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Kolsky Bar Experiment for High-rate Large Deformations of Polycarbonate

ABSTRACT

Polycarbonate (PC) is a tough, transparent engineering thermoplastic. Its impact strength and ability undergo large plastic deformations without shatter make PC an ideal protective material for impact-resilient eyewear, aircraft windows and transparent armor.

A good understanding of the response of this material to large deformations at high strain rates is critical for its utilization in these applications. To this end, a striker-less Kolsky bar device is employed in this work for the needed material characterization. The apparatus allow impulsive torsion and/or compression loadings with pulse durations sufficiently long for the plastic flow behavior to develop fully. Three new testing techniques based on the device are developed and applied to measure the response of PC to large plastic deformations of various modes at various strain rates and under various temperatures.

The first new technique is a modified torsional Kolsky bar method that loads the PC sample in high rate of simple shear. In addition to measuring the shear stress as the conventional method, the new technique also measures the axial stress induced by shear deformation.  The measurements show that the material expands as it undergoes elastic shear and contracts as the shear becomes increasingly plastic. The results for the elastic response confirm the prediction by a non-linear elastic model for PC.

The second new technique applies a static axial compression to the sample before dynamic shear loading.  The experiments with this technique seek to determine if and to what extent the deviatoric yield and flow stresses of PC are affected by the volumetric stress.  For the stress states examined, both the deviatoric yield and flow stresses show linear dependence on the compressive volumetric stress.

The final Kolsky bar technique developed uses a friction clamp to store and release a compressive pulse. This new technique allows for loading pulses that are much longer than the achievable pulses in the traditional split Hopkinson bar tests. They are sufficient for the material flow behavior to develop fully in the compressive strain rate range of mid hundreds to lower thousands per second. Tests with the technique are performed on PC over an array of temperatures and strain rates.

The temperature and strain rate dependences of the yield and flow stresses under dynamic compression are studied.  The volumetric stresses are considerably more in tense for the compression tests than for the torsion tests and combined compression-torsion tests.  The data from the three types of tests together indicates consistent pressure-dependent increases  in the deviatoric yield and flow stresses of PC subjected to
high-rate large deformation.

ANALYSIS OF STANDARD TKB

TKB Set-up:

The multi-mode friction clamp type Kolsky apparatus used in all of the methods.The friction clamp, shown  designed by Duffy (Hartley, Duffy, & Hawley, 1985) is integral for storing and quick release of torsion pulses. A hydraulic cylinder is used to tighten the clamp on the bar. Another hydraulic cylinder attached to the pulley is used to apply the desired torque to the section of the bar between the pulley and the clamp.

Multimode Kolsky Bar Apparattus.

Multimode Kolsky Bar Apparattus.

SHEAR INDUCED AXIAL STRESS

Experimental Analysis:

The shear strain rate, shear strain, and shear stress histories are determined by the methods outlined with modifications shown below. For this experiment in addition to these histories, a history of axial stress is also needed.

DYNAMIC TORSION WITH STATIC AXIAL COMPRESSION

Introduction:

Polycarbonate is an amorphous polymer, meaning that it is composed of long polymeric chains randomly arranged and has no crystal structure. The amorphous structure of the material leads to it transparency.

The chemical structure of this polymer leads to its stiffness and thermal stability (Mehta & Prakas, 2009) and therefore its engineering utility. The yield and flow behavior are heavily dependent on how these molecules move past one another. Shen (Shen, 2007) and Reitsch and Bouette (Rietsch & Bouette, 1990) studied the effects of both strain rate and temperature on the flow stress and yield stress.

Polycarbonate from  Biphenyl A Chemical Structure

Polycarbonate from Biphenyl A Chemical Structure.

Experimental Analysis:

Axial Strain Gauge Analysis

The strain gauge analysis for this series of experiments is the same as the analysis described only that in this case the bar is solid and the bar is initially loaded.

COMPRESSION TESTING

Introduction:

Split-Hopkinson pressure bar tests have traditionally been performed with a fast moving striker bar used to initiate the pulse. There are practical limits to the length of striker bars and therefore pulse duration. With limited pulse durations, there is little time for yielding and flow behavior to develop in strain rates in the low thousands and lower.  Figure 5-1 from Moy et al (Moy, Weerasooriya, Hsieh, & Chen, 2009) show the gap between traditional SHPB tests and hydraulic testing machines.

Compressional Kolsky Bar Experimental Technique:

Thermal Chamber

To observe the effects of temperature on the deformation on polycarbonate, elevated temperatures are needed. The thermal chamber used for this series of compression tests is the same device used by Shen (Shen, 2007) in his series of torsion tests. The 61 temperature controller controls based on the input of a thermo couple that is placed directly to the surface of the sample. Shen found good uniformity in temperature at multiple points along the sample surface (Shen, 2007), so uniformity in temperature can
be assumed.

Schematic of Th ermal Chamber

Schematic of Thermal Chamber.

Experimental Results:

Regression Analysis

The values for deviatoric invariant yield and flow stress, deviatoric invariant strain rate at yielding and flow, and pressure at yielding and flow in Deviatoric invariant stress and pressure vs. deviatoric invariant strain and deviatoric invariant strain rate and engineering strain rate histories for tests.

Model and Experimental Results for Deviatoric Invariant Yield Stress vs. ln(Deviatoric Invariant Strain Rate) and Pressure

Model and Experimental Results for Deviatoric Invariant Yield Stress vs. ln(Deviatoric Invariant Strain Rate) and Pressure.

CONCLUSIONS

In this thesis three new experimental methods based on a striker-less Kolsky bar apparatus are developed for the study of the response of polycarbonate (PC) to various modes of large deformations at high strain rates and for various initial temperatures. These methods take advantage of the device’s ability to achieve long pulse durations and incorporate techniques to enable specimen loading and response measurements in both axial compression/ tension and shear modes.

Hence, they provide the experimental techniques necessary for dynamic testing of a material whose response involves significant distortion-dilation coupling during large deformations. Although the methods developed have been applied only to the study of PC in this work, they are expected to be applicable for other polymeric solids displaying similar dynamic behaviors.

Source: University of Nebraska-Lincoln
Author: Jason G. Vogeler

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