Influence of Mo Segregation at Grain Boundaries on the High Temperature Creep Behavior of Ni-Mo Alloys: An Atomistic Study

Based on molecular dynamics simulations, the creep behaviors of nanocrystalline Ni before and after the segregation of Mo atoms at grain boundaries are comparatively investigated with the influences of external stress, grain size, temperature, and the concentration of Mo atoms taken into consideration. The results show that the creep strain rate of nanocrystalline Ni decreases significantly after the segregation of Mo atoms at grain boundaries due to the increase of the activation energy. The creep mechanisms corresponding to low, medium, and high stress states are respectively diffusion, grain boundary slip and dislocation activities based on the analysis of stress exponent and grain size exponent for both pure Ni and segregated Ni-Mo samples. Importantly, the influence of external stress and grain size on the creep strain rate of segregated Ni-Mo samples agrees well with the classical Bird-Dorn-Mukherjee model. The results also show that segregation has little effect on the creep process dominated by lattice diffusion. However, it can effectively reduce the strain rate of the creep deformation dominated by grain boundary behaviors and dislocation activities, where the creep rate decreases when increasing the concentration of Mo atoms at grain boundaries within a certain range.

Deformation and Instability Properties of Cemented Gangue Backfill Column under Step-By-Step Load in Constructional Backfill Mining

Constructional backfill mining with cemented gangue backfill column can solve the environmental issues caused by mining activities and the accumulation of waste gangue at a low cost. To study the deformation and instability properties of cemented gangue backfill columns during the advancement of coal mining face, five step-by-step loading paths were adapted to mimic the different loading processes of the roof. The lateral deformation at different heights and axial deformation of the sample were monitored. The results show that the deformation and instability of the backfill column have the properties of loading paths and are affected by the step-by-step loading path. When stress-strength ratio (SSR) is less than 0.6, the lateral of backfill column shrinks during the creeping process. In high-stress levels, lateral creep strain develops faster than axial creep strain. The backfill column has characteristics of axial creep hardening and lateral creep softening during the step-by-step loading process. The instantaneous deformation modulus and instantaneous Poisson’s ratio show an upward trend. The bearing capacity of backfill column under the step-by-step load is related to loading paths and is no less than uniaxial compressive strength. The non-uniformity of the lateral deformation of backfill column leads to excessive localized deformation that mainly occurs in the middle, causing the overall instability. The development of cracks of backfill column under step-by-step load could be divided into 4 stages according to SSR. Under different step-by-step loading paths, the axial creep strain rate is nearly a constant before entering the accelerated creep stage. A nonlinear creep constitutive model with a creep strain rate trigger was proposed to depict the development of axial strain under step-by-step load. This research will provide a scientific reference for the design of the advancing distance and cycle for the hydraulic support, and reinforcement of the backfill column.

Study on Relationship Between Dislocation Density and Creep Strain Rate of Single Crystal Ni Based Superalloy for Gas Turbines Using the Discrete Cosine Transform

The discrete cosine transform (DCT) is known to be able to express the relation curve between creep strain and time, or the relation curve between creep strain rate and time very well. Moreover, recently it has been found out that the DCT can draw electron density distribution maps of crystals. In addition, the DCT always passes through all the points measured at an equal interval in any continuous curves and its interpolated values between adjacent points are very reasonable. Furthermore, a new prediction method for long term creep curves from short term creep data by using the DCT was reported at TurboExpo2020. Up to the present, the strength of single crystal Nickel based superalloys for gas turbines at elevated temperatures has been advanced by controlling the interface dislocation density and the lattice misfit at the γ/γ’ interfaces. For this reason, it has to be understood how to evaluate a relationship between interface dislocation density and creep strain rate to develop more advanced single crystal Nickel based superalloys. Therefore, in this research it was studied how to evaluate the relationship between interface dislocation density and creep strain rate of a single crystal Nickel based superalloy for gas turbines by using the DCT. As a result, useful properties on the effective stress have been obtained from the coefficients of the DCT.

