Thermal cavity nucleation at intergranular inclusions in high temperature creep

The role of intergranular inclusions at the thermal cavity nucleation in high temperature creep is analysed in detail. The theoretical treatment is generalized for cavities the free surface curvature radius of which is comparable with the inclusion size and for cavities forming with inclusions the equilibrium systems. Special attention is devoted to the influence of the interface energies, the inclusions volume and the internal stress concentrations to the cavity nucleation kinetics. Each kinetics of cavity nucleation observed is qualitatively explained on the basis of the thermally activated heterogeneous cavity nucleation at intergranular inclusions.     

Dislocation nucleation at metal-ceramic interfaces

The ductile vs brittle behaviour of metal-ceramic interfaces is discussed within an atomistic framework, in which the mechanical response of an interfacial crack is assumed to be ultimately controlled by the competition between atomic decohesion and dislocation nucleation ahead of the crack tip. As in later versions of the Rice-Thomson model, this competition may be evaluated in terms of the parameters G_cleave, the energy release rate for cleavage of the metal-ceramic interface, and G_disl, the energy release rate associated with the emission of a single dislocation within the metal. The various models of dislocation nucleation are discussed, with emphasis on an approach which makes use of Peierls-like stress vs displacement relations on a slip plane ahead of a crack tip. A recent analytical result by Rice shows that for a mode II or III shear crack, with a slip plane parallel to the ack plane, a dislocation is emitted when G = γ_us (G is the energy release rate corresponding to the “screened” crack tip stress field and γ_us is the “unstable stacking” energy associated with the sliding of atomic planes past one another). This treatment permits the existence of an extended dislocation core, which eliminates the need for the core cutoff radii required by the Rice-Thomson model of emission. Results are presented here for the nucleation of dislocations under more realistic assumptions for metal-ceramic cracks, namely, the emission on inclined slip planes within a mixed-mode crack-tip field. The specific case of a copper crystal bonded on a {221} face to sapphire is analyzed, and the results are used to interpret the recent experimental observations of Beltz and Wang [Acta metall. mater.40, 1675 (1992)] on directional toughness along this type of interface.     

Theory of intergranular creep cavity nucleation,growth and interaction

Creep cavitation is modeled assuming random continuous cavity nucleation, coupled growth by diffusion and plastic deformation, diffusive cavity interactions and cavity interconnection and finally, failure at a critical a real damage fraction. Nucleation is simulated by Monte-Carlo techniques using an empirically-derived nucleation law for copper that depends on the steady-state creep strain. For initially fully-dense materials, cavity nucleation dominates the cavity number density until interconnection and coarsening become important late in rupture life. In this situation, Monkman-Grant behavior is obtained and cavity sizes approach stable log-normal distributions. However, when a small fraction of cavities pre-exist, the cavity density is dominated by cavity interactions and the density remains relatively constant despite continuous nucleation. In this case, cavity growth controls the rupture time and cavity size distributions tend to approach log-normal distribution more slowly. These diffusive interactions diminish for larger but more widely-spaced pre-existing cavities because of limited interactions between the pre-existing and nucleating cavities. The sensitivity of the rupture life on dihederal angle and nucleation rate are also examined, and the statistics of failure are quantified.     

Unified thermodynamic treatment of cavity nucleation and growth in high temperature creep

Existing models describing the creep nucleation and growth are briefly outlined in orderss to obtain a starting point for a new physical framework which unifies the stochastic treatment of nucleation with the deterministic treatment of growth. For this purpose an original hypothesis was postulated to develop the equations of motion of a thermodynamic system in non-equilibrium state at constant temperature and pressure. It is shown the application of this hypotthesis to a system of creep cavities provides the unified equations describing the evolution of cavities during their nucleation and growth stages. Particular attention is devoted to the role of the elastic relaxation of local normal stress due to deposition of atoms from a cavity its nucleation.     

