Blade materials, testing methods and structural design - Wind Power Generation and Wind Turbine Design - page 430

fi ber composites loaded in the fi ber direction,

s − and the composite shear
strength, t LTu . As for elastic properties (Section 5.1) the strength properties of an
orthotropic material, such as a unidirectional fi ber composite, must be related to
specifi c directions. The longitudinal direction is assigned the subscript L, the
(in-plane) direction orthogonal to the longitudinal direction is called the transverse
direction and given subscript T. For a unidirectional fi ber composite, the tensile
strength in the fi ber direction,

Lu

s + , is usually much higher than the tensile strength
perpendicular to the fi ber direction,

Lu

s + .
Fracture by a single sharp crack is most often characterized by linear-elastic frac-
ture mechanics concept such as fracture toughness (the critical stress intensity fac-
tor) or equivalently the fracture energy (the critical energy release rate G c ). The crack
opening is described in 3 pure opening modes: Pure normal opening (Mode I), pure
tangential crack opening/shearing (Mode II) and tearing (Mode III). The fracture
toughness and fracture energy are material constants but are infl uenced by tempera-
ture, loading rate and environmental conditions such as humidity level. In homoge-
nous materials, cracks tend to propagate under pure Mode I. Materials interfaces are
usually weaker than the surrounding materials; therefore cracks tend to remain at
interfaces. Therefore, the fracture energy, G c , of an interface between two dissimilar
materials is a function of the mode mixity y , where the mode mixity, y , is defi ned
from the complex stress intensity factor and a characteristic length scale, see [9] (in
isotropic materials, pure normal crack opening displacement corresponds to y = 0°,
whereas pure tangential opening corresponds to y = 90°). As noted earlier, the inter-
action of aerodynamic and gravity loading during blade rotation produces multiaxial
loading in wind turbine blades, which results in mixed mode loading of interfaces
and cracks. Thus, the fracture energy of interface cracks in wind turbine blades must
be measured for various load cases, corresponding to different mode mixities that
exist in a given cross section and along the blade length. This is the case for gelcoat/
laminate delamination, skin/core delamination, cracking along interfaces in adhe-
sive joints and delamination of laminates. Because fracture energy is a material con-
stant, it can be used for different geometries so long as the mode mixity is the same.
As discussed later, this simplifi es the testing requirements.
The energy required for crack initiation is less than the energy required for
crack propagation. Thus, the fracture energy of an interface is typically separated
into the energy required for initiation and the energy required for further crack
extension; however both values are strong functions of mode mixity.
As indicated in Fig. 5, laminated fi ber composites can fail by delamination,
which is a cracking mode that can involve fi ber bridging between the crack faces .
If the fi ber composite develops a large scale fi ber bridging zone, it cannot be prop-
erly characterized by linear-elastic fracture mechanics. Instead, the mechanical
behavior of a large scale fracture process zone can be characterized by non-linear
fracture mechanics, in terms of the J integral [10] and a cohesive law [11]. A cohe-
sive law is the relationship between the local crack opening, d , and the local stress,
s , across the failure process zone. The cohesive stress is assumed to depend upon
the local crack opening only, s = s ( d ). The cohesive stresses can be normal and
shear stresses (mixed mode cohesive laws). Figure 6 illustrates the concepts of
stress-strain and cohesive laws.

Tu