PSI - Issue 72

Sreten Mastilovic / Procedia Structural Integrity 72 (2025) 538–546

544

In the case of standard CT loading using pins (ASTM E1921-22a (2022)), it can be argued that the observed sequential fracture naturally results from bending of the ligament zone. It is evident that stress state significantly influences failure modes (e.g., Krajcinovic (1996), Christensen (2013)). As indicated by Fig. 3(a), due to stress concentration, the neutral axis initially lies near gage C, while the region at gage D experiences compression. To assess how this loading condition—or stress state more broadly—affects these qualitative results, Mastilovic [9] applied a longitudinal tensile load uniformly across the specimen’s top and bottom edges (see Fig. 4 shown latter). This simulation is reproduced here more systematically using the same setup as in Fig. 1 with and without the loading pins. The motivation is that pure longitudinal, uniformly-applied tension subjects the CT ligament to an opening mode only. The σ22 stress histories in Fig. 3(c) reveal that, although global failure occurs much more abruptly under this loading compared to the pin-loading CT case (Fig. 1(a))—as evidenced by fracture displacements and dynamic bond rupture progression in Fig. 3(d)—the sequential failure pattern remains evident, even in this more brittle loading scenario. The weakly disordered model (λr, λk, λε) = (0.98, 0.98, 0.98) exhibits typical brittle σ-ε behavior, marked by abrupt crack propagation along a correlated front. This fracture process progresses sequentially through localized bond failures, ultimately leading to catastrophic global failure of the system. That avalanche-like final rupture is highlighted by virtually simultaneous rupture of 113 bonds in Fig. 3(d), with only 80 bonds broken cumulatively prior to that, indicating a more sudden failure than that seen in Fig. 3(b). This confirms the expected increased brittleness under uniform tensile loading (Fig. 4) compared to standard CT loading via pins (Fig. 1). However, even in the most brittle case, failure is preceded by a small but finite accumulation of localized damage manifested as directed percolation, Krajcinovic (1996).

Fig.4. The alternative setup for the uniform tensile loading via rigid busbars at the top and bottom edges of the pre-cracked specimen: (a) the initial stage of crack propagation for the weakly disordered system, and (b) the damage pattern corresponding to the strongly disordered (damage tolerant) system. (Note: The short red lines represent nucleated microcracks associated with ruptured bonds. While their positions and orientations accurately reflect simulation results, their lengths have been uniformly scaled to an arbitrary value of 3·lch for enhanced visibility.) As is typical for damage-tolerant materials, the PD results in Fig. 4(b) show that while microcrack nucleation is mainly confined to the advancing FPZ, appreciable bond ruptures occur also outside this zone—roughly within the triangular damage-affected zone emanating from the crack tip as indicated by dashed yellow lines. The majority of these microcracks—manifested as distributed damage and not part of the cluster associated with global specimen failure—would become passive upon load reversal to longitudinal compression. All these observations challenge the assumptions underlying WL theory and extreme value statistics, which treat the 3-D solid volume as a chain of elements failing when the first link breaks. This concept applies realistically only to one-dimensional components like proper chains, where stress redistribution after micro-ruptures is minimal or nonexistent. Real 3-D structures cannot be so easily represented by a serial connection of independent random elements. This aligns with longstanding knowledge that quasi-brittle materials do not fail instantaneously but accumulate damage before brittle failure occurs, Alava et al. (2006).