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Research Papers

Void Growth and Coalescence in Porous Plastic Solids With Sigmoidal Hardening

[+] Author and Article Information
Padmeya P. Indurkar

Department of Mechanical Engineering,
National University of Singapore,
Singapore 117576, Singapore;
Visiting Scholar,
Department of Mechanical Engineering,
University of Houston,
Houston, TX 77204
e-mail: padmeya.indurkar@u.nus.edu

Shailendra P. Joshi

Assistant Professor
Department of Mechanical Engineering,
University of Houston,
Houston, TX 77204
e-mail: shailendra@uh.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received December 30, 2018; final manuscript received April 10, 2019; published online June 7, 2019. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 86(9), 091001 (Jun 07, 2019) (12 pages) Paper No: JAM-18-1734; doi: 10.1115/1.4043519 History: Received December 30, 2018; Accepted April 10, 2019

This paper presents an analysis of void growth and coalescence in isotropic, elastoplastic materials exhibiting sigmoidal hardening using unit cell calculations and micromechanics-based damage modeling. Axisymmetric finite element unit cell calculations are carried out under tensile loading with constant nominal stress triaxiality conditions. These calculations reveal the characteristic role of material hardening in the evolution of the effective response of the porous solid. The local heterogeneous flow hardening around the void plays an important role, which manifests in the stress–strain response, porosity evolution, void aspect ratio evolution, and the coalescence characteristics that are qualitatively different from those of a conventional power-law hardening porous solid. A homogenization-based damage model based on the micromechanics of void growth and coalescence is presented with two simple, heuristic modifications that account for this effect. The model is calibrated to a small number of unit cell results with initially spherical voids, and its efficacy is demonstrated for a range of porosity fractions, hardening characteristics, and void aspect ratios.

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Figures

Grahic Jump Location
Fig. 1

Canonical scenarios of the two-stage saturation behaviors: (a) fixed σf but varying ɛf and (b) fixed ɛf but varying σf

Grahic Jump Location
Fig. 2

Axisymmetric porous unit cell discretized into a fine FE mesh. The origin of the coordinate system lies at the center of the void with the global coordinate axes (r and z) oriented along bottom and left edges of the RVE, respectively.

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Fig. 3

Macroscopic responses of porous unit cells (f0 = 0.001) at T = 1, 2. Panel (a) ΣeqEeq and (b) f/f0Eeq for different ε̂ values. Panels (c) and (d) show the corresponding responses for different σ̂ values. Here, σi = 10 MPa and ɛi = 0.05 (Eq. (1)). In panels (b) and (d), black solid lines indicate porosity evolution in an elastic-perfect plastic matrix.

Grahic Jump Location
Fig. 4

FE result of the normalized porosity evolution as a function of ɛi, ε̂, and σ̂. W0 = 1, f0 = 0.01, and T = 2. The dashed vertical lines show ɛi values for reference.

Grahic Jump Location
Fig. 5

(a) Porosity evolution at T = 2 in a material with f0 = 0.01, ε̂ = 0.4, ɛi = 0.5, and σ̂ = 14. Inset shows evolution of the ligament parameter χ. Panels (b)–(d) show the stress–strain responses at stages A, B, and C of porosity evolution. The dashed curves represent the average cell response, and the thin solid curves represent the local matrix response. Panels (e)–(g) show the equivalent plastic strain distribution. Note the evolution of the differential flow hardening between the equator (E) and pole (P) regions.

Grahic Jump Location
Fig. 6

(a) Evolution of void shape corresponding to Fig. 5(a) at T = 2. Initially, L0 = Lr0 = Lz0. Panel (b) shows the evolution of the normalized void dimensions along the radial and axial directions with symbols corresponding to two strain levels in (a).

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Fig. 7

Panel (a) shows an aligned spheroidal-voided microstructure with material orthotropy and the lab-frame used. Panel (b) shows typical variation adopted for the scalar invariant h of 𝕙. Inset shows the dependence of hmax on hLS (=hTS).

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Fig. 8

Calibrated CDM responses for σi = 10 MPa, ɛi = 0.05, σ̂ = 9, and f0 = 0.01. Panels (a) and (b), respectively, show the first and second rows in Table 1. Insets in (b) and (d) emphasize the improvement in capturing the evolution of (calibrated) and χ (predicted).

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Fig. 9

Predicted responses of a material with σi = 10 MPa, ɛi = 0.05, and σ̂ = 9. Insets in (b) and (d) show the improvement in the prediction of porosity evolution in comparison to the original KB model.

Grahic Jump Location
Fig. 10

Predicted responses of a material with σi = 10 MPa, ɛi = 0.05, and ε̂ = 0.4. Insets in (b) and (d) show the improvement in the prediction of porosity evolution in comparison to the original KB model.

Grahic Jump Location
Fig. 11

Predicted responses of a material probing void shape effects (σi = 10, ɛi = 0.05, σ̂ = 9, ε̂ = 0.4, f0 = 0.01, and T = 2). Insets in (b), (c), and (d), respectively, show the improved modified , , and χ responses using the modified CDM model.

Tables

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