## 3 Illustration of the Proposed Approach: Results of Case Studies
### Fatigue Crack Growth Test
The load gating method was used to select the AE signals at the loads exceeding 0.95 of the peak load, and to remove the signals associated with crack closure on unloading. As a note, AE due to crack closure can be produced by several mechanisms such mechanisms as rubbing of the crack faces due to local compressive stresses from plastic deformation, friction between jagged crack edges and rubbing or breaking of wedged oxides [126; 127; 128; 129; 130]. AE induced by crack closure is dependent on many factors including materials properties, environment, and test frequency [86; 127]. The ductility of the material affects the roughness of the crack faces, and the susceptibility of a material to oxidation in a given environment will affect the presence of oxides in the crack region. Closure emissions are generally unwanted in the AE analysis of FCG [126], unless the crack closure phenomenon itself is of particular interest. Before discussing the AE findings of the present work, a brief excursion to the FCG related mechanisms would be in place. Acoustic emission from fatigue crack-related mechanisms has been studied experimentally for decades, and AE features specific to crack initiation, crack extension, and crack closure have been identified by many researchers on examples of various materials. Several empiric relations and qualitative explanations of the crack growth behaviour in its relation to AE have been developed, and some are described below. Fracture mechanisms associated with the opening of new surfaces and expansion of the plastic zone during crack extension produce elastic waves. The amplitude of the AE signal depends on the dynamics at the source [131; 132], and, in general, brittle fracture mechanisms produce higher amplitude signals than ductile ones [129; 133; 134; 135]. Brittle fracture mechanisms include intergranular and cleavage fracture. Ductile fracture mechanisms involve microvoid nucleation and coalescence, tearing, and shearing. [PERSON] [136] considered the elastic energy  
Figure 18: The source function plotted versus time (**a**) or loading force (**b**): the contributions from the heat dissipation and thermoelastic effect are distinguished, and the separated heat energy dissipation per cycle is shown in (**c**). conversions of a system during crack growth for characteristic ductile and brittle source events of equal magnitude. The difference in the AE signal amplitudes was explained by partitioning the released energy into three groups: energy of plastic deformation, surface energy or \"event\" energy associated with AE waves. The plastic deformation term captures the energy expended in creating the plastic zone through the dislocation generation and movement, while the surface energy refers to the disbonding of the single atomic layer to create the new surfaces. It was argued that due to a larger plastic zone and the increased surface energy due to a rougher crack surface, a lesser fraction of the released elastic energy is emitted as AE in the ductile fracture mode compared to brittle fracture of the same magnitude of the energy release at the source. For FCG, [PERSON] et al. (137,138) found a relation between the AE count rate \(\frac{dN_{AE}}{dN}\), and \(\Delta K\) in the form of the power law resembling the Paris-Erdogan FCG Equation (23) (see also (77,139,140), where the first model has been proposed to link the AE count rate with the stress intensity factor):  
\[\frac{dN_{AE}}{dN}=C_{AE}\Delta K^{n_{AE}} \tag{25}\]  
where \(C_{AE}\) is the empiric constant and the exponent \(n_{AE}\) is found to be related to the Paris exponent, \(m\), by the relation \(n_{AE}\approx m+2\) as proposed by [PERSON] et al. (129). It was suggested that both the energy released during crack extension, and the deformation and fracture related events within the plastic zone ahead of the crack, contribute to AE during FCG, see [PERSON] and [PERSON] (141,142), finding dislocation mechanisms, twin nucleation, and fracture of inclusions to be potent sources of AE in the plastic zone.