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Research Papers

Effective Yield Criterion Accounting for Microvoid Coalescence

[+] Author and Article Information
A. Amine Benzerga

Associate Professor
Mem. ASME
Department of Aerospace Engineering,
Department of Materials
Science and Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: benzerga@tamu.edu

Jean-Baptiste Leblond

Professor
Institut Jean-Le-Rond-d'Alembert,
Université Paris VI,
Tour 65-55 4, Place Jussieu,
Paris Cedex 05 75252, France
e-mail: jbl@lmm.jussieu.fr

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received May 8, 2013; final manuscript received June 26, 2013; accepted manuscript posted July 1, 2013; published online September 18, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(3), 031009 (Sep 18, 2013) (7 pages) Paper No: JAM-13-1188; doi: 10.1115/1.4024908 History: Received May 08, 2013; Revised June 26, 2013; Accepted July 01, 2013

An effective yield function is derived for a porous ductile solid near a state of failure by microvoid coalescence. Homogenization theory combined with limit analysis are used to that end. A cylindrical cell is taken to contain a coaxial cylindrical void of finite height. Plastic flow in the intervoid matrix is described by J2 theory while regions above and below the void remain rigid. Velocity boundary conditions are employed which are compatible with an overall uniaxial straining for the cell, a postlocalization kinematics that is ubiquitous during the coalescence of neighboring microvoids in rate-independent solids. Such boundary conditions are not of the uniform strain rate kind, as is the case for Gursonlike models. A similar limit analysis problem for a square-prismatic cell containing a square-prismatic void was posed long ago (Thomason, P. F., 1985, “Three-Dimensional Models for the Plastic Limit–Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids,” Acta Metallurgica, 33, pp. 1079–1085). However, to date a closed-form solution to this problem has been lacking. Instead, an empirical expression of the yield function proposed therein has been widely used in the literature. The fully analytical expression derived here is intended to be used concurrently with a Gursonlike yield function in numerical simulations of ductile fracture.

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Figures

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Fig. 1

Geometry of cylindrical RVE

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Fig. 2

Sketch of effective yield surface

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Fig. 3

Comparison of new criterion (28) with Thomason's criterion 4. (a) Limit-load constraint factors as defined in Eq. (29) versus the matrix-neck parameter. (b) Limit loads versus the void aspect ratio.

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Fig. 4

Normalized limit loads Σ33coal/σ¯ in (28) versus the ligament parameter for several values of W

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