PSI - Issue 13

Koji Uenishi et al. / Procedia Structural Integrity 13 (2018) 652–657 Uenishi et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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condition, i.e. positions of blast and dummy holes, used for the case IC-10/00 is more favorable for dynamically controlled fracture. The snapshots of fracture development in the rectangular specimens, taken by the high-speed digital video camera, clearly indicate that in the case IC-09/00 (Fig. 2(a)) cracks on the top surface emerge first in the squares of four dummy holes and then the main crack connecting the blast holes appears. On the other hand, in the case IC-10/00 (Fig. 2(b)) the main crack moving through the three blast holes and the cracks in the upmost and bottommost squares of dummy holes emerge almost at the same time. Also, Figs. 1(c) and 2 do show that, similar to the case of conventional blasting with explosives (Rossmanith et al., 1997; Uenishi and Rossmanith, 1998; Rossmanith and Uenishi, 2006), EDI-induced fracture develops first upon wave propagation in the specimen and then crack opening displacements become larger due to gas pressurization with the ejection of stemming material. If cracks were generated by gas pressurization from the initial stage, the stemming material would be ejected at earlier time, concurrently with the extension of fracture network. 3. Physical background behind the controlled fracture The experiments have indicated that the emerged main crack is connecting blast holes rather smoothly when each blast hole, located not close to the free surface on the side, is surrounded by four empty dummy holes. We can briefly confirm the influence of dummy holes and free surfaces on extension of the main fracture plane numerically by using our fully three-dimensional finite difference simulator for a PC (Windows) (Uenishi et al., 2010, 2014) and tracing the evolution of dynamic disturbances in the rectangular specimens. We assume a homogeneous, isotopic and linear elastic concrete material, with the measured density 2,320 kg/m 3 , Young’s modulus 34.2 GPa and Poisson’s ratio 0.25 (longitudinal and shear wave speeds c P  4,200 m/s and c S  2,400 m/s, respectively). We arrange orthogonal 91  91  31 grid points (constant grid spacing  x = 10 mm) for efficient and fundamental calculations with the constant time step  x /(2 c P ). For simplicity, we presume that the stemming material has the same material properties as concrete, and the diameter of every blast holes is identical to that of dummy holes. For the cartridges, we employ a simplified form of the time t -dependent pressure P ( t ) owing to the application of EDI, P ( t ) = A sin 2 (  t / T ) (for 0  t  T ) and 0 (otherwise), with A = 1 GPa and T = 260  s by referring to Uenishi et al. (2014). Since firstly we must know the mechanical characteristics of the waves caused by the application of EDI, we incorporate no specific fracture criterion at this moment. The assumptions and the geometrical and loading settings make the model almost symmetric with respect to the virtual central horizontal plane (and the source cartridges; at a height of 150 mm) as well as to the virtual central vertical plane containing the blast holes. Thus, the fundamental effect of wave interactions on ensuing fracture development is identifiable by scrutinizing only the quarter part of the specimen. The snapshots of contours of normalized volumetric strain (a strain invariant) for the cases (a) IC-09/00 and (b) IC 10/00 in Fig. 3 depict time-dependent dilatational (positive volumetric strain) and contractive (negative volumetric strain) elements in the rectangular specimen. In the case IC-09/00, initially, EDI-induced compressive waves propagate concurrently from the cartridges. Subsequently, wave reflection not only from the bottom (top) and side free surfaces but also from the dummy holes produces areas in tension near the blast holes and there tensile cracks may develop (if we can apply a tensile fracture criterion). However, the region between the blast holes on the virtual vertical plane are still in compression due to the relatively large distance between the blast holes. At a later stage, wave interaction becomes more intricate, and the region between the blast holes may also be under dynamic tension and the main crack may extend into this region. In the case IC-10/00 (Fig. 3(b)), on the contrary, tensile areas in the proximity of the free surfaces and dummy holes as well as those close to the middle blast hole appear almost concurrently, possibly because, with the relatively shorter distance between the blast holes in the model, waves reflected from the nearby holes and approaching to the middle blast hole can exist. Thus, a rather flat tensile fracture plane connecting the three blast holes will be generated at an earlier stage, as speculated from the experimental results. As seen above, slight change in the positions of blast and dummy holes may be of crucial importance for controlled smooth fracture of materials, and analyses based on wave dynamics may enhance our capability of designing more accurate geometrical and loading settings for effective dynamic fracture of solid materials. Naturally, the discussion for the modern method using EDI here holds for the conventional blasting with explosives.