Effect of stress singularities on scaling of quasibrittle fracture

Jia Liang Le, Mathieu Piechout, Roberto Ballarini

Research output: Contribution to conferencePaperpeer-review


Modern engineering structures are often made of quasibrittle materials, which are brittle and heterogeneous. Typical examples include concrete, fiber composites, woven composites, tough ceramics, and nano-composites. The salient feature of quasibrittle structures is that the size of the fracture process zone is not negligible compared to the structure size, which leads to an intricate size effect on the structural strength. The current understanding of scaling of quasibrittle fracture is limited to structures with either strong stress singularities or zero stress singularities. Nevertheless, many engineering structures are designed to have complex geometries, which could cause weak stress singularities. This paper investigates the effect of stress singularities on the scaling of quasibrittle fracture both analytically and numerically. The theoretical analysis is derived from a generalized weakest link model where the energetic scaling of quasibrittle fracture is incorporated into the classical finite weakest link model. The proposed model yields a general scaling equation, which captures the transition from the energetic scaling to statistical scaling as the stress singularity gets weaker. The proposed analytical model is then verified by a numerical study on the fracture of concrete beams with a V-notch under three-point bending, where a wide range of notch angles representing different orders of stress singularities is considered.

Original languageEnglish (US)
Number of pages9
StatePublished - 2013
Event13th International Conference on Fracture 2013, ICF 2013 - Beijing, China
Duration: Jun 16 2013Jun 21 2013


Other13th International Conference on Fracture 2013, ICF 2013


  • Deterministic analysis
  • Finite weakest link model
  • Quasibrittle materials
  • Size effect


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