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Research Papers

On Void Coalescence Under Combined Tension and Shear

[+] Author and Article Information
M. E. Torki

Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843

A. A. Benzerga

Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843
Department of Materials Science and Engineering,
Texas A&M University,
College Station, TX 77843

J.-B. Leblond

Institut Jean Le Rond d'Alembert,
Sorbonne Universites,
UPMC Univ Paris 06,
CNRS, UMR 7190,
Paris F-75005, France

Benzerga's [42] conjecture stating that the rigid zones intercept the void at the poles seems to be falsified for extremely flat voids.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 29, 2015; final manuscript received February 26, 2015; published online June 3, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(7), 071005 (Jul 01, 2015) (15 pages) Paper No: JAM-15-1059; doi: 10.1115/1.4030326 History: Received January 29, 2015; Revised February 26, 2015; Online June 03, 2015

A micromechanics-based yield criterion is developed for a porous ductile material deforming by localized plasticity in combined tension and shear. The new criterion is primarily intended to model void coalescence by internal necking or internal shearing. The model is obtained by limit analysis and homogenization of a cylindrical cell containing a coaxial cylindrical void of finite height. Plasticity in parts of the matrix is modeled using rate-independent J2 flow theory. It is shown that for the discontinuous, yet kinematically admissible trial velocity fields used in the limit analysis procedure, the overall yield domain exhibits curved parts and flat parts with no vertices. Model predictions are compared with available finite-element (FE) based estimates of limit loads on cubic cells. In addition, a heuristic modification to the model is proposed in the limit case of penny-shape cracks to enable its application to materials failing after limited void growth as well as to situations of shear-induced void closure.

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Figures

Grahic Jump Location
Fig. 1

(a) Geometry of the cylindrical RVE under combined shear and tension and (b) cell parameters

Grahic Jump Location
Fig. 2

Step 1 of graphical solution to Eq. (36): case of shear loading only. (a) The curve q=f(p)=2Σ31 is a horizontal line that lies between the curves q=g(p) and q=-g(p) for all values of p provided that 2Σ31 is greater than -T without exceeding T. (b) Corresponding yield points in the Σ33–Σ31 plane.

Grahic Jump Location
Fig. 7

Coalescence stress in absence of shear, Σ33, normalized by the matrix yield stress, σ¯, versus the void aspect ratio, W, according to the FEM results for a cylindrical cell [47] and a cubic cell [46] for two values of the porosity in the band fb

Grahic Jump Location
Fig. 5

Schematic outline of the complete yield surface

Grahic Jump Location
Fig. 8

(a) Coalescence stress in absence of shear, Σ33, normalized by the matrix yield stress, σ¯, versus the void aspect ratio, W, according to the FEM results (points from Ref. [47]), the analytical model (dashed lines), and the modified model (solid lines) using t0=-0.84,t1=12.9, and b = 0.9 for three values of the ligament parameter χ. (b) Σ33/σ¯ versus χ according to the FEM results and modified model for three values of W.

Grahic Jump Location
Fig. 6

Sketch motivating the need for model calibration in the case of penny-shaped cracks. (a) Localization zone height limited by microcrack height (situation considered in analytical model). (b) More realistic localization zones based on FE simulations [47] (situation picked up by heuristic model). (c) Alternative possible localization for random arrangement of voids.

Grahic Jump Location
Fig. 9

Effective yield loci in the Σ33–Σsh plane (one quadrant shown) using the original analytical criterion (41) (dashed) and the modified criterion (44) (solid) for various values of the ligament parameter χ and four values of the void aspect ratio: (a) W = 0.25; (b) W = 0.5; (c) W = 1.0; and (d) W = 3.0

Grahic Jump Location
Fig. 10

Effective yield loci in the Σ33–Σsh plane using the modified criterion (44) (solid lines) and available FE results [46] (points) for two values of the porosity in the band fb and four values of the void aspect ratio: (a) W = 0.5; (b) W = 1.0; (c) W = 2.0; and (d) W = 3.0

Grahic Jump Location
Fig. 11

Distinction between the simple and more precise t functions

Grahic Jump Location
Fig. 12

(a) Σ33/σ¯ versus W according to the FEM results (points from Ref. [47]) and the modified model (solid lines) using t0=-0.84,t1=12.9, and b = 1 for three values of the ligament parameter χ. (b) Σ33/σ¯ versus χ according to the FEM results and modified model for three values of W.

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