A statistical analysis of cavity nucleation at particles in grain boundaries

Cavity nucleation on grain boundary particles during creep has been examined using a classical thermodynamic method. The particle sizes and spacings are assumed to obey a log-normal distribution. It is found that a threshold shear stress is needed for cavity nucleation to occur. When the resolved shear stress on a grain boundary segment reaches the threshold stress, a critical normal stress for cavity nucleation is produced on the panicle-matrix interface by grain boundary sliding and cavity nucleation occurs. The threshold stress is determined mainly by the concentration and distribution of grain boundary particles and falls in the stress range of engineering applications. A program has been developed to calculate the fraction of particles which can serve as nucleation sites. The model is used to predict the onset of cavitation in the oxide dispersion strengthened alloy Inconel MA 754. Implications for avoiding the nucleation of cavities in engineering alloys are discussed.     

Intergranular creep cavitation with time-discrete stochastic nucleation

An empirical model for the time-discrete stochastic nucleation of intergranular creep cavities is proposed. Nucleation is assumed to occur randomly in time, with the temporal behavior being governed by an inhomogeneous Poisson process. Based upon experimental evidence, the mean function of the Poisson process is taken to be a power-law function of time. The nucleation model is then implemented in conjunction with a recent analysis which treats the growth of randomly spaced populations of voids in a simplified bicrystal configuration. Numerical simulations with the resulting model indicate, among other things, that both the times-to-failure and the cavity radii are distributed according to a Weibull cumulative distribution function. Both predictions have qualitative experimental support. Moreover the presence of nucleation is found to reduce the time-to-failure by creep rupture by approximately a factor of two to eight compared to simulations without nucleation.     

Numerical study of cavity nucleation kinetics

The numerical method of calculation of cavity nucleation kinetics under the time dependent stress has been developed. The results of computations are not in full accord with the recent concept of classical steady-state solution. The cavity nucleation kinetics in the system of cavities and the time evolution of individual cavities in the nucleation and early growth stages at intergranular inclusions under the time dependent stress have been simulated numerically.     

The rate of CO bubble nucleation at oxide metal interfaces within liquid iron alloys

Baker, Warner, and Jenkins found that levitated droplets of Fe-0.8 pet C alloys exploded when decarburized at 1660°C, whereas during the present investigation, the drops remained intact during decarburization at temperatures above 1850°C. Therefore, the object of this work was to determine whether heterogeneous nucleation of CO bubbles at an iron-iron oxide interface could occur at 1900°K but could not occur at 2200°K. An equation was developed to calculate the nucleation rate of CO bubbles at an iron-iron oxide interface in iron at 1900°K containing 0.8 pct C and in iron at 2200°K containing 0.1 pct C. The results of the calculation showed that an iron-iron oxide interface could not serve as a site for CO bubble nucleation. Therefore, a new mechanism is postulated in which cavities swept into the levitated droplet from the surface serve as nuclei for CO bubble formation instead of nuclei formed at the iron-iron oxide interface.     

An analysis of cavity nucleation in superplasticity

Superplastic alloys possess either a quasi-single phase or a microduplex microstructure: in quasi-single phase alloys, cavities are observed to nucleate predominantly at coarse grain boundary particles whereas in microduplex alloys, cavities tend to form at interphase boundaries and at triple point junctions. A general analysis is presented for cavity nucleation, in both microstructures, under the stress concentrations caused by bursts of grain boundary sliding during superplastic deformation. In quasi-single phase alloys, calculations indicate the cavities nucleate at coarse particles located at grain boundaries because local interphase diffusion creep cannot accommodate the stress concentrations sufficiently rapidly. The analysis demonstrates that it is possible for cavities to nucleate at grain boundary ledges under some limited experimental conditions. It is demonstrated also that the present analysis is in agreement with the available experimental data on a quasi-single phase Cu-based superplastic alloy and a microduplex superplastic Zn-22% Al eutectoid alloy. Calculations show that small pre-existing cavities, if present, are likely to be sintered rapidly prior to superplastic déformation at elevated temperatures.     

