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At least 685 records · Page 38

Creep fatigue life prediction for engine hot section materials (isotropic)

This Final Report covers the activities completed under the optional program of the NASA HOST Contract, NAS3-23288. The initial effort of the optional program was report-in NASA CR189221, which consisted of high temperature strain controlled fatigue tests to study the effects of thermomechanical fatigue, multiaxial loading, reactive environments, and imposed stresses. The baseline alloy used in the tests included B1900+Hf (with or without coating) and wrought INCO 718. Tests conducted on B1900+Hf included environmental tests using various atmospheres (75 psig oxygen, purified argon, or block exposures) and specimen tests of wrought INCO 718 included tensile, creep, stress rupture, TMF, multiaxial, and mean stress tests. Results of these testings were used to calibrate a CDA model for INCO 718 alloy and to develop modifications or corrections to the CDA model to handle additional failure mechanisms. The Socie parameter was found to provide the best correlation for INCO multiaxial loading. Microstructural evaluations consisting of optical, Scanning Electron Microscopy (SEM), and Transmission Electron Microscopy (TEM) techniques, and surface replication techniques to determine crack initiation lives provided data which were used to develop life prediction models.

Nelson, R. S.↗

High Temperature Superconductivity in Praseodymium Doped (0%, 2%, 4%) in Melt-Textured Y(1-x)Pr(x)Ba2Cu3O(7-delta) Systems

A study of the magnetic and structural properties of the alloy Y(1-x)Pr(x)Ba2Cu3O(7-delta) of 0%, 2%, and 4% doping of praseodymium is presented. The resulting oxides of the alloy series are a high-temperature superconductor Y-Ba-Cu-O, which has an orthorhombic superconducting crystal-lattice. Magnetic relaxation studies have been performed on the Y-Pr-Ba-CuO bulk samples for field orientation parallel to the c-axis, using a vibrating sample magnetometer. Relaxation was measured at several temperatures to obtain the irreversible magnetization curves used for the Bean model. Magnetization current densities were derived from the relaxation data. Field and temperature dependence of the logarithmic flux-creep relaxation was measured in critical state. The data indicates that the effective activation energy U(eff) increases with increasing T between 77 K and 86 K. Also, the data shows that U(eff)(T) and superconducting transition temperature, Tc, decreased as the lattice parameters increased with increasing Pr ion concentration, x, for the corresponding Y(1-x)Pr(x)Ba(x)Cu3O(7-delta) oxides. One contribution to Tc decrease in this sampling is suspected to be due to the larger ionic radius of the Pr(3+) ion. The upper critical field (H(sub c2)) was measured in the presence of magnetic field parallel to the c axis. A linear temperature dependence with H(sub c2) was obtained.

James, Claudell↗

Nondestructive Evaluation Correlated with Finite Element Analysis

Advanced materials are being developed for use in high-temperature gas turbine applications. For these new materials to be fully utilized, their deformation properties, their nondestructive evaluation (NDE) quality and material durability, and their creep and fatigue fracture characteristics need to be determined by suitable experiments. The experimental findings must be analyzed, characterized, modeled and translated into constitutive equations for stress analysis and life prediction. Only when these ingredients - together with the appropriate computational tools - are available, can durability analysis be performed in the design stage, long before the component is built. One of the many structural components being evaluated by the NDE group at the NASA Lewis Research Center is the flywheel system. It is being considered as an energy storage device for advanced space vehicles. Such devices offer advantages over electrochemical batteries in situations demanding high power delivery and high energy storage per unit weight. In addition, flywheels have potentially higher efficiency and longer lifetimes with proper motor-generator and rotor design. Flywheels made of fiber-reinforced polymer composite material show great promise for energy applications because of the high energy and power densities that they can achieve along with a burst failure mode that is relatively benign in comparison to those of flywheels made of metallic materials Therefore, to help improve durability and reduce structural uncertainties, we are developing a comprehensive analytical approach to predict the reliability and life of these components under these harsh loading conditions. The combination of NDE and two- and three-dimensional finite element analyses (e.g., stress analyses and fracture mechanics) is expected to set a standardized procedure to accurately assess the applicability of using various composite materials to design a suitable rotor/flywheel assembly.

