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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crystals structures. Tensile data on nanoscale metallic multilayers (Han et. al., 2009) show a low work-hardening rate after the initial 1-2% plastic strain. Following this treatment, the initial value chosen for  is 2%, which is then used to calculate the yield strength of Cu/W multilayers as per Eq. 5. The values of the parameters used are as follows: M=3.06, � �� � ���� GPa, � � � ��� GPa,  =0.343, b = 0.2556 nm, α=0.2 (compact core) and 1 (spread core), f =3 Jm -2 and  = 70.5º. Table 1 shows the yield strength values (obtained using Eq. 5) for the extreme values of core cut off and the experimentally measured yield strength values, � ��� . For the first case, α=1, σ ��� values increase continuously as  decreases from 60 to 10. Thereby, σ ��� values for  =60,  =30 and  =10 are 2.13, 2.73 and 4.34 GPa, respectively. These values are in good agreement with the � ��� values for  =60 and  =30. However, in the case of  =10, the σ ��� value is extremely high and it is not compatible with the � ��� value obtained above. In contrast, for the second case, α = 0.2, � ��� values continuously grow as  is reduced, therefore cannot be compared with the values obtained via direct measurement. These values are 1.81, 2.08 and 2.38 GPa for  =60,  =30 and  =10, respectively. However, if the calculation of � ��� is repeated with an in-plane plastic strain,  , value of 1%, it can be seen that � ��� values grow from 1.18 GPa, for  =60, to 1.76 GPa, for  =10. It is evident that for the highest and intermediate values of  , the correct core cut-off value used for the calculation of the yield strength through confined layer slip system has to be α=1. However, for the lowest  , its � ��� value is only compatible with a σ ��� value obtained from of a core cut off of α=0.2 and an in-plane plastic strain of  =1%. In any case, for the three values of  studied, � ��� values can be explained only through the CLS model. Therefore, the saturation value reached in the yield strength for  =30, and its subsequent decrease for  =10, is not a consequence of a change in the strain mechanism from CLS to IBS model, such as others NMMs have shown (Lai et. al., 2007; Zhang et. al., 2012). Nevertheless, this decrease in the yield strength value shows a change in the trend of the crack propagation, and therefore in its fracture toughness behaviour. Table 1.Values of true Young’s modulus, E f , and Berkovich hardness H f , as well yield strength values (obtained using Eq. 7) for the extreme values of core cut-off and the experimentally measured yield strength values, � ��� , obtained for the three periodicities studied.  (nm) � � (GPa) � � (GPa) � ��� (GPa) � ��� � � �  � �� (GPa) � ��� � � �� �  � �� (GPa) � ��� � � �� �  � �� (GPa) 4.3 Nano-repetitive-impact testing As has been revealed in ours previous works, depending on the indenter geometry, the ductility of the material and the magnitude of the initial  t , the maximum strength may be reached at the first impact. From the first impact, which is actually a high strain rate indentation, it is possible to produce a notch with the same shape as the cube-corner indenter, whose purpose is to concentrate the maximum possible stress around the impact point just underneath the apex of this notch. Therefore, if initial  t is high enough to match the material yield strength, and the capacity of the material for the accumulation of plastic deformation is negligible, the hypothetical crack (nucleated in the first impact) will be propagated from the apex of the notch throughout successive impacts. From the graphical point of view, this crack propagation is equivalent to the opening of the material surface around the indenter, as the successive increase in the impact depth (accumulated with each new impact) is similar to the length travelled by the crack. This would be reflected in big decreases in the initial growth rate of the depth, �� , along the curve of the accumulative impact depth, h, as a function of the impacts number (Fig. 5). It is important to remark that all h values shown in this figure have been obtained by subtracting the depth reached at the first impact, h 1 , since it is actually a normal indentation done at high strain rate. During this indentation, a cube-corner shape notch is created, and the plastic strain (200 %) is accumulated in a small volume underneath the apex of the footprint. The abrupt growth in the impact depth reached between the first and the second impact suggests that the crack is nucleated, progressing quickly with the successive impacts. This is attributed as a continuous opening of the surface around the cube-corner indenter. After a certain 10 30 60 5.24 7.27 6.74 166 198 183 1.93 2.70 2.48 4.34 2.73 2.13 2.38 2.08 1.81 1.76 --- 1.18