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Ivins used three relations for estimating the effective viscosity of quartzites and crustal rocks having strong quartz affinity.
Specimens of plasma-sprayed-zirconia thermal-barrier coatings with three different porosities and different initial particle sizes were deformed in compression at initial loads of 6900, 13,800, and 24,100 kPa (1000, 2000, and 3500 psi) and temperatures of 1100, 1250, and 1400 C. The coatings were stabilized with lime, MgO, and two different concentrations of Y2O3. Creep began as soon as the load was applied and continued at a constantly decreasing rate until the load was removed. Temperature and stabilization had a pronounced effect on creep rate while the stress, particle size, and porosity had a lesser effect. Creep deformation was due to cracking and particle sliding.
Understanding the thermomechanical behavior (creep and stress relaxation) of ceramic fibers is of both practical and basic interest. On the practical level, ceramic fibers are the reinforcement for ceramic matrix composites which are being developed for use in high temperature applications. It is important to understand and model the total creep of fibers at low strain levels where creep is predominantly in the primary stage. In addition, there are many applications where the component will only be subjected to thermal strains. Therefore, the stress relaxation of composite consituents in such circumstances will be an important factor in composite design and performance. The objective of this paper is to compare and analyze bend stress relaxation and tensile creep data for alpha-SiC fibers produced by the Carborundum Co. (Niagara Falls, NY). This fiber is of current technical interest and is similar in composition to bulk alpha-SiC which has been studied under compressive creep conditions. The temperature, time, and stress dependences will be discussed for the stress relaxation and creep results. In addition, some creep and relaxation recovery experiments were performed in order to understand the complete viscoelastic behavior, i.e. both recoverable and nonrecoverable creep components of these materials. The data will be presented in order to model the deformation behavior and compare relaxation and/or creep behavior for relatively low deformation strain conditions of practical concern. Where applicable, the tensile creep results will be compared to bend stress relaxation data.
The present work gives the results of experiments on the influence of zirconium carbide and tungsten on the creep properties of uranium carbide. The creep behavior of high-density UC samples follows the classical time-dependence pattern of (1) an instantaneous deformation, (2) a primary creep region, and (3) a period of steady-state creep. Creep rates for unalloyed UC-1.01 and UC-1.05 are several orders of magnitude greater than those measured for carbide alloys containing a Zr-C and/or W dispersoid. The difference in creep strength between alloyed and unalloyed materials varies with temperature and applied stress.
High-entropy alloys (HEAs) have been extensively investigated during the last two decades. While substantial progress has been made in understanding their phase stability, microstructure, and deformation mechanisms at room and cryogenic temperatures, the long-term creep behavior (>100 h) of HEAs at high temperatures (>0.6 T m , where T m is the melting temperature) remains relatively underexplored. This knowledge gap is critical, as many engineering applications, including those for power generation and propulsion, require materials with good creep resistance to maintain structural integrity over extended service lifetimes. This review provides a focused and critical assessment of the current understanding of high-temperature deformation and creep behavior of HEAs, with particular attention paid to face-centered cubic HEAs and body-centered cubic refractory HEAs. The underlying deformation mechanisms governing their creep response and the influence of phase stability at elevated temperatures are examined in detail. Recent studies reveal mechanistic differences between HEAs and conventional dilute alloys that do not always lead to improved creep resistance belying their initial promise. Based on these findings, we discuss the challenges in designing HEAs for high-temperature structural applications and outline future research directions that may lead to creep-resistant HEAs.
In this paper, we report the results of a 4-dimensional (3 spatial dimensions plus time) in-situ creep experiment on a milli-core shale plug from Barnett formation in Texas. An outstanding challenge in shale mechanics is connecting observable characteristics to predictable mechanical and hydraulic behavior. We employ novel imaging and analysis techniques to statistically link sample mineralogy and structure to observed deformation. In particular, we focus on mechanisms of porosity reduction during transient response to step changes in stress, analogous to the aseismic deformation that occurs after an episode of fracturing. Our main goal in this study is to take the first steps to visualize and capture the small-scale deformation mechanisms involved in creep of shales, using imaging techniques. To do so, we conducted a uniaxial creep experiment inside an Xradia Versa 520 micro-CT system for 12 h at room temperature under a constant uniaxial stress of 25 MPa. We employed a Digital Volume Correlation (DVC) method to measure micro-scale deforspmation of the sample by comparing the resulting volumetric images with a high-resolution scan of the sample obtained prior to the creep experiment. The results indicate that the time-dependent deformation in the compliant clay plus kerogen matrix constituents facilitates rigid grain rotation and compaction of intergranular porosity at the boundary between rigid grains and matrix.
