METHODOLOGY
The service life time of an engineering component excluding obsolescence is normally dependent on three factors acting either separately or in combination with one another; Corrosion, Mechanical failure due to fatigue or Creep and Wear (Umezurike, 2008). We now analyze the failure of the fibers of the carbon fiber composite material by replacing the composite material with an elastic material using the effective modulus theory to obtain mechanical properties of the material and determine the path of propagation of the cracks resulting from repeated or cyclic stress and loadings.
Modeling
the mechanical and failure behavior of the fibers in a composite material is
not an easy task. The materials are heterogeneous and have several types of
inherent flaws. Failure of these fiber composites is generally preceded by an
accumulation of different types of internal damage. Failure mechanisms in the
micromechanical scale include fiber breaking, matrix cracking and interface
debonding. They vary with type of loading and are intimately related to the
properties of the constituents. The damage is well distributed throughout the
composite and progresses with an increasingly applied load. It coalesces to
form a macroscopic fracture shortly before catastrophic failure. The strength
of composites with through-thickness cracks is studied by fracture mechanics
approach. Using effective modulus theory, the heterogeneous anisotropic fiber
composite material is replaced by a homogeneous anisotropic elastic material.
Through-thickness cracks reduce the carrying capacity of composite structures,
and also the damage introduced at the crack tip is taken into consideration.
Material Analysis
The
composite material is assumed as a combination of epoxy resin and carbon fiber
fabric, we will use the AS4/3501-6 Carbon/Epoxy unidirectional prepreg as a
model which is frequently used for purposes and conditions of high mechanical
loads.
The
mechanical properties of this polymer - matrix composite is mainly determined
by the fiber properties because the strength and elastic stiffness of these
fibers are more than a hundred times larger than that of the polymer matrix.
Nevertheless, the mechanical behavior of the matrix is also important because
it determines the load transfer to the fibers and must not fail if the strength
of the fibers is to be exploited fully. Because of their excellent properties,
high performance thermoset epoxy resins are the most commonly used type of
polymer matrix for fabrication of advanced materials such as carbon fiber
reinforced epoxy composite materials used in the aerospace industry with
maximum values of about 60%, which is the highest possible fiber volume
fraction that can be used. We shall now discuss the mechanical behavior of the composite
material to be modeled.
1. AS4 Carbon Fibers
Carbon
fiber is characterized by high stiffness and strength, but both parameters
cannot be maximized simultaneously. In high strength fibers, Young’s modulus
does not exceed 400GPa while in high stiffness fibers, the tensile strength is
reduced. The fiber diameter of the materials ranges from 9-17 macrometers and uses about
500,000 intertwined turbostratic fibers per square inch.
2. 3501-6 Epoxy
Although
most of the mechanical load is borne by the fibers, there are still several
requirements for the mechanical properties of the matrix. Its fracture should
be sufficiently large to avoid premature damage of the composite material by
crack formation in the matrix, and the elastic stiffness should be as large as
possible to achieve a sufficient support of the fiber under compressive loads
and to avoid buckling or kinking of the fibers. Finally, its mechanical
behavior should remain unchanged under different environmental conditions
(humidity, temperature, and irradiation). Unfortunately, these requirements are
partially contradictory.
3. AS4/3501-6 Carbon
Fiber/Epoxy Unidirectional Prepreg
The
homogeneous anisotropic model will be used to achieve the mechanical properties
of the composite material. The properties of the fiber and matrix have to be
carefully adjusted to obtain optimal properties of the composite material under
mechanical loads, i.e., the fracture strain of the epoxy has to be sufficient
for carbon fiber under mechanical loads.
4. Homogeneous
Anisotropic Model
The AS4/3501-6 carbon fiber/epoxy composite material is modeled as a homogeneous anisotropic material using micromechanical theories. For a thin lamina under a state of plane stress, the in-plane stress components are related with the in-plane strain components along the principal material axes. The validity of the homogeneous anisotropic elasticity theory for modeling the failure of fiber composite depends on the degree to which the discrete nature of the composite affects the failure modes (Gdoutos, 2005).
Fracture Analysis
Fracture in materials is usually initiated by a crack or notch-like flaw, which cause high stresses in the region of such flaw. A criterion of fracture based on the first law of thermodynamics was proposed by Griffith, that the reduction in strain energy due to propagation of a crack is used to create new crack surfaces.
In
composite materials, the presence and orientation of the fiber can change the
fatigue strength of the matrix in several ways, i.e., local effects occur at
the fiber-matrix interface due to load transfer and the corresponding change in
stress and strain fields. The shear stress at the interface between the fiber
and matrix locally increases the strain in the matrix. This strain may cause
local damage in the matrix and initiate cracks. Under cyclic loadings, the weak
interface between the fiber and matrix allows movement between them. Friction
occurring in this process can cause damage, reduce the unloading effect of the
fiber and thus enable the crack to propagate. Failure usually occurs not by
propagation of a single crack through the material, but by accumulation of
local damage.
Three independent kinematic movements are possible, by which the upper and lower crack surfaces can displace with respect to each other. The crack tip stresses are functions of the crack dimensions and applied load, and critical values of these parameters govern the phenomenon of unstable crack growth.
Composites can be more sensitive to loadings, such as impact and cyclic because they absorb energy mainly through fracture mechanics rather than elasticity or plasticity, and the internal make-up can be damaged with mechanisms such as matrix cracking, delamination, fiber breakage and local buckling.
Fracture Criteria
In
this work, we focus on the fibers of a carbon fiber composite material with a
pre-existent crack. We start by considering a stationary semi-infinite line
crack. The symmetry of the deformation implies
that the crack may only propagate in a direction perpendicular to the loading.
All that is required then is a necessary condition for the crack growth. In the
region surrounding the tip of the crack, the singular stress is characterized
by the stress intensity factor KI. It is postulated that crack
growth will occur when the equality
KI = KIc
holds,
where KIC, which behaves as a threshold value for KI, is
called the critical stress intensity factor which is a material parameter, also
known as mode I fracture toughness.
During crack propagation, the cyclic stress intensity factor increases due to the increase of crack length. Therefore, the crack growth rate also increases even if the cyclic load of the component remains constant. If the maximum stress intensity factor approaches the fracture toughness, the crack accelerates rapidly and eventually becomes unstable after a few more cycles, and failure of the material ensures.
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