Literature Review Report onSpecimen Design and its Effects for Kolsky bar ExperimentByYuvaraj Reddy Chitela

Abstract: In this report, a detailed review was done on the effects of specimen sizes, length by diameter ratios, interfacial friction, radial inertia, and non-cylindrical specimens on the characterization of material response at high strain rate loading using Kolsky bar experiment.

Introduction: In the modern world to design different kinematic applications using different materials, it is very important to know the material behavior at the applied force rate. There were many methods developed to know the behavior of material at static loading, but the applications designed considering static behavior of the material have failed to work properly because materials have a different behavior at dynamic loading conditions. This has led many researchers to work on analyzing of dynamic behavior of material. In 1918 Hopkinson introduced an experimental concept to determine the dynamic behavior of materials. In 1949 H Kolsky developed a device to determine the dynamic behavior of the material. Later this device had been modified by different researchers to achieve desired results.

To determine the dynamic behavior of the material, first the material specimen is sandwiched in between the two elastic bars and there are two strain gauges attached to the elastic bars. At first the striker bar loaded in the gas gun hits the elastic bar and a compressive wave is generated, this wave passes from the first elastic bar to the specimen at the interface of the specimen a wave is reflected back to the elastic bar and then from the specimen it passes to the to the second elastic bar and it hits the end and travel back in opposite direction. From the elasto dynamics following equations are derived to calculate stress and strain.

In the recent times Kolsky bar experiment is been widely used in determining the dynamic stress-strain relationship of various materials because it can produce the results with a reasonably acceptable accuracy and the cost is very cheap.

In SHPB test there havent been any standardized specimen length or diameter have been proposed, this is due to the complexity analyzing the material behavior, different materials with different properties require different testing conditions. Due to this while testing various materials require various specimen sizes. Previously many researchers have investigated the effects of specimen size in the test results and they have provided suitable geometries, for different materials for testing. Further in this report different types effects occurred due to specimen sizes is discussed.

Effects of Specimen Size: Initially when the SHPB test was employed the transmission of stress waves was done by the explosively loaded elastic anvil bar towards the specimen. At that time some investigators used short specimen, when short specimens were used to transmit the stress waves through the specimen they had to ignore all the inherent stresses, due to this some investigators abandoned the use of short specimen and they employed long specimen. In these experiments the transformation of experimental observations into basic mechanical properties of a material involved the specimen response for the wave propagation analysis and this analysis required additional hypothesis about the material behavior. When small specimens were used stress-strain and time were simultaneously measured. So using of small specimen have been more convenient to do the tests by making appropriate allowances for the inherent stresses.

Role of L/D ratio on the SHPB tests: The L/D ratio of SHPB test specimen is also known as slenderness ratio plays a crucial role in the test. The validity of the test results is dependent on the L/D ratios. In order to avoid size effects like inertia and interfacial friction we must choose an appropriate L/D ratios. Usually the selection of appropriate L/D is done be considering the following restrictions. The Interfacial friction effect should be negligible. The Axial inertia effect also should be negligible, this means the force should be constant throughout its length and there shall not be effect of wave propagation. Radial inertial effect shall also be small.In Kolsky work the L/D ratio of the specimen was 0.05, with this ratio kolsky considered the effect of stress in axial direction is uniform. He allowed to develop inertial stress in radial and tangential direction. The dynamic stresses of annealed copper obtained by kolsky did not present a reasonable value when extrapolated with the data obtained by Baron (1956). The difference between these two had been matched if a factor of 1.3-1.5 have been multiplied. Later analysis was done on the kolskys experiment and it was determined that this difference was due to the interfacial friction.

Later in 1962 Davies & Hunter have done a mathematical treatment to the kolsky model by considering a mathematical model shown by Siebel (1923). This analysis showed the relation between friction coefficient and the L/D ratio of the specimen. That analysis show the criterion

From Hawkyard and Freeman (1954) have estimated that the interfacial friction coefficient is being in between 0.02 to 0.06 and by substituting this value in the above equation leads to a value

There were experiments performed to observe the behavior of different L/D specimen ratios of the same material. Pankow, Attard and Waas (2009) had performed an experiment comparing the material behavior of 3 Specimens of same material,Circular SpecimenDia(mm)Length(mm) L/D

19.41.780.189

29.42.540.270

39.44.570.486

They found out that the all specimens have exhibited similar stress-strain histories and also made some observations from the following graph

With decrease in the thickness the duration of the stress-strain history duration is increased. Thin specimen with the L/D ratio=0.189 have displayed the complete history. Thick specimen with L/D ratio=0.486 had the shortest duration but it had displayed the most data in the initial regime.Another graph between strain rate and strain shows the equilibrium and holds the validity of the data.

In this graph even though the thicker specimen experiences a lower strain compared with the thin specimen at initial strains a steady straining is achieved. This point holds the validity of the experiment. From this experiment we know that to determine failure and yield strength thinner specimen can be used and to extract strain rate dependence on youngs modulus thick specimen must be used.