Abdul-Azid, Ali↗

Recommendation for Limiting Conditions for ASME BPVC Section III Division 5 Allowable Stress Criteria

Section III, Division 5 of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC) specifies rules for elevated temperature nuclear reactors. Time dependent allowable stresses are an important aspect of the high temperature design models and are related to the time to 1% strain, time to rupture, and time to onset of tertiary creep. The time to onset of tertiary creep criterion has an overly strong negative influence on the allowable stresses for some structural materials, likely due to very limited datasets and misidentification of microstructural changes rather than onset of significant creep damage, as tertiary creep is meant to represent. It is recommended that the onset of tertiary creep be determined through an alloy specific ratio between onset of tertiary creep and creep rupture time, which would give access to the significantly larger creep rupture time datasets.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Advanced Ceramic Matrix Composites: Science and Technology of Materials, Design, Applications, Performance and Integration

Overview of NASA Transformational Tools and Technologies Project's 2700F CMC/EBC Technology Challenge J. Hurst, NASA (National Aeronautics and Space Administration, Glenn Research Center, Cleveland, OH USA Key Words: ceramic matrix composites (CMCs), SiC/SiC composites, environmental barrier coatings (EBCs), CMC modeling, simulated engine testing As advanced gas turbine engine designs continue to move toward both higher operating temperatures and increased pressures, materials capable of functioning under these extreme conditions are being sought by both government and industry. As part of its mission, the NASA's Transformational Tools and Technologies Project, under the auspices of NASA's Aeronautics Research Mission Directorate, has been pursuing a five year Technology Challenge problem. This challenge problem has sought to develop high temperature materials for turbine engines that enable a 6% reduction in fuel burn for commercial aircraft, compared to current SOA materials. Specifically this is accomplished by the development and demonstration of a ceramic matrix composite (CMC) and environmental barrier coating (EBC) system capable of sustained performance at temperature of 2700F. The NASA Glenn Research Center has continued its two decade long interest in CMC/EBCs technology by pursuing this 2700F performance goal. This ambitious effort included an array of vendors, universities and engine companies. Included in this challenge was fiber development, fiber architecture considerations, ceramic matrix composition, environmental barrier compositions and processing routes as well as test development. Evaluation of the CMC/EBC materials included a variety of testing, from coupon testing for strength and creep resistance, to testing aimed at determining material behavior under more engine-like conditions. The development and validation of thermomechanical models and computational tools for design, analysis, and life prediction, have been an important part of this effort as well. Simulated engine testing of vane subcomponents by P&W was the final step following years of development. In addition to achieving the temperature goals and enhanced durability performance of the Tech Challenge, an additional goal achieved by this work was reaching a Technology Readiness Level of 5 for the 3-D CMC/EBC system. As this five year Technical Challenge comes to a conclusion, future development interests in environmental barrier coatings and environmental modeling are discussed.

SiC/SiC composites↗

FAST-1.2: A Computer Code for Thermal-Mechanical Nuclear Fuel Analysis under Steady-state and Transients

Fuel Analysis under Steady-state and Transients (FAST) is the U.S. Nuclear Regulatory Commission (NRC)’s computer code that calculates the steady-state and transient response of nuclear reactor fuel rods during long-term in-reactor burnup, anticipated operational occurrences (AOOs), design basis accidents (DBAs), and dry storage conditions. The code calculates the temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include: • heat conduction through the fuel and other materials • heat transfer from the cladding-to-coolant • cladding elastic and plastic deformation, including creep • fuel-cladding mechanical interaction • fission gas release from the fuel • rod internal pressure and void volume • cladding oxidation The code contains necessary material and coolant properties, as well as clad-to-coolant heat-transfer correlations, for normal operation through postulated accidents and AOOs for today’s U.S.-based light water reactor (LWR) fuel designs. FAST-1.2 also contains preliminary materials and models for new LWR fuel concepts, such as accident tolerant fuel (ATF), and non-LWR fuel concepts such as metallic fuels for sodium fast reactors (SFRs). FAST has been developed for use on Windows and Linux operating systems. This document describes FAST-1.2 and is one of a series of documents on the code; the other documents detail the material properties used by FAST as well as its integral assessment to experiments and commercial data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Creep, Fatigue and Fracture Behavior of Environmental Barrier Coating and SiC-SiC Ceramic Matrix Composite Systems: The Role of Environment Effects

Advanced environmental barrier coating (EBC) systems for low emission SiCSiC CMC combustors and turbine airfoils have been developed to meet next generation engine emission and performance goals. This presentation will highlight the developments of NASAs current EBC system technologies for SiC-SiC ceramic matrix composite combustors and turbine airfoils, their performance evaluation and modeling progress towards improving the engine SiCSiC component temperature capability and long-term durability. Our emphasis has also been placed on the fundamental aspects of the EBC-CMC creep and fatigue behaviors, and their interactions with turbine engine oxidizing and moisture environments. The EBC-CMC environmental degradation and failure modes, under various simulated engine testing environments, in particular involving high heat flux, high pressure, high velocity combustion conditions, will be discussed aiming at quantifying the protective coating functions, performance and durability, and in conjunction with damage mechanics and fracture mechanics approaches.

