A Kolsky Torsion Bar Technique for Characterization of Dynamic Shear Response of Soft Materials (Dynamic Behavior of Materials)

ABSTRACT

A novel Kolsky torsion bar technique is developed and successfully utilized to characterize the high strain rate shear response of a rate-independent end-linked polydimethylsiloxane (PDMS) gel rubber with a shear modulus of ~10 KPa. The results show that the specimen deforms uniformly under constant strain rate and the measured dynamic shear modulus well follows the trend determined by dynamic mechanical analysis (DMA) at lower strain rates. Contrastive Kolsky compression bar experiments are also performed on the same gel material with annular specimens. The dynamic moduli obtained from compression experiments, however, are an order of magnitude higher than those predicted by the torsional technique, due to the pressure caused by the radial inertia and end constraints.

INTRODUCTION

Characterization of dynamic response of soft biological tissues has seen a tremendous rise in the past decade. Among all the published non-oscillatory high rate results, dynamic uniaxial compression/tension has generated the most popular group of data [1], and its experimental conditions have also been extensively investigated [2]. There are two major issues associated with the axial loading conditions when the strain rate is high: 1. Dynamic stress (or force) equilibrium across the specimen length, and 2. Radial inertia induced pressure by strain rate and strain acceleration. A preliminary solution to minimize the inertia effect is to punch a hole in the center of the specimen, for which the pressure was greatly reduced by creating a stress-free inner surface. However, for materials as soft as human brain tissues whose elastic moduli are typically in the range of 0.1-10 KPa, even the reduced pressure in an annular sample can be sufficiently high to overshadow the intrinsic material response. To separate the pressure from the intrinsic mechanics response of soft materials, a pure shear loading condition is desired. In this paper, we present a newly developed desktop Kolsky torsion bar technique for the characterization of high rate shear mechanical properties of soft materials. The effectiveness of this torsion bar technique was demonstrated by our calibration experiments on the end-linked polydimethylsiloxane (PDMS) gel rubber.


EXPERIMENTS AND RESULTS

A typical oscilloscope record of the modified Kolsky torsion bar experiment is shown in Fig. 1. The trace noted as "incident bar signal" is measured by the strain gages mounted on the incident bar, while the other trace is taken from the torque sensor which connects to the external ring adapter. Since the gel material under investigation has extremely low wave impedance compared to that of the incident bar, most of the incident wave is reflected back. Consequently, the reflected pulse would not see any noticeable difference, both in shape and amplitude, from the incident pulse. We used the incident wave to calculate the shear strains in the specimen so that a better-quality signal can be used directly from the oscilloscope reading. The stress-strain curves of five different samples loaded at shear strain rate of ~1000s-1 are displayed in Fig. 2. Although some discrepancies were found on the five measured stress-strain curves, all of them exhibited linear elasticity when the strain is beyond 8%. In order to compare the shear modulus with those obtained from DMA tests, and thus evaluate the validity of our Kolsky torsion bar experiment, the tangential of these stress-strain curves in Fig. 2 were measured in the strain range from 8% to the maximum strain on each curve. As mentioned before, the purpose of conducting current dynamic torsional experiments on soft materials is to directly acquire their shear constitutive properties, which in the past were mostly inferred from the dynamic compression results. To compare the measured modulus value from uniaxial compression experiments with those obtained from DMA and Kolsky torsion bar experiments, dynamic compressive experiments on this same PDMS gel were also conducted at comparable strain rates. The results are plotted in Fig. 3. The dynamic shear elastic modulus of gel measured with torsion bar technique follows the trend of DMA test results, while the same material exhibited much higher modulus value (about an order of magnitude) when it was under dynamic compression. Such a large discrepancy between the two dynamic testing techniques and the analysis of the discrepancy reveal that the Kolsky torsion bar experiment is necessary to characterize the shear behavior of extra soft materials under high strain rate loading conditions.

The original signals of torsional experiments


Fig. 1 The original signals of torsional experiments

Shear stress-strain curve of PDMS at 1000/s by Kolsky torsion bar technique

Fig. 2 Shear stress-strain curve of PDMS at 1000/s by Kolsky torsion bar technique

Comparison of shear modulus obtained by different testing techniques at different shear rates

Fig. 3 Comparison of shear modulus obtained by different testing techniques at different shear rates

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