Cyclic creep and anelastic relaxation analysis of an ODS superalloy

This paper documents the effect of stress and temperature on the cyclic minimum strain rate at two different loading frequencies for the oxide dispersion strengthened (ODS) superalloy, INCONEL* MA 6000. The apparent stress exponent and activation energy for cyclic creep at both frequencies studied are shown to be greater than values observed for static creep. The large values of the stress exponent and activation energy for cyclic creep are proposed to result from anelastic strain storage delaying nonrecoverable creep during the on-load portion of the cyclic creep loading, such that the “effective stress” driving nonrecoverable creep is only a small fraction of the applied stress. In addition, the temperature dependence of the anelastic relaxation that occurs during the off-load portion of the cyclic creep loading is determined. The activation energy found for the relaxation process is equal to about one-half that for self-diffusion in nickel. A mechanism of localized climb of dislocations over the oxide dispersoids present in INCONEL MA 6000 is postulated to account for the observed activation energy of the relaxation process. VINCENT C. NARDONE, formerly Associate Research Scientist, Henry Krumb School of Mines, Columbia University     

Anelastic relaxation controlled cyclic creep and cyclic stress rupture behavior of an oxide dispersion strengthened alloy

Cyclic creep deceleration relative to static creep was observed in oxide dispersion strengthened alloy Inconel MA 754 at 760 °C and cyclic stresses of 221 MPa-41 MPa, 231 MPa-41 MPa, and 241 MPa-41 MPa. Tests were run over the range of frequency from 0.05 cycles per hour to six cycles per hour. The maximum cyclic deceleration, which was manifested as a reduced net creep rate and increased rupture life, was observed at the highest cyclic frequency. Considerable anelastic strain, having a magnitude of ε_a/ε_e～ 1/3, is stored in MA 754 at 760 °C under these creep loads, and this strain may be recovered in the off-load half cycle of a cyclic creep test. During the higher frequency tests, the effect of an incomplete storage of anelastic strain on the accompanying nonrecoverable creep rate provides a mechanism for the frequency dependent cyclic creep deceleration. The proposed mechanism is in agreement with mixed-mode test results and with TEM examination of interrupted-test specimens.     

A model for nano-indentation creep

A new model is developed to describe that stage of nano-intentation creep prior to “pop-in”, i.e. when the indentation load induces purely elastic stresses within the sample. Expressions for the stress fields due to a conical indenter are derived and the resulting chemical potential and diffusion fluxes established. The considerations lead to a creep rate equation which is found to fit well with existing experimental data on tungsten. The model is hence used to predict nano-indentation creep rates at various temperatures. It is found, for example, that at a temperature as low as 100°C, the indentation creep rate of tungsten can be considerable.     

A coupled damage model for creep

Alloy steels of type 9Cr1Mo are being developed worldwide for the boiler and turbine components of supercritical and ultra supercritical thermal power plants and for the pressure vessel of fast breeder reactors. These steels exhibit very complex high temperature creep cavitation processes with coupled influences of creep strain, material softening and ageing etc. A new viscoplastic model considering both deformation and damage evolution has been developed in this work to predict high temperature creep deformation and damage of a 9Cr1Mo steel. Smooth tensile specimens have been analysed using this new model and the evolution of creep damage has been predicted. The results have been compared with those of experiment from literature. From the initial results, it is observed that this approach is very promising to carry out design and fitness-for-purpose of service of actual plant components.     

A Microstructural model for primary creep

The evolution of primary creep is modelled by the formation of sub-cells in which a pattern of internal stresses exists. The internal stresses have two components, one a general isotropic impediment to dislocation movement, the other an elastic back stress leading to kinematic hardening. The stresses are built up by the polarised accumulation of dislocations and they recover by diffusional relaxation within the sub-cells. The model differs from others in focussing on the sub-cell size and misorientation as the important state variables.     

A theoretical model for creep crack growth

A theory of creep crack growth has been developed with the presumption that the crack growth occurs by the diffusion of vacancies along the grain boundaries. This is consistent with many experimental results that show that creep fracture is generally of intergranular type and the activation energies for crack growth rates fall within the range of grain boundary diffusion energies. The theory is based on the concept that creep crack growth results from a balance of two competing processes-the diffusion of point defects that contributes to the growth and the creep deformation process that retards the growth and causes even its arrest. The present analysis shows that crack growth via grain boundary diffusion occurs within some temperature range. The upper limiting temperature is determined by the bulk diffusion process which disperses the vacancies, that are diffusing to the crack tip, to the plastic zone ahead of the crack front. The lower temperature limit is set by the fact that the grain boundary diffusion rates decrease with the decrease in temperature and thus large stress intensities approaching the fracture toughness value are required to accomplish crack growth by the grain boundary diffusion. Outside these limits creep crack growth occurs via deformation which is significantly slower than growth by the grain boundary diffusion process. The importance of the present analysis rests on the fact that service conditions for many high temperature structural materials fall within the regime wherein creep crack growth occurs via grain boundary diffusion.     

