Initial Creep Stage Research Articles

Micromechanics of primary creep in Ni base superalloys

The initial stages of creep in nickel base superalloy deserve a special attention since they prevail in most of the service live of critical jet engine components. In nickel base superalloys, a very sharp minimum in creep rate is observed at strains less than 0.5% in a wide range of temperatures: the lower the applied stress the steeper the minimum, often referred to as incubation period. In this paper, the primary creep stage of Ni superalloy is investigated using 3D discrete dislocation dynamics modeling. The simulated volume corresponds to a 3D periodic cell of the cubic arrangement of γ−γ′ NiAl loaded along the (001) direction. Misfit stresses induced by the lattice mismatch (δ = -3.10−3) between the precipitate and the matrix are taken into account through a coupling of the dislocation dynamics code with a finite element code. Frank-Read sources are positioned in the horizontal channel. It is shown that most of the dislocations propagate in the horizontal channels by repeated cross-slip on activated {111} glide planes and a few invade the vertical channels. This behavior is rationalized by the model. In the γ-γ′ interfaces, the zigzagging lines of dislocations straighten out into [100] and [010] directions leading to a dislocation microstructure similar to the ideal misfit dislocation network needed to compensate the lattice mismatch. Calculations of internal stresses in the channels show that this dislocation microstructure induces biaxial planar stresses in the horizontal γ channels leading to an elastic contraction of the sample along the loading direction. Three-dimensional DDD simulations show that the plastic strain induced, in the loading direction, by the movement and multiplication of dislocations is less important than the elastic relaxation it produces along that same direction. Hence, for very low applied tensile stresses, Ni superalloys display an abnormal behavior often referred to as negative creep that can be evidenced experimentally, even in polycrystalline materials. This last observation clearly implies that the first active batches of dislocations, during creep, or static high temperature ageing are mobilized to cancel out the numerous and pervading internal elastic strain fields generated within the crystals by the γ’ precipitates due to their misfit with the γ matrix.

Creep behavior of a γ′-strengthened Co-base alloy with zero γ/γ′-lattice misfit at 800 °C, 196 MPa

Abstract

Three-dimensional elastoplastic phase-field simulation of γ′ rafting and creep deformation

A modified phase-field model coupling viscoplastic constitutive equations has been built up to simulate the creep process of nickel-base single-crystal superalloys at 1223 K/300 MPa. The kinematic and isotropic hardening effects as well as interactions of slip systems are included in the present model. Under the external tension along [001] direction, the plastic strain prefers to concentrate in the channel vertical to [001] direction, promoting γ′ precipitate to raft along the direction vertical to [001] direction. The interactions between slip systems alter the value of plastic strain and thus the stress field in inner γ channel. In turn, the stress field readjusts the plastic deformation. The simulative results and experimental data are in good agreement in the initial creep stage. In addition, this modified model gives a possibility to simulate the microstructure evolution during cycle fatigue.

Phase-field simulation of rafting kinetics in a nickel-based single crystal superalloy

Directional coarsening (rafting) of the γ′ precipitate phase during creep in a nickel-based single crystal superalloy is simulated using the phase-field method. Both the morphological change of the γ′ phase and the microstructure-dependent heterogeneous creep of the γ matrix phase are modeled in the simulation. In three-dimensional simulations considering a single γ′ particle at 1273 K under tensile stresses of 130 MPa and 100 MPa along the [001] crystallographic direction, the γ′ phase coarsens toward the direction perpendicular to the applied stress axis. The simulated macroscopic creep rate–time curve in the initial stage of creep is consistent with the experimental data. The time to rafting increases with decreasing magnitude of the applied external stress. Furthermore, the external stress is removed at an arbitrary strain in the simulation at 1273 K, and the occurrence of rafting during the subsequent heat treatment without external stress is confirmed. The simulation results show that the threshold value of macroscopic strain for inducing rafting (ɛth) is ɛth=0.12%–0.16% in the stress range of 100–160 MPa. Moreover, rafting can be accelerated by removing the external stress of 100–160 MPa when the macroscopic strain exceeds ɛth.

