Determination of stress-time histories in axially symmetric impacts with the two-gauge technique

Abstract

We present an experimental technique for the direct measurement of stress-time histories in axially symmetric dynamic impacts, where the state of strain is not uniaxial. The technique is based on placing two different well-calibrated piezoresistance gauges in the desired location on the symmetry axis. The two measured resistance changes are then substituted in a system of two equations with two unknowns from which one obtains the axial stress and the lateral strain histories. We demonstrate the technique with manganin and constantan gauges which were calibrated both under uniaxial strain and hydrostatic conditions. As an example we bring the results of stress measurements inside thick polymethyl methacrylate targets which were impacted by thick copper discs. The measured stress-time history is then compared to that predicted by a two-dimensional Lagrangian code.

Dynamic analysis of the response of lateral piezoresistance gauges in shocked ceramics

“…However, this issue has not been addressed in previous studies that used surface-mounted gauges. 8,19,26,27 To understand the role of the epoxy layer on the local dynamic response, we first carried out a series of calculations using just the epoxy-matrix system ͑Fig. 2 without the gauge͒.…”

“…Similar conclusions were also obtained from the static inclusion calculations 6,7,22 and a simplified reverse analysis. 8,19,26,27 Second, the applied load is not so large that the piezoresistive response of the gauge is significantly nonlinear. Under these conditions, simplified analyses may be used to interpret the equilibrium response of a lateral gauge with reasonable accuracy.…”

“…5,9,10,14 It was conjectured in some related studies, based on the assumption of perfect gauge bonding, that the longitudinal strain in such a gauge is the same as that in the matrix under uniaxial strain compression. 8,19,26,27 While the numerical result indicates that the thin gauge slips with respect to the matrix, the averaged longitudinal strain of the gauge ͑0.0396͒ in the equilibrium state ͑1.3 s͒ is very close to the far-field uniaxial strain value in the matrix ͑0.0395͒. Because the thin gauge does not block the passage of the epoxy flux and because the epoxy flows completely for the given load, the stress distributions across the gauge width in the equilibrium state are quite uniform, particularly for the lateral stress.…”

“…15,16 Both experimental and analytical studies have been carried out to understand the electromechanical response of manganin and ytterbium gauges. 6,7,[17][18][19][20] In particular, the studies by Gupta and coworkers have provided a fairly complete phenomenological model for piezoresistance response, and the methodologies to evaluate the model constants. 6,7,11,13,[20][21][22] Thus, the gauge resistance change can be calculated quite accurately if the mechanical state of the gauge is known and the model constants have been determined.…”

“…[5][6][7][8]13,19,23,26,27 Chartagnac suggested that the gauge calibration obtained for longitudinal gauges can be used directly for analyzing the equilibrium response of lateral gauges. 5 Rosenberg and co-workers 8,19,26,27 derived a lateral gauge analysis by neglecting the effects due to the interaction between the gauge and surrounding materials. Unfortunately, the lateral stress in a solid subjected to shock wave, uniaxial strain compression cannot be related to other field variables through the conservation equations.…”