Probabilistic Minimum-Creep-Strain-Rate and Stress-Rupture Prediction for the Long-Term Assessment of IGT Components

Time-dependent creep induced failure is a major concern for structural components (i.e. IGT components, Gen IV nuclear reactor components) operating at elevated temperature. The likelihood of a failure is aggravated by randomness in several sources of uncertainty. Creep rupture data shows expanding scatter bands for long-duration creep tests where uncertainty can span multiple logarithmic decades of life. This experimental uncertainty is exacerbated by the uncertainties that exist during service. The continuum damage mechanics (CDM) based creep-damage model readily available in literature does not consider the uncertainty effect while predicting the long-term reliability of the components; rather the problem is tackled deterministically. Introduction of probabilistic phenomena into the existing model to predict the minimum-creep-strain-rate (MCSR) and stress-rupture (SR) would present a pathway for estimation of effect of uncertainty ensuing high reliability in the assessment. The objective of this paper is to develop a probabilistic model for MCSR and SR that is capable of predicting experimental uncertainty and extrapolating the expanded scatter bands observed in long-duration creep data. The Sine-hyperbolic (Sinh) CDM model is selected. Multi-isotherm MCSR and SR data for 304 (18Cr-8Ni) and 316 (18Cr-12Ni-Mo) stainless steel are gathered from the NIMS material database. A deterministic calibration is performed where the optimal material constants are obtained with no initial damage and perfect loading conditions. Probabilistic calibration begins with adding ASTM-specified temperature and stress tolerances (± X°C, ±Y% MPa) to capture a portion of the experimental uncertainty. The initial damage tolerances is then calibrated to capture the remaining uncertainty in the data. Probability distribution functions (pdfs) are assigned to each uncertainty parameter. Monte Carlo simulations are performed over a range of stress and temperature. The probabilistic Sinh model is shown to predict the expanding scatter band observed in long-term MCSR and SR data. Parametric simulations are performed where service condition uncertainty is added to the probabilistic model. It is determined that service condition uncertainties further degrade the creep resistance of a material.

Development of “Material Specific” Creep Continuum Damage Mechanics-Based Constitutive Equations

The objective of this study is to introduce a method for creating “material specific” creep continuum damage mechanics-based constitutive models. Herein, material specific is defined as a constitutive model based on the mechanism-informed minimum creep strain rate (MCSR) equations found in deformation mechanism maps and calibrated to available material data. The material specific models are created by finding the best MCSR model for a dataset. Once the best MCSR model is found, the Monkman Grant inverse relationship between the MCSR and rupture time is employed to derive a rupture equation. The equations are substituted into continuum damage mechanics-based creep strain rate and damage evolution equations to furnish predictions of creep deformation and damage. Material specific modeling allows for the derivation of creep constitutive models that can better the material behavior specific to the available data of a material. The material specific framework is also advantageous since it has a systematic framework that moves from finding the best MCSR model, to rupture time, to damage evolution and, creep strain rate. Data for Alloy P91 was evaluated and a material specific constitutive model derived. The material specific model was able to accurately predict the MCSR, creep deformation, damage, and rupture of alloy P91.

Reliability Prediction of 304 Stainless Steel Using Sine-Hyperbolic Creep-Damage Model With Monte Carlo Simulation Method

