Model For Creep Deformation Research Articles

A unified description of creep in pure and dispersion-strengthened copper

Abstract A constitutive model for creep deformation in pure and dispersion-strengthened copper is presented. This description reproduces the characteristic features of steady-state and constant-str...

Creep deformation modelling of superalloy single crystals

A model of creep deformation in arbitrarily oriented nickel-base superalloy single crystals has been developed. This model extends the preceding model of the present authors [Svoboda, J. and Lukáš, P., Acta mater., 1998, 46, 3421] covering the case of creep in 〈001〉 oriented crystals. The calculated creep curves were compared with the creep curves of single crystals CMSX-4 of the orientations 〈001〉, 〈011〉 and 〈111〉 measured at 750°C; a fair agreement was found.

On rafting in a single crystal nickel-base superalloy after high and low temperature creep

A microstructure-sensitive crystal plasticity constitutive framework is proposed for simulating the tensile, cyclic, and creep response of single crystal Ni-based superalloys. In this framework, a non-Schmid model is used to account for the orientation- and temperature-dependent yield anisotropy. A model for the evolution of the slip system-level backstress is developed to simulate the cyclic response. The model accounts for the effect of microstructural features like precipitate volume fraction and size, and matrix channel width, on the associated hardening mechanisms. A physical model for creep deformation has also been developed that accounts for dislocation climb normal to the slip plane and the microstructure evolution due to rafting and isotropic coarsening of the precipitates. Application of the model is demonstrated by predicting the orientation- and temperature-dependent thermo-mechanical deformation of two single crystal superalloys, CMSX-4 and PWA-1484. The model is calibrated to the experimental tensile, cyclic and creep response for these alloys. Finally, the model is qualitatively validated by predicting the creep-fatigue interactions for different loading orientations and a range of thermo-mechanical conditions for CMSX-4 and PWA-1484.

Modelling of anisotropic creep deformation and damage in single crystal superalloys

Previous studies on the creep behavior of single crystal nickel base superalloys reveal that both creep deformation behavior and stress rupture properties of single crystal alloys are strongly dependent on crystal orientation and temperature. A physical model of creep deformation in single crystal superalloys has been proposed by Ghosh et al. This model accounts for the anisotropy and asymmetry of creep by viscous glide on specific crystallographic slip systems and for the tertiary creep behavior through a damage parameter that is related to the accumulation of mobile dislocations in each slip system. The model has been applied to analyze the creep curves of the single crystal nickel base superalloy SRR99, with particular reference to [001] and [111] orientations. The model also attempts to predict the change in the anisotropy of creep behavior with stress and temperature, and the changes in the orientation and specimen cross-section with creep strain. The creep model proposed by Ghosh et al has been modified and extended to describe the anisotropic creep behavior of single crystal superalloys for multiaxial stress states. The equations must be used with a general transformation procedure to relate the crystallographic deformation to the global loading directions. Three creep rupture criteria basedmore » on material damage in single crystal superalloys have been suggested. The creep damage criterion that takes into account of the different effects of damage on octahedral and cubic slip system and includes interaction effects between the two types of slip provided the best predictions of creep rupture life for the single crystal nickel base superalloy SRR99.« less

A micromechanics model of creep deformation in dispersion-strengthened metals

A micromechanics model, in which work-hardening caused by second-phase particles and a recovery process by diffusion of atoms were taken into account, has been proposed for explaining the creep deformation of dispersion-strengthened metals in high-temperature creep. A constitutive equation of the Θ projection was employed to describe the whole creep curves from the onset of loading to rupture. The results of the calculations based on the present model have been compared with those of experiments on the carbon steels containing spherical cementite particles. There was a correlation between the experimental creep curves and the calculated ones. The changes in the calculated creep strain and creep rate with time have also been compared with the experimental results on carbon steels. The micromechanics model was found to be applicable to any kind of two-phase material, if the constitutive equation was appropriately chosen.

Numerical Model of Primary Creep Deformation in a Novel Double Shear Specimen

Abstract Three-dimensional finite element calculations were performed for primary creep deformation in a novel double shear specimen. Two characteristic creep behaviors were considered: one in which the stress exponent, n, is equal to 3 and another in which n is equal to 5. Both models resulted in a quasi-stationary stress state in which the principal stresses change only slightly with time while the von Mises effective stress and principal facet stress reach essentially constant values. The uniformity of this quasi-stationary stress state throughout the gage section indicates that it may be used to characterize the overall stresses driving creep deformation and damage.

