An Improved Anisotropic Tertiary Creep Damage Formulation

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon ◽  
Young Wha Ma ◽  
Richard W. Neu
Keyword(s):  
Damage Model ◽  
Creep Damage ◽  
Cyclic Fatigue ◽  
Grain Structure ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Directionally Solidified ◽  
Stress Concentrations ◽  
Element Analysis ◽  
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.

Modeling the Temperature-Dependence of Tertiary Creep Damage of a Directionally Solidified Ni-Base Superalloy

2009 ◽  
Author(s):  
Calvin M. Stewart ◽  
Erik A. Hogan ◽  
Ali P. Gordon
Keyword(s):  
Experimental Data ◽  
Gas Turbine ◽  
Creep Damage ◽  
Time Estimation ◽  
General Purpose ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Directionally Solidified ◽  
Estimation Model ◽  
Element Analysis

Directionally solidified (DS) Ni-base superalloys have become a commonly used material in gas turbine components. Controlled solidification during the material manufacturing process leads to a special alignment of the grain boundaries within the material. This alignment results in different material properties dependent on the orientation of the material. When used in gas turbine applications the direction of the first principle stress experienced by a component is aligned with the enhanced grain orientation leading to enhanced impact strength, high temperature creep and fatigue resistance, and improve corrosion resistance compared to off axis orientations. Of particular importance is the creep response of these DS materials. In the current study, the classical Kachanov-Rabotnov model for tertiary creep damage is implemented in a general-purpose finite element analysis (FEA) software. Creep deformation and rupture experiments are conducted on samples from a representative DS Ni-base superalloys tested at temperatures between 649 and 982°C and two orientations (longitudinally- and transversely-oriented). The secondary creep constants are analytically determined from available experimental data in literature. The simulated annealing optimization routine is utilized to determine the tertiary creep constants. Using regression analysis the creep constants are characterized for temperature and stress-dependence. A rupture time estimation model derived from the Kachanov-Rabotnov model is then parametrically exercised and compared with available experimental data.

Temperature and Orientation Dependence of Creep Damage of Two Ni-Base Superalloys

2007 ◽  
Author(s):  
Ali P. Gordon ◽  
Sameer Khan ◽  
David W. Nicholson
Keyword(s):  
Gas Turbines ◽  
Damage Model ◽  
Creep Damage ◽  
General Purpose ◽  
Orientation Dependence ◽  
Tertiary Creep ◽  
Directionally Solidified ◽  
Element Analysis ◽  
Stress And Deformation ◽  
Marine Air

Both polycrystalline (PC) and directionally-solidified (DS) Ni-base superalloys are commonly applied as turbine materials to primarily withstand creep conditions manifested in either marine-, air- or land-based gas turbines components. The thrust for increased efficiency of these systems, however, translates into the need for these materials to exhibit considerable strength and temperature resistance. This is critical for engine parts that are subjected to high temperature and stress conditions sustained for long periods of time, such as blades, vanes, and combustion pieces. Accurate estimates of stress and deformation histories at notches, curves, and other critical locations of such components are crucial for life prediction and calculation of service intervals. In the current study, the classical Kachanov-Rabotnov model for tertiary creep damage is implemented in a general-purpose finite element analysis (FEA) software. Creep deformation and rupture experiments on samples from two representative Ni-base superalloys (PC and DS) tested at temperatures between 649 and 982°C and two orientations (longitudinally- and transversely-oriented for the DS case only) are applied to extend this damage formulation. The damage model coefficients corresponding to secondary and tertiary creep constants are characterized for temperature and orientation dependence. This updated formulation can be implemented for modeling full-scale parts containing temperature distributions.

Characterization of the Creep Deformation and Rupture Behavior of DS GTD-111 Using the Kachanov–Rabotnov Constitutive Model

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon ◽  
Erik A. Hogan ◽  
Ashok Saxena
Keyword(s):  
Creep Deformation ◽  
Creep Damage ◽  
General Purpose ◽  
Secondary Creep ◽  
Directionally Solidified ◽  
Element Analysis ◽  
Optimization Routine ◽  
Base Superalloy ◽  
Rupture Behavior

Creep deformation and rupture experiments are conducted on samples of the Ni-base superalloy directionally solidified GTD-111 tested at temperatures between 649°C and 982°C and two orientations (longitudinally and transversely oriented). The secondary creep constants are analytically determined from creep deformation experiments. The classical Kachanov–Rabotnov model for tertiary creep damage is implemented in a general-purpose finite element analysis (FEA) software. The simulated annealing optimization routine is utilized in conjunction with the FEA implementation to determine the creep damage constants. A comparison of FEA and creep deformation data demonstrates high accuracy. Using regression analysis, the creep constants are characterized for temperature dependence. A rupture prediction model derived from creep damage evolution is compared with rupture experiments.