Typically continuum damage mechanics (CDM) based constitutive models are applied deterministically where the uncertainty of experiments is not considered. This is also true for the Sine-hyperbolic (Sinh) CDM-based constitutive model where the model is calibrated to represent 50% reliability of creep data. There is a need to implement Sinh in a more stochastic manner. The objectives of this study is to incorporate the probabilistic feature in the Sinh creep damage model to reliably predict the minimum-creep-strain-rate, creep-rupture and creep deformation. This will be achieved using Monte-Carlo methods. Creep deformation data for 304 Stainless Steel is collected from literature consisting of tests conducted at 300 and 320 MPa at 600°C with five replicates. The replicate tests exhibited substantial scatter in the minimum-creep-strain-rate, stress-rupture, and overall creep deformation. Subsequently, upon calibration using the Sinh model, the material constants among the replicates varied. The trends of uncertainty carried by each material constant are studied. The interdependence of the material constants is evaluated to determine if the uncertainty carried by each material constant can be regressed using a co-dependence function. The Monte Carlo method was applied to determine the extent that the creep deformation curve varies taking into consideration the variability of the material constants. Monte Carlo simulations show that the predicted creep deformation persists within the bounds of the experimental data. A large number of Monte Carlo simulations using the Sinh model enabled the creation of credible reliability bands for the minimum-creep-strain-rate, stress-rupture, and creep deformation of 304 Stainless Steel. In future work, this statistical method will be applied to the variability of service conditions, pre-existing defects, and material constants to quantitatively establish the reliability of the Sinh model in simulating component-level creep deformation to rupture.

Development and Application of Minimum Creep Strain Rate Metamodeling

Numerous minimum-creep-strain-rate laws exist, creating a challenge in determining which is best for a given material database. The objective of this study is to validate the applicability of a “metamodel” and its ability to model the minimum creep strain rate (MCR). A metamodel is a model that can combine and regress into different base models, in this case, seven established MCR models. The metamodel can be exploited using a calibration algorithm to rapidly calibrate the base models. The metamodel contains ten terms and eight material constants (one is a constraint, and another is stress as an input variable). Using the metamodel and calibration software, the user can determine the best MCR model for a given material database. Using the software, the metamodel is calibrated in two approaches: constrained and pseudo-constrained. The constrained approach restricts the metamodel to regress directly into one of the base models, allowing for the base models to be equally calibrated and compared alongside each other. The pseudo-constrained approach freely optimizes all eight of the metamodel material constants; however, the metamodel is modified to include 5 Heaviside function constants that turn on/off sections of the metamodel to increase the statistical-dependencies of the final model. This pseudo-constrained approach has the potential to identify novel MCR models that exist at the interface between the seven base models. Alloy data for 9Cr-1Mo-V-Nb (ASTM P91) was used with a total of 89 points which extended over a total of three isotherms: 600°C, 625°C, and 650°C. The MCR model that best fit the data was the Johnson-Henderson-Kahn model.

Application of the Wilshire Stress-Rupture and Minimum-Creep-Strain-Rate Prediction Models for Alloy P91 in Tube, Plate and Pipe Form

There exists a challenge in predicting the long-term creep of materials (3 105 hours) where 11+ years of continuous testing is required to physically collect creep data. As an alternative to physical testing, constitutive models are calibrated to short-term data (< 104 hours) and employed to extrapolate the long-term creep behavior. The Wilshire model was introduced to predict the stress-rupture and minimum-creep-strain-rate behavior of materials and the model is well-accepted due to the explicit description of stress- and temperature-dependence allowing predictions across isotherms and stress levels. There is an ongoing effort to determine how alloy form affects the long-term creep predictions of the Wilshire model. In this study, stress-rupture and minimum-creep-strain-rate predictions are generated for alloy P91 in tube, plate, and pipe form. Data is gathered from the National Institute of Materials Science (NIMS) material database for alloy P91 at multiple isotherms. Following the establish calibration method for the Wilshire model, post-audit validation is performed using short-term data from NIMS to vet the extrapolations accuracy of each form at different isotherms. The Wilshire model demonstrates successful extrapolative techniques for the stress-rupture and minimum-creep-strain-rate of tube, plate, and pipe forms across multiple isotherms. Overall the form with the highest extrapolative accuracy for both stress-rupture and minimum-creep-strain-rate is the plate and the lowest one is the pipe. Stress-rupture design maps are provided where stress and temperature are axes and rupture-time is in contour. The design maps can be applied to: (a) given the boundary conditions, determine the design life (b) given the design life, determine the acceptable range of a boundary conditions. The latter is more useful in turbomachinery design.