A combined model to simulate the powder densification and shape changes during hot isostatic pressing

Under high temperature and pressure during Hot Isostatic Pressing (HIP), various deformation and sinter mechanisms such as plastic yielding, power law creep, and diffusion occur. They contribute either simultaneously or consecutively to the densification process depending on temperature and pressure levels. Some published works have shown that neither the pure plastic model nor the pure viscoplastic model sufficiently models the densification process during HIP, therefore a combined model which includes both a time independent plasticity and a rate dependent plasticity (creep) should be used. An innovative aspect of this work in comparison with available models in literature is the accommodation for model inaccuracies in the initial creep stage. The densification model incorporates the initial creep mechanism which occurs for a short time with a higher rate as compared to the steady stage creep rate. In this study, a combined model which consists of the influence of plasticity, primary creep, and secondary creep mechanisms is used. The authors believe that this approach can improve the quality of “near-net-shape” simulation.Innovative Aspects: The proposed model is more robust and predicts the final shape of HIP-ed components better which will support the production of Selective Net Shape or Net Shape HIP components. The reported results are of importance for companies producing big and complex shaped components through powder-HIP.

Study on nonlinear damage creep constitutive model for high-stress soft rock

Rock engineering especially deep rock engineering undergoing long-term effects of external loading and gravity all or most may gradually damage deformation or creep deformation accumulation, leading rock structures to damage, crack, such as severe plastic deformation or even progressive failure. In this paper, based on the nonlinear damage creep characteristics of rock and damage variable, a new nonlinear damage creep constitutive model of high-stress soft rock is defined in series with the improved Burgers model, Hooke model and St. Venant model. This new nonlinear damage creep constitutive model can work out fairly reasonably explanations for the soft rock creep deformation. A series of uniaxial compression creep tests were performed to study the creep damage characteristics of typical soft rock in Jinchuan No.2 Mine in the northwest of China. Using the increment step loading and single-step loading, the results of creep experiments and nonlinear damage creep constitutive model results are very consistent in this study. The new model not only can reflect the whole course of creep deformation, but also can reasonably describe the soft rock under different initial creep stage, steady-state creep stage and accelerated creep stage. Therefore, the new nonlinear creep damage model is a reasonable reference model for the research of soft rock creep.

Influence of initial microstructure on creep deformation behaviors and fracture characteristics of Haynes 230 superalloy at 900 °C

The effect of initial microstructure on creep properties at 900°C has been investigated in a solid-solution-strengthened Haynes 230 superalloy. The proprietary direct aging combined with controlled cooling rate led successfully to the transition of serrated grain boundaries. The serrated grain boundaries were found to have plane normal terminated by low-index planes. The lamellar carbides formed by discontinuous precipitation process became more significant in the serrated specimen, as the aging temperature to which the specimen was slow-cooled from 1280°C decreased. The fine intragranular carbides which precipitate during initial stage of creep are responsible for the strong hardening effect by pinning the dislocations in the standard specimen. The serrated grain boundaries with stable planar M23C6 carbides enhanced highly creep ductility due to their high resistance to cavitation cracking. However, the serrated specimens exhibited a higher creep rate, which is attributed to the promotion of intragranular deformation due to the lack of fine intragranular carbides, as well as cavitation at the lamellar carbides. Based on the relationships between microstructural factors and creep behaviors at 900°C, the optimal microstructure is discussed.

Nanoindentation characterized initial creep behavior of a high-entropy-based alloy CoFeNi

A crossover behavior in the initial creep stage during nanoindentation with a constant load for a high-entropy-based alloy CoFeNi is found. The holding time and stress in the indentation tests are evaluated to reveal the intrinsic mechanism of the crossover point. It indicated that the initial creep behavior is dominated by the strain-hardening at the beginning and then transit into the dislocation migration induced viscous stage. The transition presents the crossover, where the strain hardening effect predominates in a very short initial period while the viscous stage accounts for most of the initial creep stage with a time-dependent strain rate.

Jumpwise deformation of polymethyl methacrylate in the microplasticity region

The deformation rate with a step of 325 nm has been measured under uniaxial compression at the initial stage of creep and shape recovery of a polymethyl methacrylate (PMMA) sample after unloading. The effect of low γ-ray doses and magnetic fields on the deformation has been studied. It has been shown that a weak pre-exposure of the PMMA sample structure to radiation and magnetic fields can cause a slight hardening in the microplasticity region. The deformation jump sizes have been determined on micro- and nanoscales. The effect of irradiation and magnetic fields manifests itself as redistributed contributions of various jumps to the deformation.

