Correction to : Estimating measurement uncertainty on stress-strain curves from SHPB
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CORRECTION
Correction to : Estimating measurement uncertainty on stress-strain curves from SHPB D. Brizard1 · S. Ronel1 · E. Jacquelin1
© Society for Experimental Mechanics 2020
Equation (12) in the original article [1] gives the strain from the measured voltage on a full bridge configuration of the four strain gages. The full-bridge is intended to measure tension-compression strain (type III full-bridge), the correct equation is therefore [2] e(t) Vex
(1)
2Vr (t) κ[(1 + ν) − Vr (t)(1 − ν)]
(2)
2Vr (t) κ(1 + ν)
(3)
Vr (t) = III (t) =
which corresponds to a type II full-bridge for bending measurements (see table 12.2 in [2]). κ is the gage factor, Vr the bridge output and Vex the excitation voltage.
The online version of the original article can be found at https://doi.org/10.1007/s11340-017-0260-8.
u (II (t)) II (t)
u (κ) 2 u(ν) 2 + κ 1+ν 2 u(Vex ) u(e(t)) 2 + + Vex e(t)
2 =
(4)
which holds only in case of type II full-bridge (Equation 3). For type III full-bridge, from Equation 2 and the rules for expressing uncertainty (see [3]), the uncertainty in the strain is:
and not II (t) =
The measurement uncertainty on the strain was given as (see equation (13) in [1]):
2 u(III ) (1 + Vr )ν u(ν) 2 u(κ) 2 = + III (1+ν)−Vr (1−ν) ν κ 2 2 1+ν u(e) + (1+ν)−Vr (1−ν) e 2 1+ν u(Vex ) 2 + (5) (1+ν)−Vr (1−ν) Vex
A first order asymptotic approximation of Equation 2 gives
D. Brizard
[email protected] S. Ronel [email protected] E. Jacquelin [email protected] 1
Univ Lyon, University Claude Bernard Lyon 1, IFSTTAR, LBMC UMR T9406, F69622, Lyon, France
III =
2Vr (1 + o(Vr )) κ(1 + ν)
(6)
Finally, the order of magnitude of Vr during the experiments was of a few thousandth. The consequences of the bridge type error on the results (i.e. strain and measurement uncertainty on the strain) are therefore negligible.
Exp Mech
References 1. Brizard D, Ronel S, Jacquelin E (2017) Estimating measurement uncertainty on stress-Strain curves from SHPB. Exp Mech 57(5):735–742 2. Watson RB (2008) Bonded Electrical Resistance Strain Gages. In: William N. Sharpe, editor, Springer Handbook of Experimental Solid Mechanics, Springer Handbooks, pages 283–334. Springer US, Boston, MA
3. Farrance I, Frenkel R (2012) Uncertainty of measurement: a review of the rules for calculating uncertainty components through functional relationships. The Clinical Biochemist Reviews 33(2):49–75
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