Effect of stress reductions on the stress exponent and subgrain size in an Al-Zn alloy

Stress change and uninterrupted tests were performed on an Al-5 wt pct Zn alloy over the high temperature range (0.7 to 0.99T _m, whereT _mis the melting point) and at a normalized stress range extending from 10⁻⁵ to 2 × 10⁻⁴. Two techniques, etch-pit (EP) and transmission electron microscopy (TEM), were used to examine dislocation substructure developed during creep. The results of stress reduction tests, when compared with those of uninterrupted tests, lead to two findings: (a) there is no difference between the stress exponents determined from stress reduction tests and uninterrupted tests, and (b) after a stress reduction the subgrain size, measured by both EP and TEM, coarsens, reaching the steady-state value determined in an uninterrupted test at the reduced stress. TEM micrographs show that subgrain coarsening during the transient period after a stress reduction involves substructural activities such as subgrain boundary dissolution. Also, TEM examination of the interiors of subgrains occasionally reveals the presence of a cellular substructure which resembles very small subgrains. The characteristics of this cellular substructure are discussed with reference to recent conflicting evidence concerning the ability of the subgrain size to coarsen after a stress reduction. Formerly Graduate Student, University of California, Irvine, CA 92717.     

A model for subgrain superplastic flow in aluminum alloys

Aluminum alloys that contain low angle boundaries exhibit different superplastic behavior than alloys consisting of high angle boundaries. On a relative basis, the low angle boundaries increase the flow stress, but impart a greater resistance to cavitation; the strain-rate sensitivity of this material is generally smaller and the change in the strain-rate sensitivity with strain rate shows a minimum instead of a maximum as observed in the large angle boundary materials. As a result, the subgrain material can be deformed to large tensile strains at fast strain rates. A kinetic model for subgrain superplasticity that invokes a balance between the arrival and emission rates of dislocations at low angle boundaries is presented. It explains several features of subgrain superplasticity. It also explains why ultrafine dispersoids of intermetallics appear to stabilize the subgrain structure in aluminum. Early work on the correlation between flow stress and the subgrain size in dynamic recrystallization of metals may also be consistent with the model.     

Creep cavity growth from tritium-induced helium bubbles in nickel

The growth of grain boundary cavities in nickel under creep conditions was investigated. Growth could be studied unambiguously and without the complications of radiation damage due to a unique sample preparation technique making use of the tritium-to-helium’ decay reaction. Resultant helium bubbles served effectively as creep cavity nuclei, the growth of which led to premature intergranular fracture. Constant stress tension creep tests under argon were performed on helium embrittled samples, revealing information on the stress and temperature dependence of the creep-fracture process. The cavity spacing developed during primary creep by bubble migration and coalescence persisted to fracture. Bulk plastic deformation was strongly suppressed by a matrix bubble population which stabilized a finer subgrain network than is characteristic of virgin nickel. This enhanced creep resistance permitted observation of a stress region in which void growth was controlled by classical Hull-Rimmer grain boundary vacancy diffusion. At higher stresses a transition to plasticity control appeared to take place. These results are interpreted in terms of a coupled grain boundary diffusive/ matrix plasticity model. This paper is based on a presentation made in the symposium “Crack Propagation under Creep and Creep-Fatigue" presented at the TMS/AIME fall meeting in Orlando, FL, in October 1986, under the auspices of the ASM Flow and Fracture Committee.     

Deformation mechanisms in superplastic AA5083 materials

The plastic deformation of seven 5083 commercial aluminum materials, produced from five different alloy heats, are evaluated under conditions of interest for superplastic and quick-plastic forming. Two mechanisms are shown to govern plastic deformation in AA5083 over the strain rates, strains, and temperatures of interest for these forming technologies: grain-boundary-sliding (GBS) creep and solutedrag (SD) creep. Quantitative analysis of stress transients following rate changes clearly differentiates between GBS and SD creep and offers conclusive proof that SD creep dominates deformation at fast strain rates and low temperature. Furthermore, stress transients following strain-rate changes under SD creep are observed to decay exponentially with strain. A new graphical construction is proposed for the analysis and prediction of creep transients. This construction predicts the relative size of creep transients under SD creep from the relative size of changes in an applied strain rate or stress. This construction reveals the relative size of creep transients under SD creep to be independent of temperature; temperature dependence resides in the “steady-state” creep behavior to which transients are related.     

