Anisotropic Creep Damage Research Articles

Influence of crystal orientations on the creep fracture of a nickel-based single crystal superalloy

Due to the anisotropy of the modulus of face-centered cubic cells, the nickel-based single crystal alloys exhibits substantial anisotropy at high temperatures. Their creep properties, especially the creep rupture lives, are related to the actuation of the slip system and the magnitude of the shear stress on the slip plane. The creep orientation sensitivity has been analyzed through creep experiments, as well as the microstructure and morphology of the fracture. On the macroscale, the necking sections of [001], [011] and [111] orientations are circular, elliptical and circular, respectively. Meanwhile, on the microscopic scale, the damage evolution caused by the expansion of the internal micropores in the single crystal alloy under the three orientations shows fourfold symmetry, double symmetry and triple symmetry, respectively. Based on the crystal plasticity theory, an anisotropic creep constitutive model and damage model are established to reflect the difference in creep deformation and damage evolution caused by orientation. The numerical simulations of the whole creep process of a second generation nickel-based single crystal superalloy show that the creep constitutive model and damage model can simulate the deformation and damage of the specimen under different orientations, and the creep life can be obtained.

Coupling model for the gradient loading creep behavior of nickel-based single-crystal superalloys

The emergency situation caused by the abnormal service of an aeroengine, such as gradient loading, directly leads to blade rupture. Considering the effect of gradient loading on creep, a coupling creep model of nickel-based single crystals under gradient loading conditions is proposed based on crystal plastic theory and thermodynamic damage theory. Internal state variables—elastic strain, plastic strain and damage—are introduced to describe the thermodynamic irreversible process of a system. An anisotropic creep damage evolution equation represented by the damage strain energy release rate Y is deduced by the energy conversion method. The gradient loading creep behavior predicted by the finite element calculation is in good agreement with the experimental results.

Experimental analysis and constitutive modeling of anisotropic creep damage in a wrought age-hardenable Al alloy

Many components of aerospace and automotive engineering manufactured from forged age-hardening aluminum alloys operate at high temperature in the range 0.3Tm–0.5Tm, where Tm is the melting temperature. Experimental data for uni-axial creep on specimens sampled from a forged AA2014 alloy component show that inelastic strain rates depend significantly on the orientation of loading with respect to the material flow direction during the manufacturing stage. Based on the recently developed constitutive model of anisotropic creep, hardening/recovery, softening and overageing processes, this paper addresses experimental analysis and modeling tertiary creep regime up to the final stage of creep rupture. The emphasis is placed on the damage evolution equation in order to account for different damage mechanisms depending on the loading mode and loading direction relative to grain axis: cavitation on elongated grain boundaries as well as decohesions and microcracks around and inside coarse grain particles. Experimental data of creep strain rates for longitudinal and transverse loading directions at 130, 150 and 170 °C have been used to calibrate the model. The validation of the model was carried out by comparing experimental and modeled creep curves in the case of a 30°angle between the loading and the material flow direction during forging. The results show that the assumed damage mechanisms and the developed damage evolution equation are able to reflect both the anisotropic accelerated creep and the time to creep rupture for different stress levels and loading directions.

Nonhomogeneous microstructure related creep damage of the CrMoV multi-pass weld metal

The metallurgical notch effect of weldment is critical for the structural integrity assessment and to avoid the premature failure especially at elevated temperature. The local nonhomogeneous microstructure located in heat affected zone (HAZ) and multi-pass weld metal area (WM) is one of the largest contributions for the material weakening of the entire weldment. Although the type IV failure related to the HAZ has been intensively discussed, few researchers focus on the creep damage on the weld metal. In fact, the limited long-term creep tests of welded joints conducted by Tabuchi et al. [4]. has emphasized the necessity of monitoring creep damage not only in the HAZ but also in the weld metal. In this article, the nonhomogeneous microstructure related creep damage of the CrMoV multi-pass weld metal is discussed in detail. Different fracture morphology subjected to different weld properties are compared with each other, including the distribution of creep cavities, the precipitates and the substructures of crept specimens sampled from weld pass metal in the welding direction (WP), the overlap of different weld passes (WPO) and multiple weld passes through the thickness direction (MWP). Further, the microscopic analysis on the heterogeneous creep damage behavior are conducted. It is found that the grain length difference perpendicular to the loading direction is the dominant reason for anisotropic creep damage of multi-pass weld metal. In addition, the mismatched creep properties of subzones in the multi-pass weld metal also affect the damage field distribution.