An improved nonlinear damage model of rocks considering initial damage and damage evolution

2020 ◽  
Vol 29 (7) ◽  
pp. 1117-1137 ◽  
Author(s):  
Wenlin Feng ◽  
Chunsheng Qiao ◽  
Shuangjian Niu ◽  
Zhao Yang ◽  
Tan Wang
Keyword(s):  
Damage Evolution ◽  
Least Squares Method ◽  
Damage Model ◽  
Creep Damage ◽  
Secondary Creep ◽  
Nonlinear Creep ◽  
Creep Failure ◽  
Initial Damage ◽  
Nonlinear Damage Model ◽  
Creep Damage Model

The experimental results show that the creep properties of the rocks are affected by the initial damage, and the damage evolution also has a significant impact on the time-dependent properties of the rocks during the creep. However, the effects of the initial damage and the damage evolution are seldom considered in the current study of the rocks' creep models. In this paper, a new nonlinear creep damage model is proposed based on the multistage creep test results of the sandstones with different damage degrees. The new nonlinear creep damage model is improved based on the Nishihara model. The influences of the initial damage and the damage evolution on the components in the Nishihara model are considered. The creep damage model can not only describe the changes in three creep stages, namely, the primary creep, the secondary creep, and the tertiary creep, but also reflect the influence of the initial damage and the damage evolution on creep failure. The nonlinear least squares method is used to determine the parameters in the nonlinear creep damage model. The consistency between the experimental data and the predicted results indicates the applicability of the nonlinear damage model to accurately predict the creep deformation of the rocks with initial damage.

Modeling the Temperature Dependence of Tertiary Creep Damage of a Ni-Based Alloy

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Temperature Dependence ◽  
Creep Deformation ◽  
Mechanical Response ◽  
Axial Stress ◽  
Nauk Sssr ◽  
Damage Model ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Continuum Damage ◽  
Over Time

To capture the mechanical response of Ni-based materials, creep deformation and rupture experiments are typically performed. Long term tests, mimicking service conditions at 10,000 h or more, are generally avoided due to expense. Phenomenological models such as the classical Kachanov–Rabotnov (Rabotnov, 1969, Creep Problems in Structural Members, North-Holland, Amsterdam; Kachanov, 1958, “Time to Rupture Process Under Creep Conditions,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Mekh. Mashin., 8, pp. 26–31) model can accurately estimate tertiary creep damage over extended histories. Creep deformation and rupture experiments are conducted on IN617 a polycrystalline Ni-based alloy over a range of temperatures and applied stresses. The continuum damage model is extended to account for temperature dependence. This allows the modeling of creep deformation at temperatures between available creep rupture data and the design of full-scale parts containing temperature distributions. Implementation of the Hayhurst (1983, “On the Role of Continuum Damage on Structural Mechanics,” in Engineering Approaches to High Temperature Design, Pineridge, Swansea, pp. 85–176) (tri-axial) stress formulation introduces tensile/compressive asymmetry to the model. This allows compressive loading to be considered for compression loaded gas turbine components such as transition pieces. A new dominant deformation approach is provided to predict the dominant creep mode over time. This leads to development of a new methodology for determining the creep stage and strain of parametric stress and temperature simulations over time.

Anisotropic Creep Damage and Elastic Damage of Notched Directionally Solidified Materials

2011 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Crack Initiation ◽  
Turbine Blade ◽  
Gas Turbines ◽  
Turbine Blades ◽  
Stress Triaxiality ◽  
Creep Damage ◽  
Transversely Isotropic ◽  
Grain Structure ◽  
Directionally Solidified ◽  
Elastic Damage

Drives to improve gas turbines efficiency have lead to an increase in firing temperatures. This increase in exhaust temperature has a negative impact upon turbine blade life. Both engineers and material scientists have produced methods to improve turbine blade life under these conditions. Cooling holes have become commonplace and use relatively cool gas to create a lower temperature barrier around a turbine blade. These cooling holes creating internal and external surfaces; a common sight of crack initiation. Directionally-solidified (DS) turbine blades have also become commonplace. These turbine blades exhibit a transversely-isotropic grain structure that improves creep strength in a desired direction. To model a component under such conditions, anisotropic constitutive models are required. In this paper, an anisotropic tertiary creep damage constitutive model for transversely-isotropic materials is given. The influence of creep-damage on general linear elasticity (elastic damage) is described by a modified Hooke’s compliance tensor. Finite element simulations of a V-notched tensile specimen are conducted to replicate a crack initiation site. A discussion on stress triaxiality, stress redistribution, and damage distribution due to anisotropy is provided.

