Boundary Cavitation Research Articles

Characterization of the cavity nucleation factor for life prediction under creep-fatigue interaction

It is understood that grain boundary cavitation is one of the detrimental processes for the degradation of materials that reduces the creep-fatigue life at high temperatures. In a previous investigation, a model for life prediction under creep-fatigue conditions was proposed in terms of cavity nucleation and growth. In that model, the cavity nucleation factor (P) was introduced to correlate between the number of cavities and the plastic strain range from which athermal vacancies are generated. It was considered to be a material specific constant which was independent of the experimental conditions. However, in this study, it is found that the cavity nucleation factor is a function of the plastic strain range but is independent of the testing temperature at near 0.5 Tm. In the light of this dependency, a new cavity nucleation factor (P'), is introduced. Using this new cavity nucleation factor (P'), a modified equation for life prediction is proposed, and it is shown that there is good agreement between predicted and experimental lives. Additionally, an interesting approach has been made to find the physical meaning of the new cavity nucleation factor (P'). According to this study, it is suggested that the new cavity nucleation factor, which is regarded as a material specific constant, is found to be strongly related to the density of the grain boundary precipitates with a linear relationship existing between them.

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.

Micromechanics of intergranular creep failure under cyclic loading

This paper is concerned with a micromechanical investigation of intergranular creep failure caused by grain boundary cavitation under strain-controlled cyclic loading conditions. Numerical unit cell analyses are carried out for a planar polycrystal model in which the grain material and the grain boundaries are modelled individually. The model incorporates power-law creep of the grains, viscous grain boundary sliding between grains as well as the nucleation and growth of grain boundary cavities until they coalesce and form microcracks. Study of a limiting case with a facet-size microcrack reveals a relatively simple phenomenology under either balanced loading, slow-fast loading or balanced loading with a hold period at constant tensile stress. Next, a (non-dimensionalized) parametric study is carried out which focusses on the effect of the diffusive cavity growth rate relative to the overall creep rate, and the effects of cavity nucleation and grain boundary sliding. The model takes account of the build up of residual stresses during cycling, and it turns out that this, in general, gives rise to a rather complex phenomenology, but some cases are identified which approach the simple microcrack behaviour. The analyses provide some new understanding that helps to explain the sometimes peculiar behaviour under balanced cyclic creep.

An analysis of grain boundary sliding and grain boundary cavitation in discontinuously reinforced composites

In this study, the creep cavitation and rupture characteristics of polycrystalline matrix material and discontinuously reinforced composites are investigated including grain boundary sliding behavior, reinforcement aspect ratio and interfacial behavior between the reinforcement and surrounding matrix grains. Free sliding of the grain boundaries, a continuous nucleation of the grain boundary cavities, their diffusional growth and coalescence to form grain boundary facet cracks are fully accounted for in the analyses. 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 behavior between the reinforcement and the matrix. For the composites, the influence of grain boundary sliding on the creep life is reduced by the stress concentration effect that is seen at the end of the reinforcements. In contrast with the behavior of polycrystalline matrix material in composites after the formation of the first facet crack, resulting from the coalescence of the cavities, a significant time is required for the formation of the other grain boundary facet cracks across the ligament to cause final rupture. The results also show that experimentally observed higher creep exponents or stress dependent creep exponent values in discontinuously reinforced composites can occur as a result of creep damage evolution behavior.

The normalized coffin- manson plot in terms of a new damage function based on grain boundary cavitation under creep- fatigue condition

A new damage function based on a model for the creep-fatigue life prediction in terms of nucleation and growth of grain boundary cavities is proposed. This damage function is a combination of the terms related to the cavitational damage in the life prediction equation and is generally applicable to the materials in which failure is controlled by the grain boundary cavitational damage. The creep-fatigue data from the present and other investigations are used to check the validity of the proposed function, and it is shown that they satisfy the reliability of damage function. Additionally, using this damage function, one may realize that all the Coffin-Manson plots at the various levels of tensile hold time and temperature under strain-controlled creep-fatigue tests can be normalized to make the master curve.

