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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Li, Y. , Zheng, Y. , Lin, Z. , Hu, Z. , and Zeng, J. , 2012, “ Quantitative Analysis of Inclusions in Aluminum,” Adv. Mater. Res., 476–478, pp. 453–456.
McDanels, D. , 1985, “ Analysis of Stress-Strain, Fracture, and Ductility Behavior of Aluminum Matrix Composites Containing Discontinuous Silicon Carbide Reinforcement,” Metall. Trans. A, 16(6), pp. 1105–1115. [CrossRef]
Canal, L. P. , Segurado, J. , and Llorca, J. , 2009, “ Failure Surface of Epoxy-Modified Fiber-Reinforced Composites Under Transverse Tension and Out-of-Plane Shear,” Int. J. Solids Struct., 46(11–12), pp. 2265–2274. [CrossRef]
Totry, E. , González, C. , and Llorca, J. , 2008, “ Prediction of the Failure Locus of C/PEEK Composites Under Transverse Compression and Longitudinal Shear Through Computational Micromechanics,” Compos. Sci. Technol., 68(15–16), pp. 3128–3136. [CrossRef]
Basu, S. , Waas, A. M. , and Ambur, D. R. , 2006, “ Compressive Failure of Fiber Composites Under Multi-Axial Loading,” J. Mech. Phys. Solids, 54(3), pp. 611–634. [CrossRef]
Gamstedt, E. K. , and Sjögren, B. A. , 1999, “ Micromechanisms in Tension-Compression Fatigue of Composite Laminates Containing Transverse Plies,” Compos. Sci. Technol., 59(2), pp. 167–178. [CrossRef]
Vajari, D. A. , González, C. , Llorca, J. , and Legarth, B. N. , 2014, “ A Numerical Study of the Influence of Microvoids in the Transverse Mechanical Response of Unidirectional Composites,” Compos. Sci. Technol., 97, pp. 46–54. [CrossRef]
Puck, A. , and Schürmann, H. , 1998, “ Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models,” Compos. Sci. Technol., 58(7), pp. 1045–1067. [CrossRef]
Legarth, B. N. , and Kuroda, M. , 2004, “ Particle Debonding Using Different Yield Criteria,” Eur. J. Mech.-A/Solids, 23(5), pp. 737–751. [CrossRef]
Curtin, W. A. , 1991, “ Theory of Mechanical Properties of Ceramic-Matrix Composites,” J. Am. Ceram. Soc., 74(11), pp. 2837–2845. [CrossRef]
Tvergaard, V. , and Legarth, B. N. , 2007, “ Effects of Anisotropic Plasticity on Mixed Mode Interface Crack Growth,” Eng. Fract. Mech., 74(16), pp. 2603–2614. [CrossRef]
Ling, D. , Yang, Q. , and Cox, B. , 2009, “ An Augmented Finite Element Method for Modeling Arbitrary Discontinuities in Composite Materials,” Int. J. Fract., 156(1), pp. 53–173. [CrossRef]
Belytschko, T. , and Black, T. , 1999, “ Elastic Crack Growth in Finite Elements With Minimal Remeshing,” Int. J. Numer. Methods Eng., 45(5), pp. 601–620. [CrossRef]
Zhang, Z. J. , Paulino, G. H. , and Celes, W. , 2007, “ Extrinsic Cohesive Modelling of Dynamic Fracture and Microbranching Instability in Brittle Materials,” Int. J. Numer. Methods Eng., 72(8), pp. 893–923. [CrossRef]
Legarth, B. N. , 2005, “ Effects of Geometrical Anisotropy on Failure in a Plastically Anisotropic Metal,” Eng. Fract. Mech., 72(18), pp. 2792–2807. [CrossRef]
Yang, Q. , and Thouless, M. , 2001, “ Mixed-Mode Fracture Analyses of Plastically-Deforming Adhesive Joints,” Int. J. Fract., 110(2), pp. 175–187. [CrossRef]