The dislocation microstructure of aluminum

Aluminum of 99.999 pct purity was deformed in torsion at 644 K and an equivalent uniaxial strain rate of 5.04 × 10⁻⁴ s⁻¹ to various steady-state strains up to 16.33. The subgrain size and density of dislocations not associated with subgrain boundaries remained fixed throughout the wide steady-state strain range. The subgrain boundaries, however, underwent two important changes. At the onset of steady state (ε ~0.2) all of the subgrain boundaries had relatively small misorientation angles averaging about 0.5 deg. With increased strain, however, an increasing fraction of the subgrain facets were high-angle boundaries. At strains greater than about four nearly a third of the boundaries were high-angle. In specimens with both types of boundaries, the high-angle boundaries have misorientation angles (θ) greater than 10 deg, while θ for low-angle boundaries is nearly always less than 3 deg. Only rarely do subgrain boundaries have misorientation angles between 3 deg and 10 deg. In aluminum, the increased high-angle boundary area at larger strains originates from the extension of the initial boundaries through the mechanism, recently introduced by others, of “geometric dynamic recrystallization” in aluminum. The average misorientation across low-angle boundaries initially increases during steady state but eventually reaches a maximum value of about 1.2 deg at ε ≃ 1.2. Since the flow stress stays nearly constant, the dramatic changes in the character of the subgrain boundaries that are observed during steady state suggest that the details of the boundaries arenot an important consideration in the rate-controlling process for creep.     

Evolution of dislocation structure in martensitic steels: the subgrain size as a sensor for creep strain and residual creep life

The results on the evolution of the dislocation structure in martensitic CrMoV-steels published by two research groups are shown to be consistent: The steady state dislocation spacings vary in inverse proportion to shear modulus normalized stress, the subgrains grow with strain at a rate which is determined by the initial subgrain size w₀, the steady state subgrain size w_∞ and the strain rate, independent of the composition of the material. At constant stress and temperature the strain ? and the subgrain size w are uniquely related by ? = ?_wln[log(w₀ / w_∞)/log(w / w_∞)] with ?_w = 0.12. Thus w can be used as a sensor for strain and, if the relation between strain and time is known, for the residual creep life.     

X-ray diffraction study of subgrain misorientation during high temperature creep of tin single crystals

Creep tests in the high temperature range (0.68 T_m-0.94 T_m, where T_m is the melting temperature) have been performed on high purity tin single crystals with the [100] direction as the tensile axis. Above the transition temperature, about 0.84 T_m (150 °C), the creep activation energy was found to be almost equal to the self diffusion energy. Below the transition temperature the creep activation energy is about half of the self diffusion energy and has a value of the order expected for dislocation pipe diffusion. A method based on X-ray rocking curves was developed to measure subgrain misorientation angles of crept specimens. The average subgrain misorientation angles for specimens crept at 70 °C and 100 °C increased continuously with creep strain at rates a factor of 20 to 40 smaller than that predicted by a cross-slip controlled process. The average subgrain misorientation angles at a given strain decrease slightly with increasing temperature. However, no abrupt change of the angle was observed at the transition temperature. It was concluded that a cross-slip controlled mechanism cannot control below the transition temperature. Instead, our results lend support to Sherby and Weertman’s argument that dislocation climb controls creep over the entire high temperature regime.     

Internal stress superplasticity in anisotropic

Internal stress superplasticity is assessed in powder metallurgy and wrought polycrystalline Zn and in polycrystalline α-U. These materials are anisotropic in their thermal expansion coefficients, and, as a result, internal stresses are generated during thermal cycling. A creep model is developed based on the contribution of internal stress to the enhancement and inhibition of normal plastic flow. This creep model, which has no disposable parameters, is shown to describe quantitatively the flow behavior of anisotropic materials under thermal cycling conditions, and correctly predicts the attainment of Newtonian flow characteristics at low stresses. It is predicted that certain polycrystalline ceramics can be made superplastic in tension when thermally cycled under small applied stress.     

