PSI - Issue 77

P. Santos et al. / Procedia Structural Integrity 77 (2026) 339–347

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P. Santos et al. / Structural Integrity Procedia 00 (2025) 000 – 000

The load - CMOD curves recorded from the tests are plotted in Fig. 2a, with the load expressed in terms of the remote stress  ∞ (Fig. 1b). The relative pre-crack sizes ã 0 are included in the plot and the differences between each of them are reflected by the initial slopes of the curves. Fig. 2b complements Fig. 2a, showing the crack sizes found in each test from the unloading slopes as a function of CMOD. According to the curves of the two figures, the cracks do not show significant signs of growth until the load drop becomes clear, despite the highly prolonged load maxima over CMOD. This suggests that some unstable local deformation process is taking place at the crack front, following which crack growth onset occurs.

Fig. 2. Fracture tests of SENT specimens: a) Load – CMOD data; b) Crack sizes - CMOD records; c) J-integral registries vs CMOD values up to maximum loads. Fig. 2c shows the J-integral values measured up to the onset of load drop in the five fracture tests by applying the BS-8571 (2018) standardized method. Thus, the dependency of J-integral with CMOD is linear after a short parabolic onset. This is predicted by linear elastic fracture mechanics in the small-scale yielding (SSY) regime, since in this regime the CMOD and the J integral are respectively proportional to load and to the square. The average of the five J-integral values corresponding to the onset of load drop and crack propagation is 93 N/mm. 3. Application of the cohesive model to SENT specimen The cohesive crack was introduced by Bilby et al. (1963) to model the nonlinearities that occur at the crack front as a crack extension capable of transmitting a uniform tensile stress Y, between its two faces, so that the singularity of the stress field vanishes because of the stress intensity factor due to the extended crack, the applied load and the cohesive stress Y becomes zero. This condition determines the size of the cohesive crack extension. In the subsequent evolution of the model provided by Jemblie et al., (2017), the cohesive resistance Y is no longer a material constant and is replaced by a material law, which determines a one-to-one relationship between the separation acquired by each pair of points of the cohesive crack coming from the same initial material point, and the tensile stresses of equal value and opposed sign that they transmit to each other. The Green function of Chell (1976) allows the cohesive model to be particularized for the SENT specimen for obtaining the theoretical curves load, J-integral vs CMOD as function of the cohesive resistance Y. The Green function G(x, a) is the stress intensity factor per unit load (K p /p) for a SENT specimen with a crack depth a, when its faces are compressed by concentrated