Anisotropic creep damage and fracture mechanism of nickel-base single crystal superalloy under multiaxial stress

The influence of orientation on the creep rupture properties of a single crystal superalloy DD6 under multiaxial stress was carried out at 980 °C and 400 MPa. A circumferential V-type notched specimen had been designed to investigate the effect of multiaxial stress state on the creep behavior. It was found that the creep lifetimes of the [111] oriented notched specimen were slightly longer than that of the [011] orientation and 1.36 times longer than that of the [001] orientation. The computational results showed that the strain and damage distribution revealed fourfold symmetry, double symmetry and threefold symmetry for [001], [011] and [111] orientation respectively, which was confirmed by experimental observation. At high temperature the creep anisotropy in three different orientations exhibited mainly in primary and secondary creep stages. Through the study of notched specimens by SEM, the morphology evolution of γ′-phase proved that the directional coarsening was strongly dependent on the local effective stress and the direction of the local max principal stress with respect to loading axis. Fracture morphology displayed uneven cleavage configuration with multi-level feature, and the cleavage planes parallels (001), (011) and (111) crystal plane for [001], [011] and [111] orientation, respectively. The cleavage plane, which is attributed to the cracks propagated along the interfaces of γ/γ′phases, displayed square-like, rhombus-like and hexagon-like feature for [001], [011] and [111] orientation, respectively. Due to the higher density in dislocations of {111} planes, it is more easily as the secondary crack when the crack reach the {111} planes, which is thought to be the main reason of forming different feature on primary cleavage plane.

Analytic model of creep damage of interfaces for RCCD

The construction interfaces of RCCD have a distinctive influence on the deformation of dams. Based on the theory of damage mechanics, the characters and rules on deformation of construction interfaces were studied and the analytic model of anisotropic creep damage of construction interfaces was built as well. These models can reflect the elastic deformation, the attenuation creep deformation, the irreversible creep deformation and the accelerating creep deformation of interfaces. The example shows that the results of the proposed model can tally with that of monitoring in situ preferably, and verifies the validity of the model. The methods proposed and the analytic models can be generalized and applied to general concrete dams, especially to the analysis on deformation rules of fault and interlayer in dam base.

An Improved Anisotropic Tertiary Creep Damage Formulation

Directionally solidified (DS) Ni-base superalloys are commonly used as gas turbine materials to primarily extend the operational lives of components under high load and temperature. The nature of DS superalloy grain structure facilitates an elongated grain orientation, which exhibits enhanced impact strength, high temperature creep and fatigue resistance, and improved corrosion resistance compared with off-axis orientations. Of concern to turbine designers are the effects of cyclic fatigue, thermal gradients, and potential stress concentrations when dealing with orientation-dependent materials. When coupled with a creep environment, accurate prediction of crack initiation and propagation becomes highly dependent on the quality of the constitutive damage model implemented. This paper describes the development of an improved anisotropic tertiary creep damage model implemented in a general-purpose finite element analysis software. The creep damage formulation is a tensorial extension of a variation in the Kachanov–Rabotnov isotropic tertiary creep damage formulation. The net/effective stress arises from the use of the Rabotnov second-rank symmetric damage tensor. The Hill anisotropic behavior analogy is used to model secondary creep and tertiary creep damage behaviors. Using available experimental data for a directionally solidified Ni-base superalloy, the improved formulation is found to accurately model intermediate oriented specimen.

An anisotropic tertiary creep damage constitutive model for anisotropic materials

When an anisotropic material is subject to creep conditions and a complex state of stress, an anisotropic creep damage behavior is observed. Previous research has focused on the anisotropic creep damage behavior of isotropic materials but few constitutive models have been developed for anisotropic creeping solids. This paper describes the development of a new anisotropic tertiary creep damage constitutive model for anisotropic materials. An advanced tensorial damage formulation is implemented which includes both material orientation relative to loading and the degree of creep damage anisotropy in the model. A variation of the Norton-power law for secondary creep is implemented which includes the Hill’s anisotropic analogy. Experiments are conducted on the directionally-solidified bucket material DS GTD-111. The constitutive model is implemented in a user programmable feature (UPF) in ANSYS FEA software. The ability of the constitutive model to regress to the Kachanov-Rabotnov isotropic tertiary creep damage model is demonstrated through comparison with uniaxial experiments. A parametric study of both material orientation and stress rotation are conducted. Results indicate that creep deformation is modeled accurately; however an improved damage evolution law may be necessary.