Assessment of creep damage in austenitic steel X-8-CrNiMoNb-16-16 at elevated temperature

A phenomenological model of creep deformation is developed by introduction of a function that represents intrinsic creep resistance to damage. The Lévy-Mises relation in plasticity is modified in deriving the time dependent creep strain and/or strain rate expression. Results correlated well with the experimental creep data of the X-8-CrNiMoNb-16-16 austenitic steel.

Creep and Creep Rupture of Metallic Composites

A creep and creep damage theory is presented for metallic composites with strong fibers. Application is to reinforced structures in which the fiber orientation may vary throughout but a distinct fiber direction can be identified locally (local transverse isotropy). The creep deformation model follows earlier work and is based on a flow potential function that depends on invariants reflecting stress and the material symmetry. As the focus is on the interaction of creep and damage, primary creep is ignored. The creep rupture model is an extension of continuum damage mechanics and includes an isochronous damage function that depends on invariants specifying the local maximum transverse tension and the maximum longitudinal shear stress. It is postulated that at high temperature and low stress, appropriate to engineering practice, these stress components damage the fiber/matrix interface through diffusion controlled void growth, eventually causing creep rupture. Experiments are outlined for characterizing a co...

A Rate-Dependent Inelastic Constitutive Model—Part II: Creep Deformation Including Prior Plastic Strain Effects

In this part, a constitutive model for creep deformation is presented, which includes the effect of prior plastic straining. The model is capable of predicting the influence of plastic or creep prestrain and step loading on the subsequent creep deformation as well as cross effect between prestrain and creep strain directions in a multiaxial stress state. The predictions of the model are compared with the experimental data and the agreement is found to be very good. This model, in conjunction with that presented in Part I, would enable one to predict material response to complex loading sequences in the creep-plasticity range.

Creep deformation of single crystal superalloys—modelling the crystallographic anisotropy

A generalised model of creep deformation in cubic single crystals is developed that considers the combined effects of viscous glide on two (or more) slip systems and accounts for tertiary creep by the accumulation of mobile dislocations with plastic strain. The model is applied to analyse a database of creep curves for the nickel-base single crystal superalloy SRR99 with the assumption that creep deformation occurs by glide on both the {111}〈 1 01〉 and {001}〈110〉 systems. A procedure for the calculation of creep curves and associated crystal rotations for arbitrary crystal orientations is described. The model predicts changes in the anisotropy of creep behaviour with stress and temperature that is in general agreement with the limited available experimental data. It also includes the contributions of all possible slip vectors to predict crystal rotations that are consistent with observations.

Deformation and subcritical crack growth under static loading

Abstract To examine the effect of creep deformation rate on crack growth, an analytical relationship between the kinetics of crack growth in an inert environment and the deformation kinetics is developed by combining a tensile ligament instability model for crack growth with Hart's model for uniaxial creep deformation. The modified model was examined in terms of the steady state creep and crack growth data of Landes and Wei on AISI 4340 steel at 297, 353 and 413 K (i.e. below the homologous temperature of about 450 K). The model was found to be effective in describing the crack growth response at high stress intensity factor K levels and showed a threshold crack growth behavior at lower K levels. Changes in crack growth response with deformation mechanism and the need for additional experimental confirmation are discussed.

A dislocation network model of recovery-controlled creep

A new model of recovery-controlled creep deformation, based on the jerky glide motion of dislocations between obstacles, is proposed. A three-dimensional distribution of dislocation links is visualized such that only links which attain a certain threshold size,λ a, through recovery can glide rapidly until they are again arrested at the next obstacle. The rate of mobilization of arrested dislocations is shown to be directly proportional to the annihilation rate, ϱa. The strain rate, γ, during transient creep is related to the annihilation rate, the obstacle spacingL and the Burgers vectorb of the dislocations according to the expression $$\gamma = \alpha _1 \psi (t)\dot \varrho bL$$ where α1 is a geometrical constant and ψ(t) is a time-dependent parameter whose value is determined by the instantaneous (free) dislocation density as well as some salient features of the dislocation distribution. At steady state, ψ(t) translates into a constant which is stress and temperature independent. The average effective dislocation velocity is also shown to be directly proportional to the annihilation rate. The model is used to rationalize the familiar creep transients which are usually observed when the stress is altered abruptly during recovery creep.

