PSI - Issue 28

Koji Uenishi et al. / Procedia Structural Integrity 28 (2020) 2072–2077 Uenishi et al. / Structural Integrity Procedia 00 (2020) 000 – 000

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fracture, between time 0 and 80  s; (2) the second one is initiation and arrest of propagation of the secondary fracture, from time 80 to 140  s; and (3) the last one is reactivation of propagation of the secondary fracture, between time 340 and 400  s. Obviously, the secondary fracture propagates even without additional external loading. That is, its extension is because of the fracture-induced waves. 3. Discussion Second, in order to reveal a possible mechanism behind the above local observations, we perform another experiment and numerical speculation using a geometrically simpler specimen that contains small-scale cracks only on the line of the primary fracture (Fig. 1c). In this contribution, owing to the space limitation, we describe solely the numerical part. We conduct finite difference calculations, with the spatiotemporally second order accuracy and 361  1,201 orthogonal grids, for a homogeneous, isotopic and linear elastic material representing the polycarbonate specimens in Fig. 1, with the mass density 1,200 kg/m 3 , shear modulus 820 MPa and Poisson’s ratio 0.37. These physical quantities give the longitudinal (P), shear (S) and Rayleigh surface (R) wave speeds of the material as 1,820 m/s, 827 m/s and 775 m/s, respectively, according to the relation among the linear elastic parameters that can be found, e.g. in Viktorov (1962). For visual clarity, here, we show dynamic stresses caused by the primary fracture, with no subsidiary fracture included. As in the experimental photographs, contours of the maximum in-plane shear stress  max are depicted but  max is normalised with respect to the statically and vertically applied constant, uniform tensile stress. This assumption of constant static tensile stress during the dynamic process can be accepted, if approximate, because the dynamic phenomena experimentally recognised in Fig. 3 have occurred within about 400  s and with the displacement rate of 100 mm/min, the increment of the displacement in 400  s is 667 nm or increase of the nominal strain is some 4.44  10 − 6 (the initial effective specimen length is 150 mm here) while the maximum nominal strain carried by the specimen just before the stress drop is by far larger, approximately 4.5  10 − 2 as seen in Fig. 2. Figure 4 illustrates the numerically generated snapshots of the dynamic wave field related to the primary fracture propagation. The fracture travels at an experimentally observed sub-Rayleigh speed of 563 m/s from left to right, and around the tip of the primary fracture, the so-called rupture front wave develops (see time 60  s after the start of the fracture propagation). At this stage, regions of stress amplification can be identified at positions away from the

10 mm

RR

R

Direction of fracture propagation

Regions of stress amplification

Normalised maximum in-plane shear stress

R

Rupture front wave

R

R

RR

R

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60

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140

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Fig. 4. Dynamic wave field associated with the propagation of the primary fracture running at a constant sub-Rayleigh speed in an initially multiply cracked linear elastic specimen that is subjected to uniaxial tensile loading (specimen in Fig. 1c). Although technically possible, for graphical clarity and a wave-tracing purpose, only the primary fracture is taken into account. Upon a perfect split of the specimen by the primary fracture, propagation of relatively strong Rayleigh (R) and reflected Rayleigh (RR) waves along the vertical free surface is visible. If the secondary and further fractures are included, RR wave(s) diffracted at the initiation point(s) of the secondary fracture on the right vertical surface may propagate further along the surfaces of the arrested secondary fracture until they reach the tip of the secondary fracture to cause resumption of fracture propagation. Time elapsed after initiation of fracture propagation is 20, 60, 100, 140, 180, 220  s, respectively.