Environmental Barrier Coatings↗

Constitutive response of Rene 80 under thermal mechanical loads

The applicability of a classical constitutive model for stress-strain analysis of a nickel base superalloy, Rene' 80, in the gas turbine thermomechanical fatigue (TMF) environment is examined. A variety of tests were conducted to generate basic material data and to investigate the material response under cyclic thermomechanical loading. Isothermal stress-strain data were acquired at a variety of strain rates over the TMF temperature range. Creep curves were examined at 2 temperature ranges, 871 to 982 C and 760 to 871 C. The results provide optimism on the ability of the classical constitutive model for high temperature applications.

Kim, K. S.↗

Viscoplastic Constitutive Theory Demonstrated for Monolithic Ceramic Materials

Development of accurate three-dimensional (multiaxial) inelastic stress-strain models is critical in utilizing advanced ceramics for challenging 21st century high-temperature structural applications. The current state of the art uses elastic stress fields as a basis for both subcritical crack growth and creep life prediction efforts aimed at predicting the time dependent reliability response of ceramic components subjected to elevated service temperatures. However, to successfully design components that will meet tomorrow's challenging requirements, design engineers must recognize that elastic predictions are inaccurate for these materials when subjected to high-temperature service conditions such as those encountered in advanced heat engine components. Analytical life prediction methodologies developed for advanced ceramics and other brittle materials must employ accurate constitutive models that capture the inelastic response exhibited by these materials at elevated service temperatures. A constitutive model recently developed at the NASA Lewis Research Center helps address this issue by accounting for the time-dependent (inelastic) material deformation phenomena (e.g., creep, rate sensitivity, and stress relaxation) exhibited by monolithic ceramics exposed to high-temperature service conditions. In addition, the proposed formulation is based on a threshold function that is sensitive to hydrostatic stress and allows different behavior in tension and compression, reflecting experimental observations obtained for these material systems.

Janosik, Lesley A.↗

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials Using MALAMUTE

Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy, aims to develop and qualify additively-manufactured materials for nuclear applications. The key challenges to these efforts are the microstructural variabilities observed on the AM products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-through-put experimental and modeling techniques to accelerate the qualification efforts. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the AM process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture the microstructural variabilities is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning modeling capabilities to develop a digital twin for AM that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation for AM materials. The melting and subsequent solidification that occurs during the AM process is a complex phenomenon that requires multiscale multiphysics analysis. Idaho National Laboratory’s (INL) Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for AM materials in an efficient, reliable, and cost-effective way. This work package focuses on understanding the role of process variabilities on the various microstructural characteristics of the AM materials. Microstructures unique to AM materials, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. In fiscal year (FY) 24, we significantly advanced upon our work in the last fiscal year, both on physics-based and ML models. The alloy solidification model available in MOOSE has been extended to incorporate the thermodynamic properties and free energy relevant to 316SS. The model demonstrates the Cr segregation that occurs during solidifcation. It is demonstrated that rate of solidification and solute segregation is primarily influence by the cooling rate dictating the level of freezing. This work captures the microstructural variabilities at the subgrain level that are often missing in the part-scale models. With an aim to connect the microstructural evolution model to realistic process conditions, a reduced order model is developed for predicting the thermal conditions around meltpool from high-fidelity process simulations. Furthermore, machine learning approach is used to accelerate the temperature prediction during the AM process. In the following years, MALAMUTE will be used to connect different aspects of the models and quantitatively predict the microstructural evolution. The developed ML-based surrogate model will consider the process conditions as the input to predict the microstructural features in a cost-effective way. The generated microstructures can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work help identify the key microstructural features at the subgrain level that are significant in property/performance prediction of the AM products. This work will provide inputs to the large-scale process variability models to reevaluate and validate assumptions/simplifications made in the part-scale models. Furthermore, through active learning this work will help identify the data need from both modeling and experimental sides for development of a robust digital twin for AM.

