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.

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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.

     

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.

     

Creep crack growth by grain boundary cavitation: crack tip fields and crack growth rates under transient conditions

Transient creep crack growth due to grain boundary cavitation, and under plane strain and small scale creep conditions, is investigated. Full account is taken of the finite geometry changes accompanying crack tip blunting and 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, distributed on a given density of cavitating grain boundary facets. Our analyses show the competing effects of stress relaxation due to creep, diffusion and crack tip blunting, and the stress increase due to crack growth. Another outcome of our analyses is the crack growth rate under various conditions of loading and for various values of material properties and for various characterizations of the failure process. Prior to crack growth, Hutchinson-Rice-Rosengren type singular fields dominate over the crack tip region, outside of a finite strain zone that has dimensions of the order of the crack opening displacement. These singular fields scale with the path integral C(t), which to a good approximation decays as K _I ²/t, with t being the elapsed time since load application and K _Ithe imposed stress intensity factor. When the crack growth rate is faster than the growth rate of the creep zone, our finite element results show that Hui-Riedel singular fields dominate over the crack tip region and the magnitude of the Hui-Riedel fields scales with the crack growth rate. For a crack that grows more slowly than the creep zone, Hutchinson-Rice-Rosengren type fields dominate over the crack tip region. In these circumstances, the crack growth rate is found to scale as C(t) to a power. Regardless of which of the two singular fields dominates for the growing crack, finite strain effects are found to be significant over a size scale of the order of the crack opening displacement at crack growth initiation. The effect of increased mesh refinement is also considered and very little mesh dependence is found.

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Résumé On étudie la croissance d'une fissure en fluage transitoire, associée à la cavitation aux frontières des grains, sous des conditions d'état plan de déformation et de fluage à petite échelle. On tient compte des modifications finies de géométrie accompagnant l'arrondisement de l'extrémité de la fissure, et le matériau suit une loi de fluage elasto-parabolique, avec une contribution additionnelle à la vitesse de fluage venant d'une densité donnée de facettes de joints de grains comportant de la cavitation. On suppose que toutes les cavités sont présentes dès le début, et qu'elles sont distribuées selon une densité déterminée de ces facettes. L'analyse montre les effets rivaux d'une relaxation des contraintes associée au fluage, à la diffusion et à l'arrondisement des extrémités de fissure, et d'une augmentation de contraintes due à la croissance de fissure. Un autre résultat de l'analyse est l'établissement de la vitesse de croissance de la fissure sous diverses conditions de mise en charge, pour diverses valeurs des propriétés du matériau, et pour divers modes de caractérisation du processus de rupture. Avant croissance de la fissure, ce sont des champs singuliers de type Hutchinson-Rice-Rosengren (HDR) qui prédominent sur la région de l'extrémité de la fissure, à l'extérieur d'une zone de déformations finies dont la taille est de l'ordre de grandeur du COD. Ces champs singulier sont proportionnels à l'intégrale de parcours C(t) laquelle, avec une bonne approximation, s'atténue en fonction de K _I ²/t, où t est le temps qui s'est écoulé depuis la mise en charge et K _Ile facteur d'intensité de contraintes imposés. Lorsque la vitesse de croissance de la fissure dépasse la vitesse de croissance de la zone en fluage, les résultats de l'analyse par éléments finis montre que ce sont les champs singuliers de Hui-Riedel qui prédominent sur la zone de l'extrémité de la fissure, et que l'amplitude de ces champs est proportionnelle à la vitesse de croissance de la fissure. Pour une fissure qui croit moins vite que la vitesse de fluage, es champs de type HRR sont prédominants et on trouve que la vitesse de croissance de la fissure est proportionelle C(t) à une certaine puissance. Quel que soit le type de champs singulier qui détermine la croissance de la fissure, on trouve que les effets de déformation finies sont significatifs sur une échelle de dimension de l'ordre du COD à l'amorçage de la fissuration. On considère également l'effet d'un affinage plus important du réseau, et l'on trouve me très faible dépendance par rapport à ce paramètre.

     

A creep rupture model accounting for cavitation at sliding grain boundaries

An axisymmetric cell model analysis is used to study creep failure by grain boundary cavitation at facets normal to the maximum principal tensile stress, taking into account the influence of cavitation and sliding at adjacent inclined grain boundaries. It is found that the interaction between the failure processes on these two types of adjacent facets reduces the failure time significantly when cavitation is creep constrained. In all cases the time to cavity coalescence on transverse facets appears to be a useful lower bound measure of the material life-time. Sliding at the boundaries of the central grain of the cell model is accurately represented; but in some computations a stress enhancement factor is used to incorporate also the effect of sliding between surrounding grains. The influence of grain boundary viscosity is included in the model and it is found that even in the absence of sliding, cavitation on inclined boundaries may significantly reduce the failure time.     

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.     