Fundamental Modelling of Mechanisms Contributing to Tertiary Creep in Copper at 215 and 250°C

2018 ◽  
Author(s):  
Fangfei Sui ◽  
Rolf Sandström
Keyword(s):  
Spent Nuclear Fuel ◽  
Creep Damage ◽  
Back Stress ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Creep Tests ◽  
Long Time ◽  
Higher Temperature ◽  
Good Agreement

Extensive creep tests have been performed on oxygen free copper with 50 ppm phosphorus at both low and high temperatures. It is the candidate material for storage of spent nuclear fuel in Sweden. Basic models without fitting parameters have been formulated to reproduce primary and secondary creep. For a long time, only empirical models existed for fitting of tertiary creep. To understand the role of creep damage, including recovery, cavitation and necking, basic models that do not involve adjustable parameters are in urgent demand. Only recently, basic models taking the relevant mechanisms into account have been developed. These models were used to predict the tertiary creep for copper at 75°C. The modelled results were compared with experimental creep curves and good agreement has been found. In the present paper, the models are applied to creep tests at higher temperatures (215 and 250°C). A similar representation with good accuracy is obtained. This demonstrates that the fundamental model for back stress is applicable for the higher temperature tests as well.

Application of the Monkman-Grant Relationship for Ultrafine-Grained Metallic Materials

2013 ◽  
Vol 577-578 ◽  
pp. 137-140
Author(s):  
Marie Kvapilová ◽  
Jiří Dvořák ◽  
Petr Král ◽  
Milan Svoboda ◽  
Vàclav Sklenička
Keyword(s):  
Creep Deformation ◽  
Damage Tolerance ◽  
Creep Damage ◽  
Tolerance Factor ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Metallic Materials ◽  
Ultrafine Grained ◽  
Ultrafine Grained Materials ◽  
The Relationship

The applicability of the Monkman-Grant relationship was analyzed and validated for ultrafine-grained metallic materials under investigation. A special attention has been given to the creep damage tolerance factor which is defined as the ratio of the strain to fracture to the Monkman-Grant ductility and which describes the coupling between creep deformation and damage based on continuum creep damage approach. It was found, that ultrafine-grained materials generally obey the Monkman-Grant relationship, however, the relationship is especially suitable for materials exhibiting short secondary creep and long tertiary creep stages when dislocation-controlled creep is dominant.

scholarly journals The Stress-Sensitivity, Mesh-Dependence, and Convergence of Continuum Damage Mechanics Models for Creep

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Mohammad Shafinul Haque ◽  
Calvin Maurice Stewart
Keyword(s):  
Damage Mechanics ◽  
Damage Model ◽  
Constitutive Models ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Stress Sensitivity ◽  
304 Stainless Steel ◽  
Stress Concentrations ◽  
Local Approach ◽  
Creep Damage Model

The classic Kachanov–Rabotnov (KR) creep damage model is a popular model for the design against failure due to creep deformation. However, the KR model is a local approach that can exhibit numerically unstable damage with mesh refinement. These problems have led to modified critical damage parameters and alternative constitutive models. In this study, an alternative sine hyperbolic (Sinh) creep damage model is shown to (i) predict unity damage irrespective of stress and temperature conditions such that life prediction and creep cracking are easy to perform; (ii) develop a continuous and well-distributed damage field in the presence of stress concentrations; and (iii) is less stress-sensitive, is less mesh-dependent, and exhibits better convergence than the KR model. The limitations of the KR model are discussed in detail. The KR and Sinh models are calibrated to three isotherms of 304 stainless steel creep test data. Mathematical exercises, smooth specimen simulations, and crack growth simulations are performed to produce a quantitative comparison of the numerical performance of the models.

Modeling Creep Deformation and Damage Behavior of Tempered Martensitic Steel in the Framework of Additive Creep Rate Formulation

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
J. Christopher ◽  
B. K. Choudhary
Keyword(s):  
Creep Rate ◽  
Internal Stress ◽  
Creep Strain ◽  
Creep Deformation ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Time Behavior ◽  
Secondary Creep ◽  
Modeling Creep ◽  
Applied Stresses

Additive creep rate model has been developed to predict creep strain-time behavior of materials important to engineering creep design of components for high temperature applications. The model has two additive formulations: the first one is related to sine hyperbolic rate equation describing primary and secondary creep deformation based on the evolution of internal stress with strain/time, and the second defines the tertiary creep rate as a function of tertiary creep strain. In order to describe creep data accurately, tertiary creep rate relation based on MPC-Omega methodology has been appropriately modified. The applicability of the model has been demonstrated for tempered martensitic plain 9Cr-1Mo steel for different applied stresses at 873 K. Based on the observations, a power law relationship between internal stress and applied stress has been established for the steel. Further, a higher creep damage accumulation with increasing life fraction has been observed at low stresses than those obtained at high stresses.

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