Although spectacular advances in hydraulic fracturing, also known as fracking, have taken place and many aspects are well understood by now, the topology, geometry, and evolution of the crack system remain an enigma and mechanicians wonder: Why fracking works? Fracture mechanics of individual fluid-pressurized cracks has been clarified but the vital problem of stability of interacting hydraulic cracks escaped attention. First, based on the known shale permeability, on the known percentage of gas extraction from shale stratum, and on two key features of the measured gas outflow which are (1) the time to peak flux and (2) the halftime of flux decay, it is shown that the crack spacing must be only about 0.1 m. Attainment of such a small crack spacing requires preventing localization in parallel crack systems. Therefore, attention is subsequently focused on the classical solutions of the critical states of localization instability in a system of cooling or shrinkage cracks. Formulated is a hydrothermal analogy which makes it possible to transfer these solutions to a system of hydraulic cracks. It is concluded that if the hydraulic pressure profile along the cracks can be made almost uniform, with a steep enough pressure drop at the front, the localization instability can be avoided. To achieve this kind of profile, which is essential for obtaining crack systems dense enough to allow gas escape from a significant portion of kerogen-filled nanopores, the pumping rate (corrected for the leak rate) must not be too high and must not be increased too fast. Furthermore, numerical solutions are presented to show that an idealized system of circular equidistant vertical cracks propagating from a horizontal borehole behaves similarly. It is pointed out that one useful role of the proppants, as well as the acids that promote creation of debris in the new cracks, is to partially help to limit crack closings and thus localization. To attain the crack spacing of only 0.1 m, one must imagine formation of hierarchical progressively refined crack systems. Compared to new cracks, the system of pre-existing uncemented natural cracks or joints is shown to be slightly more prone to localization and thus of little help in producing the fine crack spacing required. So, from fracture mechanics viewpoint, what makes fracking work?–the mitigation of fracture localization instabilities. This can also improve efficiency by fracturing more shale. Besides, it is environmentally beneficial, by reducing flowback per m3 of gas. So is the reduction of seismicity caused by dynamic fracture instabilities (which are more severe in underground CO2 sequestration).

Design of large composite structures requires understanding the scaling of their mechanical properties, an aspect often overlooked in the literature on composites.This contribution analyzes, experimentally and numerically, the intra-laminar size effect of textile composite structures. Test results of geometrically similar Single Edge Notched specimens made of [0 • ] 8 epoxy/carbon twill 2×2 laminates are reported. Results show that the nominal strength decreases with increasing specimen size and that the experimental data can be fitted well by Bažant's size effect law, allowing an accurate identification of the intra-laminar fracture energy of the material, G f .The importance of an accurate estimation of G f in situations where intra-laminar fracturing is the main energy dissipation mechanism is clarified by studying numerically its effect on crashworthiness of composite tubes. Simulations demonstrate that, for the analyzed geometry, a decrease of the fracture energy to 50% of the measured value corresponds to an almost 42% decrease in plateau crushing load. Further, assuming a vertical stress drop after the peak, a typical assumption of strength-based constitutive laws implemented in most commercial Finite Element codes, results in an strength underestimation of the order of 70%.The main conclusion of this study is that measuring accurately fracture energy and modeling correctly the fracturing behavior of textile composites, including their quasi-brittleness, is key. This can be accomplished neither by strength-or strain-based approaches, which neglect size effect, nor by LEFM which does not account for the finiteness of the Fracture Process Zone.

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An accurate prediction of the orthotropic elastic constants of woven composites from the constituent properties can be achieved if the representative unit cell is subdivided into a large number of finite elements. But this would be prohibitive for microplane analysis of structures consisting of many representative unit cells when material damage alters the elastic constants in each time step in every element. This study shows that predictions almost as accurate and sufficient for practical purposes can be achieved in a much simpler and more efficient manner by adapting to woven composites the well-established microplane model, in a partly similar way as recently shown for braided composites. The undulating fill and warp yarns are subdivided into segments of different inclinations and, in the center of each segment, one microplane is placed normal to the yarn. As a new idea, a microplane triad is formed by adding two orthogonal microplanes parallel to the yarn, one of which is normal to the plane of the laminate. The benefit of the microplane approach is that it is easily extendable to damage and fracture. The model is shown to give realistic predictions of the full range of the orthotropic elastic constants for plain, twill, and satin weaves and is extendable to hybrid weaves and braids.

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