36 MATERIALS SCIENCE↗

Predicting Lifetime of a Thermomechanically Loaded Component

NASALIFE is a computer program for predicting the lifetime, as affected by low cycle fatigue (LCF) and creep rupture, of a structural component subject to temporally varying, multiaxial thermomechanical loads. The component could be, for example, part of an aircraft turbine engine. Empirical data from LCF tests, creep rupture tests, and static tensile tests are used as references for predicting the number of missions the component can withstand under a given thermomechanical loading condition. The user prepares an input file containing the creep-rupture and cyclic-fatigue information, temperature-dependent material properties, and mission loading and control flags. The creep rupture information can be entered in tabular form as stress versus life or by means of parameters of the Larson-Miller equation. The program uses the Walker mean-stress model to adjust predicted life for ranges of the ratio between the maximum and minimum stresses. Data representing complex load cycles are reduced by the rainflow counting method. Miner's rule is utilized to combine the damage at different load levels. Finally, the program determines the total damage due to creep and combines it with the fatigue damage due to the cyclic loading and predicts the approximate number of missions a component can endure before failing.

Murthy, Pappu L. N.↗

Requirements Description of GAMSOR and GAMSRC

This report presents the modeling and simulation capabilities of Argonne National Laboratory’s GAMSOR and GAMSRC code that is used in present reactor analysis activities. These capabilities will then be used to establish the set of verification tasks necessary to verify GAMSOR for use on commercial projects. A similar approach was taken for the PERSENT, REBUS and DIF3D software packages. The GAMSOR program is a modified version of DIF3D used to obtain the coupled neutron gamma flux distributions for a given reactor system. GAMSOR was first developed in the 1980s and its work has progressed in parallel with DIF3D throughout its various development phases. While GAMSOR is compatible with DIF3D-FD and DIF3D-Nodal, DIF3D-VARIANT is most commonly used today and will be the focus of the present verification effort. As covered in [1], GAMSOR was built to provide more accurate heating distributions by explicitly solving for both the gamma and neutron heating distributions. Without this consideration, gamma heat is normally assumed to be deposited locally at the site of gamma production. This is acceptable for modeling some phenomena because the total energy production is preserved, but it can lead to inaccurate approximations of fluence-dependent behaviors such as fuel performance, swelling, cladding embrittlement, radiation induced creep, and power peaking. The outputs from GAMSOR are contained in multiple intermediate and final output files: FIXSRC, VARSRC, GTFLUX, GHFLUX, PWDINT, NPDINT, and GPDINT. DIF3D normally produces a PWDINT file containing power density results, with the assumption that gamma rays are absorbed where they are emitted (i.e., energy deposition is local with no modeled transport). With GAMSOR, neutron power density (NPDINT) and gamma power density (GPDINT) are both produced, with their summed power densities replacing the results in PWDINT for total heating (i.e., recoverable) power density.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Stress studies in EFG

Stress distributions were calculated for a creep law to predict a rate of plastic deformation. The expected reduction in stresses is obtained. Improved schemes for calculating growth system temperature distributions were evaluated. Temperature field modeling examined the possibility of using horizontal temperature gradients to influence stress distribution in ribbon. The defect structure of 10 cm wide ribbon grown in the cartridge system was examined. A new feature is identified from an examination of cross sectional micrographs. It consists of high density dislocation bands extending through the ribbon thickness. A four point bending apparatus was constructed for high temperature study of the creep response of silicon, to be used to generate defects for comparison with as grown defects in ribbon. The feasibility of laser interferometric techniques for sheet residual stress distribution measurement is examined. The mathematical formalism for calculating residual stress from changes in surface topology caused by an applied stress in a rectangular specimen was developed, and the system for laser interferometric measurement to obtain surface topology data was tested on CZ silicon.

Source record↗

Computational simulation of probabilistic lifetime strength for aerospace materials subjected to high temperature, mechanical fatigue, creep, and thermal fatigue

The results of a fourth year effort of a research program conducted for NASA-LeRC by The University of Texas at San Antonio (UTSA) are presented. The research included on-going development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects or primitive variables. These primitive variables may include high temperature, fatigue, or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation was randomized and is included in the computer program, PROMISC. Also included in the research is the development of methodology to calibrate the above-described constitutive equation using actual experimental materials data together with regression analysis of that data, thereby predicting values for the empirical material constants for each effect or primitive variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from industry and the open literature for materials typically for applications in aerospace propulsion system components. Material data for Inconel 718 was analyzed using the developed methodology.