Observations of anelastic backflow following stress reductions during creep of pure metals

The anelastic contribution to creep transients in pure f.c.c. metals has been studied by conducting experiments in which nearly the entire applied stress is removed. The observed anelastic strains range from as little as one quarter of the calculated elastic contraction for Pb to 7 or 8 times the elastic contraction for pure Al. The recoverable strains in Cu are generally about equal to the elastic strains. For Al, the magnitude of the recoverable strain increases with prior creep strain. Both the magnitude and kinetics of backflow are similar for polycrystalline and single crystal specimens. Consideration of the kinetics of backflow suggests that there are at least two rate controlling mechanisms which operate during this process. An attempt has been made to determine the physical mechanisms which contribute to creep anelasticity. Based on a qualitative consideration of the kinetics and magnitude of the anelastic transients, the most likely mechanism involves motion of dislocations from subgrain interiors to the subgrain walls and is driven by long range internal back stresses. Other simple mechanisms cannot account for the large recoverable strains, although they may make additional contributions to the overall transient.     

A theory of diffusion controlled intergranular creep crack growth

A theory of intergranular creep crack growth in brittle materials has been developed. The mechanism of crack propagation is removal of atoms from the crack tip by stress induced grain boundary diffusion and their deposition at the grain boundary. The width of the crack is assumed to be constant during crack propagation. Any possible plastic deformation at the crack tip has been neglected. The stress relaxation ahead of the crack tip which arises due to the non-uniform deposition of material onto the grain boundary is calculated and the diffusion process governed by this relaxed stress studied. Thus the theory is analogous to those developed previously for the growth of r-type voids in grain boundaries. Both the steady state and the transient were considered. It was found that the rate of crack growth at any moment was determined by the nominal stress intensity factor K. A minimum stress intensity, K_min' exists below which no crack growth can take place. Conversely there is a maximum limiting rate of crack growth determined by the maximum surface diffusion rate. For K > K_min the steady state is always reached quickly and the length of the transient period t_tr is proportional to K⁻⁶. For K > K_min the rate of crack growth is proportional to K⁴. A comparison with experimental measurements on brittle ½Cr-½Mo-¼V steels show good agreement between the theory and experiment.     

Measurement of anelastic creep strains in Al-5.5 at.% Mg using a new technique: Implications for the mechanism of class I creep

The anelastic response of Al-5.5 at.% Mg has been studied in the Class I creep regime using stress change-strain transient experiments at 573 and 673 K. Conventional single drop experiments yield a nonlinear variation of total and back-extrapolated anelastic strain with stress reduction, while a linear response is found for stress increments. These results are inconsistent with the predictions of a new dislocation loop model for alloy type creep. An examination of the transient creep process using the loop model indicates that the anelastic backstrain and forward creep processes are not independent, and that the predicted anelastic response can be observed only for nearly complete unloadings. This analysis has led to the development of the constant reduced stress-dual drop experiment. The results of this new technique correlate well with the purely anelastic backstrain mechanism proposed in the loop model. This interpretation of the creep transient implies that measurements of internal stresses using the conventional single drop test are inaccurate, and suggests that the internal stress accounts for less than 10% of the applied stress for alloy type creep.     

A stochastic model for evolution of creep damage in engineering materials

In this work a stochastic model for the creep damage evolution and associated scatter has been developed in terms of a discontinuous Markov process. The magnitude of damage has been described in the form of a probability distribution function whose evolution in time characterizes the nondeterministic nature of the damage accumulation process. The model is able to describe the state of damage along with the associated scatter at a given time at any stress level. The validity of the model has been established by comparing the predicted creep curves generated for a specific loading condition with those experimentally obtained for an austenitic stainless steel (Type 316, 18Cr 8 Ni 2Mo).     

A critical strain model for the creep fracture of nickel-base superalloys

Fracture toughness samples of NIMONIC 115 were creep tested at 704°C in Mode I (tension) and Mode III (torsion) loading. In Mode III loading the rupture lives were two orders of magnitude shorter than in Mode I. The effects of loading mode are shown to agree with predictions based on a critical strain fracture model. Earlier test results with a number of different superalloys also are consistent with a strain controlled fracture model. Improved resistance to crack growth during creep at intermediate temperatures can be achieved by increasing Young’s modulus, yield strength, grain size and the critical strain value.     

