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Journal of Pressure Vessel Technology | Volume 139 | Issue 4 | research-article
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
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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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Figures

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Fig. 1

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

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

+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))
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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))
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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

+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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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)

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

+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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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

+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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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

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

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

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

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

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