Low cycle fatigue in rene 88DT at 650 °C: Crack nucleation mechanisms and modeling

Intermediate-temperature low-cycle-fatigue experiments were conducted on three microstructural conditions of the nickel-base superalloy Rene 88DT over several strain ranges. The most significant difference between the microstructural conditions was the grain size; two of the conditions had an average grain diameter of approximately 20 μm, while the third condition had an average grain diameter of 6 μm. Two dominant crack nucleation mechanisms were observed on the specimen fracture surfaces: crack nucleation from surface slip band damage accumulation and crack nucleation around subsurface inclusion clusters. The experimental results indicate that both the grain size and the applied strain range are contributing factors in the prevailing crack nucleation mechanism. The Fatemi-Socie parameter, a multiaxial fatigue damage parameter, was used to examine the ease and probability of surface slip band crack nucleation for these microstructural conditions. The parameter was modified to explicitly include grain size, fatigue R-ratio, and applied strain range, thus giving it a more physically meaningful basis. This modified Fatemi-Socie parameter was found to be a suitable parameter for characterizing the ease of surface slip band cracking for materials with different grain sizes and is able to explain the observed disparity in fatigue lives based on microstructural design.     

Evolution of internal stresses and substructure during creep at intermediate temperatures

Secondary creep has most generally been associated with a rather steady structure. Many models have been suggested to explain the constant strain rate in terms of the effective stress which is determined by the structurally-dependent internal stresses. The internal stresses deduced macroscopically have been of the order of half the applied stress. In this article, by pinning the dislocations under load in an Al-Zn alloy, the evolution of the structure and local effective stresses with strain has been identified by electron microscopy. Values of local effective stresses at the subgrain boundaries ranging between 10–20 times the applied stress have been measured. The emission of dislocations from these boundaries and the evolution of substructure within the subgrain interior indicate that the controlling mechanism during the creep process is the relaxation of internal stresses by this emission. At the same time, the subboundary stress-fields existing in different subgrains determine their different behaviour as a function of time. Hard and soft subgrains alternate in the deformation process to produce overall uniform strain.     

Asymmetric tip morphology of creep microcracks growing along bimaterial interfaces

The asymmetric tip morphology of a creep microcrack propagating along a bimaterial interface is presented based on the assumptions that the near-tip shapes are developed from surface diffusion controlled crack growth and that a steady state prevails. Following Chuang and Rice, a single master curve still can adequately describe the near-tip shapes to within 6% accuracy, but four cases of crack-tip morphology emerge depending on the ratios of surface to interfacial free energy and diffusivity of the adjoining phases. For fixed ratios of the two surface diffusivities, crack tip morphology maps in the space of specific surface energies are constructed with which areas associated with each individual case are indicated. Predicted cases on a set of bimaterial systems are tabulated and discussed. TEM photos of creep crack tips in alumina and silicon nitride are presented for illustration. The information given here is essential to a coupled analysis of diffusion and elastic deformation at a composite interface which may ultimately yield predictions of the delamination rate between the reinforcing phase and the matrix phase as a function of applied stress, temperature and other relevant materials' constants.     

Diffusive intergranular cavity growth in creep in tension and torsion

Creep experiments were performed at 500°C in tension and torsion on high conductivity copper tubes with a uniform initial coverage of implanted water vapor bubbles on all grain boundaries. No significant differences were found in the times to fracture over a wide stress range when the results were correlated according to the maximum principal tensile stress in the two fields. The results indicate that the cavities grow in a crack-like mode but at one tenth the rate predicted from the theoretical model of Pharr and Nix. This difference is attributed partly to load shedding from boundaries normal to the maximum principal tensile stress to slanted boundaries and partly to a lack of knowledge about the surface diffusion constant. The results indicate further, that the contribution to intergranular cavity growth by power-law creep in negligible in comparison to the contribution by diffusional flow. Complementary tension and torsion experiments performed in initially uncavitated samples result in shorter creep lives in torsion than in tension due to more effective cavity nucleation in the former. The times to fracture in both of these cases obey Monkman and Grant's law, indicating the presence of constraints on growth by the lagging deformations by power-law creep in the surroundings of the cavitating isolated grain facets.     

