Research Papers

Effective Yield Criterion Accounting for Microvoid Coalescence

[+] Author and Article Information
A. Amine Benzerga

Associate Professor
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

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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Gurson, A. L., 1977, “Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media,” ASME J. Eng. Mater. Technol., 99, pp. 2–15. [CrossRef]
Tvergaard, V., and Needleman, A., 1984, “Analysis of the Cup–Cone Fracture in a Round Tensile Bar,” Acta Metallurgica, 32, pp. 157–169. [CrossRef]
Koplik, J., and Needleman, A., 1988, “Void Growth and Coalescence in Porous Plastic Solids,” Int. J. Solids Struct., 24(8), pp. 835–853. [CrossRef]
Gologanu, M., Leblond, J.-B., Perrin, G., and Devaux, J., 1997, “Recent Extensions of Gurson's Model for Porous Ductile Metals,” Continuum Micromechanics (CISM Lectures Series), P.Suquet, ed., Springer, New York, pp. 61–130.
Benzerga, A. A., and Besson, J., 2001, “Plastic Potentials for Anisotropic Porous Solids,” Eur. J. Mech., 20A(3), pp. 397–434 [CrossRef]
Keralavarma, S. M., and Benzerga, A. A., 2010, “A Constitutive Model for Plastically Anisotropic Solids With Non-Spherical Voids,” J. Mech. Phys. Solids, 58, pp. 874–901. [CrossRef]
Madou, K., and Leblond, J.-B., 2012, “A Gurson-Type Criterion for Porous Ductile Solids Containing Arbitrary Ellipsoidal Voids—I: Limit-Analysis of Some Representative Cell,” J. Mech. Phys. Solids, 60, pp. 1020–1036. [CrossRef]
Benzerga, A. A., and Leblond, J.-B., 2010, “Ductile Fracture by Void Growth to Coalescence,” Adv. Appl. Mech., 44, pp. 169–305. [CrossRef]
Madou, K., and Leblond, J.-B., 2012, “A Gurson-Type Criterion for Porous Ductile Solids Containing Arbitrary Ellipsoidal Voids—II: Determination of Yield Criterion Parameters,” J. Mech. Phys. Solids, 60, pp. 1037–1058. [CrossRef]
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. [CrossRef]
Benzerga, A. A., Besson, J., and Pineau, A., 1999, “Coalescence—Controlled Anisotropic Ductile Fracture,” ASME J. Eng. Mater. Technol., 121, pp. 221–229. [CrossRef]
Zhang, Z. L., and Niemi, E., 1995, “A New Failure Criterion for the Gurson-Tvergaard Dilational Constitutive Model,” Int. J. Fracture, 70, pp. 321–334. [CrossRef]
Pardoen, T., and Hutchinson, J. W., 2000, “An Extended Model for Void Growth and Coalescence,” J. Mech. Phys. Solids, 48, pp. 2467–2512. [CrossRef]
Tekoglu, C., Leblond, J.-B., and Pardoen, T., 2012, “A Criterion for the Onset of Void Coalescence Under Combined Tension and Shear,” J. Mech. Phys. Solids, 60, pp. 1363–1381. [CrossRef]
Hosokawa, A., Wilkinson, D. S., Kang, J., and Maire, E., 2013, “Onset of Void Coalescence in Uniaxial Tension Studied by Continuous X-Ray Tomography,” Acta Mater., 61, pp. 1021–1036. [CrossRef]
Benzerga, A. A., 2002, “Micromechanics of Coalescence in Ductile Fracture,” J. Mech. Phys. Solids, 50, pp. 1331–1362. [CrossRef]
Tracey, D. M., 1971, “Strain Hardening and Interaction Effects on the Growth of Voids in Ductile Fracture,” Eng. Fracture Mech., 3, pp. 301–315. [CrossRef]
Kudo, H., 1960, “Some Analytical and Experimental Studies of Axi-Symmetric Cold Forging and Extrusion—I,” Int. J. Mech. Sci., 2, pp. 102–127. [CrossRef]
Keralavarma, S. M., Hoelscher, S., and Benzerga, A. A., 2011, “Void Growth and Coalescence in Anisotropic Plastic Solids,” Int. J. Solids Struct., 48, pp. 1696–1710. [CrossRef]
Trillat, M., and Pastor, J., 2005, “Limit Analysis and Gurson's Model,” Eur. J. Mech., 24, pp. 800–819. [CrossRef]


Grahic Jump Location
Fig. 1

Geometry of cylindrical RVE

Grahic Jump Location
Fig. 2

Sketch of effective yield surface

Grahic Jump Location
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.

Grahic Jump Location
Fig. 4

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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In