Effects of Friction on the Kolsky bar experiment:In a Kolsky bar experiment friction is produced mainly due to the use of short specimens. The friction at the interface of specimen and the elastic rods leads to a 3D stress state. Due to the friction the measured stress of the specimen greatly increases, this happens because the lateral expansion of the bar is limited by the interfacial friction, due to the limitation of length of the rod the stress is heavily increased.

The interfacial friction will act completely different with the brittle materials, as friction limits the unilateral expansion of the bar this will result in the development of multi axial stresses. Due to the multi axial stresses premature failure will occur in the specimen. So the measured stress is less than the actual stress. Use of the lubricants at the interface of specimen and the elastic rods will reduce the friction. A study was conducted by Song et al (2009), in this experiment he compared the stress-strain curves of aluminum, without lubrication and with vegetable oil and petroleum jelly as lubricants.

From the observations of above graph we can note that without proper lubrication the stresses in the specimen are highly increased.Another observation had been done by L.D. Bertholf and C.H. Karnes analyze the effect of friction in the following Effect on Material stress strain path. Uniformity of Stress-strain in specimen. Accuracy in specimen behavior predicted by Elastics bars.The observed stress-strain profile is shown below for =0.05, 0.15,0.25 with a L/d Ratio of 0.3

From the above three graphs the realistic friction effect on the Stress-Strain profile is observed.

Effects of Inertia on the SHPB test:In a Kolsky bar experiment Inertia occurs due to the dynamic event. Initially along with acceleration inertia in radial and axial direction change strain rate from 0 to the desired amount. But the stresses associated with the radial and axial strain should be every small when compared with the stress flow in Specimen. We need to find the true dynamic behavior of the material, so the inertial effect correction were proposed by Kolsky in his experiment using energy method. Kolskys analysis is done on a thin sample, so in this equation inertia in radial direction was neglected.

Davies and Hunter (1963) gave an analysis about the frictional effects and the considered the radial inertia they had resulted the following equation.

Samanta(1971) gave an analysis which is similar to hunter and Davies but he added the and his equation

In an experiment done by Bertholf and Karnes for zero friction and different L/d ratios the dynamic behavior is shown below

Effect of Radial Inertia for Kolsky bar test for an Incompressible Material:T.L Warren and M.J Forrestal derived a mathematical equation for the effect of radial inertia in a kolsky bar experiment for an incompressible material, this explain that the inertia in radial direction have a parabolic distribution.

Conclusion:Kolsky bar experiment was proposed by H. Kolsky (1949) to analyze the dynamic behavior of the materials, this is a unique experiment to determine the dynamic behavior of the material cost effectively and with reasonably accurate results. While performing the experiment a judicious care must be taken for the specimen designing, because this test dont have a standardized specimen geometry. We need to design the specimen geometry according to our application and material properties. Desired results will only be generated with the proper design of specimen.

As we discuss the geometric effects of the specimen, the size of the specimen must be always short because, when longer specimens were used considering the stress the propagation of wave must be analyzed and this makes our test process complex. So short specimens were used to directly measure stress-strain and time. L/D ratio of the specimen in the test plays a crucial role in the test due to different L/d ratios different geometric effects are produced in the results, to avoid this in most of the cases the L/D ratio should be in between 0.5 to 2 depending on the material properties. There wont be a difference in the dynamics behavior of a material for different L/d ratios.

The effect of friction must be negligible to get the proper dynamic behavior of the material. Due to the friction the stresses in the material is increased and in the brittle materials due the friction the measured stress is less that the actual material dynamic stress. So proper care must be take while designing the L/d ratio and also proper lubrication must be provided at the interface of specimen and the elastic bars to minimize the error in result caused by the friction.

Inertia effect occurs at the dynamic events and due to the inertial stress in radial and axial direction increase in stress rate is observed, as we need the intrinsic behavior of the material the correction factor has been applied to the stresses. The radial inertial effect in a incompressible material is different and according to a mathematical equation inertia in radial direction is in parabolic distribution. This is used when designing specimen with incompressible material.

References: Two dimensional analysis of SHPB system Berthlof and Karnes Dynamic compression testing of solids by the method of split Hopkinson pressure bar-Davies and Hunter Effects of Specimen size in Kolsky Bar-Srinivas Arjun Tenkalur and Oshika sen Specimen Geometry Effects in high Strain rate Testing-Eyassu Woldsenbet and Jack Winson Specimen Size and Shape Effect in Split Hopkinson pressure bar testing- Pankow, Attard, A M Waas. Split Hopkinson Bar Technique for Low Impedance material W.Chen, B.Zhang and MJ Forrestal Comments on the Effect of Radial Inertia in the Kolsky bar Test for an Incompressible material TL Warren , MJ Forrestal