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.     

The Contribution of Dislocation Density and Velocity to the Strain Rate and Size Effect Using Transient Indentation Methods and Activation Volume Analysis

Constant load indentation creep and load relaxation tests were performed on several FCC Al, Ag, and Ni metals that exhibit indentation size effect (ISE) to examine the coupled relationship between the activation volume V* at specific loads, the dislocation density ρ, and the dislocation velocity (v) from kinetics-based perspective. The influence of the ISE on the dislocation velocity and the activation volume is thoroughly examined using the two independent indentation creep and load relaxation experiments. This study is carried out based on the general experimental and theoretical hypothesis that the ISE is driven by a dislocation mechanism, specifically the increase in the geometrically necessary dislocation density at shallow depth of indentation due to the presence of a large strain gradient. Geometrically necessary dislocations dominate the material’s propensity to work harden when their density exceeds the density of statistically stored dislocations and are primarily considered responsible for the size effects observed in indentation. Based on the preestablished bilinear behavior and the decrease in the activation volume with hardening due to dislocation–dislocation interaction in indentation creep experiments by Elmustafa and Stone, 2003, we demonstrate that the dislocation velocity exhibits a bilinear behavior when plotted vs hardness using the Orowan’s relation. Ag and Ni distinctively depict a bilinear behavior in the dislocation velocity with hardness, whereas Al exhibited a rather linear behavior. This can be explained by the fact that aluminum’s work-hardening rate is higher due to the increase in the rate and intensity of cross-slip and dislocation climbing.

     

The effect of particle reinforcement on the creep behavior of single-phase aluminum

The effect of TiC particle reinforcement on the creep behavior of Al (99.8) and Al-1.5Mg is investigated in the temperature range of 150 °C to 250 °C. The dislocation structure developed during creep is characterized in these materials. The addition of TiC increases creep resistance in both alloys. In pure aluminum, the presence of 15 vol pct TiC leads to a factor of 400 to 40,000 increase in creep resistance. The creep strengthening observed in Al/TiC/15_p is substantially greater than the direct strengthening predicted by continuum models. Traditional methods for explaining creep strengthening in particle-reinforced materials(e.g., threshold stress, constant structure, and dislocation density) are unable to account for the increase in creep resistance. The creep hardening rate(h) is found to be 100 times higher in Al/TiC/15_p, than in unreinforced Al. When incorporated into a recovery creep model, this increase inh can explain the reduction in creep rate in Al/TiC/15_p. Particle reinforcement affects creep hardening, and thus creep rate, by altering the equilibrium dislocation substructure that forms during steady-state creep. The nonequilibrium structure generates internal stresses which lower the rate of dislocation glide. The strengthening observed by adding TiC to Al-1.5Mg is much smaller than that found in the pure aluminum materials and is consistent with the amount of strengthening predicted by continuum models. These results show that while both direct (continuum) and indirect strengthening occur in particle-reinforced aluminum alloys, the ratio of indirect to direct strengthening is strongly influenced by the operative matrix strengthening mechanisms. This article is based on a presentation made in the symposium entitled “Creep and Fatigue in Metal Matrix Composites” at the 1994 TMS/ASM Spring meeting, held February 28–March 3, 1994, in San Francisco, California, under the auspices of the Joint TMS-SMD/ASM-MSD Composite Materials Committee.     

Novel oxide-dispersion-strengthened copper alloys from rapidly solidified precursors: Part 2. Creep behavior

Yttria- and zirconia-dispersion-strengthened copper alloys produced by hot pressing and hot extrusion of internally oxidized melt-spun Cu-0.33 at. pct Y and Cu-0.32 at. pct Zr ribbons were subjected to compressive creep tests at 923 and 973 K. Creep strengths and stress exponents were higher for the Cu-ZrO₂ alloy than for Cu-Y₂O₃, and both were higher than those of pure copper. Comparisons of the creep properties with published data for pure copper along with microscopic evidence indicated that at least two creep mechanisms were operating in these alloys. These are attractive dislocation/particle interactions in the matrix and particle-inhibited diffusional creep. The experimental data at low stresses could be described reasonably well by the Arzt-Ashby-Verrai model for particle-restricted diffusional creep, using plausible values for the structure-related parameters. Fitting the higher stress creep data to the Rösier-Arzt model of dislocation/particle interaction resulted in values of the relaxation parameter (k) within the bounds predicted by the theory. The estimated k values for Y₂O₃ and ZrO₂ are in the vicinity of ～0.8, compared with ～0.9 for the γ-Al₂O₃ dispersoids in conventional oxide-dispersion-strengthened (ODS) Cu. The analysis suggests that these alternate dispersoids with fluorite-related structures may interact more effectively with dislocations during creep.     

