Research Papers: Materials and Fabrication

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

[+] Author and Article Information
Mohammad Shafinul Haque

Department of Mechanical Engineering,
University of Texas El Paso,
500 West University Avenue,
El Paso, TX 79902
e-mail: mhaque@miners.utep.edu

Calvin Maurice Stewart

Department of Mechanical Engineering,
University of Texas El Paso,
500 West University Avenue,
El Paso, TX 79902

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 13, 2016; final manuscript received February 28, 2017; published online April 20, 2017. Assoc. Editor: Haofeng Chen.

J. Pressure Vessel Technol 139(4), 041403 (Apr 20, 2017) (10 pages) Paper No: PVT-16-1171; doi: 10.1115/1.4036142 History: Received September 13, 2016; Revised February 28, 2017

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.

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Rouse, J. P. , Sun, W. , Hyde, T. H. , and Morris, A. , 2013, “ Comparative Assessment of Several Creep Damage Models for Use in Life Prediction,” Int. J. Pressure Vessel Piping, 108–109, pp. 81–87. [CrossRef]
Yu, T. , Yatomi, M. , and Shi, H.-J. , 2009, “ Numerical Investigation on the Creep Damage Induced by Void Growth in Heat Affected Zone of Weldments,” Int. J. Pressure Vessel Piping, 86(9), pp. 578–584. [CrossRef]
Murakami, S. , 2012, Continuum Damage Mechanics, Solid Mechanics and Its Applications, Springer, Dordrecht, The Netherlands.
Kachanov, L. M. , 1999, “ Rupture Time Under Creep Conditions,” Int. J. Fract., 97, pp. 11–18. [CrossRef]
Rabotnov, Y. N. , 1969, Creep Problems in Structural Members, North-Holland Publishing, Amsterdam, The Netherlands.
Hayhurst, D. R. , Dimmer, P. R. , and Morrison, C. J. , 1984, “ Development of Continuum Damage in the Creep Rupture of Notched Bars,” Philos. Trans. R. Soc. A, 311(1516), pp. 103–129. [CrossRef]
Liu, Y. , and Murakami, S. , 1998, “ Damage Localization of Conventional Creep Damage Models and Proposition of a New Model for Creep Damage Analysis,” JSME Int. J. Ser. A, 41(1), pp. 57–65. [CrossRef]
Hutchinson, J. W. , 1983, “ Constitutive Behavior and Crack Tip Fields for Materials Undergoing Creep-Constrained Grain Boundary Cavitation,” Acta Metall., 31(7), pp. 1079–1088. [CrossRef]
Riedel, H. , 1987, “ Fracture at High Temperatures,” Springer, Berlin.
Saanouni, K. , Chaboche, J. L. , and Bathias, C. , 1986, “ On the Creep Crack Growth Prediction by a Local Approach,” Eng. Fract. Mech., 25(5–6), pp. 677–691. [CrossRef]
Needleman, A. , and Tvergaard, V. , 1994, “ Mesh Effects in the Analysis of Dynamic Ductile Crack Growth,” Eng. Fract. Mech., 47(1), pp. 75–91. [CrossRef]
Haque, M. S. , and Stewart, C. M. , 2015, “ A Novel Sin-Hyperbolic Creep Damage Model to Overcome the Mesh Dependency of Classic Local Approach Kachanov–Rabotnov Model,” ASME Paper No. IMECE2015-50427.
Penny, R. K. , 1996, “ The Use of Damage Concepts in Component Life Assessment,” Int. J. Pressure Vessel Piping, 66(1–3), pp. 263–280. [CrossRef]
Haque, M. S. , and Stewart, C. M. , 2015, “ Comparison of a New Sin-Hyperbolic Creep Damage Constitutive Model With the Classic Kachanov–Rabotnov Model Using Theoretical and Numerical Analysis,” TMS2015 Supplemental Proceedings, Wiley, Hoboken, NJ, pp. 937–945.
Peerlings, R. H. J. , De Borst, R. , Brekelmans, W. A. M. , and Geers, M. G. D. , 2002, “ Localization Issues in Local and Nonlocal Continuum Approaches to Fracture,” Eur. J. Mech. A/Solids, 21(2), pp. 175–189. [CrossRef]
Murakami, S. , and Liu, Y. , 1995, “ Mesh-Dependence in Local Approach to Creep Fracture,” Int. J. Damage Mech., 4(3), pp. 230–250. [CrossRef]
Jiang, J. , Wang, W. , Zhao, N. , Wang, P. , Liu, Y. , and Jiang, P. , 2016, “ Application of a Creep-Damage Constitutive Model for the Rotor of a 1000 MW Ultra-Supercritical Steam Turbine,” ASME J. Eng. Gas Turbines Power, 138(2), p. 022606. [CrossRef]
Shen, L. , Jin, P. , Wang, Y. , and Gong, J. , 2016, “ Numerical Simulation of Damage Evolution and Life Prediction for Two Commercial Fe–Cr–Ni Alloys Subjected to Mechanical and Environmental Factors,” ASME J. Pressure Vessel Technol., 138(5), p. 051403. [CrossRef]
Yu, Q. , and Zhou, H. , 2016, “ Study on Creep Damage and Life Prediction of Threaded Connections at High Temperature,” Adv. Mech. Eng., 8(1), pp. 1–9. [CrossRef]
Larson, R. , and Miller, J. , 1952, “ A Time-Temperature Relationship for Rupture and Creep Stress,” Trans. ASME, 74, pp. 765–775.
Monkman, F. , and Grant, N. , 1956, “ An Empirical Relationship Between Rupture Life and Minimum Creep Rate in Creep-Rupture Tests,” Proc. ASTM, 56, pp. 593–596.
ASME, 2015, “ Subsection NH—Class 1, Components in Elevated Temperature Service,” ASME Boiler and Pressure Vessel Code, Section III, Division 1, American Society of Mechanical Engineers, New York.
AFCEN, 2002, “ Règles de Conception et Construction—Mécanique Rapide (RCC-MR),” Design and Construction Rules for Mechanical Components of FBR Nuclear Islands, AFCEN, Paris, France.
Ainsworth, R. A. , ed., 2003, R5: An Assessment Procedure for the High-Temperature Response of Structures, British Energy Generation Ltd., Barnwood, UK.
EDF Energy, 2011, AGR Materials Data Handbook R66 Revision 9, EDF Energy, Gloucester, UK.
Stewart, C. M. , and Gordon, A. P. , 2010, “ Analytical Method to Determine the Tertiary Creep Damage Constants of the Kachanov–Rabotnov Constitutive Model,” ASME Paper No. IMECE2010-39153.
Haque, M. S. , and Stewart, C. M. , 2016, “ Finite-Element Analysis of Waspaloy Using Sinh Creep-Damage Constitutive Model Under Triaxial Stress State,” ASME J. Pressure Vessel Technol., 138(3), p. 031408. [CrossRef]
Stewart, C. M. , 2013, “ A Hybrid Constitutive Model for Creep, Fatigue, and Creep-Fatigue Damage,” Ph.D. dissertation, University of Central Florida, Orlando, FL.
Haque, M. S. , and Stewart, C. M. , 2016, “ Modeling the Creep Deformation, Damage, and Rupture of Hastelloy X Using MPC Omega, Theta, and Sin-Hyperbolic Models,” ASME Paper No. PVP2016-63029.
Haque, M. S. , and Stewart, C. M. , 2016, “ Exploiting Functional Relationships Between MPC Omega, Theta, and Sinh-Hyperbolic Continuum Damage Mechanics Model,” ASME Paper No. PVP2016-63089.
Kim, S. J. , Kong, Y. S. , Roh, Y. J. , and Kim, W. G. , 2008, “ Statistical Properties of Creep Rupture Data Distribution for STS304 Stainless Steels,” Mater. Sci. Eng., A, 483–484, pp. 529–532. [CrossRef]
Stewart, C. M. , and Gordon, A. P. , 2012, “ Methods to Determine the Critical Damage Criterion of the Kachanov–Rabotnov Law,” ASME Paper No. IMECE2012-88389.
Lemaitre, J. , 1992, A Course on Damage Mechanics, Springer, Berlin.
Saanouni, K. , Chaboche, J. L. , and Lesne, P. M. , 1989, “ On the Creep Crack-Growth Prediction by a Non-Local Damage Formulation,” Eur. J. Mech. A. Solids, 8(6), pp. 437–459.
Ling, X. , Zheng, Y. , You, Y. , and Chen, Y. , 2007, “ Creep Damage in Small Punch Creep Specimens of Type 304 Stainless Steel,” Int. J. Pressure Vessels Piping, 84(5), pp. 304–309. [CrossRef]
Hambli, R. , 2001, “ Comparison Between Lemaitre and Gurson Damage Models in Crack Growth Simulation During Blanking Process,” Int. J. Mech. Sci., 43(12), pp. 2769–2790. [CrossRef]
Sun, Y. , Maciejewski, K. , and Ghonem, H. , 2012, “ A Damage-Based Cohesive Zone Model of Intergranular Crack Growth in a Nickel-Based Superalloy,” Int. J. Damage Mech., 22(6), pp. 905–923.
Lin, G. , 1999, “ ANSYS USER Material Subroutine USERMAT,” ANSYS, Canonsburg, PA.
Findley, W. N. , Lai, J. S. , and Onaran, K. , 2011, Creep and Relaxation of Nonlinear Viscoelastic Materials, Courier Dover Publications, Mineola, NY.