Boyce, Lola↗

Creep-rupture reliability analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Peralta-Duran, A.↗

Creep-rupture reliability analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Peralta-Duran, A.↗

Time-dependent THMC properties and microstructural evolution of damaged rocks in excavation damage zone

Modeling coupled thermo-hydro-mechanical-chemical (THMC) processes in host rocks near high-level nuclear waste (HLW) repositories at various time scales is an extremely challenging task. The current study integrates experimental, theoretical, and numerical methods in assessing the evolution of excavation damage zone (EDZ) over time and its implication on the long-term migration of hazardous species. Argillite and rock salt and are the focus of this study. The first part of the report presents a novel time-dependent directional microcrack damage theory for generic brittle rocks. It features detailed statistical description of the microcracks within a damaged solid, permitting a direct upscaling of microscale processes such as crack growth kinetics, crack closure/opening, sliding friction to explain the macroscopic creep, nonlinear elasticity, shear dilation, and loading-unloading hysteresis. This provides a basic platform for describing the anisotropic mechanical and transport properties of damaged rocks during excavation and subsequent THMC loadings. The model is validated and numerically implemented to Finite Element (FE) package ABAQUS through the user-defined material (UMAT) interface and have demonstrated great potential in resolving the time-dependent and anisotropic evolution of damage in the EDZ. The second part of the report presents a multi-scale experimental effort in characterizing the thermal, hydraulic, and mechanical properties of Mancos shale and Avery Island salt. For the Mancos shale, triaxial compression tests are performed at different confining pressures and temperatures to probe its thermomechanical properties relevant to HLW repositories. The obtained stress-strain data are interpreted using the proposed directional damage theory. Post-test specimens are subjected to gas permeability tests to reveal the correlation between permeability and the degree of microcracking. At microscale, temperature-controlled nanoindentation tests are performed and found a linear correlation between fracture toughness and elastic modulus from 25°C to 300°C. For Avery Island salt, we have designed and manufactured a novel relative-humidity controlled uniaxial creep device. Long-term creep tests at low stresses (< 5 MPa) are performed at different levels of relative humidity (RH). Besides confirming the much higher creep rates as one would expect through extrapolating the high-stress creep data, the results reveal that the steady-state creep rate of rock salt is strongly dependent on the ambient RH, an aspect that is often neglected in the literature. Both behaviors can be attributed to the pressure-solution creep mechanism which dominates at low stress and high RH levels. The third part of the report explores a set of numerical strategies in modeling the THMC behavior of porous geomaterials. A fully implicit, monolithic FE solution that can flexibly interface with different material models and coupling mechanisms for THMC problems is developed and verified through the ABAQUS user-defined element (UEL) interface. The scheme is used to study the THM response of a hypothetical HLW storage site with reference to an existing in-situ heater test. Strategies for integrating the UEL and the microcrack UMAT are suggested. Another numerical endeavor of this study is to implement a higher-order asymptotic homogenization method to account for the heterogeneous porous structures. The same method is then extended to perform microstructure-informed thermo-mechanical modeling of generalized continua. The above outcomes of this project provide a strong thrust towards enhancing the fundamental understanding and modeling capability of the long-term evolution of host rocks in EDZ, thus helping achieve the design goal of 1-million-year isolation of high-level nuclear wastes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Mantle devolatilization and rheology in the framework of planetary evolution

We investigate the thermal history of an Earth-like planet with the help of a parameterized mantle convection model including the volatile exchange between mantle and surface reservoirs. The weakening of mantle silicates by dissolved volatiles is described by a functional relationship between creep rate and water fugacity. We use flow law parameters of diffusion creep in olivine under dry and wet conditions. The mantle degassing rate is considered as directly proportional to the seafloor spreading rate, which is also dependent on the mantle heat flow. To calculate the spreading rate, we assume that the heat flow under the mid-ocean ridges is double the average mantle heat flow. The rate of regassing also depends on the seafloor spreading rate as well as on other factors like the efficiency of volatile recycling through island arc volcanism. Both mechanisms (de- and regassing) are coupled self-consistently with the help of the parameterized convection model under implementation of a temperature and volatile-content-dependent mantle viscosity.

Franck, S.↗