PSI - Issue 2_A

E. Frutos et al. / Procedia Structural Integrity 2 (2016) 1391–1404 Author name / Structural Integrity Procedia 00 (2016) 000–000

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at maximum load, respectively. In Eq. (2),  and  i, and E f and E i denote the Poisson’s ratio and the Young’s modulus for the film and the indenter, respectively. E R refers to the reduced Young’s modulus of the specimen determined according to Oliver and Pharr procedure. Young’s modulus (E i ) and Poisson’s coefficient (  i ) of the diamond Berkovich tip are 1141 GPa and 0.07, respectively. Both hardness and Young’s modulus results for a given load correspond to average values of at least 10 experiments. The impact pendulum configuration of the Nanotest-Advantage was used for the cyclic impact testing solenoid connected to a timed relay was used to produce the repetitive impacts on the surface. A cube-corner diamond tip was accelerated from a distance, S, of 500 nm to the surface, producing an impact force, P, of 1 mN. The experiments were computer-controlled so that repetitive impacts occurred at the same position every 4 seconds over 300 seconds (75 impacts in total). The penetration depth was registered after every impact. Average values were obtained from at least 10 experiments performed in randomly selected areas on the surface of the coating. 3. Background and approaches The plastic region localized ahead of the tip of an existing defect, i.e. at the origin of the crack tip, has to be very small so as not to affect the overall load-deflection response of cracked samples. Only then is it possible to assume a linear elastic fracture mechanism, and therefore classical indentation models can be used to calculate fracture toughness values. Selection of the most appropriate expression for evaluating K C requires a proper knowledge of the crack morphology and its evolution with each new impact. If c/a  3.5, the crack profile corresponds to a half-penny type and, therefore, the Anstins model is the most suitable for calculating the fracture toughness by using the expression: ܭ ூ௖ ൌ   ோ ቀ ு ா ቁ ଵൗଶ ௖ ௉ యൗమ , (3) where P is the indentation load, c is the crack length, E is the Young’s reduced modulus, H is the hardness and   ோ is the calibration coefficient, which depends on the tip and crack geometries. For half-penny cracks and for a cube-corner indenter geometry, this parameter is 0.040. On the other hand, if 1.1  l/a  2.5 or c/a  3.5, the crack profile corresponds to the Palmqvist type, and therefore the Laugier model is the most suitable for calculating the fracture toughness from the expression: ܭ ூ௖ ൌ   ቀ ௔ ௟ ቁ ଵൗଶ ቀ ு ா ቁ ଶൗଷ ஼ ௉ యൗమ , (4) where a and l are the lengths related to the half of the diagonal and the crack length from the apex of the footprint, respectively, while   is a constant similar to   ோ , for which the most indicative value for cube-corner geometry is 0.057. 4. Results and discussion 4.1 Microstructure characterization Figure 1 shows scanning transmission electron microscopy high-angle annular dark field (STEM-HAADF) micrographs for  =60. Although the layering structure is well defined in all cases, the layers, which are initially flat close to the coating/silicon interface, quickly develop a wavy character from the 2 nd or 5 th layer from the substrate interface to the top of the surface, depending of the periodicity (  =10 and  =60, respectively). This morphology results in the formation of large folds similar to a valley in both layers. In the case of W layers, the presence of disorder areas and large cavities is more than evident inside of the folds. As  is reduced from 60 to 10, i.e., as the thickness of both layers is reduced, the Cu layers are no longer continuous. In fact, in some cases the successive W layers become interconnected. Furthermore, in the case of  =10, these valleys give rise to the formation of channels with a high