Anisotropic Creep Model Research Articles

Normalized Parameter Creep Model of DD6 Nickel-Based Single Crystal Superalloy

For nickel-based single crystal superalloy DD6 (AECC Beijing Institute of Aeronautical Materials, Beijing, China) material, a method for predicting creep rupture time was proposed based on a newly defined equivalent stress method. An anisotropic creep model for describing the orientation-dependent creep behavior and lifetime of a nickel-based single crystal superalloy was proposed. The creep subroutine was written based on the proposed nickel-based single crystal creep model. The stability of the model was improved by adjusting the iterative algorithm. The creep calculation results in [001], [011], and [111] loading directions were compared with the experimental results. The accuracy of the calculation results by the nickel-based single crystal creep subroutine was verified. The initial time step and maximum time step of the creep subroutine were studied.

An anisotropic creep model for continuously and discontinuously fiber reinforced thermoplastics

Objective of the present study is the definition and implementation of a constitutive creep model for fiber reinforced thermoplastics. Both, unidirectionally as well as discontinuously long fiber reinforced materials are considered. Assuming that creep deformation is restricted to the thermoplastic matrix, a three term Kelvin–Voigt formulation is employed as a base material model. For continuously unidirectionally fiber reinforced materials, the thermoplastic matrix is superimposed with a standard linear elastic model. For discontinuously long fiber reinforced thermoplastics, an anisotropic generalization of the original, isotropic Kelvin-Voigt model is proposed. Both models are implemented into a finite element program and validated against an experimental data base consisting of tensile creep experiments on neat matrix material, unidirectionally fiber reinforced material as well as discontinuously long fiber reinforced material with different fiber volume fractions. Different fiber orientations as well as different temperatures are considered. As a structural example for further validation, creep experiments on loading points for hybrid thermoplastic sandwich structures are performed and simulated numerically. In all cases, the experimental results and the numerical prediction are found in a good agreement.

Anisotropic creep characteristics and mechanism of shale under elevated deviatoric stress

The time-dependent characteristics of anisotropic shale are important for accurately predicting a reservoir's behavior over a long period of time. To study the transverse isotropic creep characteristics of shale, a series of shale creep tests using specimens with 4 different bedding layer orientations (0°, 45°, 75° and 90°) under multiple levels of deviatoric stress were conducted. The experimental results indicate that shale presents creep behavior even when the deviatoric stress is relatively low. Anisotropy has significant influences on the creep deformation and steady creep rate. When the bedding plane inclined angle is 45° and under the same deviatoric stress, the creep deformation and steady creep rate are the highest, while the smallest creep deformation and steady creep rate are generated when the bedding plane orientation is 90°. Time-dependent deformation appears the tertiary creep stage when the deviatoric stress is crack damage threshold, which implies that crack damage stress can be regarded as the shale's long term strength. The steady creep rate increases exponentially with increasing deviatoric stress as the stress is larger than the crack initiation threshold. The rationality of the empirical creep law is evaluated. It is concluded that the empirical creep model can only fit the existing creep data, but it is almost impossible to predict the creep deformation. The mechanism for generating anisotropic creep behavior of shale is analyzed in detail, and three basic creep patterns for shale are proposed based on the action mechanism of the stress tensor components. A general methodology for proposing the anisotropic creep model is finally suggested.

An anisotropic creep model for continuously and discontinuously fiber reinforced materials

AbstractThe present study is concerned with the formulation, implementation and validation of anisotropic creep laws for neat thermoplastic matrix materials, discontinuously long fiber reinforced thermoplastic (LFT) composite materials with process dependent fiber preference directions as well as unidirectionally fiber reinforced thermoplastic tapes. Based on a simple three term Kelvin‐Voigt approach, an anisotropic model is formulated and implemented into a finite element program. The model is validated against an experimental data base of creep experiments on continuously and discontinuously fiber reinforced materials.

Modelling of anisotropy and consolidation effect on behaviour of sunshine embankment: Australia

This paper investigates the time-dependent behaviour of Sunshine embankment on soft clay deposit with and without prefabricated vertical drains. An elasto-viscoplastic model was used to investigate the influence of anisotropy and creep effect on the settlement behaviour of the embankment. The constitutive model, namely ACM accounts for combined effects of plastic anisotropy and creep. For comparison, the problem is also analysed with isotropic Modified Cam Clay model which does not consider creep effect. To analyse the PVD improved subsoil, axisymmetric vertical drains were converted into equivalent plane strain conditions using two different mapping approaches. The results of the numerical analyses are compared with the field measurements. The numerical simulations suggest that the anisotropic creep model is able to give a better representation of soft clay response under an embankment loading. The isotropic model which neglects the effects of anisotropy and creep may lead to inaccurate predictions of soft clay response. Additionally, the numerical results show that the mapping method used for PVD improved soft clays can accurately predict the consolidation behaviour of the embankment and provide a useful tool for engineering practice.