Engineering grain boundary sliding and cavitation effects in superplastic alloys employing thermodynamics

Plastic deformation by grain boundary sliding in superplastic alloys is described by a novel thermostatistical approach. The Gibbs free energy for cavity formation at moving grain boundaries is obtained. It equals the competition between the stored energy at the boundaries and the energy dissipated by grain boundary sliding. The latter is approximated by an entropy term induced by moving dislocations to facilitate boundary displacement. Strength loss evolution is estimated from the cavity evolution rate. The theory describes superplastic behaviour of Zn22Al, Zn21Al2Cu and Mg3Al1Zn for various temperatures, strain rates, grain sizes, and specimen geometries. Transition maps are defined for finding the optimal conditions for achieving superplastic behaviour in terms of composition, temperature, geometry and strain rate.     

Crack trapping effect of persistent grain boundary islands

In the polycrystalline Fe–Si alloy, when a cleavage front transmits from one grain to another, it first penetrates stably across the grain boundary at a number of breakthrough points (BTPs) that distribute along the front quasi‐periodically. As the critical energy release rate is reached, unstable crack jump occurs and the persistent grain boundary islands (PGBI) between the BTPs are left behind the verge of propagating, bridging across the crack flanks, which leads to a 10–30% increase in fracture resistance. In this article, this process is investigated through an energy analysis. The influence of the size/spacing ratio of PGBI on the grain boundary toughness is discussed in detail.     

The Measurement of Compressive Creep Deformation and Damage Mechanisms in a Single-Phase Alumina Part II Correlation of creep cavitation and grain boundary sliding

It has been theorized that stochastic grain boundary sliding (GBS) is the primary driving force for the nucleation, growth, and coalescence of cavities located on the grain boundaries of polycrystalline ceramics undergoing creep. This paper reports on the results of co-ordinated measurements of both GBS and creep cavitation during the creep of a single-phase alumina. Constant compressive stress creep experiments were performed at a temperature of 1600 °C, and stress levels of 70, 100, and 140 MPa. Small angle neutron scattering measurements (SANS) show that cavities nucleate continuously due to creep at all three stress levels, and that since negligible cavity growth was measured, creep cavitation appears to be ruled by a nucleation rather than a growth process. Also, at a constant creep temperature, the number and volume of cavities measured was observed to decrease with a decrease in the applied stress. GBS displacements reported in Part 1 of this paper [1] are related to the number of cavities nucleated per unit volume and shown to relate directly, thereby providing experimental evidence that GBS may act as the driving force for creep cavitation.     

Irradiation induced grain boundary flow-a new creep mechanism at the nanoscale

A new mechanism of irradiation enhanced creep is proposed for nanocrystalline materials. It derives from local relaxations within the grain boundaries as they absorb point defects produced by irradiation. The process is studied by inserting point defects into the grain boundaries and following the materials response by molecular dynamics. Calculated creep compliances are found in good agreement with those measured in dilute nanocrystalline Cu-W alloys [Tai, K.; Averback, R. S.; Bellon, P.; Ashkenazy Y. Scr. Mater.2011, 65, 163]. The simulations provide a direct link between irradiation induced creep in nanocrystalline materials with radiation-induced viscous flow in amorphous materials, suggesting that grain boundaries in these materials can be treated as an amorphous phase. We provide a simple analytic model based on this assumption that reproduces the main features of the observed creep rates, a linear dependence on stress, inverse dependence of grain size, a weak dependence on temperature, and a reasonable estimate of the absolute creep rate.     

Computer simulation of grain growth by grain boundary migration during liquid phase sintering

From many experiments with mixtures of small and large particles, it can be concluded that during liquid phase sintering, smaller particles partially dissolve and a solid phase precipitates on the larger particles. Therefore, the number of smaller particles decreases due to coarsening. The growth rate can be controlled either by the solid-liquid phase boundary reaction or by diffusion through the liquid phase. This dissolution-reprecipitation process leads to further densification by rearrangement of smaller and larger particles. The microstructure may change either by larger particles growing during the Ostwald ripening process or by shape accommodation. In this study, two-dimensional simulation of grain growth by grain boundary migration based on such a physical and corresponding numerical modeling of liquid phase sintering was considered. The simulation method developed is based on the defined submodels for model system definition, for solution-precipitation, and for grain coarsening process.     

Cavity growth and grain boundary sliding in polycrystalline solids

A basic method is presented for the estimate of the overall mechanical response of solids which contain periodically distributed defects (inhomogeneities, regions undergoing inelastic flow, voids, and inclusions). This method is then applied to estimate the shape and growth pattern of voids that are periodically distributed over the grain boundaries in a viscous matrix. The interaction effects are fully accounted for, and the results are compared with calculations for a single void in an infinitely extended viscous solid, by Budiansky, Hutchinson, and Slutsky. Then, for a polycrystalline solid that undergoes relaxation by grain boundary sliding, the relaxed moduli are obtained, again fully accounting for the interaction effects. Finally, the overall inelastic nonlinear response at elevated temperatures is discussed in terms of a model which considers nonlinear power law creep within the grains, and linear viscous flow in the grain boundaries.     

Impact of grain boundary junctions on grain growth in polycrystals with different grain sizes

Effect of finite mobility of triple and quadruple grain boundary junctions on grain growth is studied by numerical simulation. They retard the growth process and transform its kinetics from parabolic one into a sequence consisting of exponential, linear and parabolic steps. This relates even to polycrystals with large initial grain sizes. Such junctions can contribute to microstructure stabilization in nanomaterials.     

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.