## Fi F Fo Ff

Strength for certain values of R and v is predicted using the equation:

provided the three S-N curves X(N), Y(N), and S(N) are derived for the same loading conditions, R, v. In case the complex stress field is produced by multiaxial loading of nonproportional characteristics, resulting in different Ri ratios and vi values for each stress component, oi, then, the corresponding X(N), Y(N), and S(N) strengths, to be used in Eq. (1.17), must be known experimentally for the same Ri, vi conditions.

The experimental characterization of X(N), Y(N) is performed through uniaxial testing of straight-edge flat coupons cut along the respective principal material direction. For S(N), it was proposed in [20] to use the value of half the fatigue strength of a flat coupon cut off-axis at 45° and loaded uniaxially. This choice yielded satisfactory results for alternating loads, R = —1, but its performance was less effective for other loading types. Therefore, it is proposed to determine S(N) by fitting Eq. (1.17) to the experimental S - N data derived from uniaxial testing at a suitable off-axis orientation.

### 1.9.2 Stiffness Reduction During Fatigue Life

Monitoring and evaluation of stiffness changes during operation can give useful information on the integrity of a composite structure. Prediction of gradual decrease of elastic moduli due to the cyclic loading is essential, inter alia, for design purposes. Many investigators, even from the early years of composite material applications, were considering stiffness as a suitable damage metric and used stiffness degradation to account for damage accumulation in the material under consideration, for example, [3, 33-38]. However, to the author's knowledge, no fatigue theory based on stiffness degradation has gained wide acceptance among scientists nor has inspired confidence to designers. One could mention several reasons, but the truth is that prediction of stiffness degradation during fatigue life is not a simple matter. There is a number of parameters that influence the variation of stiffness, such as material system, loading conditions, cyclic stress level, stress multiaxiality, and the like. The knowledge of interaction rules of all these factors is essential for the formulation of a viable theory for prediction of stiffness degradation. Therefore, for design purposes, simple as possible models predicting stiffness reduction should be used, having parameters that can be reliably defined through standard fatigue tests under specific loading conditions.

For GFRP composites and especially those material systems and stacking sequences used in the fabrication of wind turbine rotor blades, stiffness degradation measurements were intensively carried out the last decade and reported in the literature [8-12, 21, 22, 28]. The resulting trend from all the experimental studies on stacking sequences of practical interest, that is, usually combinations of (0°) and (±45°) fabrics, is that after the very few first cycles there is an abrupt stiffness reduction, followed by a long period of slow linear degradation and finally a steepest stiffness variation is observed prior to final failure.

Based on the experimental evidence, an empirical model for the description of stiffness changes and the prediction of stiffness-controlled design curves was introduced in [28] and further validated for different material systems and loading conditions in [21, 22]. A brief outline of the model, which is further exploited in the present study for predicting stiffness degradation and derive corresponding design allowables, is given below.

The degree of damage in a polymer matrix composite coupon can be evaluated by measuring stiffness degradation, EN/E1, where E1 denotes the Young's modulus of the material measured at the first cycle, different in general from the static value E0, and EN the corresponding one at the Nth cycle. It is assumed that stiffness degradation can be expressed by [28]:

Material constants, K and c, inEq. (1.18) are determined by curve fitting therespec-tive experimental data for EN/E1, depending on the number of stress cycles, N, and the level of applied cyclic stress amplitude, oa. Recasting Eq. (1.18) in the following form:

allows easy determination of model constants. Notice that these model characteristics depend strongly on applied stress ratio R and stress multiaxiality. Relation (1.18) also establishes a stiffness-based design criterion since for a predetermined level of En/E1, for example, p, one can solve for aa to obtain an alternative form of design curve, henceforth denoted by Sc-N, corresponding not to material failure but to a specific stiffness degradation percentage (1 - p)%. The Sc-N curves for any specific stiffness degradation level, EN/E1, can be easily calculated by means of the following equation:

1.9.3 Statistical Evaluation of Fatigue Strength Data

Strength data from each set of on- and off-axis fatigue tests were subjected to statistical analysis to determine characteristic values. The methodology used [39, 40] is briefly discussed below. The form of the S-N equation is assumed to be given by:

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