An Anisotropic Creep Damage Model for Anisotropic Weld Metal

Past studies from creep tests on uniaxial specimens and Bridgman notch specimens, for a P91 weld metal, showed that anisotropic behavior (more specifically transverse isotropy) occurs in the weld metal, both in terms of creep (steady-state) strain rate behavior and rupture times (viz., damage evolution). This paper describes the development of a finite element (FE) continuum damage mechanics methodology to deal with anisotropic creep and anisotropic damage for weld metal. The method employs a second order damage tensor following the work of Murakami and Ohno (1980, “A Continuum Theory of Creep and Creep Damage,” Creep in Structures, A. R. S. Ponter and D. R. Hayhurst, eds., Springer-Verlag, Berlin, pp. 422–444) along with a novel rupture stress approach to define the evolution of this tensor, taking advantage of the transverse isotropic nature of the weld metal, to achieve a reduction in the number of material constants required from test data (and hence tests) to define the damage evolution. Hill’s anisotropy potential theory is employed to model the secondary creep. The theoretical model is implemented in a material behavior subroutine within the general-purpose nonlinear FE code ABAQUS (ABAQUS User’s Manual, Version 6.6, 6006, Hibbitt, Karlsson and Sorenson, Inc., Providence, RI). The validation of the implementation against established isotropic continuum damage mechanics solutions for the isotropic case is described. A procedure for calibrating the multiaxial damage constants from notched bar test data is described for multiaxial implementations. Also described is a study on the effect of uniaxial specimen orientation on anisotropic damage evolution.

Development and use of an anisotropic damage model for the high-temperature life assessment of a P91 weldment

This paper describes the development of a finite element (FE) continuum damage mechanics methodology to deal with anisotropic creep and anisotropic damage for a P91 weld metal. The method employs a second-order damage tensor, together with a novel rupture stress approach to define the evolution of this tensor. The method takes advantage of the transverse isotropic nature of the weld metal, to achieve a reduction in the number of material constants required from test data (and hence tests) to define the damage evolution. Hill's anisotropy potential theory is employed to model the secondary creep. An FE implementation of the model is applied to the creep life assessment of an internally pressurized axisymmetric P91 pipe weldment. The study also considered the effect of various material mismatch ratios in the various zones of the weldment. Here material mismatch is considered to be a combination of the difference in uniaxial minimum strain rates and in the uniaxial rupture times.

An FE-analysis of anisotropic creep damage and deformation in the single crystal SRR99 under multiaxial loads

Multidimensional stress–strain and damage analyses of engineering structural components with the help of numerical simulations are of great interest. These can only be done by using adequate material models and suitable numerical methods. Bertram and Olschewski (Computational modelling of anisotropic materials under creep conditions, Math. Modelling Sci. Comp. 5 (1995) 100–109; Anisotropic creep modeling of the single crystal superalloy SRR99, J. Comp. Mater. Sci. 5 (1996) 12–16), proposed a three-dimensional creep model for single crystals. An anisotropic creep damage model for single crystals was also suggested by Qi and Bertram (W. Qi, A. Bertram, Anisotropic creep damage modeling of single crystal superalloys, Tech. Mech. 17 (1997) 313–322; W. Qi, Modellierung der Kriechschadigung einkristalliner Superlegierungen in Hochtemperaturbereich, Ph.D. dissertation, Technical University Berlin, VDI Verlag, Düsseldorf, 1998; W. Qi, A. Bertram, Damage modeling of the single crystal superalloy SRR99 under monotonous creep, Comput. Mater. Sci. 13 (1998) 132–141). The coupled model has been used to predict the creep deformation and the lifetime of the single crystal SRR99 under uniaxial creep loads at 760°C. The purpose of this work is the application of the coupled model to the simulation of multiaxial creep behavior and damage development, and its dependence upon non-proportional loading paths of SRR99 at 760°C.

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

An anisotropic creep damage model for multiaxial cyclic loading histories

The purpose of this study is the development of an anisotropic creep damage theory within the continuum damage mechanics, applicable to creep-dominated cyclic loading histories. A damage distribution is expressd in rate form as a symmetric tensor of rank necessary to match physically measured damage. A theoretical model which expresses general anisotropic creep damage phenomena with power law cavity growth is proposed. The coupling of damage with a bounding surface cyclic viscoplasticity theory is also accomplished. Comparison with experimental results are made for weakly anisotropically damaging materials, type 304 stainless steel at 593°C. Good correlation of rupture time, secondary creep, and tertiary creep has been obtained for proportional and nonproportional, isothermal, constant isochronous nominal stress loading histories. A modification of the isochronous stress (the set of stress state which have a same rupture time) for compressive hydrostatic stress state has been offered.

