脆性破壊伝播に関する研究(第2報) : 円孔が定速で拡大する場合の応力場の厳密解

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This report is the second part on the theoretical studies of propagation of brittle fracture. An exact solution of dynamical stress field around a circular hole, enlarging or propagating at the constant speed, under the uniform tensile stress at infinity was obtained.The equation of motion was solved by introducing a new conception of "expanding coordinates", in which the radial coordinate expands proportionally with the time. In addition, the released elastic strain energy, the kinetic energy, and the cirtical stress were also obtained.The general conclusions obtained are as follows : (1) The radial displacement and the dynamical stress varies only in the region, in which the longitudinal plane stress wave propagates. (Figs.2,3,and 4)(2) The released elastic strain energy decreases as the crack speed increases. (Fig.6)(3) The kinetic energy increases and then decreases with the increased crack speed, and its maximum value is obtained at a speed on about 40% of the sonic speed, (Fig.6)(4) The critical stress for brittle crack propagation at a speed of 60% of the sonic speed becomes about 70% greater than that at the extremely low speed. at some temperature. (Fig.7)
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