Diffusional Cavity Growth Research Articles

Correlation of creep fracture lifetime with microstructure evolution and cavity behaviors in G115 martensitic heat-resistant steel

In order to deepen the understanding towards the creep rupture lifetime of G115 martensitic heat-resistant steel, a series of creep tests using 130–200MPa loading stresses at 923K were carried out to investigate the as-crept microstructural characteristics and cavity behaviors. The significant microstructure deformation and a dramatic increase in the areal density of high-angle grain boundaries occur when the stress loading is over 160MPa. Apart from the strain concentration at elongated grain boundaries and refined grains, the elevated stress also leads to the appearance of a strong α-fiber texture with {001}<110>//RD. The nucleation and growth of cavities can be effectively accelerated by the stress elevation, and ductile fracture is determined as the dominate mechanism within the test stresses. However, a transition towards brittle intergranular fracture is observed due to the rapid coarsening of Laves phase. Furthermore, a good prediction for creep lifetimes of G115 steel has been obtained based on the constrained diffusional cavity growth model.

Comparative creep damage assessments using the various models

The creep fracture characteristics of a conventionally cast (CC) MARM-002 superalloy were studied for creep conditions of 1173 K/200–400 MPa using different approaches including the Kachanov-Rabotnov type continuum damage mechanics, grain boundary damage accumulation, and Chen-Argon diffusional cavity growth. A rapid improvement in creep rupture life can be achieved by reducing the Kachanov-Rabotnov damage rate (ώ) below a critical value of this rate. It is possible that a large improvement in creep resistance would be made by decreasing grain boundary damage rate rather than continuum damage rate since the minimum creep rate (έm) accelerates rapidly without changing the parameter ώ.

Cavity formation and early growth in a superplastic Al–Mg alloy

Knowledge of the exact physical mechanism of cavity formation and early growth is important for the prediction of the extent of internal damage following superplastic deformation. To this end, the early stages of cavitation in a superplastic Al–Mg–Mn–Cu alloy have been experimentally studied and reported here. Small cavities (<0.5 μm) were detected by scanning electron microscopy and the number of cavities per unit volume was monitored by image analysis through optical microscopy. Before deformation, some cavities were seen at the particle–matrix interfaces. However, during tensile deformation in the temperature range of 450–550°C (and strain rates ∼10 −4 to 10 −2 s −1), additional cavities emerge and grow. Most cavities are observed at the interface between particles and the matrix from submicrometer size range, and grow initially along the interface. This suggests that early cavity growth is by matrix/particle decohesion, possibly starting from interfacial defects, and this growth has rapid kinetics. The density of observable cavities increases with strain, i.e. “nucleation” is continuous. The number of cavities increases at higher strain rates and at lower test temperatures. This is due to the higher flow stresses, reduced strain-rate sensitivity and poorer diffusional accommodation process, which assist in the initial growth of the submicrometer and nanoscale interface defects. But the evidence for diffusional cavity growth in the initial stages was not found.

Observations related to healing of interface damage and cavity nucleation during superplastic flow

Two critical observations related to the nucleation of superplastic cavities are reported. Cavities preexisting in a fine grain Al–Mg alloy prior to superplastic deformation have been minimized, but not completely eliminated by a high temperature annealing treatment. This has reduced the density of emerging cavities during subsequent deformation, however nucleation of cavities occur continuously with superplastic strain, starting possibly from partially healed defects of imperceptible (nanoscale) size. The observations raise doubts about the often-used cavity nucleation criterion based on a thermodynamically stable void size. Diffusional cavity growth model, used in conjunction with this assumed “stable” size artificially enlarges its perceived contribution, but still predicts less growth than the observed cavitation levels in superplastic metals. Alternate growth mechanism for submicron size cavities is suggested.

Inhomogeneous nucleation and growth of cavities in irradiated materials

The origin of the effect of inhomogeneous swelling observed near grain boundaries in irradiated materials is examined taking into account both nucleation and diffusional growth of cavities, and the interaction of cavities with mobile interstitial clusters produced in collision cascades. The model shows the formation of a characteristic profile of inhomogeneous swelling that exhibits features similar to those observed experimentally. The rate of swelling is found to be strongly dependent on the size of cavities, with cavities growing near the boundary being able to reach substantially larger sizes than those growing in the interior area of the grain. The distance ${z}^{*}$ between the peak of swelling and the grain boundary scales with the density of cavities ${N}_{0}$ as ${z}^{*}\ensuremath{\sim}{N}_{0}^{\ensuremath{-}\ensuremath{\beta}},$ where $\ensuremath{\beta}$ is close to 1/3.