Plastic and viscous deformation of metals

Deformation characteristics of tensile specimens of several alloys, including electrolytic copper, α-brass, and 304 stainless steel, have been studied by application of stress and measurement of change of length in a soft tensile machine. By means of experiments in which the stress rate is reduced suddenly from a positive value to zero and the strain rate measured, both during loading and during creep, it is found that permanent deformation consists of two components, a plastic component for which the strain rate is a function of stress and stress rate, and a viscous component which is functionally dependent on stress and temperature. Plastic deformation is relatively more evident at increasing stress rate but declines in importance through the series copper, a-brass, and stainless steel. As a consequence, for a fixed strain rate during loading, the initial creep rate is low in copper and little creep occurs; in stainless steel, however, the initial creep rate is nearly equal to the loading strain rate and creep is pronounced. The theory is not fully developed but is based on a competition between thermal and mechanical release of dislocation segments from obstacles or sources. Release produces a strain increment which may be small or large depending on the relative values of stress and structural resistance. Plastic deformation occurs when the applied stress is close to the mechanical threshold, mechanical release is relatively easy, and the strain consists, at a given strain rate, of a few large strain increments per unit time. For viscous flow the relative stress is low, thermal release easy, and the strain rate is composed of many small strain increments in each unit of time.     

The production and utility of recovered dislocation substructures

The production of dislocation substructures by cold working and recovery, fatigue, creep and hot working are reviewed. The relationships of subgrain size and dislocation density to the causal parameters of strain, strain rate, strain amplitude, temperature, stress and time (as applicable) are presented for each process. The importance of dislocation mechanisms such as climb, cross-glide, annihilation and subboundary formation are explained. The relative capabilities and limitations of each mode of creation with respect to both external processing and internal mechanisms are explored. The effects of the metal's stacking fault energy, of solid solution and of particle dispersion on structure and behavior are presented. The properties of the different kinds of substructures for room temperature and creep service are examined. The need for modification of the Petch relationship between yield strength and subgrain size is explored. The thermal stability is shown to be an important factor for creep service. It is concluded that the most suitable modes of substructure preparation are either cold working and recovery or hot working both from the view point of fitting into current industrial practice and from that of dependable, useful service properties. This paper is based on a presentation made at a symposium on “Mechanical-Thermal Processing and Dislocation Substructure Strengthening”, held at the Annual Meeting in Las Vegas, Nevada, on February 23, 1976, under the sponsorship of the TMS/IMD Heat Treating Committee.     

Denuded zones, diffusional creep, and grain boundary sliding

The appearance of denuded zones following low stress creep in particle-containing crystalline materials is both a microstructural prediction and observation often cited as irrefutable evidence for the Nabarro-Herring (N-H) mechanism of diffusional creep. The denuded zones are predicted to be at grain boundaries that are orthogonal to the direction of the applied stress. Furthermore, their dimensions should account for the accumulated plastic flow. In the present article, the evidence for such denuded zones is critically examined. These zones have been observed during creep of magnesium, aluminum, and nickel-base alloys. The investigation casts serious doubts on the apparently compelling evidence for the link between denuded zones and diffusional creep. Specifically, denuded zones are clearly observed under conditions that are explicitly not diffusional creep. Additionally, the denuded zones are often found in directions that are not orthogonal to the applied stress. Other mechanisms that can account for the observations of denuded zones are discussed. It is proposed that grain boundary sliding accommodated by slip is the rate-controlling process in the stress range where denuded zones have been observed. It is likely that the denuded zones are created by dissolution of precipitates at grain boundaries that are simultaneously sliding and migrating during creep. 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 Dan 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.     

