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Research Papers

# Mismatch Constraint Effect of Creep Crack With Modified Boundary Layer Model

[+] Author and Article Information
Yanwei Dai

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: daiyw13@mails.tsinghua.edu.cn

Donghuan Liu

Department of Applied Mechanics,
University of Science and Technology Beijing,
Beijing 100083, China
e-mail: liudh@ustb.edu.cn

Yinghua Liu

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: yhliu@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 10, 2015; final manuscript received November 11, 2015; published online December 11, 2015. Editor: Yonggang Huang.

J. Appl. Mech 83(3), 031008 (Dec 11, 2015) (16 pages) Paper No: JAM-15-1548; doi: 10.1115/1.4032025 History: Received October 10, 2015; Revised November 11, 2015

## Abstract

Mismatch effect plays a crucial role in weldments, and an independent mismatch constraint parameter $M*$ is proposed to characterize the material mismatch constraint effect in this paper. A mismatched modified boundary layer (MBL) model for creeping solids is developed to simulate the stress field of creep cracks in mismatched weldments. It can be found that there still exists the similarity between creep crack tip stress fields under different mismatch factors. Numerical results show that $M*$ obtains the minimum value on the under match condition and the maximum value on the over match condition. Comparisons between $M*$ and other geometric constraint parameters ($A2(t)$ and $Q22$) are carried out and the applicability of $M*$ is verified. A modified assessment formula for creep crack growth rate ratio is proposed based on the parameter $M*$. It is found that $M*$ is a reasonable and remarkable parameter to characterize the mismatch constraint effect of creeping cracks.

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## Figures

Fig. 1

Typical weldments with HAZ in MBL model

Fig. 2

FE mesh of the whole MBL model

Fig. 3

Grids of (a) local FE model and (b) crack tip

Fig. 4

Dimensionless angular distribution functions under mismatch factor 0.46 at different creep time: (a) p11, (b) p22, (c) p12, and (d) p1

Fig. 5

Dimensionless angular distribution functions under mismatch factor 0.79 at different creep time: (a) p11, (b) p22, (c) p12, and (d) p1

Fig. 6

Dimensionless angular distribution functions under mismatch factor 1.00 at different creep time: (a) p11, (b) p22, (c) p12, and (d) p1

Fig. 7

Dimensionless angular distribution functions under mismatch factor 1.58 at different creep time: (a) p11, (b) p22, (c) p12, and (d) p1

Fig. 8

Dimensionless angular distribution functions under mismatch factor 2.00 at different creep time: (a) p11, (b) p22, (c) p12, and (d) p1

Fig. 9

Dimensionless amplitudes of stress field at r = 0.1 mm under different mismatch factors with different creep time: (a) M11′/σ0, (b) M22′/σ0, (c) M12′/σ0, and (d) M1′/σ0

Fig. 10

Amplitudes of angular distribution for n = 3 under different mismatch factors: (a) M11′ and (b) M22′

Fig. 11

Amplitudes of angular distribution for n = 7 under different mismatch factors: (a) M11′ and (b) M22′

Fig. 12

Variations of mismatch constraint parameter M* with mismatch factors and creep time: (a) d = 0.5 mm, (b) d = 0.3 mm, and (c) d = 0.1 mm

Fig. 13

Variations of M* in the radial direction under different mismatch factors

Fig. 14

Variations of mismatch constraint parameter M*+Q with mismatch factors and creep time: (a) T = −0.5, (b) T = −1.0, (c) T = −1.5, and (d) T = −2.0

Fig. 15

C(t)-integrals under different mismatch factors and crack locations

Fig. 16

C(t)-integrals under different T-stresses: (a) d = 0.1 mm, m = 0.46; (b) d = 0.1 mm, m = 2.0; (c) d = 0.3 mm, m = 0.46; (d) d = 0.3 mm, m = 2.0; (e) d = 0.5 mm, m = 0.46; and (f) d = 0.5 mm, m = 2.0

Fig. 17

Variations of –A2(t) under different mismatch factors

Fig. 18

Variations of Q22 with creep time under different mismatch factors

Fig. 19

Variations of M* with creep time under different mismatch factors

Fig. 20

Interpretation of M*-parameter

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