Analysis of Creep Crack Growth at High-Temperature Components by Diffusive Growth Model of Grain Boundary Cavities (I)-Effect of Grain Boundary Cavitation on Stress Field and Crack Growth Rate-

The crack growth under creep condition is one of the major damage mechanisms which determines remaining life of the component operating at high temperatures. In this paper, the creep crack growth by grain boundary cavitation is studied, which is frequently observed failure mechanism for creep brittle materials. As a result of diffusive growth of creep cavities, it is shown that the crack-tip stress field is modified from the original stress distribution by the amount of singularity attenuation parameter which is function of crack growth rate and material properties. Also, the stress relaxation at crack-tip results in the extension of cavitating area by the load dump effect to meet the macroscopic force equilibrium conditdion.

Thermal activation analysis on the bubble-strengthening mechanism at high temperatures in [formula omitted] tungsten fine wires

The doping elements such as Al, K and Si in P/M tungsten develop many arrays of small bubbles, the diameter of which ranges from 10 to 150 nm depending on annealing temperatures, along the wire axis during fabrication. In the present work, the authors consider the effects of bubbles on the flow stress at high temperatures from a point of view of thermal activation process of dislocation motion. The small activation energy for steady state creep in doped wire results from a combination of the effect of grain boundary cavitation on creep rates and the deformation of the constraining surroundings which is controlled by the Peierls-Nabarro mechanism. The elementary process of steady state creep in non-doped wire is the surface diffusion which rate-controls the grain boundary sliding. The increase in flow stress of doped wire must result from the athermal strengthening due to bubbles which block the climb of dislocations.

Ductility degradation of vacuum-plasma-sprayed NARloy-Z at elevated temperatures

Vacuum plasma spray forming is being used in the near-net fabrication of aerospace components at the Marshall Space Flight Center (MSFC), Alabama. For example, vacuum-plasma-sprayed (VPS) NARloy-Z (a copper-based alloy with high thermal conductivity) is used to form the combustion chamber liner of liquid rocket engines. VPS NARloy-Z possesses properties comparable with the wrought alloy at temperatures ranging from −259 to 316 °C. However, VPS material exhibits lower ductility than the wrought material at chamber operating temperatures (ranging from 427 to 649 °C). Because of these findings, an investigation was initiated into the mechanisms responsible for the loss of high-temperature ductility. Fracture analysis indicated that ductility loss at elevated temperatures is associated with a transition in fracture mode from transgranular to intergranular. Low-ductility specimens featured extensive grain boundary cavitation with limited grain elongation in the stress direction. Grain size also influenced the high-temperature ductility; finer grained material is more ductile. VPS NARloy-Z had more cavities at grain boundaries and a higher bulk oxygen content than wrought NARloy-Z. The ductility loss at high temperatures appears to have been caused by compounding effects of excessive oxygen and grain boundary cavitation. High-temperature ductility was improved by altering the thermal processing (pre-hot isostatic pressing (HIP) vacuum anneal, HIP and post-HIP vacuum aging) to reduce oxygen and enhance grain boundary integrity.

Relationship between Recrystallization Kinetics and Rate of Creep Cavitation in Bubble Strengthened Tungsten

The kinetics of secondary recrystallization and high temperature creep fracture behaviour of bubble-strengthened (KSiAl-doped) tungsten wires have been investigated using emission electron microscopy and scanning electron microscopy. Two different doped wires were chosen that exhibited different creep properties, and their recrystallization and fracture behaviour were compared. In addition, creep and fracture behaviour of an undoped wire was also investigated. Under the applied creep conditions (T = 2900 K ; = 5 MPa), fracture of the samples was caused by grain boundary cavitation, due to the coarsening and growth of the bubbles in doped wires, and due to the growth of deformation-induced microcracks in the undoped material. The results suggested that, in the case of bubble-strengthened tungsten, the high temperature fracture behaviour of the wire can be predicted from its recrystallization kinetics.