Wang, J. , and Suo, Z. , 1990, “ Experimental-Determination of Interfacial Toughness Curves Using Brazil-Nut-Sandwiches,” Acta Metall. Mater., 38(7), pp. 1279–1290. [CrossRef]
Fang, X. J. , Zhou, Z. Q. , Cox, B. N. , and Yang, Q. D. , 2011, “ High-Fidelity Simulations of Multiple Fracture Processes in a Laminated Composite in Tension,” J. Mech. Phys. Solids, 59(7), pp. 1355–1373. [CrossRef]
Ling, D. S. , Fang, X. J. , Cox, B. N. , and Yang, Q. D. , 2011, “ Nonlinear Fracture Analysis of Delamination Crack Jumps in Laminated Composites,” J. Aerosp. Eng., 24(2), pp. 181–188. [CrossRef]
Moës, N. , and Belytschko, T. , 2002, “ Extended Finite Element Method for Cohesive Crack Growth,” Eng. Fract. Mech., 69(7), pp. 813–833. [CrossRef]
Legarth, B. N. , 2004, “ Unit Cell Debonding Analyses for Arbitrary Orientations of Plastic Anisotropy,” Int. J. Solids Struct., 41(26), pp. 7267–7285. [CrossRef]
Paris, F. , Correa, E. , and Mantič, V. , 2007, “ Kinking of Transversal Interface Cracks Between Fiber and Matrix,” ASME J. Appl. Mech., 74(4), pp. 703–716. [CrossRef]
Ashouri Vajari, D. , 2015, “ A Micromechanical Study of Porous Composites Under Longitudinal Shear and Transverse Normal Loading,” Compos. Struct., 125, pp. 266–276. [CrossRef]
Tvergaard, V. , and Hutchinson, J. , 1992, “ The Relation Between Crack-Growth Resistance and Fracture Process Parameters in Elastic Plastic Solids,” J. Mech. Phys. Solids, 40(6), pp. 1377–1397. [CrossRef]
Park, S. J. , Lee, B. K. , Na, M. H. , and Kim, D. S. , 2013, “ Melt-Spun Shaped Fibers With Enhanced Surface Effects: Fiber Fabrication, Characterization and Application to Woven Scaffolds,” Acta Biomater., 9(8), pp. 7719–7726. [CrossRef] [PubMed]
Edie, D. D. , Fox, N. K. , Barnett, B. C. , and Fain, C. C. , 1986, “ Melt-Spun Non-Circular Carbon Fibers,” Carbon, 24(4), pp. 477–482. [CrossRef]
Yeom, B. Y. , and Pourdeyhimi, B. , 2011, “ Web Fabrication and Characterization of Unique Winged Shaped, Area-Enhanced Fibers Via a Bicomponent Spunbond Process,” J. Mater. Sci., 46(10), pp. 3252–3257. [CrossRef]
Yingde, W. , Xuguang, L. , Wanglei , Xinyan, L. , Jingen, X. , Yonggang, J. , and Wenli, Z. , 2010, “ Preparation and Properties of Non-Circular Cross-Section SiC Fibers From a Preceramic Polymer,” Ceram. Trans., 213, pp. 121–126.
Needleman, A. , 1987, “ A Continuum Model for Void Nucleation by Inclusion Debonding,” ASME J. Appl. Mech., 54(3), pp. 525–531. [CrossRef]
Tvergaard, V. , and Hutchinson, J. , 1993, “ The Influence of Plasticity on Mixed-Mode Interface Toughness,” J. Mech. Phys. Solids, 41(6), pp. 1119–1135. [CrossRef]
Sou, Z. , Shih, C. , and Varias, A. , 1993, “ A Theory for Cleavage Cracking in the Presence of Plastic-Flow,” Acta Metall. Mater., 41(5), pp. 1551–1557. [CrossRef]


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.

Grahic Jump Location
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.




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