Grahic Jump Location
Fig. 1

Damage variation in front of the crack tip due to stress variation across an element

Grahic Jump Location
Fig. 2

Damage variation, ∂ω(t), versus damage, ω, at a fixed stress variation, ∂σ(t), for the (a) KR model (Eq. (8)) and (c) Sinh model (Eq. (14))

Grahic Jump Location
Fig. 3

Creep deformation and analytical damage evolution of the KR and Sinh models at (a) and (b) 700 °C, (c) and (d) 650 °C, and (e) and (f) 600 °C for 304SS

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Fig. 4

Two-dimensional center-hole plate: (a) dimensions and (b) ansys mesh (Δe  = 0.05 mm)

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Fig. 5

Damage at the crack tip for 0.01 mm: (a) mesh, (b) KR model (t = 1100 h), and (c) Sinh model (t = 1073 h)

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Fig. 6

Length of damage distribution with ω ranging from 0.11 to 0.99 on the (a) X-axis and (b) Y-axis relatively to the crack tip

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Fig. 7

Damage contour near fracture of center-hole plate with 0.05 mesh: (a) KR and (b) Sinh model

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Fig. 8

Mesh-size effect on crack growth rate: (a) KR and (b) Sinh models

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Fig. 9

Timestep and CPU time versus simulated time: (a) 0.05 mm and (b) 0.01 mm meshes

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Fig. 10

Mesh sensitivity and convergence using (a) simulated rupture time and (b) CPU time




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