New perspective of fracture mechanics inspired by gap test with crack-parallel compression

Abstract

The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials’ fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. 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. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress–displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.

Conversion of explicit microplane model with boundaries to a constitutive subroutine for implicit finite element programs

“…(4) In the vectorial forms, it is easy to take into account the strain dependence of the boundary limits, while for the yield limits in the tensorial formulation with invariants it would be difficult, (5) The microplane model automatically predicts the effect of crack-parallel stress on the Mode I fracture energy, G f , which was recently demonstrated by a new kind of experiment-the "gap test." 41,42 Under high crack-parallel compression, G f of concrete can get doubled or reduced to almost zero. This phenomenon is caused by frictional dilatant slip on microcracks inclined to the crack direction and spiltting bands ahead of the crack tip.…”

“…Another, perhaps more important, cause is a high crack-parallel compression, which probably greatly reduces the Mode II fracture energy, as suggested by the gap tests. 41,42 Both causes come to play in the double-edge-notched specimen if the opposite loads are placed close to the notches, as in Figure 7(A). The crack will then run straight ahead in pure shear, Mode II, as demonstrated in the 1996's experiments of Bažant and Pfeiffer 64 (Figure 7).…”

“…The ability of capturing fracture under mixed-mode load and fracture in the last two examples is essential to represent the effect of crack-parallel stress xx . 41,42 This is because the triaxial state of the crack tip is appropriately captured by interaction among the stress components on microplanes. Thanks to this feature, complex phenomena such as friction interlock and dilatant expansion corresponding to different level of parallel stress can be appropriately quantified, which will be discussed next.…”

“…This is automatically captured by the microplanes but not by tensorial models based on invariants such as Mohr–Coulomb or Drucker–Prager. There is no need for nonassociated plasticity to describe dilatant frictional slip. Thanks to interactions among microplanes, M7 automatically exhibits nonassociated dilatancy observed in concrete, and does so without violating the dissipation inequality of thermodynamics. In the vectorial forms, it is easy to take into account the strain dependence of the boundary limits, while for the yield limits in the tensorial formulation with invariants it would be difficult, The microplane model automatically predicts the effect of crack‐parallel stress on the Mode I fracture energy, G f , which was recently demonstrated by a new kind of experiment—the “gap test.” 41,42 Under high crack‐parallel compression, G f of concrete can get doubled or reduced to almost zero. This phenomenon is caused by frictional dilatant slip on microcracks inclined to the crack direction and spiltting bands ahead of the crack tip.…”

“…The microplane model automatically predicts the effect of crack‐parallel stress on the Mode I fracture energy, G f , which was recently demonstrated by a new kind of experiment—the “gap test.” 41,42 Under high crack‐parallel compression, G f of concrete can get doubled or reduced to almost zero. This phenomenon is caused by frictional dilatant slip on microcracks inclined to the crack direction and spiltting bands ahead of the crack tip.…”