A Bayesian optimization procedure is presented for calibrating a multimechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on Fe(8–9)%Cr are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600°C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework (Huang et al., 2021, “Bayesian optimization of functional output in inverse problems,” Optim. Eng., 22, pp. 2553–2574). Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. In conclusion, validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel.
A Bayesian optimization procedure is presented for calibrating a multi-mechanism micromechanical model for creep to experimental data of F82H steel. Reduced activation ferritic martensitic (RAFM) steels based on are the most promising candidates for some fusion reactor structures. Although there are indications that RAFM steel could be viable for fusion applications at temperatures up to 600 °C, the maximum operating temperature will be determined by the creep properties of the structural material and the breeder material compatibility with the structural material. Due to the relative paucity of available creep data on F82H steel compared to other alloys such as Grade 91 steel, micromechanical models are sought for simulating creep based on relevant deformation mechanisms. As a point of departure, this work recalibrates a model form that was previously proposed for Grade 91 steel to match creep curves for F82H steel. Due to the large number of parameters (9) and cost of the nonlinear simulations, an automated approach for tuning the parameters is pursued using a recently developed Bayesian optimization for functional output (BOFO) framework [1]. Incorporating extensions such as batch sequencing and weighted experimental load cases into BOFO, a reasonably small error between experimental and simulated creep curves at two load levels is achieved in a reasonable number of iterations. Validation with an additional creep curve provides confidence in the fitted parameters obtained from the automated calibration procedure to describe the creep behavior of F82H steel at 600 °C. The model is further extended using a temperature dependent scaling law approach to simulate creep response between 550 °C and 650 °C. The efficacy of this extension is compared with the previously used scaling law approach for Grade 91 steel.
This report describes a physics-based model for creep and thermal aging in Alloy 709. Alloy 709 is an advanced austenitic alloy, targeted for use in future Sodium Fast Reactors (SFRs) and other advanced reactors. The material has superior high temperature properties compared to currently qualified 316 and 304 stainless steels. However, the available creep and thermal aging test database for Alloy 709 is significantly more limited compared to the historical materials. The physics-based model developed here is one way to accelerate the qualification of the material by providing more accurate long-term predictions for creep properties and thermal aging, compared to current empirical time-extrapolate techniques. The crystal plasticity finite element model is used to predict the deformation and failure of alloy 709. The same setup for the CPFE model is used in both the baseline model calibration process and the simulation campaigns for parameter inference. Specific constitutive choices are made for Alloy 709 to capture the primary deformation mechanisms. The dislocation creep formulation developed by Hu and Cocks is extended to account for coupled precipitation formation and the grain boundary cavitation model developed by Sham, Needleman, et al. is used to model grain boundary cavitation-induced failure. A novel update algorithm is proposed to render the semi-discrete constitutive update for the Sham-Needleman model unconditionally stable. A progressive calibration approach is adopted based on the observations that several types of material responses can be effectively decoupled. A surrogate model is trained based on full-fledged CPFE simulations to accelerate the forward model evaluations, and stochastic variational inference (SVI) is used to calibrate the unknown microstructural model parameters. The calibrated mechanistic model is used to predict the long-term creep life of Alloy 709, and the predictions are compared against classical empirical approaches.
The applicability of a thermodynamic constitutive theory of deformation to the prediction of primary creep and creep strain relaxation behavior in metals is examined. Constitutive equations derived from the theory are subjected to a parametric analysis in order to determine the influence of several parameters on the curve forms generated by the equations. A computer program is developed which enables the solution of a generalized constitutive equation using experimental data as input. Several metals were tested to form a data base of primary creep and relaxation behavior. The extent to which these materials conformed to the constitutive equation showed wide variability, with the alloy Ti-6Al-4V exhibiting the most consistent results. Accordingly, most of the analysis is concentrated upon data from that alloy, although creep and relaxation data from all the materials tested are presented. Experimental methods are outlined as well as some variations in methods of analysis. Various theoretical and practical implications of the work are discussed.
