Issue 78

M. Adel et.al, Frattura ed Integrità Strutturale, 78 (2026) 168-185; DOI: 10.3221/IGF-ESIS.78.10

(A) (B) Figure 16: Effect of a/d on the behavior of MC and TTC specimens; deflection measurements were limited to a maximum of 13 mm. Fracture toughness response of MC and TTC The fracture energy was calculated from the experimental test results based on Griffith’s energy-based criterion [1]. The methodology involved calculating the differential energy absorption by subtracting the ascending region of the load displacement response up to crack initiation of the matrix-cracked specimen against the corresponding energy area of the uncracked reference specimen (dW). The energy difference was then normalized by dividing by the total crack surface area (dA = 2×a×b, where a is the crack length and b is the specimen breadth). This calculation gave the fracture energy parameter ( Δ G=dW/dA). Then, the Mode I critical stress intensity factor (K IC ) was computed from the value of fracture energy using the relation: K IC = √Δ GE, where E is the elastic modulus according to the load-deflection relation for each specimen. The computational approach is based on classical principles of fracture mechanics and predicts the Mode I stress intensity parameter from the energy release rate of the cracked region and the rigidity properties of the material [24]. The complex stress field and material deterioration in the crack tip vicinity are represented by a single quantifiable parameter, the critical stress intensity factor. Only the macroscopic strain and stress components are considered in standard fracture mechanics models, such as the K IC approach. Alternative damage characterization models, such as microplane-based formulations, consider material responses at discrete material orientations and microstructural domains. The application of such advanced approaches enables a more accurate representation of the heterogeneous and anisotropic nature of damage evolution and material softening in brittle materials, such as plain and fiber-reinforced concrete. Nevertheless, such advanced models necessitate enhancement to adequately represent the influence of steel and fiber reinforcement inclusions within concrete members [25]. beam code Crack energy absorption, dW (N.mm) Energy release rate, Δ G (N/mm) Stress intensity factor, K IC (MPa √ mm) MC-RC-FRC [0.25] 16769.5 0.745 90.62 MC-RC-FRC [0.5]

43618.7 7304.8 35794.8 14128.8 32076.4 5704.1 2809.4

0.969 0.324 0.795 0.627 0.712 0.253 0.062

103.34 56.18 87.94 78.13 83.24 64.86 32.19

TTC-RC [0.25] TTC-RC [0.5]

TTC-RC-FRC [0.25] TTC-RC-FRC [0.5] MC-FRC [0.25]

MC-FRC [0.5]

. for cracked beams IC of fracture energy and K Experimental results Table 7:

It is noted that the MC-NC [0.25] and MC-FRC [0.5] rows reported in Tab. 7 differ simultaneously in both fiber content and notch-depth ratio; the corresponding stress-intensity values are reported for completeness but are not used to draw a direct quantitative comparison in the discussion that follows. Quantitative comparisons of K I C with respect to a/d are instead confined to same-series pairs, i.e., TTC-RC-FRC [0.25] versus TTC-RC-FRC [0.5], and TTC-RC [0.25] versus TTC RC [0.5], consistent with the comparison scope defined in the experimental work section

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