Creep Of Single Crystal Superalloy Research Articles

Microstructure based model for creep of single crystal superalloys in the high temperature and low stress creep regime

A new constitutive creep model for Ni-base superalloys has been developed that links the instantaneous creep response to incremental microstructure changes occurring during creep. The structure starts with cuboidal γ′- particles embedded in the γ-phase, and transitions to a rafted structure. In the present Kocks-Mecking type of model, the dislocation density ρ is considered as a state variable that evolves during creep. The increase of ρ depends on the γ-channel width in the γ/γ′-microstructure. Recovery, i.e., the reduction of ρ, is modelled from thermally activated, mechanically assisted climb. The strain rate is also modelled from the very same recovery process. The model successfully describes creep curves in a range of temperatures and load stresses with a maximum of five physical parameters. Once the model has been calibrated, it can be used to predict creep curves for other temperatures, stresses, and microstructures if the channel width evolution is known. The model is even capable of making reasonable predictions when fitted only to a single experiment. Extrapolations to different alloys with moderately varying compositions are possible.

Misfit and the mechanism of high temperature and low stress creep of Ni-base single crystal superalloys

The present work proposes a new elementary deformation mechanism which governs high temperature and low stress creep of single crystal superalloys (SXs), where the misfit between the γ- and the γ′-phase plays a central role. In the coherent two phase SX microstructure, there is a tendency to minimize the overall elastic strain energy. This is accomplished by the formation of dislocation networks in the γ-phase close to the γ/γ’-interfaces. The stress fields of the network dislocations and misfit stresses accommodate each other to keep the overall strain energy of the system at a minimum. Previous work has shown that dynamic recovery is associated with knitting-out reactions, where dislocations from the network shear the γ’-phase and annihilate with dislocations of opposite sign on the other side of the γ’-phase region. Due to the presence of the misfit this results in an increase of elastic strain energy which is counteracted by coupled knitting-in reactions where newly arriving γ-channel dislocations re-establish the minimum energy configuration. Here we provide microstructural evidence for knitting-out and knitting-in reactions and show that while these reactions clearly occur, dislocation network spacings stay constant. The misfit between the γ- and the γ′-phase accounts for a constant network spacing. Dislocation networks are not static but represent dynamic steady state equilibrium structures in an evolving microstructure. Knitting regular networks requires climb processes which are suggested to be rate controlling. This new view of high temperature and low stress creep mechanism of SXs allows to rationalize previous results published in the literature.

Features and uniform description of I, II, and III stages of the creep in single-crystal superalloys

Features of the creep process in single-crystal nickel-based superalloys are studied in a wide range of temperatures and holding time for different crystallographic orientations. The results of experimental study of high-temperature creep obtained for different single-crystal superalloys are presented. The dominance of stage III of creep is observed for considered temperature range and loads. Uniform creep models describing I, II, and III stages, are proposed taking into account damage accumulation based on the Norton – Bailey relations and power law of evolution for the scalar damage measure of Kachanov – Rabotnov. A hierarchical sequence of creep models of various degrees of complexity is suggested depending on the necessity of taking into account stage I. A material model including six constants is sufficient to describe stages II and III. Simultaneous accounting of all three stages of creep can be carried out using model with nine constants. The assumption on the absence of damage at the first stage leads to a material model with ten constants. The entered additional tenth parameter characterizes the duration of the first stage. Identification methods for the parameters of the introduced models based on using the least-squares method and Nedeler – Mead method for solving the problem of minimizing the error functional are proposed. The results of verification of the proposed inelastic deformation models are presented for various nickel-based single-crystal superalloys. The standard deviation between the experimental and computation results for all the proposed creep models does not exceed 10%. This allows us to recommend the developed approach for estimating the level of irreversible accumulated strains and durability of the structural elements made of single-crystal superalloys.