A number of possible morphologic indicators of ground ice on Mars are discussed, with emphasis on rampart craters and terrain softening. Geologic evidence indicates that the Martian surface has been substantially modified by the action of liquid water, and that much of that water still resides beneath the surface as ground ice. Calculations of the thermodynamic stability of ground ice on Mars suggest that it can exist very close to the surface at high latitudes, but can persist only at substantial depths near the equator. A variety of observed Martian landforms can be attributed to creep of the Martian regolith abetted by deformation of ground ice. Global mapping of creep features also supports the idea that ice is present in near-surface materials at latitudes higher than +/- 30 deg, and suggests that ice is largely absent from such materials at lower latitudes.
A creep apparatus has been constructed for an in situ determination of length and length change. Using this apparatus, the creep behavior of PVC thin films associated with quenching and aging was studied. The more severe the quench through the glass transition temperature, the greater is the instantaneous elastic deformation and the subsequent creep behavior. As aging proceeds, the quenched films gradually lose the ductility incurred by quenching. These results agree well with the well-known phenomena of physical aging. Thus, the changes reflecting molecular mobilities due to quenching and aging can be properly monitored by such a creep apparatus.
Characteristics of premature creep failure in the over-tempered base metal (OT-BM) of a Grade 91 steel weldment are investigated with specially designed creep experiments and advanced microstructure characterization. In situ digital image correlation (DIC) strain measurements reveal that local creep strain as high as 100% accumulated in the OT-BM, compared with only 10% nominal strain over the gauge length. The creep strain rate in the OT-BM is identical to that in the intercritical heat-affected zone and fine-grained heat-affected zone at the secondary creep stage and early tertiary stage, but faster at the late tertiary stage. Microstructural analysis shows that highly recovered microstructure in the OT-BM leads to the lowest hardness, the largest grain size, the lowest fraction of coincidence site lattice boundaries, and the lowest localized strain energy. Dislocation creep and transgranular creep fracture are the dominant deformation and fracture mechanisms in the OT-BM under the current creep testing condition of a low temperature (550 °C) and a high stress (215 MPa).
The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.
The activities performed during the first year of the NASA HOST Program, Creep Fatigue Life Prediction for Engine Hot Section Materials (Isotropic), being conducted by Pratt & Whitney Aircraft are summarized. The program is a 5 year, two part effort aimed at improving the high temperature crack initiation prediction technology for gas turbine hot section components. Significant results of the program produced thus far are discussed. Cast B1900 + Hf and wrought IN 718 were selected as the base and alternate materials, respectively. A single heat of B1900 + Hf was obtained and test specimens fabricated. The material was characterized with respect to grain size, gamma prime size, carbide distribution, and dislocation density. Monotonic tensile and creep testing has shown engineering properties within anticipated scatter for this material. Examination of the tensile tests has shown a transition from inhomogeneous planar slip within the grains at lower temperatures to more homogeneous matrix deformation. Examination of the creep tests has shown a transgranular failure mode at 1400 F and an intergranular failure mode at 1600 F and 1800 F.
A study has been made of the kinetics of the directional coarsening of the gamma-prime precipitates in Ni-5.8Al-14.6Mo-6.2Ta single crystals during creep at 982 C. In this alloy, which is characterized by a large negative lattice misfit between the gamma-prime precipitate and the gamma matrix, the formation of gamma-prime rafts begins during primary creep, and the rafts grow in length as the deformation proceeds into steady-state creep. After that, the length of the rafts stabilizes. The thickness of the rafts remains constant from primary up to tertiary creep. The directional coarsening behavior of the alloy studied is similar to that of a more conventional single-crystal superalloy having a substantially smaller negative misfit.
A physics-informed recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear, time-dependent constitutive behavior of ceramic matrix composites (CMCs) driven by matrix damage and constituent creep at the microscale. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the high-fidelity generalized method of cells (HFGMC) approach which calls appropriate creep and damage models for each of the constituents. This coupling permits simulating the nonlinear behavior of CMCs based on constituent response at the microscale along with microstructural features such as fiber and porosity volume fraction and fiber radius. The microscale repeating unit cell is loaded under creep fatigue conditions to replicate the material loading experienced in a turbine engine. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input stress sequence, temperature, and microstructural features, the resulting strain history response while satisfying physical constraints related to creep rate, isochoric inelastic deformation, and strain energy density. The trained surrogate model is shown to effectively match the strain history over quantified distributions of microstructural features and relevant loading regimes and temperatures. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore, the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex microstructures, nonlinear time-dependent material response, and under non-monotonic loading conditions.
The role of pull aparts and pushups in transcurrent systems, the rotation of faults and blocks within transcurrent fault systems, the role of accretion tectonics in plate boundary deformation, and power law creep behavior and the yielding at plate boundaries were investigated.