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Research Papers

Effect of Contact Conditions on Void Coalescence at Low Stress Triaxiality Shearing

[+] Author and Article Information
Jonas Dahl

 Department of Mechanical and Manufacturing Engineering, Aalborg University, DK-9220 Aalborg, Denmarkjda@m-tech.aau.dk

Kim L. Nielsen1

Solid Mechanics, Department of Mechanical Engineering,  Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmarkkin@mek.dtu.dk

Viggo Tvergaard

Solid Mechanics, Department of Mechanical Engineering,  Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmarkviggo@mek.dtu.dk

1

Address all correspondence to this author.

J. Appl. Mech 79(2), 021003 (Feb 09, 2012) (7 pages) doi:10.1115/1.4005565 History: Received March 20, 2011; Revised June 20, 2011; Posted January 31, 2012; Published February 09, 2012; Online February 09, 2012

Recent numerical cell-model studies have revealed the ductile failure mechanism in shear to be governed by the interaction between neighboring voids, which collapse to micro-cracks and continuously rotate and elongate until coalescence occurs. Modeling this failure mechanism is by no means trivial as contact comes into play during the void collapse. In the early studies of this shear failure mechanism, Tvergaard (2009, “Behaviour of Voids in a Shear Field,” Int. J. Fract., 158 , pp. 41-49) suggested a pseudo-contact algorithm, using an internal pressure inside the void to resemble frictionless contact and to avoid unphysical material overlap of the void surface. This simplification is clearly an approximation, which is improved in the present study. The objective of this paper is threefold: (i) to analyze the effect of fully accounting for contact as voids collapse to micro-cracks during intense shear deformation, (ii) to quantify the accuracy of the pseudo-contact approach used in previous studies, and (iii) to analyze the effect of including friction at the void surface with the main focus on its effect on the critical strain at coalescence. When accounting for full contact at the void surface, the deformed voids develop into shapes that closely resemble micro-cracks. It is found that the predictions using the frictionless pseudo-contact approach are in rather good agreement with corresponding simulations that fully account for frictionless contact. In particular, good agreement is found at close to zero stress triaxiality. Furthermore, it is shown that accounting for friction at the void surface strongly postpones the onset of coalescence, hence, increasing the overall material ductility. The changes in overall material behavior are here presented for a wide range of initial material and loading conditions, such as various stress triaxialities, void sizes, and friction coefficients.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Periodic array of circular cylindrical voids with radius R0 and void spacing 2A0 in the x1 -direction and 2B0 in the x2 -direction, and (b) a representative mesh used in modeling the ductile shear failure (B0 /A0  = 4 for all results presented). The applied load is characterized by κ=∑22/∑12.

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Figure 2

Curves of constant effective plastic strain, ɛep, at: (a) ψ = 0.093, (b) ψ = 0.164, (c) ψ = 0.195, (d) ψ = 0.525 (just before coalescence), and (e) ψ = 0.666 (just after coalescence) under simple shear, κ = 0, and accounting for frictionless sliding, μ = 0, (R0 /A0  = 0.25)

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Figure 3

Average shear stress versus average shear angle showing the effect of the employed contact algorithm. Here, a comparison between fully accounting for frictionless sliding, μ = 0, (contact) and the pseudo-contact approach by Tvergaard [2], using different lower limits on the void aspect ratio (ρ∈[0.05,0.2], κ = [–0.3,0,0.6], R0 /A0  = 0.25).

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Figure 4

Critical average shear angle at the onset of coalescence (ψ=ψC) versus applied loading κ showing the effect of the employed contact algorithm. Here, a comparison between fully accounting for frictionless sliding, μ = 0, (contact) and the pseudo-contact approach by Ref. [2] (ρ = 0.15), respectively.

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Figure 5

Curves of constant effective plastic strain ɛep at the onset of coalescence (ψ=ψC) for (a) κ = 0.6 (ψC=0.193), (b) κ = 0 (ψC=0.580), and (c) κ = –0.3 (ψC=0.689) when fully accounting for frictionless sliding, μ  =  0, (R0 /A0  = 0.25)

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Figure 6

Average shear stress versus average shear angle showing the effect of Coulomb friction, τ=μσn, with μ = [0,0.3,0.7,1] and κ = [0.3,0.6], (R0 /A0  = 0.25)

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Figure 7

Critical average shear angle at the onset of coalescence (ψC) versus the applied friction coefficient for both Coulomb friction, τ = μσn , and Wanheim-Bay friction (τ=μσn)withτmax=σY/3. The results are here shown for combined shear and tension (κ = [0.3,0.6]) and different initial void sizes (R0 /A0  = [0.20,0.25,0.30]).

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Figure 8

Critical average shear angle at the onset of coalescence (ψC) versus the applied friction coefficient for both Coulomb friction, τ = μσn , and Wanheim-Bay friction (τ=μσn)withτmax=σY/3. Here, showing the effect of the material strain hardening (N = [0.05,0.1,0.2]) for combined shear and tension (κ = 0.3) and an initial void sizes of R0 /A0  = 0.25.

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