60
3
Mechanics of composites is an important study in the understanding of the mechanical responses and their mechanisms due to
anisotropy. Micromechanics and macromechanics of composites
deal with a material at its constituent and bulk levels, respectively.
The understanding of the properties of the constituents—their
interaction and bonding mechanisms—plays a vital role in understanding micromechanics. On the other hand, macromechanics
primarily deals with engineering aspects of composite material and
its responses to applied loads. This chapter explains in detail the
concepts of micromechanics and macromechanics.
3.1 Micromechanics of Polymeric Composites
Micromechanics is the study and analysis of composite materials at
the level of the individual constituents. It also can be said that
micromechanics is the study of the behaviour of fibres and filaments, matrices, interfaces, and interphases in a composite material
under load. It discusses the phenomenon of the interaction of fibres
with the matrix, the role of the interface, the role of the interphase,
and the interaction between fibres through the matrix under the
influence of external forces.
3.1.1 Rule of Mixtures
Some of the properties of a composite material can be expressed as
the sum of the product of the volume fraction of the constituents
and their properties. The volume fraction of a constituent in a composite material is defined as the ratio of the volume of the constituent to the total volume of the composite material. The resulting
expression is commonly referred to as the rule of mixtures [1]. In
order to achieve optimum properties in advanced composite materials as per the rule of mixtures, the volume fractions of reinforcement and matrix should be 0.5 for each. For example, the tensile
strength of the fibre-reinforced composite may be calculated as
σ
σ
σ
C
f f
m m
=
+
V
V
(3.1)
where
5 σ c = Tensile strength of composite
5 σ f = Tensile strength of fibre
5 σ m = Tensile strength of matrix
5 V f = Volume fraction of fibre
5 V m = Volume fraction of matrix
Similarly, other properties of the composites may be evaluated theoretically using the rule of mixture. The longitudinal modulus is
given as
E E V E V
c
f f
m m
=
+
(3.2)
Chapter 3 · Micromechanics and Macromechanics of Polymeric Composites
3
Mechanics of composites is an important study in the understanding of the mechanical responses and their mechanisms due to
anisotropy. Micromechanics and macromechanics of composites
deal with a material at its constituent and bulk levels, respectively.
The understanding of the properties of the constituents—their
interaction and bonding mechanisms—plays a vital role in understanding micromechanics. On the other hand, macromechanics
primarily deals with engineering aspects of composite material and
its responses to applied loads. This chapter explains in detail the
concepts of micromechanics and macromechanics.
3.1 Micromechanics of Polymeric Composites
Micromechanics is the study and analysis of composite materials at
the level of the individual constituents. It also can be said that
micromechanics is the study of the behaviour of fibres and filaments, matrices, interfaces, and interphases in a composite material
under load. It discusses the phenomenon of the interaction of fibres
with the matrix, the role of the interface, the role of the interphase,
and the interaction between fibres through the matrix under the
influence of external forces.
3.1.1 Rule of Mixtures
Some of the properties of a composite material can be expressed as
the sum of the product of the volume fraction of the constituents
and their properties. The volume fraction of a constituent in a composite material is defined as the ratio of the volume of the constituent to the total volume of the composite material. The resulting
expression is commonly referred to as the rule of mixtures [1]. In
order to achieve optimum properties in advanced composite materials as per the rule of mixtures, the volume fractions of reinforcement and matrix should be 0.5 for each. For example, the tensile
strength of the fibre-reinforced composite may be calculated as
σ
σ
σ
C
f f
m m
=
+
V
V
(3.1)
where
5 σ c = Tensile strength of composite
5 σ f = Tensile strength of fibre
5 σ m = Tensile strength of matrix
5 V f = Volume fraction of fibre
5 V m = Volume fraction of matrix
Similarly, other properties of the composites may be evaluated theoretically using the rule of mixture. The longitudinal modulus is
given as
E E V E V
c
f f
m m
=
+
(3.2)
Chapter 3 · Micromechanics and Macromechanics of Polymeric Composites