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RESEARCH PAPERS

# Fatigue Crack Modeling and Simulation Based on Continuum Damage Mechanics

[+] Author and Article Information
Masakazu Takagaki

Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo, 153-8505 Japanmtak@iis.u-tokyo.ac.jp

Toshiya Nakamura1

Aviation Program Group, Japan Aerospace Exploration Agency, 6-13-1 Osawa, Mitaka, Tokyo, 181-0015 Japannakamt@chofu.jaxa.jp

Square root of a tensor: $A=X1∕2$ or $A2=X$ is defined for a positive semi-definite tensor $X$(15-16).

1

Corresponding author.

J. Pressure Vessel Technol 129(1), 96-102 (Mar 10, 2006) (7 pages) doi:10.1115/1.2388993 History: Received April 20, 2005; Revised March 10, 2006

## Abstract

Numerical simulation of fatigue crack propagation based on fracture mechanics and the conventional finite element method requires a huge amount of computational resources when the cracked structure shows a complicated condition such as the multiple site damage or thermal fatigue. The objective of the present study is to develop a simulation technique for fatigue crack propagation that can be applied to complex situations by employing the continuum damage mechanics (CDM). An anisotropic damage tensor is defined to model a macroscopic fatigue crack. The validity of the present theory is examined by comparing the elastic stress distributions around the crack tip with those obtained by a conventional method. Combined with a nonlinear elasto-plastic constitutive equation, numerical simulations are conducted for low cycle fatigue crack propagation in a plate with one or two cracks. The results show good agreement with the experiments. Finally, propagations of multiply distributed cracks under low cycle fatigue loading are simulated to demonstrate the potential application of the present method.

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## Figures

Figure 13

Propagation of two cracks (H0W15, N=2000)

Figure 14

Propagation of two cracks (H10W0, N=2000)

Figure 15

Simulation of crack propagation for distributed cracks

Figure 1

Two-dimensional crack

Figure 2

FE model for elastic analyses (angle of the crack θ=30deg)

Figure 3

Contour of stress σy (angle of crack θ=30deg)

Figure 4

Comparison of σy distribution (angle of crack θ=30deg)

Figure 5

Yield surface (plane stress)

Figure 6

Assumption of damage evolution

Figure 7

Specimen straight section and analysis model with location of initial cracks (displacement controlled push-pull: Δδ∕L=0.5%)

Figure 8

Nominal stress-strain response

Figure 9

Analysis result of crack propagation (H0W0, single crack)

Figure 10

Analysis of crack propagation

Figure 11

Propagation of two cracks (H2.5W15, N=2000)

Figure 12

Propagation of two cracks (H10W20, N=1200)

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