PSI - Issue 72

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

539

1. Introduction Ferritic steels in the ductile-brittle transition (DBT) region exhibit significant variability in fracture toughness even under nominally identical experimental conditions. This randomness is mainly due to aleatory uncertainty, as the problem has been extensively analyzed theoretically (e.g., Ruggieri et al. (2024), Djordjevic et al. (2023), and references therein). A critical micro-mechanical aspect of brittle cleavage involves Griffith crack nucleation triggered by the activation of the dominant defect

. const

(1)

a c c  

randomly located ahead of the crack tip, causing an unstable damage propagation leading to an abrupt global failure. InEq. (1), σ c is the critical (fracture) stress, a c - the critical half-length of the elliptic microcrack (formed, e.g., by the fracture of the largest carbide particle at the crack front), while the constant combines the elastic properties and the rate of work expanded per unit area of the crack.

Nomenclature CT compact tension

DBT ductile-brittle transition FPZ fracture process zone MD molecular dynamics PD particle dynamics WL weakest link

The particle dynamics (PD) method is employed to simulate a standard fracture toughness test on compact tension (CT) specimens of (quasi)brittle materials under quasistatic loading, incorporating different levels of quenched disorder. The primary objective is to evaluate the stress field at the crack tip and examine how it may vary with specimen size. Qualitative results from this established method of computational mechanics of discontinua, Mastilovic (2022) offer valuable insights that can support ongoing modeling efforts using a data-driven, scaling based framework grounded in weakest-link (WL) theory, extreme value theory, and Weibull statistics. 2. Simulation Methodology PD models are among several discrete approaches aimed at bridging the gap between microscopic and macroscopic spatial scales. They can be viewed as engineering adaptations of molecular dynamics (MD) applied at an arbitrarily chosen, coarser spatial scale—often referred to as quasi-MD, Mastilovic (2022), Krajcinovic (1996). The key difference between PD and MD lies in this coarser scale and the resulting phenomenological load-transfer rules (force-displacement relationships) that govern interparticle interactions. Aside from these differences, the simulation techniques used in PD closely follow those established in traditional MD methodologies (e.g., Allen et al. (1987)). In brief, the particle system consists of N “continuum particles”, Mastilovic (2022), each with mass m i and position r i ( i = 1,…, N ), randomly distributed in 2-D space following the topology of an underlying lattice specific to the material being modeled. (Hereafter, bold symbols represent vectors and tensors.) The known initial configuration establishes a reference state. In the absence of geometric disorder, this system is equivalent to plane-strain conditions [3]. The computational approach involves approximately solving a system of differential equations governing the particles’ motion

 r F 

) , ( 1,..., i N 

(2)

m

i i

i