JEC COMPOSITES MAGAZINE - Issue #74 - July 2012 - 49

the fibres has on the crack resistance, the characterisation can be performed for specified fibre volume fractions.

Generic approach to fatigue
From the above discussion, it is evident that the S-N curve for an un-notched composite specimen is dependent on individual fracture phenomena that either occur subsequently or interact simultaneously. Rather than approaching this with a stress-based S-N approach, it is highly recommended to follow a fracture mechanics approach where the individual fractures modes are described as they occur. This implies that the fatigue life, which is currently only a number of cycles for a given load, becomes a damage propagation life of individual damage mechanics. This further implies that individual damage mechanisms should be described using linear elastic fracture mechanics (LEFM), with a necessary adaptation for potential plasticity effects (analogue to the metallic approach to crack closure). Similarly, this means that the resistance of the material to damage growth (interlaminar – delamination, intralaminar – matrix cracking) should be experimentally determined to provide the input in damage growth mechanistic descriptions. In other words, similarly to crack growth resistance curves determined for metallic sheet materials (Paris curves), where growth rates are plotted versus an LEFM parameter (ΔK), resistance curves must be obtained for delamination and matrix cracking, plotted against a relevant LEFM parameter. For delamination resistance, it has been proven accurate to describe the growth rate versus the SERR, experimentally characterized with ply-interrupt specimens [10]. Once the resistance data is available for both mode I and mode II, both transverse ply crack growth and splitting can be described, and delamination growth under shear and peel. For deflection of transverse ply cracks into delamination, criteria can be used that relate the offered energy for both modes to the critical energy of both.

Fig. 6: The various matrix cracking modes: transverse ply cracking (mode I), splitting (mode II), cracking in plies under 45°

This may lead to under- or overestimation of the fatigue response, depending on whether splitting occurs and whether it redistributes the local peak stresses to a larger area. However, from a physical point of view, splitting does not differ that much from transverse ply cracking. Where splitting is predominantly driven by shear (mode II), transverse ply cracks are driven by the tensile mode (mode I). The damage types in both cases remains intralaminar, i.e. cracks along but in-between the fibres. One should note here that the matrix cracks that occur in the ±45° plies are driven by the combination of the two modes, as illustrated in Fig. 6. In this respect, the proposed mechanistic approach will ease the evaluation. Rans et al. [9] demonstrated that the empirical relations often determined based on mode I, II and several mixed modes are not necessary. Once the modes I and II are available and properly defined against the strain energy release rate (SERR), the mixedmode cracking or delamination growth can be calculated theoretically by substituting these two individual modes (see Fig. 7).

Implication of the damage-tolerance approach
The advantage of the generic damage-growth descriptive approach is that it allows assessing damage growth from existing or impact damage in a damage-tolerance evaluation in an identical way. Rather than applying two different approaches to the same structure, a single generic approach can thus be developed for strength evaluation. Even if a no-growth principle is preferred for structural design, the mechanistic approach to growth can be used to determine the theoretical growth over the specified design service goal. By doing so, the change of operational load spectra, or life extension after the fact, can still be evaluated with this approach. In fact, this approach specifies the no-growth concept more precisely into a limited-growth concept. The calculated growth may be so limited that macroscopic observation will not reveal the extension of damage, as it remains too small. However, it would give more insight into the concept, rather than failing to determine whether any damage extension did occur. This has been illustrated for FMLs with the case where interlaminar doubler run-out specimens were fatigue tested for 180 kcycles with no delamination reported. Analysis of No74 July 2012 /

Fig. 7: Pure mode I and II delamination growth data for glass/epoxy laminates with corresponding Paris relation constants (a) and mixed-mode data with corresponding predictions using superposition of modes I and II contributions to growth (b) [9]

The reason why most studies were not able to do so is based on the improper formulation of the SERR [9]. The advantage is that mode I and II tests for intralaminar matrix cracking can be defined, whereas a more complex end-notch flexure (ENF) test for this case is no longer required. Knowing the influence the resin volume in-between

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JEC COMPOSITES MAGAZINE - Issue #74 - July 2012

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #74 - July 2012