Crystal Plasticity Study of Heterogeneous Deformation Behavior in γ Matrix Channels during High Temperature Low Stress Creep of Single Crystal Superalloys

Abstract Single crystal nickel-based superalloys have high temperature creep resistance due to particle strengthening by high volume fraction of coherent γ′ precipitates distributed within nickel-based solid solution γ matrix. In the high temperature low stress regime, published experimental studies reveal that the creep deformation mechanism during the secondary stage is predominantly by dislocation glide in the γ matrix only, and that there is a preferential motion of dislocations in the matrix, oriented in a direction perpendicular to the stress. In this work, the crystal plasticity finite element method is employed to perform creep simulations on a representative volume element in the high temperature and low stress regime. A sine-hyperbolic–based material creep model was used for the matrix, while the precipitates are assumed to be elastic. A softening model incorporating the evolution of mobile dislocation density was used to capture the transition from secondary to tertiary creep. The predicted creep curves agree well with the published experimental measurements on single crystal superalloy CMSX-4. The simulations predict a higher creep strain distribution in the horizontal channel of the matrix (perpendicular to the applied stress) as compared with the vertical channel (horizontal to the applied stress). Local creep strain distributions in the channels were found to be greater than twice their average creep strain. The results provide key insights into the distribution of macroscopic creep strain in the local channels of the γ matrix to further aid in the microstructural design of creep-resistant superalloys.

Critical assessment 31: on the modelling of tertiary creep in single-crystal superalloys

ABSTRACTModelling of tertiary creep in single-crystal superalloys – operative over the majority of the temperature/stress regime of relevance – is assessed. Traditional, empirical approaches are useful for the prediction of component life; a modern trend is for more physically faithful models which account for microstructure and alloy composition. Calculations are made using different methods, to identify advantages/disadvantages, in an effort to approach best practice. The predictions are tested against experimental data. The creep resistance can be estimated to within approximately one-half of a Larson–Miller parameter, from an input of alloy composition, deformation conditions, and estimates of microstructural parameters, rate laws (and parameters therein), and physical constants. Different merit indices are considered to identify the most appropriate for compositional optimisation.

Testing of Ni-base superalloy single crystals with circular notched miniature tensile creep (CNMTC) specimens

The present work introduces a novel circular notched miniature tensile creep (CNMTC) specimen which is used to study the influence of notches on creep and of multiaxial stress states on microstructural evolution in Ni-based single crystal (SX) superalloys. It is briefly discussed how mild circular notches affect the stress state in the notch root of a tensile bar during elastic loading. Then the stress redistribution under creep conditions is calculated using the finite element method (FEM), assuming isotropic material behavior. Two series of interrupted creep experiments with the Ni-based single crystal superalloy ERBO1 (CMSX-4 type) were then performed at 950°C, with flat uniaxial miniature tensile creep (FUMTC) and CNMTC <100> specimens, respectively. The evolution of cavities and microcracks in both types of specimens was carefully analyzed after 81, 169, and 306h. In the uniaxial experiments, a growth of cast pores and the formation of new creep cavities were observed. These degradation processes were much less pronounced in the circular notched specimens. The results of the present work are discussed in the light of previous findings on the influence of multiaxial stress states on creep in single crystal superalloys.

Interfacial dislocation motion and interactions in single-crystal superalloys

The early stage of high-temperature low-stress creep in single-crystal superalloys is characterized by the rapid development of interfacial dislocation networks. Although interfacial motion and dynamic recovery of these dislocation networks have long been expected to control the subsequent creep behavior, direct observation and hence in-depth understanding of such processes has not been achieved. Incorporating recent developments of discrete dislocation dynamics models, we simulate interfacial dislocation motion in the channel structures of single-crystal superalloys, and investigate how interfacial dislocation motion and dynamic recovery are affected by interfacial dislocation interactions and lattice misfit. Different types of dislocation interactions are considered: self, collinear, coplanar, Lomer junction, glissile junction, and Hirth junction. The simulation results show that strong dynamic recovery occurs due to the short-range reactions of collinear annihilation and Lomer junction formation. The misfit stress is found to induce and accelerate dynamic recovery of interfacial dislocation networks involving self-interaction and Hirth junction formation, but slow down the steady interfacial motion of coplanar and glissile junction forming dislocation networks. The insights gained from these simulations on high-temperature low-stress creep of single-crystal superalloys are also discussed.

