PSI - Issue 33

Michal Vyhlídal et al. / Procedia Structural Integrity 33 (2021) 966–981 Vyhlídal et al./ Structural Integrity Procedia 00 ( 2019) 000 – 000

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The measured F – d diagrams were used to estimate values for the maximal force F max , Young’s modulus of elasticity E , specific fracture energy G F , fracture toughness K Ic and effective fracture toughness K Ic,e . Young’s modulus of elasticity E was estimated from the first, almost linear part of these diagrams – see Karihaloo (1995). Specific fracture energy G F was calculated using the work-of-fracture method. It represents the energy necessary for the creation of a unit area of a crack (RILEM, 1985). Fracture toughness K Ic was estimated from F max according to Karihaloo (1995). It represents a linear elastic brittle material's resistance to crack propagation. In contrast, the effective fracture toughness K Ic,e was determined based on the Effective Crack Model (Karihaloo, 1995), in which the difference between the initial tangent stiffness and the secant stiffness of the specimen at peak load F max is considered. The determined mechanical fracture parameters can be seen in Table 4.

Table 4. Mechanical fracture parameters (Vyhlídal et al., 2019 ).

F max [kN] 0.53 0.79 0.83 0.83

E [GPa]

G F [J∙m – 2 ]

K Ic [MPa∙m 1/2 ]

K Ic,e [MPa∙m 1/2 ]

Inclusion material

Amphibolite

37.7 42.1 46.5 39.8

30.5 42.0 42.4 57.7

0.295 0.443 0.462 0.462

0.40 0.74 0.67 0.97

Basalt Granite Marble

4.3. Nanoindentation measurements The results for E , H , CIT and J ( t ) were evaluated with regard to their dependence on distance from an inclusion. E , H exhibit a gradual increase with distance, defining a weaker ITZ around the rock inclusion in the region of 0 – 20  m. The region is characterized by a lower modulus and a lower hardness compared to the bulk for all specimens, as already detected in (Zacharda et al., 2018, see Table 5). Slightly lower E and H values among the specimens can be found for specimens with amphibolite inclusions. The CIT parameter in the ITZ around inclusions is always higher due to the higher creep encountered in this zone. The highest amount of creep and the highest CIT and J ( t ) are exhibited by the specimens with amphibolite inclusions, especially in the ITZ of these specimens. Microstructurally, the ITZ can be described as having a higher porosity around the aggregate (Scrivener et al., 2004). Consistently, the evolution of Young’s modulus and ha rdness has a negative correlation with porosity, while CIT and the amount of creep scales with porosity. To quantify the influence of micromechanical parameters measured by nanoindentation, the mean hardness ( H 50 ) and average creep compliance J 50 ( t ) values were calculated over an ITZ region of 50 µm, while the mean Young’s modulus values were calculated over ITZ regions of 20 µm ( E mic,20 ) and 50 µm ( E mic,50 ) due to the higher values of porosity in the first 20 µm of the ITZ ; see (Bourdette et al., 1995) or (Scrivener et al., 1987).

Table 5. Results of nanoindentation measurements (Zacharda et al., 2018).

E mic,20 [GPa]

E mic,50 [GPa]

H 50 [GPa]

J 50 (t) [GPa – 1 ]

Inclusion material

Amphibolite

23.2 32.8 34.2 34.4

25.8 36.1 37.9 34.5

0.75 1.32 2.12 1.33

0.188 0.053 0.045 0.063

Basalt Granite Marble

4.4. Microstructure of the ITZ In the following four figures, the micrographs display the hardened cement that adhered to the inclusions after the mechanical tests; the microstructures of the specimens with amphibolite, basalt and granite are very similar in