Simulation of subgrain growth by subgrain rotation: A one-dimensional model

It has been known for many years that subgrain growth can occur by subgrain rotation. However, the kinetics of such a growth process have not been worked out. In this investigation, a simple model for such a process, namely, a single row of subgrains, has been studied by computer simulation. The rate of growth of the mean subgrain size and the variation in the distribution of the subgrain misorientations with time have been established. The differences between subgrain growth by rotation and normal grain growth are also discussed.     

On grain and subgrain rotations in two dimensions

Computer simulations of subgrain growth by coalescence in two dimensions have been carried out. The model governing the dynamics allows the subgrains to rotate in order to reduce the sub-boundary energies. The purpose of the model is to study this mechanism separately; thus, the sub-boundaries are not allowed to migrate out of their initial positions. Hence, a coarsening of the subgrain structure occurs due to coalescence only. Results from several simulations are discussed. It was found that the mean subgrain size increased as an exponential function of time. The effect of the initial distribution of orientations and angles of misorientation has also been studied. It was found that the width of the distribution of orientations is important for the evolution of the mean subgrain size. The model and, consequently, the simulations concern subgrain rotations leading to coalescence. Based on these results, the general case of grain rotations in two dimensions has been discussed. It has been suggested that grain rotations depend on the grain boundary energy as a function of the misorientation.     

Creep Behavior and Degradation of Subgrain Structures Pinned by Nanoscale Precipitates in Strength-Enhanced 5 to 12 Pct Cr Ferritic Steels

Creep behavior and degradation of subgrain structures and precipitates of Gr. 122 type xCr-2W-0.4Mo-1Cu-VNb (x = 5, 7, 9, 10.5, and 12 pct) steels were evaluated during short-term and long-term static aging and creep with regard to the Cr content of steel. Creep rupture life increased from 5 to 12 pct Cr in the short-term creep region, whereas in the long-term creep region, it increased up to 9 pct Cr and then decreased with the addition of Cr from 9 to 12 pct. Behavior of creep rupture life was attributed to the size of elongated subgrains. In the short-term creep region, subgrain size decreased from 5 to 12 pct Cr, corresponding to the longer creep strength. However, in the long-term creep region after 10⁴ hours, subgrain size increased up to 9 pct Cr and then decreased from 9 to 12 pct, corresponding to the behavior of creep rupture life. M₂₃C₆ and MX precipitates had the highest number fraction among all of the precipitates present in the studied steels. Cr concentration dependence of spacing of M₂₃C₆ and MX precipitates exhibited a V-like shape during short-term as well as long-term aging at 923 K (650  °C), and the minimum spacing of precipitates belonged to 9 pct Cr steel, corresponding to the lowest recovery speed of subgrain structures. In the short-term creep region, subgrain coarsening during creep was controlled by strain and proceeded slower with the addition of Cr, whereas in long-term creep region, subgrain coarsening was controlled by the stability of precipitates rather than due to the creep plastic deformation and took place faster from 9 to 12 pct and 9 to 5 pct Cr. However, M₂₃C₆ precipitates played a more important role than MX precipitates in the control of subgrain coarsening, and there was a closer correlation between spacing of M₂₃C₆ precipitates and subgrain size during static aging and long-term creep region.     

Deformation mechanisms of a rapidly solidified Al-8.8Fe-3.7Ce alloy

The mechanisms of deformation of a rapidly solidified and compacted Al-8.8Fe-3.7Ce (wt pct) alloy were investigated in the stress range 20 to 115 MPa and temperature range 523 to 623 K. The stress dependence of the steady state strain rates indicated a transition from diffusional creep to power law creep, the transition stress decreasing with increasing temperature from 70 MPa (σ/G = 3.1 × 10^-3) at 523 K to 40 MPa (σ/G = 1.9 × 10^-3) at 623 K. The activation energy in the power law creep regime was close to that of bulk self-diffusion in aluminum, while the activation energy in the diffusional creep regime was close to that of grain boundary self-diffusion in Al. The creep strain rates in the power law creep regime were found to be predicted much better by the substructure-invariant creep law (Sherby, 1981) than by the semi-empirical Dorn equation for Al, with the inclusion of a “threshold” stress. In the Coble creep regime, it was found that the cell/subgrain boundaries are inefficient vacancy sources/sinks and that their contribution to Coble creep is totally suppressed in this alloy. The Coble creep rates could be explained by using the average diameter of the powder particles as the effective grain size in the Coble creep equation.     

