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Abstract The recently conceived gap test and its simulation revealed that the fracture energy Gf (or Kc, Jcr) of concrete, plastic-hardening metals, composites, and probably most materials can change by ±100%, depending on the crack-parallel stresses σxx, σzz, and their history. Therefore, one must consider not only a finite length but also a finite width of the fracture process zone, along with its tensorial damage behavior. The data from this test, along with ten other classical tests important for fracture problems (nine on concrete, one on sandstone), are optimally fitted to evaluate the performance of the state-of-art phase-field, peridynamic, and crack band models. Thanks to its realistic boundary and crack-face conditions as well as its tensorial nature, the crack band model, combined with the microplane damage constitutive law in its latest version M7, is found to fit all data well. On the contrary, the phase-field models perform poorly. Peridynamic models (both bond based and state based) perform even worse. The recent correction in the bond-associated deformation gradient helps to improve the predictions in some experiments, but not all. This confirms the previous strictly theoretical critique (JAM 2016), which showed that peridynamics of all kinds suffers from several conceptual faults: (1) It implies a lattice microstructure; (2) its particle–skipping interactions are a fiction; (4) it ignores shear-resisted particle rotations (which are what lends the lattice discrete particle model (LDPM) its superior performance); (3) its representation of the boundaries, especially the crack and fracture process zone faces, is physically unrealistic; and (5) it cannot reproduce the transitional size effect—a quintessential characteristic of quasibrittleness. The misleading practice of “verifying” a model with only one or two simple tests matchable by many different models, or showcasing an ad hoc improvement for one type of test while ignoring misfits of others, is pointed out. In closing, the ubiquity of crack-parallel stresses in practical problems of concrete, shale, fiber composites, plastic-hardening metals, and materials on submicrometer scale is emphasized. 

Abstract In the standard fracture test specimens, the crack-parallel normal stress is negligible. However, its effect can be strong, as revealed by a new type of experiment, briefly named the gap test. It consists of a simple modification of the standard three-point-bend test whose main idea is to use plastic pads with a near-perfect yield plateau to generate a constant crack-parallel compression and install the end supports with a gap that closes only when the pads yield. This way, the test beam transits from one statically determinate loading configuration to another, making evaluation unambiguous. For concrete, the gap test showed that moderate crack-parallel compressive stress can increase up to 1.8 times the Mode I (opening) fracture energy of concrete, and reduce it to almost zero on approach to the compressive stress limit. To model it, the fracture process zone must be characterized tensorially. We use computer simulations with crack-band microplane model, considering both in-plane and out-of-plane crack-parallel stresses for plain and fiber-reinforced concretes, and anisotropic shale. The results have broad implications for all quasibrittle materials, including shale, fiber composites, coarse ceramics, sea ice, foams, and fone. Except for negligible crack-parallel stress, the line crack models are shown to be inapplicable. Nevertheless, as an approximation ignoring stress tensor history, the crack-parallel stress effect may be introduced parametrically, by a formula. Finally we show that the standard tensorial strength models such as Drucker–Prager cannot reproduce these effects realistically.