Crystal Plasticity Modeling of Hydrogen and Hydrogen-Related Defects in Initial Yield and Plastic Flow of Single-Crystal Stainless Steel 316L

Understanding of and accounting for various mechanisms that affect inelastic deformation of crystalline metals in the presence of hydrogen remains an unsettled issue. Macroscopic experimental observations contradict limited atomistic simulations, complicating the situation. In this work, we extend a recent physically based crystal viscoplasticity framework to include constitutive equations with a direct dependence on relevant hydrogen and hydrogen-related defect concentrations. Focusing on initial yield and post-yield strain hardening, we consider hydrogen solute drag on mobile dislocations as well as the role of dilute concentrations of hydrogen-vacancy complexes as obstacles to dislocation motion. Furthermore, the evolution of hydrogen and hydrogen-affected defect concentrations is explicitly considered via evolving hydrogen trap concentrations. The resulting framework is used to investigate hydrogen effects on the quasistatic, monotonic, strain-controlled uniaxial loading of single-crystal stainless steel 316L smooth specimens at room temperature in an attempt to connect atomistic insight and the resulting mesoscale model framework with experimental interpretations. Attributing the primary role of hydrogen in this manner is shown to produce good agreement with experiments in the initial yield and post-yield regime. The dominance of various hydrogen effects mechanisms is discussed.

     

On Rösler and Arzt's new model of creep in dispersion strengthened alloys

The model of creep in dispersion (non-coherent particle) strengthened alloys assuming thermally activated detachment of dislocations from particles to be the rate controlling process, recently presented by Rösler and Arzt, is correlated with some available creep and structure data for aluminium alloys strengthened by Al₄C₃ and Al₂O₃ particles. It is shown that though the model requires applied stress dependent apparent activation energy of creep, the stress dependence of creep rate can be satisfactorily accounted for even when this activation energy is stress independent, admitting a strong stress dependence of the pre-exponential structure factor, i.e. of the mobile dislocation density. On the other hand, the model is not able to account for the temperature dependence of creep rate if it is significantly stronger than that of the coefficient of lattice diffusion as is usually the case with alloys strengthened by non-coherent particles in which the attractive dislocation/particle interaction can be expected.     

Numerical models of creep and boundary sliding mechanisms in single-phase, dual-phase, and fully lamellar titanium aluminide

Finite element simulations of the high-temperature behavior of single-phase γ, dual-phase α₂+γ, and fully lamellar (FL) α₂+γTiAl intermetallic alloy microstructures have been performed. Nonlinear viscous primary creep deformation is modeled in each phase based on published creep data. Models were also developed that incorporate grain boundary and lath boundary sliding in addition to the dislocation creep flow within each phase. Overall strain rates are compared to gain an understanding of the relative influence each of these localized deformation mechanisms has on the creep strength of the microstructures considered. Facet stress enhancement factors were also determined for the transverse grain facets in each model to examine the relative susceptibility to creep damage. The results indicate that a mechanism for unrestricted sliding of γ lath boundaries theorized by Hazzledine and co-workers leads to unrealistically high strain rates. However, the results also suggest that the greater creep strength observed experimentally for the lamellar microstructure is primarily due to inhibited former grain boundary sliding (GBS) in this microstructure compared to relatively unimpeded GBS in the equiaxed microstructures. The serrated nature of the former grain boundaries generally observed for lamellar TiAl alloys is consistent with this finding.     