Hot deformation characteristics of INCONEL alloy MA 754 and development of a processing map

The characteristics of hot deformation of INCONEL alloy MA 754 have been studied using processing maps obtained on the basis of flow stress data generated in compression in the temperature range 700 °C to 1150 °C and strain rate range 0.001 to 100 s-1. The map exhibited three domains. (1) A domain of dynamic recovery occurs in the temperature range 800 °C to 1075 °C and strain rate range 0.02 to 2 s-1, with a peak efficiency of 18 pct occurring at 950 °C and 0.1 s-1. Transmission electron microscope (TEM) micrographs revealed stable subgrain structure in this domain with the subgrain size increasing exponentially with an increase in temperature. (2) A domain exhibiting grain boundary cracking occurs at temperatures lower than 800 °C and strain rates lower than 0.01 s-1. (3) A domain exhibiting intense grain boundary cavitation occurs at temperatures higher than 1075 °C. The material did not exhibit a dynamic recrystallization (DRX) domain, unlike other superalloys. At strain rates higher than about 1 s-1 the material exhibits flow instabilities manifesting as kinking of the elongated grains and adiabatic shear bands. The material may be safely worked in the domain of dynamic recovery but can only be statically recrystallized.

Creep and intergranular cracking of Ni-Cr-Fe-C in 360 °C argon

The influence of carbon and chromium on the creep and intergranular (IG) cracking behavior of controlled-purity Ni-xCr-9Fe-yC alloys in 360 °C argon was investigated using constant extension rate tension (CERT) and constant load tension (CLT) testing. The CERT test results at 360 °C show that the degree of IG cracking increases with decreasing bulk chromium or carbon content. The CLT test results at 360 °C and 430 °C reveal that, as the amounts of chromium and carbon in solution decrease, the steady-state creep rate increases. The occurrence of severe IG cracking correlates with a high steady-state creep rate, suggesting that creep plays a role in the IG cracking behavior in argon at 360 °C. The failure mode of IG cracking and the deformation mode of creep are coupled through the formation of grain boundary voids that interlink to form grain boundary cavities, resulting in eventual failure by IG cavitation and ductile overload of the remaining ligaments. Grain boundary sliding may be enhancing grain boundary cavitation by redistributing the stress from inclined to more perpendicular boundaries and concentrating stress at discontinuities for the boundaries oriented 45 deg with respect to the tensile axis. Additions of carbon or chromium, which reduce the creep rate over all stress levels, also reduce the amount of IG fracture in CERT experiments. A damage accumulation model was formulated and applied to CERT tests to determine whether creep damage during a CERT test controls failure. Results show that, while creep plays a significant role in CERT experiments, failure is likely controlled by ductile overload caused by reduction in area resulting from grain boundary void formation and interlinkage.

Delaunay-Network Modelling of Creep Failure in Regular Polycrystalline Aggregates by Grain Boundary Cavitation

In polycrystalline materials at elevated temperatures subjected to station ary loading, creep fracture occurs as a result of failure mechanisms on the size scale of grains, namely the nucleation and diffusive growth of cavities until coalescence leads to microcracks. In this paper, a polycrystalline aggregate is modelled by so-called Delaunay elements associated with individual grain boundary facets, whose constitutive behaviour represents dislocation creep inside the grains as well as the cavitation processes on the associated grain facet. Free grain boundary sliding and the elastic deformation of the grain material are also taken into account. Unit cells of polycrystalline aggregates containing many grains are investigated, assuming regular hexagonal grains and allowing for cavita tion on all facets, possibly at different rates. The development of creep damage is simulated numerically, starting from nearly no initial damage until an excessive number of microcracked grain boundaries cause disintegration of the polycrystal. It is demon strated that continuous stress redistributions take place during the failure process, and that nonuniformities in the nucleation activity can cause the formation of "zones" of stress at tenuation, where the grain boundaries damage and microcrack relatively quickly, sepa rated by "shielded" regions. As a result of this, it is found that the orientation of the first microcracks is perpendicular to the macroscopic largest principal tensile stress, as ex pected, but that the orientation of the microcrack pattern is not necessarily in the same direction.

