At high temperatures metallic materials behave in a viscous manner exemplified by strain rate dependence, stress relaxation and creep deformation. At low temperatures however, these effects are extremely small, and the behaviour is strain rate independent and shows no or very small relaxation effects. Finally there exists an intermediate region, in which the material behaviour is close to strain rate independent for high strain rates but at the same time shows time dependent inelastic effects, such as stress relaxation and creep. For IN792 this occurs at temperatures around 650 °C. The article describes the extension of a power-law viscoplastic model describing the behaviour of IN792 at 850 °C, also to describe the behaviour at 650 °C, by bounding the elastic-viscoplastic stress-space by a plastic yield surface. The model parameters have been estimated using data from creep test and tailored step relaxation tests, and the model fits well to both the step relaxation data aimed at resembling relevant component conditions and long term creep data. © 2003 Published by Elsevier B.V.
The material parameters for two isothermal viscoplastic models with deliberately limited sets of material parameters have been estimated. The models are to describe the behaviour of the nickel based superalloy IN792 in a gas turbine hot part application. The models are based on a power law flow equation and the state variable used is backstress. The model calibration is done by least-squares optimization using non-standard constitutive tests that are aimed at describing relevant component conditions. The constitutive tests give information about the kinematic hardening effects for the backstress evolution equations, while secondary creep data provides stress versus inelastic strain rate information for the flow equation. All tests are uniaxial and isothermal. With the estimated parameter sets the models give relatively good fits to the data. The results suggest that the models can be used to describe the high temperature behaviour of IN792. ⌐ 2002 Elsevier Science B.V. All rights reserved.
The accuracy of the exact muffin-tin orbitals method combined with the coherent potential approximation (EMTO-CPA) for total energy calculations for systems with magnetic and chemical disorder, which is present simultaneously, is investigated. The mixing enthalpy of ordered, as well as disordered FeCo, FeNi, and FeCu equiatomic ferromagnetic alloys is calculated with the EMTO-CPA method and with the full-potential projector augmented wave (PAW) method. The results are compared and found to be in excellent agreement with each other. The EMTO-CPA method, in combination with disordered local moment model, is then applied to calculate the mixing enthalpy of the random paramagnetic face-centered cubic (fcc) FeCo alloy, as well as body-centered cubic (bcc) FeCr and FeV alloys over the whole concentration range. The results are compared with experimental data and a very good agreement is found again.
The structural phase transitions in molybdenum under pressures are investigated on the basis of first principle analysis of elastic constants behavior and phonon dispersions. The definition of the effective elastic constants of nth order ( nP2), governing the elastic properties of a loaded crystal, is given. The effective elastic constants of second and third order and the phonon dispersions are calculated by DFT methods in the pressure range of P = 0 - 1400 GPa, T = 0 K. The calculation results at P = 0 are in good agreement with the available experimental data. On the basis of the obtained results the stability of the bcc phase of molybdenum under pressure and the possibility of the phase transition are investigated. It is shown that the effective elastic constant eC0 which corresponds to the tetragonal uniform strain of a loaded crystal undergoes significant softening at P andgt; 400 GPa. In the same pressure range the frequencies of the transverse branch T-[110](-) [zeta zeta 0] also begin to soften and already at P approximate to 1000 GPa they become imaginary near the wave vector [1/4 1/4 0]. The bcc -andgt; dhcp phase transition associated with the softening of eC0 and the soft mode T-[110](-)[1/4 1/4 0] is discussed.
Coarse grained superalloys are of large interest in high temperature applications, and can be found in e.g.gas turbine components, where great care must be given with respect to high temperature fatigue. Due tothe large grain size, the material behaviour at e.g. sharp notches cannot be considered homogeneous. As aconsequence, the fatigue behaviour is likely to expose a large variation. In order to numerically investigatethis variation, a Monte Carlo analysis has been carried out by 100 FE-simulations of notched specimens,where placements and orientations of the grains were randomised. Furthermore, each grain wasmodelled as a unique single-crystal, displaying both anisotropic elastic and plastic behaviour and tension/compression asymmetry. The effect of randomness was investigated by the obtained dispersion infatigue crack initiation life. It was concluded that the fatigue life behaviour of coarse grained nickel-basesuperalloys may show a considerable variation, which cannot be captured by one single deterministicanalysis based on data for a homogenised material. Furthermore, the dispersion is of such a magnitudethat it needs to be taken into account in industrial applications where highly stressed coarse grainedmaterials are used.