Anisotropic elasticity-anisotropic damage coupling in creep damage.

Modelling of elastic anisotropy induced by creep damage and its application to the analysis of creep crack growth in a copper plate are discussed. The elasticity theory of damaged materials developed by M. Kachanov is combined with the anisotropic creep damage theory of the present authors to formulate the anisotropic elastic-damage coupling in creep. The theory is implemented into the finite element analysis of the creep damage process in a thin plate with an internal crack subject to non-proportional loading. The material constants of elastic-damage coupling were identified by performing an experiment. The influence of the reduction in elastic modulus due to creep damage on the stress distribution at the crack tip, on the pattern of creep crack extension and on the final rupture time are discussed in detail.

Finite element analysis of creep crack growth by local approach.

The applicability of a local approach to the analysis of creep crack growth in a plate is discussed from the view point of continuum damage mechanics. The anisotropic creep damage theory developed by the present authors is implemented into the finite element analysis based on two-dimensional simplex elements and the creep damage process leading to the initiation and propagation of creep cracks in a thin plate with an inner crack under proportional and non-proportional loadings is elucidated. The dependence of the rupture times and the crack extension pattern on the mesh discretization are discussed in detail.

異方損傷の模型化とそのクリープき裂進展解析への応用

Description of anisotropic damage state in terms of mechanical variables and its application to anisotropic creep damage theory were discussed. The notion of the classical Kachanov-Rabotnov theory of creep damage was first extended to the general three-dimensional state of damage by introducing fictitious undamaged state and the fictitious deformation on gradient. Then, these results were applied to formulate the evolution and the constitutive equations of creep crack growth analysis of copper plates under proportional and non-proportional biaxial loadings.

Finite element analysis of creep crack growth by a local approach

The applicability of a local approach to the analysis of creep crack growth in a plate under biaxial tension is discussed from the point of view of continuum damage mechanics. The anisotropic creep damage theory developed by the present authors is implemented into a finite element analysis based on two-dimensional simplex elements, and the creep damage process leading to the initiation and propagation of creep cracks in a thin plate with an internal crack under proportional and non-proportional loadings is analysed. Special emphasis is placed on the discussion of the dependence of the rupture times and the crack extension pattern on the mesh discretization. The effects of damage anisotropy on the creep crack extension and the rupture times are elucidated; the numerical results are compared with the corresponding results based on isotropic damage theory. The effects of a local rupture criterion are also discussed.

Mathematical modelling of materials behaviour

In this paper some possible ways of representing constitutive equations involving (initial) anisotropy of the material (e.g. from rolling) and involving anisotropic creep-damage are dealt with. The formulations of such equations are based upon theorems concerning tensor-valued functions. Furthermore, some simplified constitutive equations for more practical use are discussed.The paper is devided into two parts. The main problem of the first part is: to find an irreducible set of tensor generators in order to formulate constitutive equations. Besides this problem it is very important to determine the scalar coefficients in constitutive equations as functions of irreducible invariants and experimental data. The second part of the paper is concerned with the determination of these scalar functions. This can be done by using tensorial interpolation methods as pointed out in detail.

Finite element analysis of the creep damage process based on anisotropic creep damage theory.

Finite element analysis of the creep damage process based on anisotropic creep damage theory.

Formulation of Cross-Hardening in Creep and its Effect on the Creep Damage Process of Copper

The present paper is concerned with the modelling of creep and creep damage in polycrystalline metals and the experimental evaluation of the proposed model. By ascribing the reduction of creep rates caused by the principal stress rotation (i.e., cross-hardening) to the intersection mechanism of dislocations on active slip planes in crystal grains, a constitutive equation of creep describing the cross-hardening is first formulated. Then, in view of the metallurgical observations on the nucleation and the growth of grain boundary cavities in the creep damage process, an evolution equation of anisotropic creep damage is expressed as a function of the stress, a second rank damage tensor and the creep rate of the material. Finally, the validity of the proposed theory is discussed by performing systematic creep damage tests of thin-walled copper tubes under nonsteady multiaxial states of stress at 250°C.