Issue 78

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

(a) LVDT1 to measure deflection

(b) LVDT2 to measure CMOD

Figure 6: Measuring deflection and CMOD during test.

Figure 7: Test setup for beams.

Fracture energy was determined using test results in accordance with Griffith’s theory. This involved calculating the difference in area between the ascending portion of the P- δ curve leading up to the crack initiation in the matrix-cracked beam and the area of the corresponding uncracked (smooth) beam (dW), as illustrated in Fig. 8. This value is then divided by the area of the two surfaces of the pre-existing matrix crack (dA = 2 × a × b). From this, the fracture energy ( Δ G = dW/dA) can be calculated, which then allows for the determination of fracture toughness (K IC = √Δ G ), where E represents the modulus of elasticity (beam elastic stiffness). The modulus of elasticity (E), (beam elastic stiffness) was not measured by a dedicated compression-cylinder test (e.g., ASTM C469), but was instead back-calculated from the initial linear-elastic slope of the measured load–midspan-deflection curve of each smooth (uncracked) reference beam, using classical elastic beam theory for the corresponding three-point bending configuration (E = k·L 3 /(48·I) type relation, where k is the measured initial elastic stiffness in kN/mm and I is the second moment of area of the gross, or transformed, cross-section, as appropriate for the plain-FRC and RC/RC-FRC beams, respectively.

Figure 8: Schematic Diagram for Matrix Crack Approach Fracture Energy Calculations.

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