# Dynamic material properties

## Strain measurements in a split-Hopkinson bar

Material constants like Young's modulus and Poisson's ratio are important characteristic quantities of materials that are used in components, designs and structures. Depending on the design, it is absolutely essential to exactly know the respective parameters valid for the materials used, since they provide information, for example, about how much a component is deformed when a force is applied to it. The values specified in standard works and tables have usually been measured in testing machines under quasi-static conditions. However, other methods are required to determine material behavior under dynamic conditions.

Young's modulus is a material constant that is a measure for how much a component is deformed when a force is applied to it. In other words, the stiffer a material is, the higher is its modulus of elasticity. Values for commonly used materials are specified in Dubbel's Handbook of Mechanical Engineering. The  stress-strain curve is usually determined using a testing machine under quasi-static conditions - i.e. with (very) small strain rates. However, material behavior may differ substantially with dynamic loads. Depending on whether dynamic loads, too, occur in a structure, the design engineer needs to know the material's dynamic properties as well.

## Strain gages measure pressure waves

Normally a simple material testing machine is not able to apply the required high strain rates. Therefore, a so-called split-Hopkinson bar is used for measuring such dynamic quantities. British electrical engineer Bertram Hopkinson first suggested such measurements in 1914. The setup used today is based on a modification developed by Herbert Kolsky in London in 1949. It is sometimes also called split-Hopkinson Kolsky bar.

The material sample is positioned between two bars in the split-Hopkinson bar: the incident bar and the transmission bar. A so-called striker - for example, a projectile accelerated by compressed air - strikes the incident bar causing a pressure wave. This pressure wave runs through the first bar. Part of the wave is reflected at the bar end, the other part runs through the material sample into the transmission bar. Strain gages (SG) installed on the surfaces of the incident bar and the transmission bar measure the strains caused by the pressure waves. This enables the amplitudes of the pressure wave originally applied to the incident bar, of the reflected pressure wave and of the transmitted pressure wave to be determined. The strain gages are interconnected in Wheatstone bridge circuits. Since the pressure waves run through the bars at the speed of sound, a very dynamic measurement system is required offering a correspondingly high bandwidth of about 100 kHz.

## High-speed measurement data acquisition ...

### ... and calculation of material characteristics

Test and measurement expert HBM offers the Genesis HighSpeed measurement system that satisfies high demands on dynamics and bandwidth. The modular measurement system offers extremely high sample rates even for systems with high channel counts. Its modularity allows users to optimally adapt the measurement system to their measurement task. For example, corresponding data acquisition cards are available to enable direct connection of the required strain gages in a quarter bridge circuit. Connecting the strain gages is very easy. No additional compensating circuits or preamplifiers are required. Perception software is available for analysis of the acquired signals.

Some prerequisites need to be met to infer the required material characteristics from the acquired signals. Both the incident bar and the transmission bar need to be made from the same material and need to have a great length in comparison to their diameter. In addition, it is essential to know the speed of sound C0 at which the pressure waves run through the bars. Provided that the bars' diameter is small, as described above, the speed of sound can easily be calculated from Young's modulus E and the density ρ:

The above-described strain signals of the pressure wave applied to the incident bar εI, of the reflected pressure wave εR, and of the transmitted pressure wave εT are measured. The resulting material stress is:

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with E being Young's modulus for the transmission bar and A0 the transmission bar's cross-section and A the material sample's cross-section. The strain rate of the material sample under test together with the original length L of the material sample is:

Forming the integral, the resulting strain is:

## Conclusion

The split-Hopkinson bar has been used for measurements already for more than 50 years. Over the past years, however, this measurement method has been used significantly more often. This is due to the fast test and measurement equipment available today, which substantially facilitates the required measurements. Matching software and powerful modern computers also permit calculation of the required material characteristics without any major problems. HBM offers a complete spectrum of products for this application, ranging from strain gages through matching measuring amplifiers and measurement systems to analysis software. The result: reliable measurements on materials used by design engineers in many different branches of industry.