Dislocation-Activation analysis of diffusion-controlled creep processes

Typically, the analysis of high-temperature creep is based upon “diffusion-controlled processes”,i.e., establishing boundary conditions at certain “sinks” and then solving the diffusion equation to obtain the rate of mass transport and from this calculating the dislocation velocity. This automatically establishes a fixed value for the activation energy of the process, namely that for self-diffusion, and normally no other “activation parameter” is considered, although sometimes the activation volume has been considered and shown to be equivalent in several materials to that for self-diffusion. On the other hand, investigators of low-temperature creep typically invoke activation analysis, often without positing any specific mechanism, for the movement of the dislocation and consider the work done by the applied stress to decrease the required activation energy. These analysts then calculate activation energy, volume and area from their data and compare these with values expected for specific mechanisms. No real attempt at a synthesis of these two methods of analysis has been presented. We discuss here a specific model, namely the movement of a screw dislocation containing jogs, and perform the analysis both by the diffusion-control approach and by the activation analysis approach. In so doing we show specifically that certain restrictive assumptions concerning activation areas are implicit in the diffusion-control approach even though they are never dealt with explicitly. The techniques here can be applied to other mechanisms as well.     

Creep Performance Modeling of Modified 9Cr-1Mo Steels with Oxidation

In this study, the deformation-mechanism-based true-stress (DMTS) creep model is modified to include oxidation influence on the long-term creep performance of modified 9Cr-1Mo steels. An area-deduction method is introduced to evaluate oxide scale formation on the creep coupons, which is incorporated into the DMTS model formulated based on intragranular dislocation glide (IDG), intragranular dislocation climb (IDC), and grain boundary sliding (GBS) mechanisms, in modifying the true stress. Thus, the modified DMTS model can not only describe the creep curve, but also predict the long-term creep life and failure mode, which is shown to be in good agreement with the creep data generated in the authors’ laboratory as well as by the National Institute for Materials Science (NIMS) of Japan for long-term (> 104 hours) creep life prediction on Grade 91 steels. In particular, the predictability of the model is demonstrated in comparison with the Larson–Miller parameter method. In addition, the modified DMTS model provides quantitative information of mechanism partitioning, insinuating the failure mode via intragranular/intergranular deformation. Therefore, it has advantages over the empirical models in providing physical insights of creep failure, which can be useful to material design for performance optimization.     

Creep of an AISI 310 type stainless steel and its numerical simulation using the Öström-Lagneborg creep model

The creep behaviour of an AISI 310 type stainless steel was determined under constant load (stress range 80–320 MPa) at a temperature of 700°C. The stress exponent, n, monotonically increased with the applied stress from a value of 2.8 to 16. The activation energy for creep, Q_c, measured at 170, 200 and 230 MPa over the temperature range 650–800°C, is 341 kJ/mol. An activation energy of this magnitude indicates that the alloying elements in this steel are involved in the recovery climb process of the dislocation network. A simple and practical simulation was made of the experimental creep results by using the Öström-Lagneborg creep model, and the results are compared to other independent models and experimental results. A good fit between the experimental results and the calculated strain-time curves can be obtained by adjustment of model parameters to out material. The applicability of the Öström-Lagneborg theory to the creep involving subgrain structure formation is evaluated in light of the elastic theories for subgrain boundaries and recent experimental findings. By considering only forest dislocations not incorporated in subgrain boundaries and introducing a subgrain structure function S_g(t), the Öström-Lagneborg model is able to simulate the creep behaviour where a subgrain structure is formed during the creep test. Further refinement of the theory is suggested whereby an assessment is made of the dislocation network coarsening kinetics.     

Creep characteristics of single crystalline Ni3Al(Ta,B)

The creep characteristics, including the nature of the creep transient after a stress reduction and activation energy for creep of single crystalline Ni₃Al(Ta,B) in the temperature range 1083 to 1388 K, were investigated. An inverse type of creep transient is exhibited during stress reduction tests in the creep regime where the stress exponent is equal to 3.2. The activation energy for creep in this regime is equal to 340 kJ mol⁻¹. A normal type of creep transient is observed during stress reduction tests in the regime where the stress exponent is equal to 4.3. The activation energy for creep in this regime is equal to 530 kJ mol⁻¹. The different transient creep behavior and activation energies for creep observed in this investigation are consistent with the previous suggestion that then = 4.3 regime is associated with creep controlled by dislocation climb, whereas then = 3.2 regime is associated with a viscous dislocation glide process for Ni₃Al at high temperatures.     

