Stress–strain relationships of polycarbonate over a wide range of strain rate, including a shock wave regime

Abstract

Stress–strain relationships of polycarbonate (PC) are determined over a very wide range of strain rates , including a shock wave regime. Plate impact tests, drop-weight tests, and quasi-static tests using universal and Instron testing machines are used for the high strain rate (10 7 s −1 ), medium strain rate (10 2 s −1 ) and low strain rate (10 −4 s −1 ) tests, respectively. A newly modified unsteady wave sensing system (NM-UWSS) for plate impact tests is developed to determine the stress–strain relationships of PC. The system consists of a powder gun for plate impact tests, three embedded polyvenyliden fluoride (PVDF) gauges, and NM-UWSS. As originally proposed, UWSS is aimed at obtaining experimental inputs for the Lagrangian analysis used in determining the dynamic behavior of materials. We revise this standard system (UWSS) twice to gain a higher time resolution. In the past, the conventional charge mode ( Q 2 method) was used. The first modified system (M-UWSS) has been used to study two classes of materials: (1) metallic materials and (2) polymeric materials, where the Q 1 method coupled with a transient differential equation for the equivalent circuit of the measurement circuit for the PVDF stress gauge was used. The latest method ( Q t method) for gaining the highest time resolution of shock wavefront structure by considering the effects of a piezofilm's thickness is proposed for PC at particle velocities of up to 1 km/s. Here we show from basic equations of piezoelectricity that the charge density q , i.e., the charge release per unit area, of the active electrode is proportional to the ratio of the thickness of the shocked region to the total thickness of the piezofilm. It is demonstrated that the rise time of shock charge density q in the piezofilm induced by such shock in the Q 2 , Q 1 and Q t methods, in this order, is becoming much shorter. The latest Q t method has the highest accuracy among these three methods. Power law relations between stress and strain rate are observed again with PC under conditions of uniaxial strain over a very wide range of strain rates, i.e., 10 −4 –10 7 s −1 including a shock wave regime. For the PC, the effects of strain rate on the stress–strain relationships are estimated using empirical formula.