Features and effect factors of creep of single-crystal nickel-base superalloys

The creep behavior of two single-crystal nickel-base superalloys with [001] orientation has been studied by measuring the creep curves, internal friction stress of dislocation motion, transmission electron microscopy (TEM) observation and energy-dispersive X-ray analysis (EDAX) composition analysis. The results show that over the stress and temperature range, there are different creep activation energies, time exponents, and effective stress exponents in two alloys at different creep stages. The size and volume fraction of the γ′ phase in the tantalum-free alloy is obviously decreased with the elevated temperature. This results in the decrease of the internal friction stress during steady-state creep. Higher levels of tungsten in the alloy result in a smaller strain value and lower directional-coarsening rate during primary creep. During steady-state creep, the primary reason for the better creep resistance of the other alloy is that it contains more Al and also Ta, which maintains a high volume fraction of γ′ phase. The dislocation climb over the γ′ rafts is the major deformation mechanisms during steady-state tensile creep. The fact that the strain rate is decreased with the increase of the size and volume fraction of the γ′ rafts may be described by a modified constitutive equation that is based on a model of the rate of dislocation motion.     

Microstructural changes in a 12% chromium steel during creep

A quantitative metallographic study was performed using transmission electron microscopy (TEM) to describe the microstructural changes in a 12% chromium steel (X 20 CrMoV 12 1) during creep at 650°C. The creep experiments were conducted under constant load conditions corresponding to initial stresses of 175 and 80 N/mm². The heat treatment for this steel consists of austenitizing followed by tempering which results in a high density of free dislocations within small elongated subgrains with carbides on or very near some of the subgrain boundaries. During creep, the mean subgrain size increases for both the high and low stress levels. Carbide particle coarsening is observed for the low stress level. These processes result in a softening of the microstructure during creep deformation.     

Effect of matrix hardness on the creep properties of a 12CrMoVNb steel

Using a creep-ductile 12CrMoVNb steel, constant-load creep tests were conducted in air at 650 °C, and the effects of matrix hardness on the creep properties were investigated. Specimens with a matrix hardness (Rc) of 30, 25, and 20 were prepared using different tempering conditions. The creep behaviors were well described by the power-law creep equation, with the stress exponents of strain rate (n) and rupture time (χ) decreasing with matrix hardness. Rupture-time analyses showed that creep rupture occurred by the nucleation of creep cavities on second-phase particles and growth by creep flow of the surrounding matrix. A hardness decrease tends to lower the rupture time and increase the strain rate (ε), and the effect of hardness was quite distinct at high applied stresses due to the short creep times, but not so at low applied stresses due to elongated creep times. After 10⁴ hours, there were almost no effects. The hardness decrease during the creep test was more severe for the specimens with higher hardness and was also more severe in the gage section than in the head section, the latter due to the stress-assisted diffusion in the coarsening of carbides. Microstructural examinations showed that subgrain boundaries grew during creep, and equiaxed carbide particles coarsened during the creep test, the rates of coarsening being greater for specimens with a higher hardness.     

Strength softening and stress relaxation of nanostructured materials

A composite model is proposed to rationalize the phenomena of strength softening with decreasing grain size for nanostructured materials, which is assumed to consist of a grain interior and an amorphous grain-boundary layer. The grain interior deforms elastically under external stresses, while the linear viscoelastic flow is responsible for the plastic deformation of the grain-boundary layer, whose stress “relaxation” follows Maxwell’s equation. The results indicate that the strength of a nanostructured material decreases linearly with decreasing grain size, when the grain size is below a certain threshold. The model is compared with the experimental data from the published studies on nanostructured Cu and Ni. The relevant creep mechanisms for nanostructured materials are also discussed in light of model predictions.