PSI - Issue 47

Ezio Cadoni et al. / Procedia Structural Integrity 47 (2023) 630–635

631

2

Author name / Structural Integrity Procedia 00 (2023) 000–000

a) b) Fig. 1. a) Specimen gauge lengths investigated; b) Raw signals of direct tensile test with SHTB.

(Forni et al. (2017)). Reinforced concrete is used in many critical infrastructures, protective structures, and other buildings. A dynamic response is required for both concrete and reinforced steel. During the last decade, a variety of studies have been conducted on the dynamic behavior of reinforcing steels (Cadoni et al. (2001, 2012, 2013); Cadoni and Forni (2015); Riganti and Cadoni (2014); Cadoni et al. (2018); Cadoni and Forni (2019)). Reinforcing steel B500A analysed in work has been studied in Cadoni et al. (2015) and Cadoni and Forni (2021) where composition and details can be found. Split Hopkinson Bars (or Kolsky Bars) are widely recognised as the most e ff ective method for mechanical charac terising materials at strain rates between 100 and 1000 s − 1 . Due to the equilibrium and uniform stresses, it is generally recommended that the specimen should be as short as possible. This common belief has been criticised by Osovski et al. (2013) and Rotbaum and Rittel (2014) highlighting for the gauge length and the boundary conditions analysed both stress equilibrium, strain localisation and stress uniformity along gauge length. In this study several gauge lengths (5, 10 and 15 mm) were selected to investigate the influence of gauge length on high strain-rate direct tensile tests. Tthe specimens analysed are shown in Fig. 1a. In order to study the e ff ects of gauge length on direct tensile test, a Split Hopkinson Tensile Bar (SHTB) apparatus located at the DynaMat SUPSI Laboratory of the University of Applied Sciences and Arts of Southern Switzerland (Mendrisio) was used. It consists of two circular high strength steel bars, having a diameter of 10 mm, with a length of 9 and 6 m for input and output bar, respectively. The specimen was screwed in the input and output bars by two fillets. The first 6 m of the input bar is used as pretensioned bar the remaining as incident bar. The functioning is described in Cadoni et al. (2012). In SHTB test the relative amplitudes of the incident ( I ), reflected ( R ) and transmitted pulses ( T ), depend on the mechanical properties of the specimen. On both half-bars, strain gauges are used to measure the elastic deformation caused by incident / reflected and transmitted pulses (as a function of time). The raw signals are depicted in Fig. 1b. The application of the elastic, uniaxial stress wave propagation theory to the Hopkinson bar system and equations (1) and (2) allow the calculation of the forces F input and F output and the displacements δ input and δ output acting on the two 2. Direct tensile test

faces of the specimen in contact with the input and output bars, respectively. F input ( t ) = A bar · E bar · [ I ( t ) + R ( t )] and F output ( t ) = A bar · E bar · T ( t )

(1)

δ input ( t ) = C 0

t 0 [ I ( t ) − R ( t )] dt and δ output ( t ) = C 0 t 0

[ T ( t )] dt

(2)

where A bar , E bar , and C 0 are the area of the bar cross-section, the elastic modulus, and elastic wave velocity of the bar, respectively while t is the time. Fig. 2 compares input and output loads versus time curves. There is a negligible di ff erence between gauge lengths of 5 and 15 mm. Therefore the average engineering values of stress σ eng , strain eng and strain-rate ˙ eng in the specimen are: σ eng ( t ) = F input ( t ) + F output ( t ) 2 · A sp. = E bar · A bar 2 · A sp. · [ I ( t ) + R ( t ) + T ( t )] (3)

Made with FlippingBook - Online Brochure Maker