Gap Test of Crack-Parallel Stress Effect on Quasibrittle Fracture and Its Consequences

In all the widely used fracture test specimens, the normal stress parallel to the plane of the notch and growing crack is negligible, and so its effect cannot get revealed. However, this stress can double the fracture energy or reduce it to zero. Why hasn't this been detected earlier?--Because the crack-parallel stress in all standard fracture specimens is negligible and is anyway unaccountable by line-crack models. These results were shown via a new type of experiment consisting of a simple modification of the standard three-point-bend test, called gap test. We develop a surprisingly simple test of notched beams with three crucial features: (i) plastic support pads with near-perfect plastic yielding introduce first notch-parallel compression $\sig_{xx}$; (ii) rigid supports are installed with gaps and engage only after $\sig_{xx}$ acts, which (iii) delivers a support system that switches from one statically determinate configuration to another, thus allowing unambiguous interpretation. Thanks to this setup, the test beam transits from one statically determinate loading configuration to another, making evaluation unambiguous. For concrete, a moderate crack-parallel compressive stress was shown to double the Mode I (opening) fracture energy and to reduce it to almost zero on approach to the compression strength limit. Further, it was demonstrated that the fracture of quasi-brittle materials must be characterized tensorially. The experimental results can be matched by crack band finite element analysis with microplane model M7 as a tensorial damage constitutive law. Here we present further detailed aspects of this experiment, and discuss the experimental approach more broadly. The numerical crack band microplane simulations of the effects of both in-plane and out-of-plane crack parallel stresses are then extended to high-strength and fiber-reinforced concretes, and to shale. These results have broad implications for all other quasi-brittle materials, including various rocks, stiff soils, coarse-grained ceramics, fiber composites, sea ice, wood, stiff foams, printed materials, bone and many bio-materials. Except when the crack-parallel stress is a priori known to be negligible, the line crack models with constant G_f, such as the linear elastic fracture mechanics, cohesive crack model or XFEM, are shown to be unusable for quasi-brittle materials, although, as an approximation ignoring stress history, the crack-parallel stress effect on fracture energy and characteristic fracture process zone length may be introduced parametrically, by a simple formula. Finally, we show that the standard tensorial strength models such as Drucker-Prager, Mohr-Coulomb and the commercial software models cannot reproduce these effects at all.