The constitutive behaviour at room temperature of a single-crystal nickel-base superalloy is presented in a new model. This model is based on crystal plasticity and takes Schmid- as well as non-Schmid stresses, elastic anisotropy and tension/compression asymmetry into account. By comparison with uniaxial tensile and compressive tests, the model is shown to reproduce the real behaviour well, including the tension/compression asymmetry. The model also shows that typically encountered deviations in orientations ofcastings have a non-negligible influence on stiffness and yield limit, which must be taken into account for industrial applications.
The thermomechanical fatigue (TMF) stress relaxation of the single-crystal nickel-base superalloy MD2 has been analysed and modelled in this paper. In-phase and out-of-phase TMF experiments in the nominal [001],[011] and [111] crystal orientations have been performed. The TMF cycle consists of two loadings each with a 100 h long hold-time. A simple crystallographic creep model, based on Norton’s creep law, has been developed and used in conjunction with a crystal plasticity model. The model takes anisotropy and tension/compression asymmetry into account, where the anisotropic behaviour is based on the crystallographic stress state. The values of the creep parameters in the anisotropic expression were determined by inverse modelling of the conducted TMF experiments, a parameter optimisation were performed. The developed model predicts the stress relaxation seen in the TMF experiments with good correlation.
This paper gives a bibliographical review of the finite element methods applied to the analysis and simulation of quenching and other heat treatment processes. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subjects that were published between 1976 and 2001. The following topics are included: quenching - quenching process in general, heat transfer and thermomechanical modelling, residual stresses in quenching, and other topics, hardening, annealing, tempering, and carburizing and nitriding. Three hundred and fifty references are listed. © 2003 Elsevier Science B.V. All rights reserved.
The special quasirandom structure (SQS) approach is a successful technique for modelling of alloys, however it breaks inherently the point symmetry of the underlying crystal lattice. We demonstrate that monocrystalline and polycrystalline elastic moduli can scatter significantly depending on the chosen SQS model and even on the supercell orientation in space. Also, we demonstrate that local disturbances, such as vacancies or interfaces change the SQS configuration in a way, that significantly affects the values of the calculated physical properties. Moreover, the diversity of local environments in random alloys results in a large variation of the calculated local properties. We underline that improperly chosen, generated or handled SQS may result in erroneous theoretical findings. The challenges of the SQS method are discussed using bulk Ti0.5Al0.5N alloy and TiN/Ti0.5Al0.5N multilayer as model systems. We present methodological corrections for the mindful application of this approach in studies of advanced properties of alloys.
Methods based on first-principles calculations have proven effective for predicting the thermodynamic stability of materials that have not previously been considered. However, the vast majority of these predictions are based on 0 K calculations, which means that little is known about the effects of temperature on their accuracy. This causes considerable uncertainty with respect to stability predictions of new hypothetical phases. In this work we combine first-principles calculations with an optimization procedure to calculate the phase stability as a function of temperature for Ti2AlC, Ti3AlC2 and Ti4AlC3 MAX phases with respect to their most competing phases in the Ti-Al-C phase diagram, in a temperature interval from 0 to 2000 K. To model nonzero temperatures, we include effects from the electronic and vibrational free energies to the Gibbs free energy for all relevant competing phases. We show that, due to a mutual cancellation of the temperature dependent energy terms, the results of neither the harmonic nor the quasiharmonic calculations differ significantly from the calculated 0 K formation energies. We thus provide a plausible explanation for the success of previous 0 K predictions, an explanation which also serves as evidence for the hypothesis that the phase stability in many materials systems is primarily governed by the 0 K energy terms.
The binding and electronic properties of monoatomic nanowires, dimers and bulk structures of Cu, Ag, Au and Ni, Pd, Pt have been studied by the projector augmented-wave method (PAW) within the density functional theory (DFT) using the local density approximation (LDA) as well as generalized gradient approximation (GGA) in both Perdew–Wang (PW91) and Perdew–Burke–Ernzerhof (PBE) parameterizations. Our results show that the formation of atomic chains is not equally plausible for all the studied elements. In agreement with experimental observations Pt and Au stand out as most likely elements to form monoatomic wires. Changes in the electronic structure and magnetic properties of metal chains at stretching are analyzed.