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Research Papers: Materials and Fabrication

# Three-Dimensional Crack Growth in Ductile Materials: Effect of Stress Constraint on Crack Tunneling

[+] Author and Article Information
Jianzheng Zuo, Michael A. Sutton

Department of Mechanical Engineering,  University of South Carolina, Columbia, SC 29208

Xiaomin Deng1

Department of Mechanical Engineering,  University of South Carolina, Columbia, SC 29208deng@engr.sc.edu

Chin-Shan Cheng

GM R&D Center,  Vehicle Development Research Laboratory, Warren, MI 48090

1

Corresponding author.

J. Pressure Vessel Technol 130(3), 031401 (Jun 03, 2008) (8 pages) doi:10.1115/1.2937738 History: Received January 20, 2006; Revised March 15, 2007; Published June 03, 2008

## Abstract

Crack tunneling is a crack growth feature often seen in stable tearing crack growth tests on specimens made of ductile materials and containing through-thickness cracks with initially straight crack fronts. As a specimen is loaded monotonically, the midsection of the crack front will advance first, which will be followed by crack growth along the rest of the crack front, leading to the formation of a thumbnail shaped crack-front profile. From the viewpoint of fracture mechanics, crack tunneling will occur if the operating fracture criterion is met first in the midsection of the crack front, which may be due to a higher fracture driving force and∕or a lower fracture toughness in the midsection. A proper understanding of this fracture behavior is important to the development of a three-dimensional fracture criterion for general stable tearing crack growth in ductile materials. In this paper, the phenomenon of crack tunneling during stable tearing crack growth in a single-edge crack specimen is investigated by considering the effect of stress constraint on the fracture toughness. Crack growth in the specimen under nominally Mode I loading conditions is considered. In this case, crack tunneling occurs while the initially flat crack surface (which is normal to the specimen’s lateral surfaces) evolves into a final slanted fracture surface. A mixed-mode crack tip opening displacement (CTOD) fracture criterion and a custom three-dimensional (3D) fracture simulation code, CRACK3D , are used to analyze the crack tunneling event (but not crack slanting) in the specimen. Results of this investigation suggest that the critical CTOD value (which is the fracture toughness) has a clear dependence on the crack-front stress constraint $Am$ (the constraint measure in this work is the stress triaxiality, which is the ratio of the mean normal stress to the von Mises effective stress). For simplicity, this dependence can be approximated by a straight line within the range of stress constraint values found, with the toughness decreasing as the constraint increases. It is found that crack tunneling in this case is mainly the result of a higher stress constraint (hence a lower fracture toughness) in the midsection of the crack front. Details of the crack growth simulation and other findings of this study will also be presented.

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## Figures

Figure 1

Schematic of a single-edge crack test specimen (all dimensions in millimeters)

Figure 2

Crack-front profiles from a Mode I stable tearing crack growth test

Figure 3

Frontal views of the finite element mesh: (a) mesh for the entire problem domain and (b) zoomed-in mesh around the crack front

Figure 4

COD comparison between two finite element meshes

Figure 5

Stress constraint comparison between two finite element meshes

Figure 6

Crack-front profiles used in stable tearing crack growth analyses

Figure 7

A 3D crack-front profile from a stable tearing crack growth test

Figure 8

Variation of CTOD and its components along Crack Front No. 4

Figure 9

Variation of CTOD and its components along Crack Front No. 5

Figure 10

Variation of CTOD and its components along Crack Front No. 6

Figure 11

Variation of total CTOD along Crack Front Nos. 3–6 at 0.5mm behind the crack front

Figure 12

Variation of total CTOD along Crack Front Nos. 3–6 based on improved CTOD calculations in the middle region of the crack front

Figure 13

Variation of stress constraint Am along Crack Front Nos. 3–6

Figure 14

Correlation between the critical CTOD and the stress constraint Am: (a) correlation based on averaged CTOD and Am values and (b) correlation based on all CTOD and Am pairs from four crack fronts

Figure 15

Finite element mesh on the fracture surface

Figure 16

Predicted crack-front profiles (with nodal release)

Figure 17

Comparisons of predicted (solid lines, with local remeshing) and measured (symbols) crack-front profiles

Figure 18

Crack-front tunneling during crack growth: (a) definition of a nondimensional crack tunneling depth and (b) comparisons of measured and predicted crack tunneling depth variations with crack growth

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