The role of impurities during creep and superplasticity at very low stresses

It is well documented that impurities play an important role in the deformation and fracture of polycrystalline materials. For example, the results of a number of studies have demonstrated that the presence of a very small of amount of impurities in polycrystalline materials can explain many phenomena such as temper embrittlement in steels, creep embrittlement, and enhancement of ductility in the intermetallic compound Ni₃Al. This article reviews the details of two high-temperature deformation phenomena whose characteristics are, according to very recent experimental evidence, influenced or controlled by impurities. The first phenomenon, micrograin superplasticity, deals with the ability of fine-grained materials (d<10 μm, where d is the grain size) to exhibit extensive neck-free elongations during deformation at elevated temperatures above 0.5 T _m, where T _m is the melting point. The second phenomenon, Harper-Dom creep, refers to the anomalous creep behavior of large-grained materials at very low stresses and temperatures near the melting point. It is shown that while these two phenomena are different in terms of the conditions of occurrence and the characteristics of deformation, they share three common features: (1) stresses applied to produce deformation are very small; (2) impurities control the deformation characteristics such as the shape of the creep curve, the value of the stress exponent, and the details of the substructure; and (3) boundaries play a key role during deformation. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in San Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

Density measurements as an assessment of creep damage and cavity growth

The change in density during creep of several polycrystalline metals may be correlated through the expression —Δρ/ρ =B(∈t/d)(σ/G)^q exp (—Q _gb /RT) where —Δρ is the density change, p is the original density, e is the strain,t is the time,d is the linear intercept grain size,σ is the applied stress,G is the shear modulus,Q _gb is the activation energy for grain boundary diffusion,R is the gas constant,T is the absolute temperature, andB andq are constants withq ≃2 to 3. This expression is consistent with the theory of unconstrained grain boundary diffusion growth of cavities provided there is also concomitant strain-dependent nucleation. The expression does not support the power-law growth of cavities, growth by surface diffusion, or constrained grain boundary diffusion growth. Formerly Research Associate, University of Southern California.     

Analysis of cavity nucleation in solids subjected to external and internal stresses

The thermodynamics of cavity nucleation in solids subjected to external and internal stresses are analyzed. We show that the critical nucleus for cavity nucleation can be formed by alternative reversible work paths; either by condensation of pre-existing vacancies or by removal of atoms from the site of nucleation to sinks within the solid or at the surface. These two nucleation paths are shown to be equivalent, Strain energy terms which are quadratic in stress are found to arise in the free energy of the nucleus when relaxation of the void surface is taken into account. Two different cases of internally stressed solids are treated: one in which vacancy sources and sinks at the site of nucleation are locked and another in which vacancy sources and sinks are unlocked. In the former case the internal stress appears only quadratically or as crossterms in the formation free energy of the critical sized nucleus, while in the latter case, it appears in a linear term, additive to the applied stress, and has a strong effect on cavity nucleation. Problems involving complex nucleus shapes and the effects of plastic relaxation in cavity nucleation are also discussed.     

Morphological changes of carbides during creep and their effects on the creep properties of inconel 617 at 1000 °C

Creep tests have been correlated with microstructural changes which occurred during creep of Inconel 617 at 1000 °C, 24.5 MPa. The following results were obtained: 1) Fine intragranular carbides which are precipitated during creep are effective in lowering the creep rate during the early stages of the creep regime (within 300 h). 2) Grain boundary carbides migrate from grain boundaries that are under compressive stress to grain boundaries that are under tensile stress. This is explained in terms of 1 the dissolution of relatively unstable carbides on the compressive boundaries, 2 the diffusion of the solute atoms to the tensile boundaries and 3 the reprecipitation of the carbides at the tensile boundaries. The rate of grain boundary carbide migration depends on grain size. 3) M₂₃C₆ type carbides, having high chromium content, and M₆C type carbides, having high molybdenum content, co-exist on the grain boundaries. M₂₃C₆ type carbides, however, are quantitatively predominant. Furthermore, M₆C occurs less frequently on the tensile boundaries than on the stress free grain boundaries. This is attributed to the difference of the diffusion coefficients of chromium and molybdenum. 4) The grain boundaries on which the carbides have dissolved start to migrate in the steady state creep region. The creep rate gradually increases with the occurrence of grain boundary migration. 5) The steady state creep rate depends not so much on the morphological changes of carbides as on the grain size of the matrix.