Precis of gap test results requiring reappraisal of line crack and phase-field models of fracture mechanics

Bazant Z. P. , Dönmez A. A. , Nguyen H. T.

ENGINEERING STRUCTURES, vol.250, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 250
  • Publication Date: 2022
  • Doi Number: 10.1016/j.engstruct.2021.113285
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Agricultural & Environmental Science Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Geobase, ICONDA Bibliographic, INSPEC, Metadex, DIALNET, Civil Engineering Abstracts
  • Keywords: Fracture mechanics, Crack-parallel stresses, T-stress, Cohesive crack model, Crack band model, Nonlocal models, Material characteristic length, Fracture testing, Concrete, Quasibrittle behavior, Fracture process zone, XFEM, Phase-field models, Yielding zone, MICROPLANE MODEL, TRIAXIALITY PARAMETER, PLASTIC ZONE, PLANE-STRAIN, SIZE, CONCRETE, TIP, ELEMENT, SHEAR, BAND
  • Istanbul Technical University Affiliated: Yes


This paper presents a brief review of the recent advances in fracture mechanics at Northwestern University and Istanbul Technical University, prompted by the recent discovery of the gap test-a test that makes it easy and unambiguous to determine the effects of crack-parallel stresses on the mode-I fracture energy and, in consequence, on the nominal strength of structures of different sizes (aka, the size effect). The standard fracture specimens cannot reveal these effects since they have zero or negligible crack-parallel stresses. In addition, these effects cannot be reproduced by the standard, widely used, fracture models including the linear elastic fracture mechanics (LEFM), the cohesive crack model (CCM), as well as the popular computational models such as the extended finite element (XFEM) and the phase-field models (PFM). Therefore, it will be necessary to adopt fracture models that can reflect the tensorial damage behavior in the fracture process zone (FPZ), which is governed by at least two characteristic lengths, one for the FPZ length and one for the FPZ width. The modeling of elasto-plastic metals is even more complicated since the FPZ of micrometer-scale width is surrounded by a millimeter-scale plastic-hardening (yielding) zone. This role of the yielding zone has been understood well since the 1980s except for the scaling laws which are helpful for determining the effect of crack-parallel stresses more accurately. As a general conclusion, the line crack and phase field models cannot be used for practical problems with significant crack-parallel stress components (sigma(xx),sigma(zz),sigma(xz)). However, thanks to the finite width of its fracture front, the crack band model can be used, provided that its tensorial damage law is realistic. A new challenge for the nonlocal and gradient models is that they, too, will need to distinguish two independent material characteristic lengths, one for the direction of damage band and one transverse to it.