A model of creep deformation in the lithosphere as a non-isothermal linear viscous circular plate on a Winkler foundation

The lithosphere is known to deform under geologic loads such as those due to surface volcanoes and submerged magma chambers. The lithosphere is modelled here as a linear viscous circular plate supported on the underlying asthenosphere, which in turn is modelled as a Winkler foundation. A two-dimensional steady creep relation is used to derive the governing partial differential equations for deflection, stress and bending moment. The temperature variation through the thickness of the lithosphere is of major importance and is included in the analysis. Solutions to the governing equations are obtained both in general and for an illustrative set of geometric, loading, material and thermal parameters.

A model for high-temperature creep incorporating both recovery and thermally activated glide

A computer model of creep deformation incorporating the thermodynamics of glide and recovery is presented. The model is able to provide possible explanations for the results of stress drop experiments in which either a delay time or a sharp change in strain rate is observed. The effect of the ease of glide on the recovery controlled creep rate is also explained. Ein Rechnermodell über Kriechveränderung einschließlich der Thermodynamik der Gleit- und Rückbildung wird dargestellt. Das Modell ist in der Lage, eine mögliche Erklärung der Resultate des Spannungsabfallsversuchs zu geben, in welchem entweder Verzugszeit oder ein scharfer Wechsel des Spannungsverhältnisses beobachtet wird. Der Einfluß der Leichtigkeit des Gleitens auf die rückbildungskontrollierte Kriechgeschwindigkeit wird ebenfalls erklärt.

On the creep characteristics of β-zircaloy

A recent model of creep deformation in pure materials is compared with published data on β-zirconium and β-zircaloy. It is shown that the zircaloys behave like the pure metal in this phase range and that the model is capable of predicting their creep rates to within a factor of 2 on tubing material. A condition is that the curved Arrhenius plot for diffusion in zirconium represents the intrinsic behaviour of point defects in the lattice and that solute atoms have an insignificant effect on the process. A corollary is that the contribution from dislocation short-circuiting both to diffusion and to creep is negligible.

An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures

A new, unified model simulates many of the structurally significant deformation phenomena associated with both creep and short-time plasticity, including cyclic hardening/softening, Bauschinger effect, strain-rate effects, and annealing, among others. It is phenomenological and macroscopic in nature, but is strongly related to the underlying microscopic physical mechanisms. It consists of a single hyperbolic sine strain-rate equation, plus two work-hardening/recovery equations for the rates of change of the two history variables. The derivation, behavior, and use of the model are explained, and the procedure for calculation of materials constants from standard test data is given. Comparisons are made with some other current strain-rate formulations.

Discussion: “An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures and Part II—Application to Type 304 Stainless Steel” (Miller, A., 1976, ASME J. Eng. Mater. Technol., 98, pp. 97–105, 106–112)

Discussion: “An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures and Part II—Application to Type 304 Stainless Steel” (Miller, A., 1976, ASME J. Eng. Mater. Technol., 98, pp. 97–105, 106–112)

Closure to “Discussion of ‘An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures and Part II—Application to Type 304 Stainless Steel’” (1976, ASME J. Eng. Mater. Technol., 98, p. 112)

Closure to “Discussion of ‘An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures and Part II—Application to Type 304 Stainless Steel’” (1976, ASME J. Eng. Mater. Technol., 98, p. 112)

An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part II—Application to Type 304 Stainless Steel

For the deformation model developed in Part I, material constants are calculated from standard test data on type 304 stainless steel. With them, simulations are made of various types of tests, including tensile tests, strain-rate sensitivity, creep tests with stress drops, strain-controlled cycling, and creep-fatigue interaction. The simulations show general agreement with the corresponding experimental data for type 304, but in a few respects, quantitative improvements are required. Implications of the strengths and weaknesses of the new model are discussed.

Analysis of creep deformation under cyclic loading conditions

A mathematical model for creep deformation under cyclic loading is reformulated with the objective of achieving more quantitative comparison with experimental results. Introduction of a more general creep relation and inclusion of a cyclic hardening effect in the improved model lead to prediction of creep behavior in good agreement with experimental results. Experimental methods are indicated whereby materials constants appearing in the formulations can be independently determined and used in the prediction of cyclic creep behavior. The application of this improved model is demonstrated for the case of interstitial free iron at room temperature.