Fatigue graphs: load-number of cycles curves

The most common method to present fatigue dates is to plot stress (S) versus the number of cycles (N), these graphs are called S-N curves. The ordinate is usually the maximum stress or stress range. The abscissa is usually the number of cycles to failure for fixed cycle of stress or deformation and it is usually plotted on a logarithmic scale. Stress ratio (R) and test frequency (Hz) are kept constant for all the specimens. All materials have a negative slope, so the number of cycles to failure increases with decreasing load. S-N curves of the composites generally depend on several factors:

• variables of material:

• material and fibre volume fraction (Vf);

• matrix (resin);

• guidance plan;

• test variables:

• load type (traction or traction-compression);

• average stress;

• frequency;

• environmental conditions.

S-N curves usually are linear for less than one million life cycles and can be expressed by linear equations like this:

a

= A + B log N (1)

astat

oapp and ostat are applied and static stress respectively, A and B are constants that depend on the material. The fatigue limit depends on many factors such as the reinforcement type, matrix and fibres orientation. Unlike metallic materials, stress-number of cycles curves of composite materials are not characterized by a fatigue limit, in fact, these curves show a continuous gradient (downwards) towards zero as the number of cycles. The criteria for the fatigue life are numerous for composite materials; usually the criterion N1o is used, which indicates the number of cycles to have a decrease in stiffness of 10%. In other words, the criterion N10 is the number of cycles required for the stress drops to 90% of initial value.

A composite material, in the its simplest form, has unidirectional fibres aligned with the direction of stress (load on axis); the fibres bear most of the load in the case of fatigue load. It is easy to think that the fatigue behaviour of a composite depends exclusively on the fibre; in reality the experimental results show that the fatigue behaviour of a composite material depends mainly on the stress in the matrix. The fatigue life increases with increasing angles layers (Marannano & Virzi’ Mariotti, 2008) in multidirectional composite materials. The presence of fibres causes damage and delamination among layers in the case of transverse loads and off-axis.

4.3 Composite damage

The damage process has two predominant phases: an initial stage where the development of non-interacting cracks leads to the Characteristic Damage State (CDS), in which a model of stable crack is developed. In the second phase, cracks of different nature interact among them with the increase of the number of cycles, causing an increase in localized cracks and the consequent fracture.

In the first phase, the cracks of matrix are generated in the plane if stresses, orthogonal to the fibres direction, exceed the strength of the matrix. These cracks usually occur in composites with brittle matrix (epoxy resin), but can also occur if the matrix is ductile (metal matrix).

Innate micro defects in the material increase continuously with fatigue loads, and when the size of the defects reaches a characteristic dimension, a first crack (original or primary crack) is formed at the beginning of CDS. First cracks in the matrix are due to consequent development of the damage under fatigue loads, and are a basis for the development of localized defects, buckling and growth of delamination in compressive loads.

The CDS is a property of the laminate, and it depends on the properties of individual layers, thickness and sequence. The CDS is independent of the loading history, boundary conditions, treatments, residual stress and humidity. It is the starting point for those processes that control the strength, stiffness and fatigue life of the laminates. It also represents a state of the damage that can be accurately described.

Characteristic of second phase is the delamination. Primary cracks propagate due to the propagation of the secondary cracks near the interface of the layers. Secondary cracks are usually perpendicular to primary and are due to stress directed along primary axis of the cracks. High interlaminar stresses generate interlaminar cracks that cause the delamination within the laminate, in the region where there are primary and secondary cracks. Then the fibres break heavily (third phase), and cause the final break. In many cases, it was noted that two thirds of the broken fibre occur in the first third of total number of cycles. However, the final failure occurs when the broken fibres are aligned with principal stress. The phases of the damage model do not occupy separate regions within material life; however, the cracks formation in the matrix characterizes the first phase of the damage model while the delamination characterizes the second phase.