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Research Papers

Prediction of Ductile Fracture Surface Roughness Scaling

[+] Author and Article Information
Alan Needleman

Department of Materials Science and Engineering,  University of North Texas, Denton, TX 76207needle.unt@gmail.com

Viggo Tvergaard

Department of Mechanical Engineering,  The Technical University of Denmark, Lyngby, 2800 Denmarkviggo@mek.dtu.dk

Elisabeth Bouchaud

Solid State Physics Division (SPEC), CEA-Saclay, F-91191 Franceelisabeth.bouchaud@cea.fr

J. Appl. Mech 79(3), 031015 (Apr 05, 2012) (8 pages) doi:10.1115/1.4005959 History: Received July 14, 2011; Revised October 29, 2011; Posted February 13, 2012; Published April 04, 2012; Online April 05, 2012

Experimental observations have shown that the roughness of fracture surfaces exhibit certain characteristic scaling properties. Here, calculations are carried out to explore the extent to which a ductile damage/fracture constitutive relation can be used to model fracture surface roughness scaling. Ductile crack growth in a thin strip under mode I, overall plane strain, small scale yielding conditions is analyzed. Although overall plane strain loading conditions are prescribed, full 3D analyses are carried out to permit modeling of the three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. An elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid is used to model the material. Two populations of second phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and various three dimensional distributions of the larger particles are considered. The scaling properties of the predicted thickness average fracture surfaces are calculated and the results are discussed in light of experimental observations.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

Initial inclusion distribution 411. (a) On y3=0. (b) On y3=hz.

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Figure 3

Initial inclusion distribution 447. (a) On y3=0. (b) On y3=hz.

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Figure 4

Contours of Mises effective stress σe at J/σ0 b0  = 12.1

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Figure 5

Curves of normalized crack opening b/b0  − 1 versus normalized applied J, J/σ0 b0 for the four distributions analyzed

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Figure 6

Void volume distribution showing the mode of crack growth for inclusion distribution 411 at J/σ0 b0  = 9.56. (a) On y3=0. (b) On y3=hz. Note that the positive y-axis is in opposite directions in (a) and (b).

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Figure 7

Void volume distribution showing the mode of crack growth for inclusion distribution 419 at J/σ0 b0  = 10.3. (a) On y3=0. (b) On y3=hz. Note that the positive y-axis is in opposite directions in (a) and (b).

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Figure 8

Void volume distribution showing the mode of crack growth for inclusion distribution 421 at J/σ0 b0  = 10.2. (a) On y3=0. (b) On y3=hz. Note that the positive y-axis is in opposite directions in (a) and (b).

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Figure 9

Void volume distribution showing the mode of crack growth for inclusion distribution 447 at J/σ0 b0  = 12.1. (a) On y3=0. (b) On y3=hz. Note that the positive y-axis is in opposite directions in (a) and (b).

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Figure 10

Average crack profile through the thickness as a function of the distance from the initial crack tip

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Figure 1

The finite element mesh in the vicinity of the initial crack tip. Here, and in subsequent figures, x, y, and z denote the coordinates y1 , y2 , and y3 , respectively.

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Figure 11

Average crack profile through the thickness as a function of the distance from the initial crack tip, modified to exclude the effect of small connected ligaments. The fracture surface is calculated starting at y2  =  − 0.003 m, as described in procedure 3A so that, with the log-log scale in Figs.  1415, β is the slope of the curves. For comparison purposes, lines corresponding to β = 0.4 and β = 0.5 are shown. A value of β = 0.5 corresponds to a random walk; i.e., a step of magnitude ΔX is as likely to lead to an increase in Δh as it is to a decrease. For a value of β < 0.5 a decrease is likely to be followed by another decrease and for β > 0.5 an increase is likely to be followed by another increase.

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Figure 12

Average crack profile through the thickness as a function of the distance from the initial crack tip, modified to exclude the effect of small connected ligaments. The fracture surface is calculated starting at y2  =  +0.003 m, as described in procedure 3B.

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Figure 13

The difference between the crack profiles in Figs.  1112

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Figure 14

Scaling of the thickness averaged roughness based on the crack profiles in Fig. 1

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Figure 15

Scaling of the thickness averaged roughness based on the crack profiles in Fig. 1

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