributed to average nanoscale roughness and high surface hydrophilicity of the nanoengineered surface.     

Size and shape effects on creep and diffusion at the nanoscale

In this paper, we have investigated the size and shape effects on creep and diffusion phenomena at the nanoscale. From a classical thermodynamic model, the higher diffusion of nanostructures is explained. As creep is particularly due to diffusion processes, it is therefore important to consider it at the nanoscale. Therefore, to be able to control creep in the nanoworld, temperature and stress thresholds, taking into account the size and shape of the nanostructure, are defined.     

Crack growth by grain boundary cavitation in the transient and extensive creep regimes

Crack growth due to cavity growth and coalescence along grain boundaries is analyzed under transient and extensive creep conditions in a compact tension specimen. Account is taken of the finite geometry changes accompanying crack tip blunting. The material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset and distributed on a given density of cavitating grain boundary facets. The evolution of the stress fields with crack growth under three load histories is described in some detail for a relatively ductile material. The full-field plane strain finite element calculations show the competing effects of stress relaxation due to constrained creep, diffusion and crack tip blunting, and of stress increase due to the instantaneous elastic response to crack growth. At very high crack growth rates the Hui-Riedel fields dominate the crack tip region. However, the high growth rates are not sustained for any length of time in the compact tension geometry analyzed. The region of dominance of the Hui-Riedel field shrinks rapidly so that the near-tip fields are controlled by the HRR-type field shortly after the onset of crack growth. Crack growth rates under various conditions of loading and spanning the range of times from small scale creep to extensive creep are obtained. We show that there is a strong similarity between crack growth history and the behaviour of the C(t) and C _t parameters, so that crack growth rates correlate rather well with C(t) and C _t .A relatively brittle material is also considered that has a very different near-tip stress field and crack growth history.Visiting Professor, Brown University, August 1988 through December 1989.     

Effect of dopants on alumina grain boundary sliding: implications for creep inhibition

We investigate by means of periodic density functional theory the mechanism of grain boundary sliding along the α-alumina Σ11 tilt grain boundary. We identify minimum and maximum energy structures along a preferential sliding pathway for the pure grain boundary, as well as for grain boundaries doped with a series of early transition metals, as well as barium, gadolinium, and neodymium. We predict that the segregation of those dopants results in a considerable increase in the grain boundary sliding barrier. Grain boundary sliding occurs by a series of bond breaking and forming across the grain boundary. Our results suggest that the presence of large cations inhibits the regeneration of bonds during sliding, which results in a decrease in total number of bonds across the grain boundary interface, thereby raising the barrier to sliding. Trends in predicted grain boundary sliding energies are in good agreement with recently measured creep activation energies in polycrystalline alumina, lending further credence to the notion that grain boundary sliding plays a dominant role in alumina creep.     

A new model for radiation-induced grain boundary segregation with grain boundary movement in concentrated alloy system

We have developed a new model for radiation-induced grain boundary migration (RIGM) and radiation-induced segregation (RIS) for austenitic iron-chromium-nickel alloy system. It was assumed that the RIS was induced by diffusional and annihilation processes of excess point defects at the grain boundary, and the RIGM occurred due to rearrangement process of atoms on one of the interfacial planes by annihilation of point defects. The calculated results indicated that the region of RIS was enlarged by the RIGM and asymmetrical concentration profiles were observed around the migrated grain boundary. The present model could explain the RIS behavior with or without grain boundary migration as comparing with our previous experimental results.     

A new computer model of grain boundary segregation

Improvements have been made to an earlier model of grain boundary segregation. The new model includes an influx of vacancies into the region of the material considered by the model, and accounts for the effect of a grain boundary on defect-binding energies. The model predictions for boron segregation in steel are compared with the original model.