A model for high temperature creep of single crystal superalloys based on nonlocal damage and viscoplastic material behavior

A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown.

Effect of climb on dislocation mechanisms and creep rates in γ′-strengthened Ni base superalloy single crystals: A discrete dislocation dynamics study

Creep of single-crystal superalloys is governed by dislocation glide, climb, reactions and annihilation. Discrete three-dimensional (3D) dislocation dynamics (DDD) simulations are used to study the evolution of the dislocation substructure in a γ/γ′ microstructure of a single-crystal superalloy for different climb rates and loading conditions. A hybrid mobility law for glide and climb is used to map the interactions of dislocations with γ′ cubes. The focus is on the early stages of creep, where dislocation plasticity is confined to narrow γ channels. With enhancing climb mobility, the creep strain increases, even if the applied resolved shear stress is below the critical stress required for squeezing dislocations into the γ channels. The simulated creep microstructure consists of long dislocations and a network near the corners of the γ′ precipitate in the low-stress regime. In the high-stress regime, dislocations squeeze into the γ channels, where they deposit dislocation segments at the γ/γ′ interfaces. These observations are in good agreement with experimentally observed dislocation structures that form during high-temperature and low-stress creep.

Lattice strain evolution during creep in single-crystal superalloys

In situ neutron diffraction studies are carried out to characterize the micromechanical deformation occurring during tensile creep of a typical single-crystal nickel-based superalloy, CMSX-4. The loading responses of the matrix γ phase and the precipitate γ′ are distinct. Moreover, the behaviour in the tertiary creep regime (in which the γ′ phase remains intact) is qualitatively different from that in the primary creep regime (when γ′ is sheared). In tertiary creep, initial deformation of the matrix leads to a release of misfit between the phases in the (100), resulting in elastic compression of the γ in the loading direction. The load state then remains fairly constant during creep. During the initial stages of primary creep, elastic compression of the γ phase is observed until at around 2–4% creep strain this compression stabilizes as the (100) misfit is released. This is the point at which γ′ shearing is thought to begin. Subsequently, the load in the γ increases by around 200MPa until a maximum is reached at around 8% creep strain. This load is then suddenly released, which may be due to the release of back-stress.

Nonlocal damage‐viscoplastic model for high temperature creep of single crystal superalloys

AbstractA new nonlocal damage‐viscoplastic model for high temperature creep of single crystal superalloys is developed. It is based on the variational formulation consisting of free energy, plastic and damage dissipation potentials. Evolution equations for plastic strain and damage variables are derived from the minimum principle for dissipation potentials [1]. The model is capable of describing different stages of creep in a unified way. The evolution of dislocation densities of gamma and gamma prime phases in superalloys incorporates plastic deformation. It results in the time‐dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage variables. Herein the nonlocal one is considered as numerical treatment to remove mesh‐dependence. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown. (© 2011 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Directional Diffusion and Effect Factors of the Elements during Creep of Nickel-Base Single Crystal Superalloys

By means of the calculation of the elements diffusion mobility, an investigation has been made into the influence of the elements interaction on the rates of the elements diffusion and  phase directional coarsening during creep of single crystal superalloys. Results show that the elements diffusion and  phase directional coarsening during creep are related to the applied stressed and elastic modulus. And the rate of  phase directional coarsening is enhanced with the applied stresses. Due to the interaction between the elements, the rates of the elements diffusion and  phase directional coarsening decrease with the increment of the elements Ta+Mo gross and Ta/W ratio. In the diffusion field of the elements during creep, the Al, Ta atoms with bigger radius are diffused to {100} planes to form the N-type rafted structure along the direction vertical to the applied stress axis, and the change of the strain energy density in the interfaces of the cubic  phase is thougth to be the driving force of the elements diffusion.