HIGH TEMPERATURE CREEP AND FATIGUE BEHAVIOR AND LIFE PREDICTION METHOD OF A TiAl ALLOY

Creep (at 700 degrees C) and low cycle fatigue (at 700 and 750 degrees C) tests of Ti-43Al-9V-Y alloy with duplex (DP) and fully lamellar (FL) microstructures are carried out to study the creep, fatigue deformation and life prediction. Firstly, Omega method is employed to characterize the creep deformation and to predict the rupture life. Secondly, the proposed fatigue life model based on walker strain is employed to predict the fatigue life for these two types of TiAl alloy. The results show that: (1) high temperature creep curves of the material of both DP and FL microstructure contain steady and accelerated creep stages other than initial creep stage, and Omega method is able to characterize the creep deformation of TiAl alloy with DP and FL microstructure; (2) the rupture time of the material of FL microstructure is longer than that of DP microstructure, and the predicted rupture time by Omega method agrees well with the test data; (3) the fatigue life of DP is longer than that of FL under the same test condition, and the predicted fatigue life is well located in the scatter band of 3 of the test fatigue life.

Effects of residual stress on creep damage and crack initiation in notched CT specimens of a Cr–Mo–V steel

In this work, the effects of residual stress on creep damage and crack initiation were investigated by numerical analyses. Two cases of residual stress alone and residual stress combined with primary load were analyzed. The results show that larger residual stress relaxation occurs at initial creep stage, and creep strain and damage are accumulated ahead of notches during residual stress relaxation. It has been demonstrated that the effects of residual stress on creep crack initiation time are related to the creep ductility of materials and primary load levels. This was analyzed by the change in residual stress relaxation time in materials.

Microstructure and creep behavior of A 9%W single crystal nickel-based superalloy

By means of the measurement of creep curves and microstructure observation, an investigation has been made into the microstructure evolution and creep behaviors of 9%W single crystal nickel-base superalloy. Results show that the alloy displays an obvious sensibility on the applied stress when applied stress is more than 160 MPa at 1040 °C. In the ranges of the applied temperatures and stresses, the apparent creep activation energy is measured to be about 465 kJ/mol. In the initial stage of creep, the cubical γ′ phase in the alloy is transformed into the N-type rafted structure along the direction vertical to the applied stress axis, the deformed mechanism of the alloy during steady state creep is dislocations climbing over the rafted γ′ phase, the dislocation shearing into the rafted γ′ phase is thought to be the creep mechanism of the alloy during later stage of creep. After crept up to fracture, the various morphology of the rafted γ′ phase is displayed in the different regions of the sample, the rafted γ′ phase vertical to the stress axis displays in the region far from the fracture, but the coarser twisted γ′ phase is detected in the regions near the fracture, which is attributed to the bigger plastic deformation occurred in the region near the fracture.

Phosphorus grain boundary segregation under an intermediate applied tensile stress in a Cr–Mo low alloy steel

Phosphorus grain boundary segregation under an intermediate applied tensile stress of 200 MPa at 520 °C in a 0.025 wt.% P-doped 2.25Cr1Mo steel, which has already been thermally equilibrated, is observed using Auger electron spectroscopy. The segregation during stress ageing has a non-equilibrium nature. There are two phosphorus segregation peaks over its thermal equilibrium level, and between them there is a depletion trough of phosphorus below its thermal equilibrium level. The first segregation peak is mainly caused by the vacancy-phosphorus complex effect and the second one by the diffusional creep effect. The depletion trough of phosphorus at the initial creep stage may be attributed to the strain hardening bias effect.

Grain Boundary Sliding during Diffusion and Dislocation Creep in a Mg-0.7 Pct Al Alloy

Early studies on grain boundary sliding (GBS) in Mg alloys have suggested frequently that the contribution of GBS to creep is high even under conditions corresponding to dislocation creep. The role of creep strain and grain size in influencing the experimental measurements has not been clearly identified. Grain boundary sliding measurements were conducted in detail over experimental conditions corresponding to diffusion creep as well as dislocation creep in a single-phase Mg-0.7 wt pct Al alloy. The results indicated clearly that the GBS contribution to creep was very high during diffusion creep at low stresses (∼75 pct) and substantially reduced during dislocation creep at high stresses (∼15 pct). These measurements were consistent with the observation of significant intragranular slip band activity observed in most grains at high stresses and very little slip band activity at low stresses. The experimental measurements and analysis indicated also that the GBS contribution to creep was high during the initial stages of creep and decreased to a steady-state value at large strains.

Ni 基単結晶超合金のクリープ構成式による長時間クリープ予測

We have proposed and developed a new creep constitutive equation for Ni-base superalloys. In this paper, an application of the creep constitutive equation for long time creep test is discussed. Several creep curves of the test conditions of 1000°C/137 MPa and 900°C/245 MPa are fitted and achieved a good reproducibility. It is also examined to predict the rupture time of a continuing long time creep test from the behavior of the initial stage creep. The initial part of the creep data is fitted by the creep constitutive equation to extract initial creep stage parameters, and parameters belongs to the later creep stage are got by multi regression analysis.