A critical strain model for the creep fracture of nickel-base superalloys

Fracture toughness samples of NIMONIC 115 were creep tested at 704°C in Mode I (tension) and Mode III (torsion) loading. In Mode III loading the rupture lives were two orders of magnitude shorter than in Mode I. The effects of loading mode are shown to agree with predictions based on a critical strain fracture model. Earlier test results with a number of different superalloys also are consistent with a strain controlled fracture model. Improved resistance to crack growth during creep at intermediate temperatures can be achieved by increasing Young’s modulus, yield strength, grain size and the critical strain value.     

A micromechanical model for creep in short fibre reinforced aluminium alloys

Three elementary microstructural processes control creep of short fibre reinforced, squeeze cast aluminium alloys: (i) loading of fibres by dislocations through the formation of a work hardened zone (WHZ), (ii) a recovery mechanism which decreases the dislocation density in the WHZ, and (iii) multiple breakage of fibres. A uniaxial micromechanical model is presented which is based on these three elementary processes. The model rationalizes the shape of individual creep curves as well as the temperature and stress dependence of the minimum creep rate. The minimum creep rate is shown to result from a superposition of primary (loading of fibres by dislocations) and tertiary (breakage of fibres and shortening of the length of the recovery path) processes.     

The influence of thermal and surface treatments on the anelastic creep of Al-Zn and Al-Cu alloys

In many industrial applications, like high precision force measurements or nanopositioning, the elastic and dimensional stabilities of materials are required at a nanometric scale. Therefore, some aspects of room temperature creep of commercial Al-Zn and Al-Cu alloys have been studied. The anelastic creep was measured at room temperature by means of a high resolution laser interferometer. The irreversible component of the deformation was quantified by measuring the viscoelastic after-effect. The anelastic relaxation of Al-Zn has been studied as a function of annealing time and temperature. The results are correlated with the size and the density of precipitates and the extension of the precipitate free zone. The influence of a surface treatment (sandblasting, electropolishing, Cu-galvanizing, chroming, Zn-plating) on anclastic relaxation has also been considered and explained in terms of the anelastic and elastic properties of both the surface layer and the bulk.     

Diffusion and deformation controlled creep crack growth

A mechanism for creep crack growth is proposed by which the crack grows by formation of grain boundary cavities ahead of the crack tip. Two cases are considered; firstly, when cavity growth is diffusion controlled and secondly, where growth is deformation controlled. The resultant crack growth rates predicted by these theoretical models are compared with experimental data.     

A model for creep-fatigue interaction in terms of crack-tip stress relaxation

A model was developed to explain the mechanism of the degradation of fatigue lives caused by the growth of transgranular crack without cavitational damage in spite of the creep-fatigue loading condition for some type 304L stainless steel and 1Cr-Mo-V steel. The model was developed by incorporating the stress relaxation effect during tensile hold time into the pure fatigue crack growth model based on the crack-tip shearing process. In the crack-tip region, the stress relaxation during hold time at the tensile peak stress reduces the maximum stress level but accumulates inelastic strain, which induces creep crack growth during hold time and enhances subsequent fatigue crack growth during subsequent loading by promoting the crack-tip shearing process. The predicted creep-fatigue lives by the model were in good agreement with the actual lives for type 304L stainless steel at 823 and 865 K and for 1Cr-Mo-V rotor steel at 823 K. The model was further expanded to explain the degradation of the life under the conditions of compressive hold cycling for 1Cr-Mo-V and 12Cr-Mo-V steels.     

A model for creep based on the climb of dislocations at grain boundaries

A model for creep based on the climb of dislocations at grain boundaries is presented. It is shown that when a sliding interface or slip band intersects a grain boundary, a traction distribution is established on the boundary. The diffusional flow induced by these tractions results in a steady state creep process. This slip band model predicts an activation energy corresponding to grain boundary self diffusion, with a stress exponent and a grain size dependence which increase and decrease, respectively, as the applied stress increases. The theoretically determined creep rates are in good agreement with the data for metals and alloys which deform by grain boundary sliding and exhibit superplastic flow properties. Other models for creep controlled by grain boundary diffusion are briefly reviewed and compared with the present model. It is concluded that superplastic deformation involves both purely diffusional flow and dislocation motion.