Primary creep in single crystal superalloys: some comments on effects of composition and microstructure

Creep at low temperatures in current single crystal superalloys is characterised by a large but orientation dependent primary creep strain followed by prolonged secondary creep at a rate closely linked to the primary creep strain. The processes of incubation, nucleation and propagation are described and the linked effects of alloy composition and microstructure are discussed in relation to these processes. It is shown that the incubation period is relatively insensitive to the alloy composition but that heat treatments which vary the γ′ size can have a larger effect on the early stages of creep. The key to high primary creep appears to be the mobility of the dislocation ribbons nucleated and this is sensitive to the alloy composition. Fault energies in both the γ and the γ′ are important in determining the form of the dislocation ribbons. Early results suggest that ruthenium may have a beneficial effect reducing the primary creep of fourth generation alloys.

Mechanisms for tertiary creep of single crystal superalloy

During the thermal-mechanical loading of high temperature single crystal turbine components, all three creep—stages: primary, secondary and tertiary, manifest themselves and, hence, none of them can be neglected. The development of a creep law that includes all three stages is especially important in the case of non-homogeneous thermal loading of the component where significant stress redistribution and relaxation will result. Thus, local creep analysis is crucial for proper design of damage tolerant airfoils.

Primary creep in single crystal superalloys: Origins, mechanisms and effects

Creep deformation of the CMSX-4 nickel-base single crystal superalloy is studied in the range 750–850°C. Emphasis is placed on elucidating the factors causing primary creep when the tensile stress is orientated within 20°C of the technologically important 〈001〉 direction. It is demonstrated unambiguously that primary creep occurs only if a threshold stress of approximately 500MPa is exceeded; thereafter the accumulated primary creep strain is proportional to the magnitude by which the threshold stress is surpassed. A very high dependence of the strain rate on the applied stress is observed. Transmission electron microscopy confirms that the stress threshold is associated with the movement of a〈112¯〉 dislocation ribbons through the γ′ precipitates by so-called stacking fault shearing. The conditions necessary for the nucleation and propagation of a〈112¯〉 dislocation ribbons and the cessation of their movement are considered; it is demonstrated that the anisotropy of creep deformation for tensile loading within 20°C of 〈001〉 can be rationalised.

A continuum model for the creep of single crystal nickel-base superalloys

In this paper, we develop a constitutive theory within a thermodynamic setting to describe the creep of single crystal superalloys that gainfully exploits the fact that the configuration that the body would attain on the removal of the external stimuli, referred to as the “natural configuration”, evolves, with the response of the body being elastic from these evolving natural configurations. The evolution of the natural configurations is determined by the tendency of the body to undergo a process that maximizes the rate of dissipation. Here, the elastic response is assumed to be linearly elastic with cubic symmetry associated with the body which remains the same as the configuration evolves. A form for the inelastic stored energy (the energy that is ‘trapped’ within dislocation networks) is utilized based on simple ideas related to the motion of the dislocations. The rate of dissipation is assumed to be proportional to the density of mobile dislocations and another term that takes into account the damage accumulation due to creep. The model developed herein is used to simulate uniaxial creep of 〈001〉 oriented single crystal nickel-base superalloys. The predictions of the theory agree well with the available experimental data for CMSX-4.

Characterisation and Modelling of Crystal Rotations during Multiaxial Creep in Single Crystal Superalloys

Characterisation and Modelling of Crystal Rotations during Multiaxial Creep in Single Crystal Superalloys

Extension of an Anisotropic Model of Creep in Single Crystal Superalloys to Variable Loading and Multiaxial Loading

Extension of an Anisotropic Model of Creep in Single Crystal Superalloys to Variable Loading and Multiaxial Loading

Modelling of high-temperature mechanical behaviour of a single crystal superalloy

A model describing the anisotropic creep deformation of single crystal superalloys has been developed and evaluated using both a database of creep tests and validatory experiments on the alloy SRR9...

Modelling the orientation dependence of tertiary creep in single crystal superalloys

Extension du formalisme utilise par Ion et coll. et par Barbose et coll. pour rendre compte de l'anisotropie cristallographique inherente des superalliages monocristallins