Unlike homogeneous materials, FRP composites accumulate damage in general rather than developing localized damage, and fracture does not always occur by propagation of a single macroscopic crack. The damage accumulation in these materials is micro structural, which includes fiber/matrix debonding, matrix cracking, delamination and fiber fracture [Mathews, 2000]. Fatigue damage mechanism in unidirectional composites primarily depends on loading mode (e.g., tensile, compressive, bending, torsion or combinations) and on the loading direction i.e., parallel or inclined to the fiber direction. In unidirectional fiber reinforced composites, fractures in fibers occur but the accumulation is slower and the life of the composite is not dependent on fatigue fractures in fibers. But matrix micro cracks transverse to the loading axis develops and propagates, thus breaking fibers or causing interfacial failure, leading to the failure of the composite. In uni-directional composites, fatigue damage is initiated by debonding between fiber and matrix. Typically, the damage mechanism in tensile fatigue is of three stages as shown in Figure 4-20 [Talreja, 1987] namely:
Fiber breakage Matrix cracking
Interfacial shear failure
Figure 4-20: Fatigue Damage Mechanism in Unidirectional Composites Under Loading Parallel to Fibers: (a) Fiber Breakage, Interfacial Debonding; (b) Matrix Cracking; (c) Interfacial Shear Failure [Talreja, 1987]
Mechanical fatigue is the most common type of failure of structures in service. The fatigue behavior of composite materials is conventionally characterized by a Wöhler or S-N curve. For every new material with a new lay-up, altered constituents or different processing procedure, a whole new set of fatigue life tests has to be repeated for such a characterization. If the active fatigue damage micromechanisms and the influence of the constituent properties and interface were known, it would be possible, at least qualitatively, to predict the macroscopic fatigue behavior. A study of the fatigue damage mechanisms would also give indications of the weakest microstructural element, which is useful information in materials selection for improvement in service properties. In tensile fatigue of a multidirectional laminate, the critical elements are the longitudinal plies, which are the last to fail.
Fiber breakage is due to the failure of the weakest fiber in the laminate due to excess stress, which causes shear-stress concentration at the interface i.e., close to the tip of the broken fiber, leading to debonding of the fiber from surrounding matrix. The debonded area leads to matrix cracking when the stresses exceed the fatigue limit. Under low strains, approximately 50% of ultimate tensile strain of matrix, a matrix crack stops at the interface. However, at high strains, the stresses at crack tips exceed the fracture stress leading to fiber pullout or breakage of adjoining fibers due to higher stresses. Strength degradation is assumed also to take place in these two stages reflecting the development of the underlying damage process.
In the first stage, a general weakening of the material is assumed and is considered dependent on damage parameters representing the stage of damage. A power law is assumed for the rate of increase of the damage parameter [Talreja, 1987], taking it as a function of an effective stress. A relationship between the residual strength (R) and the initial strength (R0) is then given as:
(
)
m' c c 0 c N N 1 R R R R ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − − + = …(4.28)(
1 m)
1 ' m + = …(4.29)(
)
m c S m k N + = 1 1 …(4.30)where Rc, Nc - residual stresses and number of cycles at the CDS, respectively;
m’, m, k - material constants, and S- maximum applied stress, respectively.
In the second stage, strength degradation is assumed to result from the localized zones of damage which are conceptually replaced by a single crack capable of releasing the same amount of elastic energy as that released collectively by the various crack growth mechanisms. Residual strength (R) is related to a characteristic dimension of the "equivalent” crack C through a fracture mechanics type relationship
2 / 1
C
R=α − …(4.31)
where α is the material constant characterizing material toughness [Talreja, 1987].
The evolution of damage is expressed by the rate of growth of the crack dimension, which is assumed to depend on the current state of damage given by the current crack dimension. Assuming a power law for the crack growth, a relationship between residual strength and the applied maximum stress is derived. This relationship forms the basis for determining the probability distribution of the residual strength and the probability distribution of the number of cycles to attain the Characteristic Damage
analysis of composites is illustrated in Figure 4-21 where R is the initial strength, Rc and
Nc are the residual strength and the number of cycles corresponding to CDS, S is the
maximum applied stress and Nf is the number of cycles to failure.
Figure 4-21: Two-Stage Strength Degradation Model for Fatigue Reliability of Composites [Talreja, 1987]
4.3.3.2.2
Fatigue in Unidirectional Composites
The S-N curve for carbon fiber, glass fiber and aramid fiber in the same standard epoxy matrix is shown in Figure 4-22. The use of stiff fibers such as carbon fibers results in low strains (1.0 - 1.8%) to failure and less stiff fibers like glass lead to relatively higher strains (2.5 – 3.5 %) to failure. Hence, the curve is steep for glass fibers while it is shallow for carbon fibers in Figure 4-22. The slope of the curve (Figure 4-21) is a function of the strain in the matrix [Curtis and Dorey 1986]. The S-N curve for carbon fibers with different stiffness in the same standard epoxy resin is shown in Figure 4-21.
Figure 4-22: Comparison of S-N Curve for Three Different Unidirectional Composite Materials [Curtis and Dorey, 1986]
It can be seen that there is little improvement in the fatigue behavior with change in fiber stiffness. This is because the fatigue behavior of composites is dependent on the strain in the matrix and interfacial characteristics rather than fiber strength. Due to this reason, plots of mean strain rather than stress versus log cycles to failure are commonly used for composite materials (Figures 4-22 and 4-23).
Figure 4-23: Comparison of S-N curve for Four Different Materials with Different Carbon Fibers in Same Epoxy Resin [Curtis and Dorey, 1986]
A typical fatigue life diagram (Figure 4-24a) for a unidirectional composite under loading parallel to fibers is shown. In Figure 4-24a, fatigue limit of the matrix is defined as the maximum strain below which no cracks or only non-propagating cracks maybe initiated in the matrix material. This matrix material property is taken as the lower limit of the progressive matrix damage. It can be seen that as the fiber stiffness reduces, distinct progressive damage band (matrix cracking) is observed before fiber breakage.
Figure 4-24: Fatigue Life Diagram of Unidirectional Composites Under (a) Loading Parallel to Fibers, (b) Off-Axis Loading (Dotted line correspond to on-axis loading) [ Talreja, 1987]
For off-axis loading angles between 0o and 90o, the tip of crack initiated in the matrix will be subjected to two displacement components, i.e., an opening normal to the fibers and a sliding parallel to the fibers. This leads to a mixed mode crack growth parallel to the fibers. The limiting values of crack tip displacement will depend on the off-axis angle; with crack tip displacement increasing with an increase in off -axis angle. The fatigue life diagram for off-axis loading is shown in Figure 4-24 (b). It was found that for off-axis angles more than a few degrees, the fiber breakage bond would be lost, as matrix and/or interfacial cracking will become the predominant damage mechanism for strain up to fracture strain. [Talreja, 1987]