Determination of mean and deviatoric stresses in shock loaded solids

Abstract

Models for the behavior of solids submitted to shock waves include an equation of state and a plastic yield surface, which represents the plastic potential. The general purpose of this work concerns various methods used to obtain these equations by means of the determination of the mean and deviatoric shock streeses. Emphasis is placed on the method of ’’piezoresistive deviatoric gauges’’ that we have been using since 1973. This method does not include any theoretical hypothesis, and is suitable for all materials that can be gauged. Examples of applications on polymethyl metacrylate, limestone, and steel are reported and show that the precision of the piezoresistive deviatoric gauges method depends upon the material, namely the deviator magnitude, and upon the stress range explored.

Dynamic flow and failure of confined polymethylmethacrylate

“…These domains are the pressure-sensitive (brittle) and pressureinsensitive (ductile-plastic) regimes, respectively. Chartagnac (1981) provides analogous results for shocked PMMA, plotting the deviatoric stress as a function of the pressure. His data show that the linear domain ends at S 11 ¼ 210 MPa and p ¼ 500 MPa.…”

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

“…The gauge-matrix interaction is expected to be less significant if the gauge is very thin compared to the epoxy layer ͑e.g., commercial manganin foil gauges 5,9,10,14 ͒. As a demonstration, we show in Fig.…”

“…A potentially attractive method for measuring the lateral stress in a shocked solid is to monitor the response of a piezoresistance foil gauge embedded in a sample such that the normal to the gauge foil surface is perpendicular to the shock compression direction. [3][4][5][6][7][8][9][10][11][12][13][14] Throughout this paper, the term ''lateral gauge'' will be used to denote such a gauge. Since the lateral gauge package ͑foil plus the epoxy encapsulation͒ is considerably more compliant than ceramic samples, its insertion disturbs the uniaxial strain condition at the sample-gauge package interface.…”

“…[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.…”

“…7,23 Consequently, there is not a fundamental method to independently verify the simplified lateral gauge analyses. Hence, despite the fact that lateral gauge measurements have been reported in various shocked solids ͑including ceramics͒, 5,9,10,14 questions regarding the analyses of lateral gauge data and their relationship to lateral stresses in shocked solids have not been resolved convincingly.…”