Modelling creep behaviour of anisotropic soft soils

This paper presents a three dimensional constitutive model that describes the creep behaviour of natural clays with anisotropic stress–strain response, focussing on robust model implementation. Creep is formulated using the concept of a constant rate of visco-plastic multiplier, resulting in a formulation with easily determined creep parameters. A key assumption in the model formulation is that there is no purely elastic domain. Of the 10 input parameters that can be defined based on standard laboratory testing, five are similar to those used in the Modified Cam-Clay model. The performance of the model at element level and boundary value level is demonstrated, for the latter by comparing the simulations with the measured response of Murro test embankment in Finland. For comparison, the simulations are also done using the previously published anisotropic creep model and an equivalent rate-independent model. This enables studying the role of evolution anisotropy and creep at boundary value level by systematic comparisons.

Comparison of Anisotropic Rate-Dependent Models for Modeling Consolidation of Soft Clays

Two recently proposed anisotropic rate-dependent models are used to simulate the consolidation behaviour of two soft natural clays: Murro clay and Haarajoki clay. The rate-dependent constitutive models include the EVP-SCLAY1 model and the Anisotropic Creep Model (ACM). The two models are identical in the way the initial anisotropy and the evolution of anisotropy are simulated, but differ in the way the rate-effects are taken into consideration. The models are compared first at the element level against laboratory data and then at boundary value level against measured field data from instrumented embankments on Murro and Haarajoki clays. The numerical simulations suggest that at element the EVP-SCLAY1 model is able to give a better representation of the clay response under oedometric loading than ACM, when the input parameters are defined objectively. However, at boundary value level the issue is not as straightforward, and the appropriateness of the constitutive model may depend heavily on the in situ overconsolidation ratio (OCR).

Anisotropic continuum damage modeling for single crystals at high temperatures

In single crystals, the process of creep damage is generally anisotropic. Indeed, the damage evolution does not only depend on the loading conditions, but also on the lattice orientation. And the current state of damage has an anisotropic influence on the effective stress state, so that it is represented by a tensorial damage variable. Based on the continuum damage mechanics theory, a creep damage model for F.C.C. single crystals has been developed and implemented in a three-dimensional anisotropic creep model. It is shown that the resulting material model is capable of describing the orientation dependence of the creep and damage evolution of nickel-based superalloys in the high temperature regime.

Extension of an anisotropic creep model to general high temperature deformation of a single crystal superalloy

Abstract: A physics based model has been developed that accounts for the principal features of anisotropic creep deformation of single crystal superalloys. The present paper extends this model to simulate other types of high temperature deformation under strain controlled test conditions, such as stress relaxation and tension tests at constant strain rate in single crystals subject to axial loading along an arbitrary crystal direction. The approach is applied to the SRR99 single crystal superalloy where a model parameter database is available, determined via analysis of a database of constant stress creep curves. A software package has been generated to simulate the deformation behaviour under complex stress-strain conditions taking into account anisotropic elasticity.

A Formulation of Creep Behavior with Anisotropic Hardening. 2nd Report. Verification.

The main purpose of the present study is to evaluate the validity of the anisotropic creep model proposed in the prior report through comparison with experimental results. A comparison with the well-known anisotropic creep models proposed by Murakami-Ohno and Mroz-Trampczynski-Hayhurst is also made; we discuss the structural similarities and/or differences and the predictive capability of these anisotropic creep models. The proposed creep model has a framework of unified constitutive models and assumes an auxiliary hardening rule for creep analyses. The auxiliary rule is characterized by the concept of material memory surface in which the isotropic hardening is suppressed and at the same time the rate of anisotropic hardening is increased by the amount by which the isotropic hardening rate is reduced. The comparison with the experimental results shows an acceptable accuracy of the proposed model. With other creep models, the present model has a comparable accuracy.

Creep Model for Metallic Composites Based on Matrix Testing

An anisotropic creep model is formulated for metallic composites with strong fibers and low to moderate fiber volume percent (< 40%). The idealization admits no creep in the local fiber direction and assumes equal creep strength in longitudinal and transverse shear. Identification of the matrix behavior with that of the isotropic limit of the theory permits characterization of the composite through uniaxial creep tests on the matrix material. Constant and stepwise creep tests are required as a data base. The model provides an upper bound on the transverse creep strength of a composite having strong fibers embedded in a particular matrix material. Comparison of the measured transverse strength with the upper bound gives an assessment of the integrity of the composite. Application is made to a Kanthal composite, a model high-temperature composite system. Predictions are made of the creep response of fiber-reinforced Kanthal tubes under interior pressure.

Requirements for in-reactor Zircaloy creep measurements for application in the design of PWR fuel

The ability to describe the irradiation creep of Zircaloy reactor components is dependent upon a well characterized data base, an anisotropic creep model, and, in the majority of cases, a multi-dimensional description of the stress state of the material. In the present paper, the interplay between these three areas is illustrated by a description of a model developed to utilize experimental data in the calculation of the creepdown of Zircaloy cladding that is subjected to an external pressure in a PWR. Design requirements are reviewed and the influence of several variables on creep measurements are presented. These include the interaction of the fuel with the cladding, the effect of anisotropy, the separation of creep and growth, the effect of initial ovality and eccentricity, and the scatter observed in data sets. Application of the model outside the data base is discussed and the model is validated by comparing the diametrical deformation calculated analytical with measurements obtained from post-irradiation examination of fuel cladding.