Dynamic grain growth and ductility enhancement at intermediate temperature

Dynamic grain growth has been observed during hot tensile tests of copper at intermediate temperatures from 0.50 to 0.75 T m over the strain rate range of about 3 × 10 −5 3 × 10 −3 s −1. Microstructural examination revealed that at strain rates < 3 × 10 −5 s −1, dynamic recovery dominates and the grain sizes of the specimens after the test are comparable to that of the original material. When the strain rate is increased above 3 × 10 −5 s −1, dynamic grain growth occurs in that the sparsely nucleated grains are able to glow freely during the test, resulting in the formation of exceedingly large grains. As the strain rate is increased further above 3 × 10 −3 s −1, dynamic recrystallization sets in and the final grain size drops to below the original value. When dynamic grain growth occurs, the stress-strain curves become serrated with a few coarse ripples of gradually decreasing peaks. Interrupted tests further revealed that the stress drop during the test is associated with the occurrence of rapid grain growth in the material. Boundary serration is also a common feature under the test conditions when dynamic grain growth is observed. Detailed metallographic and fractographic studies further showed that the occurrence of dynamic grain growth is responsible for the upturn of the hot tensile ductility of copper with increasing temperature, during which the fracture mechanism changes from profuse grain boundary cavitation with low ductility to sparse wedge cracking with considerable ductility.

Continuum damage mechanics modelling of circumferentially notched tension bars undergoing tertiary creep with physically-based constitutive equations

The paper reports the result of finite element computations, based on Continuum Damage Mechanics (CDM), carried out on circumferentially notched tension bars undergoing tertiary creep and failure. The material constitutive equations are physically based and generalised from thos applicable to polycrystalline nickel-based superalloys. The equations describe the stress level dependence of creep rate using a sinh function and two damage state parameters to model tertiary softening caused by: (i) grain boundary cavity nucleation and growth, and (ii) the multiplication of mobile dislocations. The paper presents values of the computed lifetimes, normalised with respect to plain bar lifetimes at the same average applied stress across the notch throat, and determines their sensitivity to a wide range of material parameters. The parameters include those which determine: the relative strength of the two damage rate mechanisms; the power v, to which the stress-state sensitivity parameter ( Σ 1/ Σ e ) is raised for damage evolution due to grain boundary cavitation; and, their dependence upon the applied stress levels. The effects of the material parameters on the predicted transition from notch strengthening to notch weakening are rationalised analytically using a stress state modified Skeletal Point stress methodology. The predictive capability of this methodology was found to be extremely good in most circumstances but broke down seriously when the uniaxial ductility was reduced to approximately 1%.

Simulation of Microcrack Propagation in Creeping Polycrystals Due to Diffusive Grain Boundary Cavitation

Creep rupture in random polycrystalline aggregates is investigated numerically in terms of multi-grain cell studies using a Delaunay network modelling technique. The model involves a representation of the crystalline aggregate by means of special purpose elements attributed to each grain facet. These Delaunay elements account for elastic and creep deformations of the grains, free grain boundary sliding, as well as for the nucleation and diffusive growth of grain boundary cavities until coalescence leads to a facet microcrack. Damage accumulation is simulated numerically, until an excessive number of microcracks cause des-integration of the polycrystal. Primary attention is on the influence of randomness in the microstructure on creep rupture, either in terms of random variations of the size and shape of hexagonal grains, or in terms of random variations in the nucleation properties of grain boundaries. It is found that randomness always tends to decrease the life time. In particular, it is found that the life time depends sensitively on random variations of the geometry of the microstructure.

Creep and Fracture Mechanisms in an Oxide-Dispersion Strengthened Ni3Al-Based Alloy Between 649°C and 982°C

AbstractAn oxide-dispersion strengthened (ODS) Ni3Al-based alloy has been fabricated and creep tested. Previously reported data for minimum creep rate as a function of stress indicated that two creep mechanisms operate at intermediate temperatures of 732 and 816°C [1]. This paper reports the results of recent interrupted creep tests and fractographic studies which serve to identify the two creep mechanisms. Creep at low stresses or low creep-rates occurs by constrained growth of cavities on transverse grain boundaries. In this low stress region an apparent stress exponent of 5.1 is observed. Creep at high stresses or high creep-rates results from the bulk deformation of grains by power law creep with a much smaller contribution due to grain boundary cavitation. The stress exponents of 13 and 22 observed in this high stress region are typical of ODS alloys. In both regions fracture is observed to be mixed mode with a large transgranular component due to the high grain aspect ratio developed in this material. Limited data at 982°C indicate the occurrence of only one mechanism which can be described by a stress exponent of 9.1. It was not possible, based on fractographic studies, to associate the creep mechanism at 982°C with either of those observed at the intermediate temperatures. No fractographic studies were performed at 649°C due to lack of valid specimens; however, the stress exponent of 13.5 observed at 649°C suggests that creep occurs by deformation of the grains.

