PSI - Issue 72

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

542

nondimensional units into the physical (SI) units could be performed analogously to traditional MD (e.g., Mastilovic (2022), Allen et al (1987)). In discrete fracture modeling of computational mechanics of discontinua, disorder can be explicitly incorporated. The impact of disorder on fracture behavior and properties has been extensively discussed by researchers for decades, e.g. Krajcinovic (1996), Mastilovic (2008), Alava et al. (2006). Alava et al. (2006) note neatly that “the influence of randomness on fracture can have many disguises.” Although not universally applicable, it is commonly observed that the Weibull distribution fits experimental data well under conditions of weak disorder, whereas strong disorder tends to result in a lognormal strength distribution. Ordered materials, such as crystalline metals, typically feature well-defined slip planes that promote localized deformation and more-or-less abrupt failure through mechanisms like cleavage or slip band propagation (e.g., Fig. 2(a)). In contrast, disordered materials—such as rocks, granular and amorphous materials—exhibit more heterogeneous stress distributions; this heterogeneity facilitates various meso scale dissipation mechanisms dispersed across numerous local sites, enabling progressive damage absorption rather than localized failure at a single weak point. Consequently, disordered systems generally exhibit greater damage tolerance due to enhanced stress redistribution, crack deflection, energy dissipation, and heterogeneous deformation (e.g., Figs. 2(b) and 4(b)). The current study employs PD-CT simulations primarily to capture the qualitative features of brittle cleavage fracture in ferritic steels within the DBT temperature region. Accordingly, the base case of the PD-CT model assumes very weak geometrical and structural disorder, defined by the parameter set ( λ r , λ k , λ ε ) = (0.98, 0.98, 0.98). This scenario is deemed relevant as it qualitatively represents a brittle, damage-intolerant system within the model’s limitations. For comparison, a damage-tolerant quasibrittle case—defined by ( λ r , λ k , λ ε ) = (0.02, 0.9, 2/3)—is also included, albeit in a limited manner, as it has been detailed elsewhere [9]. Since the rupture of interparticle bonds is the only dissipative mechanism included in the present model, the bond parameters define the damage energy, E D 2 2 c 2 0 / kr    (summation over all ruptured bonds)—tracked throughout simulations—as the cohesive energy released in the course of the macrocrack propagation. 3. Results and Discussions This section presents a selection of PD-CT simulation results, focusing primarily on the weak-disorder (brittle) system, which is the main subject of this study. Damage propagation arises from the progressive nucleation of microcracks within the fracture process zone (FPZ) and their coalescence, leading to a localized, abrupt fracture. Snapshots illustrating this process for two levels of quenched disorder are shown in Fig. 2.

Fig.2. The PD-CT configurations at the onset of the macro-fracture (directed percolation): (a) the weak-disorder (brittle) system, and (b) the strong-disorder (damage-tolerant, quasibrittle). These snapshots vividly illustrate a stress-driven dilution process in which only a single component of the compliance tensor becomes singular at the percolation threshold, Krajcinovic (1996). Specifically, Fig. 2(a) depicts PD-CT configurations of the weak-disorder (brittle) system upon macro-fracture while Fig. 2(b) shows the strong-disorder (damage-tolerant, quasibrittle) system. Although some diffuse damage occurs in both cases, Mastilovic (2025), the fracture path in the weak-disorder system is not wandering so much. Importantly, the highly localized, flat fracture observed in Fig. 2(a) is characteristic of quasistatic uniaxial tension in weakly disordered, damage-intolerant brittle materials—such as the brittle cleavage fracture typical of ferritic steels.