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Research Papers

Homogenization Based 3D Continuum Damage Mechanics Model for Composites Undergoing Microstructural Debonding

[+] Author and Article Information
Jayesh R. Jain

Computational Mechanics Research Laboratory, Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210

Somnath Ghosh1

Computational Mechanics Research Laboratory, Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210ghosh.5@osu.edu

1

Corresponding author.

J. Appl. Mech 75(3), 031011 (Apr 08, 2008) (15 pages) doi:10.1115/1.2870265 History: Received March 26, 2007; Revised August 29, 2007; Published April 08, 2008

This paper develops a microscopic homogenization based continuum damage mechanics (HCDM) model framework for fiber reinforced composites undergoing interfacial debonding. It is an advancement over the 2D HCDM model developed by Raghavan and Ghosh (2005, “A Continuum Damage Mechanics Model for Unidirectional Composites Undergoing Interfacial Debonding  ,” Mech. Mater., 37(9), pp. 955–979), which does not yield accurate results for nonproportional loading histories. The present paper overcomes this shortcoming through the introduction of a principal damage coordinate system (PDCS) in the HCDM representation, which evolves with loading history. The material behavior is represented as a continuum constitutive law involving a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. The current work also extends the model of Raghavan and Ghosh to incorporate damage in 3D composites through functional forms of the fourth order damage tensor in terms of macroscopic strain components. The model is calibrated by homogenizing the micromechanical response of the representative volume element (RVE) for a few strain histories. This parametric representation can significantly enhance the computational efficiency of the model by avoiding the cumbersome strain space interpolations. The proposed model is validated by comparing the CDM results with homogenized micromechanical response of single and multiple fiber RVEs subjected to arbitrary loading history.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

A 2D microstructural RVE model of Voronoi cell elements with 20 circular fibers

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Figure 2

Finite element mesh for (a) RVE with a cylindrical fiber, (b) RVE with an elliptical fiber, (c) RVE with two parallel fibers, and (d) RVE with two perpendicular fibers

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Figure 3

κ-Wd plot for a RVE with circular fiber subjected to uniaxial tension

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Figure 4

Comparison of macroscopic stress-strain curve obtained using the 2D homogenized CDM model and HMM under nonproportional loading

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Figure 5

Comparison of results of 2D plane strain VCFEM and 3D ABAQUS models: (a) macroscopic stress-strain curve and (b) degradation of secant stiffness

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Figure 6

Degradation of components of secant stiffness in third direction

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Figure 7

Rotation of the PDCS for (a) proportional and (b) nonproportional loading paths

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Figure 8

Functional representation of the κ-Wd relation

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Figure 9

Functional representation of variation of Pijkl′ with macroscopic strain for uniaxial tension

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Figure 10

Comparison of macroscopic stress-strain curve obtained using HCDM and HMM for a 3D RVE with a cylindrical fiber (Fig. 2) for load cases (a) L1, (b) L2, and (c) L3

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Figure 11

Comparison of macroscopic stress-strain curve obtained using HCDM and HMM for RVE with an elliptical fiber (Fig. 2) for load cases (a) L1, (b) L2, and (c) L3

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Figure 12

Comparison of macroscopic stress-strain curve obtained using HCDM and HMM for RVE with two parallel fibers (Fig. 2) for load cases (a) L1, (b) L2, and (c) L3

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Figure 13

Comparison of macroscopic stress-strain curve obtained using HCDM and HMM for RVE with two perpendicular fibers (Fig. 2) for load cases (a) L1, (b) L2, and (c) L3

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Figure 14

Comparison of macroscopic stress-strain curve obtained using HCDM and HMM for RVE with 20 circular fibers (Fig. 1) for load cases (a) L1, (b) L2, and (c) L3

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Figure 15

Microscopic stress contour plot of RVE with (a) a cylindrical fiber, (b) an elliptical fiber, (c) two parallel fibers, and (d) two perpendicular fibers, subjected to uniaxial tension of e11=0.004

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