6.7 Micromechanical Constitutive Model of the Particulate
Composite
The nature of the bond between particles and the matrix material has a significant
effect on the mechanical behavior of particulate composites. Most analytical and
numerical models assume that the bond between the filler and matrix is perfect and
can be modeled using the continuity of tractions and displacements across a discrete
interface. However, internal defects and imperfect interfaces are well-known to exist
in composites, and the incorporation of such phenomena into the general theory
requires modification and relaxation of the continuity of displacements between the
constituents. The imperfect interface bond may be due to the compliant interfacial
layer known as interphase or interface damage, which may have been created
deliberately by coating the particles with a debonding agent. It may also develop
during the manufacturing process due to chemical reactions between the particles
and the matrix material or due to interface damage from cyclic loading. Most
importantly, the strength of the bond at the interface controls the mechanical
response and fatigue life of the composite (Basaran and Nie 2004). By controlling
the stress-strain response of the interphase, it is possible to control overall behavior
of the composite.
In the following section, a micromechanical model for particulate composites
with imperfect interface between the filler particle and the matrix and CTE mismatch
is presented, based on the work of Ju and Chen (1994a, b) and Ju and Tseng (1996),
which was for perfectly bonded particle-matrix interfaces. In the micromechanical
model, particulate composites are treated as three-phase composites consisting of
agglomerate of particles, the bulk matrix, and the interfacial transition zone around
the agglomerate as shown in Fig. 6.2. The interfacial transition zones are assumed to
have perfect bonding with matrix and particles. The inner composite sphere assemblage (CSA), consisting of the particle and the interfacial transition zone, is regarded
as an equivalent spherical particle with the effective mechanical and thermal properties derived in the previous section.
6.7.1 Modeling Procedures for Particulate Composites
In this section, we will discuss the modeling procedures for a particulate composite,
including how the interface properties, CTE mismatch between the particle and the
matrix, and an isotropic damage parameter are introduced.
The modeling process consists of four steps. The first step is the simplification of
the real particulate composites, which is shown in Fig. 6.9. A is a representation of
the real microstructure for a particulate composite, where particles have different
sizes and shapes. In order to get an analytical expression for the effective behavior of
the particulate composite, we must make some assumptions. For simplicity, we
assume that the particles are uniform spherical. The interfacial layer is used to
316
6 Unified Micromechanics of Particulate Composites
Composite
The nature of the bond between particles and the matrix material has a significant
effect on the mechanical behavior of particulate composites. Most analytical and
numerical models assume that the bond between the filler and matrix is perfect and
can be modeled using the continuity of tractions and displacements across a discrete
interface. However, internal defects and imperfect interfaces are well-known to exist
in composites, and the incorporation of such phenomena into the general theory
requires modification and relaxation of the continuity of displacements between the
constituents. The imperfect interface bond may be due to the compliant interfacial
layer known as interphase or interface damage, which may have been created
deliberately by coating the particles with a debonding agent. It may also develop
during the manufacturing process due to chemical reactions between the particles
and the matrix material or due to interface damage from cyclic loading. Most
importantly, the strength of the bond at the interface controls the mechanical
response and fatigue life of the composite (Basaran and Nie 2004). By controlling
the stress-strain response of the interphase, it is possible to control overall behavior
of the composite.
In the following section, a micromechanical model for particulate composites
with imperfect interface between the filler particle and the matrix and CTE mismatch
is presented, based on the work of Ju and Chen (1994a, b) and Ju and Tseng (1996),
which was for perfectly bonded particle-matrix interfaces. In the micromechanical
model, particulate composites are treated as three-phase composites consisting of
agglomerate of particles, the bulk matrix, and the interfacial transition zone around
the agglomerate as shown in Fig. 6.2. The interfacial transition zones are assumed to
have perfect bonding with matrix and particles. The inner composite sphere assemblage (CSA), consisting of the particle and the interfacial transition zone, is regarded
as an equivalent spherical particle with the effective mechanical and thermal properties derived in the previous section.
6.7.1 Modeling Procedures for Particulate Composites
In this section, we will discuss the modeling procedures for a particulate composite,
including how the interface properties, CTE mismatch between the particle and the
matrix, and an isotropic damage parameter are introduced.
The modeling process consists of four steps. The first step is the simplification of
the real particulate composites, which is shown in Fig. 6.9. A is a representation of
the real microstructure for a particulate composite, where particles have different
sizes and shapes. In order to get an analytical expression for the effective behavior of
the particulate composite, we must make some assumptions. For simplicity, we
assume that the particles are uniform spherical. The interfacial layer is used to
316
6 Unified Micromechanics of Particulate Composites