Skeletal point stresses in circumferentially notched tension bars undergoing tertiary creep modelled with physically based constitutive equations

Constitutive equations are proposed in which the stress level dependence of creep rate is described by a sinh function, and two damage state-parameters are used to model the tertiary softening caused by: (i) grain boundary cavity nucleation and growth, and (ii) the multiplication of mobile dislocations. These constitutive equations are applicable to polycrystalline nickel-base superalloys and are used together with a continuum damage mechanics finite element based solver, DAMAGE XX, to study the behaviour of axisymmetrically notched tension bars and simulate the complex stress states that may be encountered at geometrical stress-raisers in high temperature components. Numerical studies of such bars show that their behaviour can be accurately represented in terms of a ‘skeletal effective stress’ located at a point within the notch throat, and the stress state at this point. It is shown that this conclusion is valid not only for those materials that fail by grain boundary cavitation alone, but also for materials such as superalloys where grain boundary cavitation is accompanied by mobile dislocation multiplication.

Rate-Controlling Process of Power Law Creep at High Temperatures in Powder Metallurgy Tungsten Wires

Creep tests and scanning electron microscopy (SEM) observation of grain boundary cavitation are made to decide the most likely mechanism which rate-controls the power law creep at high temperatures in powder metallurgy tungsten wires. The modified Monkman-Grant relation holds for the overall time, the strain to fracture and the minimum creep rate during creep. The activation energy for steady state creep is obtained to be about 130 kJ/mol which is much less than the energies for surface, dislocation, grain boundary and lattice diffusion of tungsten. The value does not approach the activation energy for lattice diffusion as the mechanism of dislocations climb even if the effect of grain boundary cavitation on creep rates is taken into account

Necking of Creep‐Cavitating Bars

This paper is a finite element study of the nonuniform (necking) deformation of creep‐cavitating bars under constant load or constant load with superimposed hydrostatic pressure. The multiaxial constitutive model used in the analysis is a finite strain generalization of a physically based model that incorporates Dyson's micromechanical mechanism of constrained cavity growth. The mechanism governs the phenomenon of coupled grain boundary cavitation and creep in polycrystalline metals at elevated temperatures and within the low‐to‐moderate stress regime. The finite element study, which is based on the principle of virtual work and constitutive model in the convected Lagrangian view, includes calculations of elongation, area, stress, and damage histories. Comparisons of elongation history as well as necked profiles of various cases are carried out. The results predict (1) Transitional behavior of catastrophic necking and brittle fracture to the tendency for diffuse necking and ductile rupture under a constan...

Effects of notch geometry and impurity on creep fracture of low alloy steel

he effects of stress state and impurity on the high temperature intergranular fracture of a commercial grade of 2·25Cr–1Mo steel have been investigated. Fracture surfaces and creep cavities were examined using scanning electron microscopy. Elemental segregation to the grain boundaries in the blunt and chevron notched specimens was analysed using Auger electron spectroscopy, which showed P segregation on the grain boundary facets and high contents of S on transgranular facets and in cavities. Whereas an increase of P content with time at 550°C was observed for the chevron notched samples up to 50 h (the time range used), a steady level had been found during creep aging for the blunt notch. However, in both cases, step cooling showed no effect on the segregation content of P after about 10 h at 550°C. The damage studies indicate that wedge cracking controls the damage, while a very few isolated cavities were found ahead of cracks, suggesting that cavities link up rapidly with the growing cracks. Energy dispersive analysis revealed the presence of Mn, Cr, and S in the cavities. It is suggested that P segregation, which is promoted strongly by the presence of Mn, could alter the grain boundary cavitation as could the cosegregation of Cr and P.MST/1489