Grain boundary sliding in the presence of grain boundary precipitates during transient creep

A constitutive rate equation for grain boundary sliding (GBS), in the presence of grain boundary precipitates, is developed. Langdon’s GBS model is modified by incorporating physically de-fined back stresses opposing dislocation glide and climb and by modifying the grain size de-pendence of creep rate. The rate equation accurately predicts the stress dependence of minimum creep rate and change in activation energy occurring as a result of changing the grain boundary precipitate distribution in complex Ni-base superalloys. The rate equation, along with the math-ematical formulations for internal stresses, is used to derive a transient creep model, where the transient is regarded as the combination of primary and secondary stages of creep in constant load creep tests. The transient creep model predicts that the transient creep strain is dependent on stress and independent of test temperature. It is predicted that a true steady-state creep will only be observed after an infinitely long time. However, tertiary creep mechanisms are expected to intervene and lead to an acceleration in creep rate long before the onset of a true steady state. The model accurately predicts the strain vs time relationships for transient creep in IN738LC Ni-base superalloy, containing different grain boundary carbide distributions, over a range of temperatures.     

Radiation effects on time-dependent deformation: Creep and growth

Observations of irradiation creep strain as well as irradiation growth strain and related microstructures are reviewed and compared to mechanisms for radiation effects on time-dependent deformation. Composition, microstructure, stress, and temperature affect irradiation creep less than thermal creep. Irradiation creep rates can often dominate thermal creep rates, particularly at low temperatures and low stresses. Irradiation creep mechanisms are classified in two general categories: (1) stress-induced preferential absorption and (2) climb glide. In the former, creep results from dislocation climb, whereas in the latter, creep results from dislocation glide. The effects of irradiation creep on failure modes in nuclear environments are discussed. This paper is based on a presentation made in the symposium “Irradiation-Enhanced Materials Science and Engineering” presented as part of the ASM INTERNATIONAL 75th Anniversary celebration at the 1988 World Materials Congress in Chicago, IL, September 2–29, 1988, under the auspices of the Nuclear Materials Committee of TMS-AIME and ASM-MSD.     

Primary creep of TiN dispersion hardened 20%Cr-25%Ni stainless steel at 160 MPa and 1123 K—II. Annealing behaviour

The annealing response of specimens of TiN dispersion hardened 20%Cr-25%Ni stainless steel after primary creep to a range of strains at 160 MPa, 1123 K is described (the microstructural development during primary creep has been reported elsewhere). It is shown that there is a driving force not only for reduction of the density, but also for an increase in perfection of the creep-induced matrix dislocation network. Moreover, it is shown that there is a driving force for the recovery of the dislocation tangles which develop at TiN particles during deformation. The details of the way in which the network characteristics change in annealing as a function of prior creep strain are fully consistent with the development during primary creep of an internal stress distribution. The latter is modelled as arising due to the presence of the dislocation tangles, which themselves occur as a result of stress relaxation associated with Orowan bypass at TiN particles. In the presence of such an internal stress during deformation, load removal produces a negative effective applied stress in the matrix, which dominates the network behaviour. It is concluded that the model of primary creep response described earlier is realistic, and emphasised that the observed strain/time variation during deformation depends on the mutually interdependent behaviour of all the components of the dislocation substructure.     

Radiation effects on time-dependent deformation: Creep and growth

Observations of irradiation creep strain as well as irradiation growth strain and related microstructures are reviewed and compared to mechanisms for radiation effects on time-dependent deformation. Composition, microstructure, stress, and temperature affect irradiation creep less than thermal creep. Irradiation creep rates can often dominate thermal creep rates, particularly at low temperatures and low stresses. Irradiation creep mechanisms are classified in two general categories: (1) stress-induced preferential absorption and (2) climb glide. In the former, creep results from dislocation climb, whereas in the latter, creep results from dislocation glide. The effects of irradiation creep on failure modes in nuclear environments are discussed.     

NiAl-28Cr-5.5Mo-0.5Hf-0.012P合金的蠕变性能研究

研究了热等静压态NiAl-28Cr-5．5Mo-0.5Hf-0．012P合金的高温蠕变行为。结果表明：实验合金具有较短的减速蠕变阶段和相当长的稳态蠕变阶段以及很高的蠕变应变；在研究的实验条件范围内，合金的蠕变变形机制为低温高应力下的位错粘滞滑移控制和高温低应力下的位错攀移控制；蠕变后合金的显微组织变化不大，表明蠕变断裂受孔洞及裂纹的形成和扩展所控制，而且蠕变断裂行为符合修正后的Monkman-Grant规律：Intf＋0.775lnε=1.104。