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Research Papers

Micromechanical Analyses of Debonding and Matrix Cracking in Dual-Phase Materials

[+] Author and Article Information
Brian Nyvang Legarth

Associate Professor
Department of Mechanical Engineering,
Solid Mechanics,
Technical University of Denmark,
DK-2800 Kgs. Lyngby, Denmark
e-mail: bnl@mek.dtu.dk

Qingda Yang

Associate Professor
Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124
e-mail: qdyang@miami.edu

Manuscript received November 6, 2015; final manuscript received February 1, 2016; published online March 4, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(5), 051006 (Mar 04, 2016) (9 pages) Paper No: JAM-15-1600; doi: 10.1115/1.4032690 History: Received November 06, 2015; Revised February 01, 2016

Failure in elastic dual-phase materials under transverse tension is studied numerically. Cohesive zones represent failure along the interface and the augmented finite element method (A-FEM) is used for matrix cracking. Matrix cracks are formed at an angle of 55deg60deg relative to the loading direction, which is in good agreement with experiments. Matrix cracks initiate at the tip of the debond, and for equi-biaxial loading cracks are formed at both tips. For elliptical reinforcement the matrix cracks initiate at the narrow end of the ellipse. The load carrying capacity is highest for ligaments in the loading direction greater than that of the transverse direction.

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Figures

Grahic Jump Location
Fig. 1

The plane strain cell model for rigid elliptical reinforcing inclusions. (a) Assumed periodically arranged reinforcement in the overall heterogeneous material. (b) The cell used for modeling is shown with initial dimensions, loads, supports, and coordinate system.

Grahic Jump Location
Fig. 2

Examples of finite element meshes used. (a) ai/bi=ac/bc=1, (b) ai/bi=2, and ac/bc=1 for βi=30 deg. A magnification near the reinforcement is inserted.

Grahic Jump Location
Fig. 3

Representation of a matrix crack using A-FEM (reproduced from [12]). (a) Cracked element in domain Ωe=Ω1e+Ω2e. (b) Mathematical element of domain Ω1e (ME1). (c) Mathematical element of domain Ω2e (ME2).

Grahic Jump Location
Fig. 4

Stress–strain curves for ai/bi=ac/bc=1 for two different sets of strength parameters. The ratio of the matrix to interface strength is 40 times larger for the dashed line compared to that of the solid line.

Grahic Jump Location
Fig. 5

Contours of maximum principal strain, εmax, at ε1=0.018 in Fig. 4. Matrix cracks are shown by gray color and the deformations are three times magnified. (a) Low matrix to interface strength ratio (solid line in Fig. 4). (b) Forty times larger matrix to interface strength ratio (dashed line in Fig. 4).

Grahic Jump Location
Fig. 6

Contours of maximum principal strain, εmax, at ε1=0.010. Matrix crack is shown by gray color and the deformations are three times magnified. Only the central reinforcement is allowed to debond.

Grahic Jump Location
Fig. 7

Stress–strain curves for ai/bi=ac/bc=1 for three different values of the loading parameter, κ, see Eq. (4)

Grahic Jump Location
Fig. 8

Contours of maximum principal strain, εmax, at ε1=0.018 in Fig. 7. Matrix cracks are shown by gray color and the deformations are three times magnified. (a) Biaxial loading, κ=0.5. The conditions in Eq. (3) are also illustrated. (b) Equi-biaxial loading, κ = 1.

Grahic Jump Location
Fig. 9

Stress–strain curves for ai/bi=1 for three different values of ac/bc under uniaxial plane strain tension

Grahic Jump Location
Fig. 10

Contours of maximum principal strain, εmax, at ε1=0.018 in Fig. 9. Matrix cracks are shown by gray color and the deformations are three times magnified; (a) ac/bc=1/2 and (b)ac/bc=2.

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Fig. 11

Stress–strain curves for ai/bi=2 and ac/bc=1 for three different values of the orientation, βi

Grahic Jump Location
Fig. 12

Contours of maximum principal strain, εmax, at ε1=0.018 in Fig. 11. Matrix cracks are shown by gray color and the deformations are three times magnified; (a) β=0 deg, (b) βi=30 deg, and (c) βi=60 deg.

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