Int J Fract (2009) 158:99–105
DOI 10.1007/s10704-009-9351-6
ORIGINAL PAPER
Simulation of damage evolution in discontinously reinforced
metal matrix composites: a phase-field model
S. B. Biner · S. Y. Hu
Received: 4 September 2008 / Accepted: 20 April 2009 / Published online: 12 May 2009
© Springer Science+Business Media B.V. 2009
Abstract In this study, a phase-field model is intro-
duced to model the damage evolution, due to
particle cracking in reinforced composites in which
matrix deformation is described by an elastic-plastic
constitutive law exhibiting linear hardening behavior.
In order to establish the viability of the algorithm, the
simulations are carried out for crack extension from a
square hole in isotropic elastic solid under the complex
loading path, and composites having the same volume
fraction of reinforcements with two different particle
sizes. The observed cracking patterns and development
of the stress-strain curves agree with the experimen-
tal observations and previous numerical studies. The
algorithm offers significant advantages to describe the
microstructure and topological changes associated with
the damage evolution in comparison to conventional
simulation algorithms, due to the absence of formal
meshing.
Keywords Metal matrix composites ·
Phase-field model · Damage · Simulation
S. B. Biner (B )
Ames Laboratory, Iowa State University, Ames, IA 50011,
USA
e-mail: sbbiner@iastate.edu
S. Y. Hu
Pacific Northwest National Laboratory, Richland, WA 99352,
USA
1 Introduction
The metal matrix composites may offer significant
advantages over conventional alloys in terms of their
specific stiffness, better fatigue properties, and in some
cases, better toughness and resistance to wear. It is now
well established that in composite systems in which
matrix deforming with a nonlinear behavior (e.g. elas-
toplastic, viscoplastic), the dominant damage mecha-
nisms leading to failure are: Brittle failure of the
reinforcements, interfacial debonding between the rein-
forcements and the matrix, and ductile failure of the
matrix by nucleation, growth and coalescence of voids
(Gungor and Liaw 1991; Suresh et al. 1993; Chawla
and Chawla 2006). These damage mechanisms have
been extensively studied by well-known constitutive
models of void growth (Gurson 1975; Needleman and
Tvergaard 1987; Tvergaard and Needleman 1995) and
cohesive zone models (Needleman 1990) within the
framework of FEM, for example as given in references
(Llorca et al. 1991; Biner 1994; Llorca and Gonzalez
1998; Bohm and Han 2001; Drabek and Bohm 2006;
Segurado and Llorca 2006).
In this study, an alternative approach, based on the
phase-field model, is introduced to elucidate the mech-
anisms of damage evolution due to particle cracking in
metal matrix composite systems. The algorithm offers
significant advantages to describe the microstructure
and topological changes associated with the damage
evolution in comparison to conventional simulation
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