Simulation of the creep of materials with different strengths

It is well known that certain materials, such as cast iron, titanium and aluminum‐magnesium alloys, beryllium copper, carbon plastic, granite, sandstone, coal, etc., behave in different ways under compressive and tensile loads [1‐3]. This difference is due to various internal microprocesses, such as the generation and growth of microcracks and microvoids, disclination distribution, sliding of grain boundaries, etc. This phenomenon is observed in both reversible [4‐6] and irreversible [7‐10] deformation processes and affects the entire spectrum of the mechanical and physical properties of materials. In this study, a creep model for materials with different moduli is constructed using piecewise-linear deformation potentials, and a technique for determining the material constants responsible for its mechanical properties is discussed. The creep model with piecewise-linear potentials for materials with different moduli is constructed on the basis of the assumption that, in the initial creep stage, the total strains of a material remain small, and the stresses are moderate and do not lead to plastic flow. Therefore, the total strain tensor e ij is the sum of the elastic strain tensor and the creep strain tensor :

The contribution of viscous flow to creep deformation of silicon nitride

For silicon nitride ceramics, in which a less refractory grain boundary amorphous film bonds more deformation-resistant Si 3 N 4 grains, one of the possible creep mechanisms is the redistribution of this amorphous film. Although this mechanism has been confirmed by measuring the film thickness distribution before and after creep, it is not clear whether viscous flow occurs only in the initial stage of creep or throughout the creep process. In this paper, compression creep tests were conducted and the film thickness distributions at different strain values were examined using high-resolution electron microscopy. A bimodal distribution of the film widths was observed after creep for all the strains examined, with the peak positions essentially unchanged after creep ranging from 7to 200 h at 1400°C. This demonstrates that viscous flow contributes principally to the initial stage of creep. In general, creep continues at a much lower rate after this cavity-free viscous flow process, entering the second stage. However, once cavities have nucleated, a local film thickness change may occur in the neighbouring areas by viscous flow. Therefore, viscous flow due to cavitation and its contribution to creep deformation are also discussed.

Isothermal creep of metallic glasses: a new approach and its experimental verification

An extended version of the theory of structural relaxation in metallic glasses under the action of external stress is presented. The theory explains the structural relaxation as a set of irreversible noncorrelated two-stage elementary shear atomic rearrangements with continuously distributed activation parameters in distinct regions of structure—relaxation centres. In loaded samples structural relaxation results in an accumulation of plastic deformation in accordance with magnitude and orientation of the applied stress. General equations are obtained for the creep strain rate as a result of the irreversible directed structural relaxation. Specially designed experiments were performed to test the theory. It is shown that the theory gives an adequate interpretation of experimental creep kinetics except for the time interval that covers 10 1–10 2 s after loading. This initial creep stage is supposed to result from reversible atomic rearrangements in relaxation centres with a symmetrical two-well potential.

Kinetics of isothermal creep in metallic glasses including the statistical distribution of activation parameters

A generalized theoretical model is proposed for the structural relaxation of metallic glasses under load. Structural relaxation is treated as a set of irreversible, uncorrelated, two-stage atomic displacements in some regions of the structure, the “relaxation centers.” In loaded samples structural relaxation acquires a directional character, leading to the buildup of plastic deformation in accordance with the magnitude and orientation of the applied mechanical stress. General equations are obtained for creep kinetics including a continuous statistical distribution of the principal activation parameters. These equations are compared with the results of a special experiment. The model is found to provide an adequate interpretation of the observed creep kinetics, except for the first 101–102 seconds after loading. It is argued that the initial stage of creep is determined by reversible atomic realignments in relaxation centers having symmetric two-well potential.

The role of microstructural instability on creep behavior of a martensitic 9Cr-2W steel

The microstructural instability during creep and its effect on creep behavior were investigated for a martensitic 9Cr-2W steel. The steel was developed as a low radioactive steel suitable for fusion reactor structure. Creep testing was carried out at 873 K for up to 15,100 ks (4200 hours). The creep curve consisted of transition creep, where creep rate decreased with time, and acceleration creep, where creep rate increased with time. During creep, microstructural instability, such as the recovery of dislocations, the agglomeration of carbides, and the growth of martensite lath subgrains, was observed to occur, which resulted in softening but no hardening. The transition creep was a consequence of the movement and annihilation of excess dislocations, resulting in the decrease in dislocation density and the increase in martensite lath size with time. The acceleration creep was a consequence of a gradual loss of creep strength due to the microstructural instability which occurred from the initial stage of creep.