On the Size-Effect Landscape of Crack-Growth Initiation in the Presence of Stress Gradients

  • Latyshev, Andrey (University of Luxembourg)
  • Hale, Jack (University of Luxembourg)
  • Maurini, Corrado (Sorbonne Université)

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The reconciliation of stress- and toughness-based fracture criteria gives rise to the classical size-effect, with strength-controlled initiation arising for small defects and Griffith-type toughness-controlled initiation for large defects, both relative to a characteristic process length. In [2] this behaviour was reproduced for a uniformly loaded plate with central crack using a variational phase-field model of brittle fracture. However, many practical configurations impose macroscopic non-uniform stresses at the specimen scale, for which the classical size-effect framework is less firmly established, see e.g. [1]. In this work we examine the effect of macroscopic stress gradients on initiation and the resulting size-effect landscape through the case of a square plate with edge crack in the presence of a macroscopic tensile stress gradient. Our results show that the tensile stress gradient exerts a stabilising effect on nucleation and significantly alters the size-effect evident in the uniformly loaded problem. We identify a critical defect size that minimises the crack initiation load, separating small, unstable defects from large, stable ones, and further highlighting the important interplay between material and structural length scales in predicting crack initiation. This research was funded in whole, or in part, by the Luxembourg National Research Fund (FNR), grant reference PRIDE/21/16747448/MATHCODA. References [1] Tuan Hiep Pham, Jérôme Laverne, and Jean-Jacques Marigo. “Stress Gradient Effects on the Nucleation and Propagation of Cohesive Cracks”. In: Discrete and Continuous Dynamical Systems - S 9.2 (2016), pp. 557–584. ISSN: 1937-1632. DOI: 10.3934/dcdss.2016012. [2] E. Tanné et al. “Crack Nucleation in Variational Phase-Field Models of Brittle Fracture”. In: Journal of the Mechanics and Physics of Solids 110 (Jan. 1, 2018), pp. 80–99. ISSN: 0022-5096. DOI:10.1016/j.jmps.2017.09.006.