Crack-parallel stress effect on fracture energy of plastic hardening polycrystalline metal identified from gap test scaling

Dönmez A. A., Nguyen H. T., Xu H., Bažant Z. P.

Journal of the Mechanics and Physics of Solids, vol.173, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 173
  • Publication Date: 2023
  • Doi Number: 10.1016/j.jmps.2023.105222
  • Journal Name: Journal of the Mechanics and Physics of Solids
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Ductile fracture, Aluminum, Fracture experiments, Structural strength scaling, Size effect, Scaling laws, Fracture energy dissipation, J-integral, Material toughness, Asymptotic matching
  • Istanbul Technical University Affiliated: Yes


The gap test is a new type of fracture test developed in 2020, in which the end supports of a notched beam are installed with gaps that close only after the elasto-plastic pads next to notch introduce a desired constant crack-parallel compression σxx (also called the T-stress). The test uses the size effect method to identify how such a compression alters the material fracture energy, Gf, and the characteristic size cf of the fracture process zone (FPZ). In 2020, experiments showed that a moderate σxx doubled the Gf of a quasibrittle material (concrete) and a high σxx reduced its Gf to almost zero. A preliminary study by Nguyen et al. (2021) showed that the gap test can be extended to plastic-hardening polycrystalline metals. A generalized scaling law with an intermediate asymptote for large-scale yielding in small structures was derived, and limited tests of aluminum alloy showed its applicability. In this study, geometrically scaled gap tests of notched three-point bend fracture specimens of aluminum are conducted at three different levels of σxx. An extended structural strength scaling law that captures the transition from the micrometer-scale FPZ through millimeter-scale yielding zone (YZ) to large-scale structures which follow linear elastic fracture mechanics (LEFM) is derived and then applied to analyze the effect of σxx. Presented here are the gap tests of aluminum alloy, in which three different levels of σxx are applied to scaled notched four-point-bend beams of depths D = 12, 24, 48 and 96 mm. Using an extended size effect law for plastic-hardening metals, it is found that, at crack-parallel stress σxx≈−40% of the yield strength, the critical J-integral value gets roughly quadrupled, not only because of the well-known enlargement of the hardening YZ whose width is of millimeter scale, but also because of the increase of the FPZ width of micrometer scale. These results can be reproduced neither by line crack models, including the LEFM, cohesive crack and phase-field models, nor by peridynamic and various nonlocal models that ignore the tensorial nature of the material stress at the crack tip. The crack band models, being able to represent an FPZ of finite width and a YZ whose size evolves depending on σxx, can capture the effect of crack-parallel stresses provided that a realistic 3D tensorial damage constitutive model is used. Here, Bai–Wierzbicki's model is shown to capture the σxx effect on the Gf and Jcr qualitatively.