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TECHNICAL PAPERS

Studies on the Effect of Cyclic Loading on Grain Boundary Rupture Time

[+] Author and Article Information
J. Oh

Equipment Development, Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201-2693joonyoung.oh@samsung.com

F. W. Brust

Equipment Development, Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201-2693brust@battelle.org

N. Katsube

Department of Mechanical Engineering, Ohio State University, 2075 Robinson Lab, 206 West 18th Avenue, Columbus, Oh 43210-1154

J. Eng. Mater. Technol 129(1), 1-10 (Feb 03, 2005) (10 pages) doi:10.1115/1.2400253 History: Received June 16, 2003; Revised February 03, 2005

This paper studies intergranular creep failure of high-temperature service material under a stress-controlled unbalanced cyclic loading condition. The experimentally verified Murakami–Ohno strain-hardening creep law and Norton’s creep law are incorporated into the Tvegaard’s axis-symmetric model for the constrained grain boundary rupture analysis. Based on the physically realistic Murakami–Ohno creep law, it is shown that the cavity growth becomes unconstrained upon the stress reversal from compression to tension. This leads to the prediction that the material life under a cyclic loading condition is shorter than that under a constant loading. Based on the classical Norton’s law, the predicted material life under a cyclic loading condition remains the same as that under a constant loading. The obtained numerical results qualitatively match recent experimental results by Arai, where the life under a cyclic loading can be much shorter than that under a constant loading. There are many cases where engineers use a simple Norton’s creep law because of its simplicity. The present work suggests that more physically realistic creep laws should be used when cyclic loading must be considered.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 4

Stress-controlled remote loading condition is shown. To simplify the problem, compressive loading time (tc) and transition time (tm) are set to be small compared to the reference time. Norton’s flow law is used to calculate the effective creep strain rate in the reference time (tr).

Grahic Jump Location
Figure 5

Normalized cavity radius increase with time for cavity at r∕d=0 with initial conditions (a∕L∞)I=0.01, aI∕bI=0.1, and bI∕dI=0.1. When Murakami–Ohno+Norton material property is applied, grain boundary damage accelerates under the cyclic loading condition, tt∕tc=100, compared to the constant loading case. When Norton’s type material property is employed, there is not difference in the final grain boundary rupture time. The same trend is observed for the cavity at r∕d=0.5. The overall cavity growth rate is slightly faster at the center of grain boundary.

Grahic Jump Location
Figure 6

Normalized cavity radius increase with time for cavity at r∕d=0 with initial conditions (a∕L∞)I=0.015, aI∕bI=0.1, and bI∕dI=0.1. The overall cavity growth results are similar to those in Fig. 6.

Grahic Jump Location
Figure 7

Normalized cavity radius increase with time for cavity at r∕d=0 with initial conditions (a∕L∞)I=0.03, aI∕bI=0.1, and bI∕dI=0.1. The overall cavity growth results are similar to those in Fig. 6.

Grahic Jump Location
Figure 8

Normalized cavity radius increase with time for the cavity at r∕d=0 with initial conditions (a∕L∞)I=0.055, aI∕bI=0.1, and bI∕dI=0.1. Both material flow rules (“Murakami–Ohno+Norton” and “Norton”) predict similar final grain boundary rupture time under constant loading condition. Grain material constraint is not significant when (a∕L∞)I⩾0.06. Therefore, initial fast creep strain rate predicted by Murakami–Ohno law does not result in a significant change in the overall cavity growth rate.

Grahic Jump Location
Figure 9

Development of the normalized normal stress around the cavity at r∕d=0 with (a∕L∞)I=0.01, aI∕bI=0.1, and aI∕dI=0.1 under constant loading condition. The initial normal stress (σn∕σ∞=1 at t∕tr=0) is decreased due to material constraint. For the “MO+N” case, this constraint process is slower than the “N” case due to the fast creep strain rate by Murakami–Ohno flow rule. After this transition time, local normal stress saturates to the same value for both cases.

Grahic Jump Location
Figure 10

Normal stress variation after stress transition from compression to tension (at second and 21st cycles) around the cavity at r∕d=0 for (a∕L∞)I=0.01, aI∕bI=0.1, bI∕dI=0.1, and tt∕tc=100. The normal stress increase after stress reversal explains the fast cavity growth rate under cyclic loading condition for the “MO+N” case especially at the second cycle. At the 21st cycle, stress increase upon stress reversal is similar for both “MO+N” and “N” cases.

Grahic Jump Location
Figure 11

Mises type effective creep strain rate variation after stress transition from compression to tension (at second and 21st cycles) around the cavity at r∕d=0 for (a∕L∞)I=0.01, aI∕bI=0.1, bI∕dI=0.1, and tt∕tc=100. The effective creep strain rate increase upon stress reversal for the “MO+N” case at the second cycle shows the possibility that creep flow enhanced cavity growth (shorter diffusion length) can happen for constrained cavity growth under cyclic loading conditions.

Grahic Jump Location
Figure 12

Development of the normal stress state around the cavity at r∕d=0 with (a∕L∞)I=0.055, aI∕bI=0.1, and bI∕dI=0.1 under constant loading conditions. Grain material constraint is not significant when (a∕L∞)I⩾0.06. Therefore, the initial normalized normal stress value decreases gradually compared to the result ((a∕L∞)I=0.01) in Fig. 9.

Grahic Jump Location
Figure 13

The effect of the number of cycles on the grain boundary rupture time for: (a) cavity at r∕d=0; and (b) cavity at r∕d=0.5. For every case, the compressive loading time(tc) and the transition time(tm) are set fixed and the loading time(tt) is changed to give a different number of cycles. The grain boundary rupture time under cyclic loading condition decreased up to 12% compared to the constant loading case. The grain boundary rupture time slightly increases when the number of cycles exceeds 300. Increase of total compressive loading time is relevant with this behavior but the reason is not clear at this time.

Grahic Jump Location
Figure 3

Verification of ABAQUS UMAT code based on Murakami–Ohno constitutive equation with the experimental result (displacement controlled cyclic test for inconel 617 at 1469°C): (a) displacement controlled cyclic condition; (b) stress prediction based on classical strain hardening creep law+Norton creep law; and (c) stress prediction based on Murakami–Ohno cyclic creep law+Norton creep law. The suggested cyclic creep law more accurately predicts the stress relaxation than the result in (b).

Grahic Jump Location
Figure 2

Verification of ABAQUS UMAT code for Murakami–Ohno cyclic creep flow law. The numerical prediction (solid line) by UMAT code is compared with the experimental results (hollow circle) and numerical prediction by traditional strain hardening type constitutive law (dotted line). Murakami–Ohno law predicts experimental creep strain variation more accurately than the traditional strain hardening law.

Grahic Jump Location
Figure 1

(a) Isolated cavitating grain boundary in the polycrystal. σ∞ is the remote axial stress and σn is the local normal stress. Since cavity growth causes grain boundary displacement, the local stress can be different from the remote stress depending on the material deformability. (b) Cavitites on the grain boundary (c) axis-symmetric finite element model used in this study.

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