Inhomogeneous Swelling Near Grain Boundaries in Irradiated Materials: Cavity Nucleation and Growth Saturation Effects

ABSTRACTThe effect of inhomogeneous nucleation and growth of cavities near grain boundaries illustrates the failure of the standard rate theory to describe the kinetics of phase transformations in irradiated materials under cascade damage conditions. The enhanced swelling observed near grain boundaries is believed to result from the competition between the diffusional growth of cavities and their shrinkage due to the interaction with mobile interstitial clusters. Swelling rates associated with the two processes behave in a radically different way as a function of the size of growing cavities. For a spatially homogeneous distribution of cavities this gives rise to the saturation of swelling in the limit of large irradiation doses.We investigate the evolution of the population of cavities nucleating and growing near a planar grain boundary. We show that a cavity growing near the boundary is able to reach a size that is substantially larger than the size of a cavity growing in the interior region of the grain. For a planar grain boundary the magnitude of swelling at maximum is found to be up to eight times higher than the magnitude of swelling in the grain interior.

Modeling Stress Evolution in Electromigration

ABSTRACTDiffusional mechanisms of electromigration and stress relaxation involve the flow of atoms in response to a gradient in chemical potential along an interface. This gradient in chemical potential may be provided by the component of an electric field parallel to the interface, or it may be established by the normal component of stresses along it. In either case, considerations of continuity of the potential dictate that diffusive flow must also be induced along any other boundary that intersects the interface. As an example, in this paper, a model system that contains grain boundaries normal to an applied electric field is analyzed. While the electric field does not directly induce diffusion along these grain boundaries, it is shown that a complimentary flux must be induced along them. The effect of this flux on electromigration is discussed in this paper. Furthermore, it is well-known that non-homogeneous diffusion of matter along boundaries induces elastic distortions and stress gradients. These in turn, influence the diffusion process. The effect of these elastic distortions on the atomic flux has been examined by considering diffusion along a single interface in an elastic medium. Prior studies of diffusional cavity growth have established the magnitudes of non-dimensional time-scales over which the deposition of atoms along the grain boundaries can be assumed to be essentially uniform. Such an assumption considerably simplifies analyses for stress evolution in these problems. The appropriate time-scales over which such a simplification can be made for electromigration are discussed in this paper, and illustrated by some model calculations.

High temperature embrittlement of metals due to helium: is the lifetime dominated by cavity growth or crack growth?

Helium produced by (n, α)-reactions can degrade the mechanical stability of fusion reactor materials by reducing their ductility and lifetime, particularly at elevated temperatures. This high-temperature He embrittlement (HTHE) has been attributed to the diffusional growth of cavities on grain boundaries, which is slow in an initial gas-driven (bubble) growth stage and fast in the subsequent stages of stress-driven (void) growth, and crack formation by cavity coalescence. In cases of severe HTHE, the time to rupture t R has been suggested to be dominated by gas-driven bubble growth. Recently, it has been proposed that t R is, instead, controlled by gas-driven crack growth (Borodin et al., 1992). In the present paper, it is shown that, in the temperature range of HTHE, gas-driven crack growth is not possible because of diffusional stress relaxation and would result, at lower temperatures, in unstable growing cracks only at bulk helium concentrations in the percentage range. Experimental evidence for the interpretation of HTHE in terms of gas- and stress-driven diffusional growth of cavities on grain boundaries is presented.

Mechanical Properties of Plated Copper

AbstractBoth electrodeposited and electroless copper are widely used in the electronics industry to form signal lines and plated-through holes in printed circuit cards and boards. Because of widely differing thermal expansion coefficients of copper and of the ceramic and polymeric substrates, large mechanical stresses develop in the metallization during thermal cycles, as e.g. during solder reflow. To safeguard against premature fracture it is imperative that the metallization is sufficiently ductile. Plated thin foil copper of poor ductility is known to be susceptible to cracks in plated-through holes which, besides causing problems in the manufacture, poses a threat to device reliability in service. In this paper we show that such cracks arise as a combination of reduced ductility due to presence of initial porosity in copper and due to grain boundary sliding and diffusional cavity growth during the soldering cycle. We emphasize that there exists strong interactions between these ductility reducing effects, such that their coupled action may exceed the effect when each mechanism operates independently. We review recent research on deformation and fracture of bulk and plated copper between RT and 300°C. Finally, we briefly discuss approaches to improve mechanical properties of plated thin foil copper.

Observations on diffusional cavity growth in superplastic materials

Observations on diffusional cavity growth in superplastic materials

Steady-state creep crack growth by continually nucleating cavities

F or creep crack growths by the nucleation and growth of grain boundary cavities, steady-state crack growth rates ( ȧ) are derived when the cavity nucleation is assumed to be continual and strain controlled. For the crack growth under HRR fields, a is linearly proportional to C∗ as reported in other models. However, when the crack growth occurs under elastic fields, a ̇ K 1 2 + 3n 5 (n > 8 3 ) for diffusional cavity growth and a ̇ ∼ K n 1 (n > 2) for cavity growth by power law creep. Predictions of the model are applied to a Ni-Cr steel and a Nimonic 80A, and compared with other models through analyses on the dependence of a on macroscopic load parameters and the activation energy of a.

