Abstract
The minimum required distance of the strain gauge on the transmitted bar of the split Hopkinson bar has been determined from the position of a metallic specimen via an explicit finite element analysis. The minimum required distance was determined when the strain-time profiles at r = 0, 0.5Ro and 1.0Ro, were coincident (r is the radial position and Ro is the radius of the bar.). The determined minimum required distance, f(x), is presented as a function of the relative specimen diameter to that of the bar (x = D/D0): j(x) = - 0.9385.x3 + 0.6624.x2 - 0.7459.x + 1.4478 (0.1 ≤ x ≤ 0.9). This result demonstrates the Saint-Venant's principle of rapid dissipation of localized stress in transient loading. The result will be useful for the design/modification of the pseudo-one-dimensional impact instruments that utilise a stress pulse transmitted through the specimen. The result will also allow one to avoid unnecessarily remote strain gage position from the specimen.
Highlights
IntroductionA strain rate-dependent constitutive equation [1, 2] is indispensable for the modelling and simulation-based design of solids and structures exposed to high strain rate events [3,4,5,6] such as crashes in high-speed transportation systems (airplanes, express trains, and automobiles), high-speed machining, blasting of rock and buildings, impact, penetration, and explosion
A strain rate-dependent constitutive equation [1, 2] is indispensable for the modelling and simulation-based design of solids and structures exposed to high strain rate events [3,4,5,6] such as crashes in high-speed transportation systems, high-speed machining, blasting of rock and buildings, impact, penetration, and explosion
The strain gauge on the incident bar has to be sufficiently away from the specimen (x > L, where L is the striker length) to avoid the superposition of the incident and reflected pulses. For both the direct impact bar (DIB) and split Hopkinson bar (SHB), the strain gauge in the transmitted bar is essential for measuring the specimen stress
Summary
A strain rate-dependent constitutive equation [1, 2] is indispensable for the modelling and simulation-based design of solids and structures exposed to high strain rate events [3,4,5,6] such as crashes in high-speed transportation systems (airplanes, express trains, and automobiles), high-speed machining, blasting of rock and buildings, impact, penetration, and explosion. The strain gauge on the incident bar has to be sufficiently away (a distance of x) from the specimen (x > L, where L is the striker length) to avoid the superposition of the incident and reflected pulses For both the DIB and SHB, the strain gauge in the transmitted bar is essential for measuring the specimen stress. Knowledge on minimum required distance will allow one to avoid unnecessarily remote strain gage position from the specimen because an overly long distance will only increase the necessity of dispersion correction In these regards, this study reveals the minimum required distance of the strain gauge on the transmitted bar that allows the measurement of the evenly distributed stress (strain) in the bar when the specimen diameter is smaller than that of the bar. Compression is denoted with a positive sign
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