A model for diffusional cavity growth in superplasticity

There is an enhancement in the diffusional growth of cavities in superplastic materials if the cavity size exceeds the grain size so that vacancies diffuse into the cavity along a number of grain boundary paths. A model for this process is developed, and it is shown that the rate of change of cavity radius with strain due to superplastic diffusion growth is given by dr dϵ ∼- 45ΩδD gb d 2kT ( σ ε ̇ ) where r is the cavity radius, ε is the total strain, Ω is the atomic volume, δ is the grain boundary width, D gb is the coefficient for grain boundary diffusion, d is the spatial grain size, k is Boltzmann's constant, T is the absolute temperature, σ is the applied stress and ε is the strain rate. Superplastic diffusion growth is therefore independent of the instantaneous cavity radius and inversely proportional to the square of the grain size; in practice, this process becomes important at the lower testing strain rates and when the specimen grain size is typically less than ~5 μm. It is demonstrated that the occurrence of superplastic diffusion growth is capable of providing an explanation for the experimental observations of large rounded cavities in several superplastic materials.

The development of cavity growth maps for superplastic materials

Superplastic alloys usually deform to very large extents but excessive cavitation can lead to premature cavitation failure in these materials. Several mechanisms can contribute to the growth of cavities during superplastic deformation although, generally, there is only one mechanism that controls cavity growth. Cavity growth mechanisms of relevance to superplastic materials are analysed in detail and the possible transitions in rate-controlling cavity growth mechanisms are considered. The contribution of lattice diffusion to the diffusional growth of cavities is included in the overall analysis of cavity growth. Cavity growth maps are constructed to show the dominant cavity growth mechanisms under different experimental conditions. Equations are developed to predict the appropriate transitions in cavity growth mechanisms with increasing cavity radii. Finally, it is demonstrated that the predictions of the cavity growth maps are consistent with the experimental results in several superplastic materials.

The effect of hydrostatic pressure on the uniaxial creep life of a 2 ¼ % Cr 1% Mo steel

The effect of a superimposed hydrostatic pressure on the ductility, the creep life and the failure mechanism of a 2 ¼ % Cr 1 % Mo steel, with an over-aged upper bainite microstructure, subject to different uniaxial stresses is described. Creep tests have been made at 923 K with uniaxial stresses in the range 55-80 MPa and superimposed hydrostatic pressures up to 35MPa. Optical and electron optical microscopy have been used to assess the accumulation of grain boundary damage arising from creep deformation. When failure is controlled by intergranular cavitation, increasing the hydrostatic pressure causes an increase in the creep ductility and a decrease in cavitation, and thus an increase in time to failure. In addition, increasing pressure effects a change in failure mode from one controlled by the nucleation and growth of intergranular cavities to one controlled by plastic flow. The results for the creep of this 2¼ % Cr 1 % Mo steel are discussed in terms of a diffusional cavity growth model which includes continuous nucleation. Moreover, these results are compared with data previously obtained for single phase materials tested with a superimposed hydrostatic pressure. The relative contributions of the principal and equivalent stresses to the creep fracture of this low alloy steel are also examined. The estimation of realistic long-term creep life from the results of short-term creep tests is also discussed.

Intergranular fracture in bicrystals

Fracture experiments, at elevated temperatures, were carried out on bicrystals of copper containing silica particles. Fracture in each instance was intergranular. In all cases except one, fracture was caused by cavitation. The cavities grew either by diffusional transport or by plastic flow. In the rate equation for time to fracture, diffusional growth led to a linear stress dependence and an activation energy equal to that for boundary self-diffusion. Growth by plastic flow was manifested by a non-linear stress dependence and a higher activation energy. In one instance, when fracture occurred in only a few seconds, grain boundary separation was caused by the incompatibility of matrix slip at the grain boundary. Data in the literature indicates that the diffusional mechanism for the growth of cavities is suppressed in polycrystals; an explanation for this anamolous behavior is given. It is postulated that diffusional growth of cavities is possible in polycrystals in a hydrostatic state of stress.

Constraints on diffusional cavity growth rates

AbstractThere have been a number of rate equations proposed in the literature for the growth of grain-boundary cavities during creep. Implicit in all these analyses is the assumption that growth occurs freely and that no constraints exist that would attenuate the predicted rates. It is shown that a constraint on growth rate can occur in polycrystals because creep cavities are inhomogeneously distributed amongst the various grain boundaries. This attenuation of growth rate is predicted to be greatest when high-strength alloys with large cavity populations are deformed slowly and least when pure metals with low cavity populations are deformed quickly. The application of these ideas to multiaxial stress states and extrapolation procedures is discussed in the knowledge that the rate of unconstrained cavity growth is directly proportional to the maximum principal tensile stress, whereas constrained growth is proportional to the nth power of the octahedral shear stress.