Split Hopkinson (Kolsky) Bar

A Kolsky bar, also widely known as a split Hopkinson pressure bar (SHPB), is a characterization tool for the mechanical response of materials deforming at high strain rates (10² – 10⁴ s^–1). This chapter presents the brief history, general working principles, considerations in design, and data reduction process of a Kolsky bar, illustrated by its compression version.

In a material property characterization experiment, the specimen should deform uniformly under well-controlled testing conditions in order for the experimental results to be clearly documented and interpreted. In quasi-static experiments, testing conditions are monitored and adjusted in real time by closed-loop feedback control systems such that the specimen deforms under specified conditions throughout the test. In Kolsky-bar experiments, feedback control systems are not available. Furthermore, due to the relatively low stiffness of the bars, even under identical loading conditions, the testing conditions on the specimen depend on the specimen response. Therefore, it is challenging to subject the specimen to specified loading conditions in Kolsky-bar experiments. Both the loading processes in the specimen and their relations to the commonly defined testing conditions need to be carefully examined. In addition, the development of Kolsky bar and its data reduction scheme involves many idealized assumptions. However, in actual Kolsky-bar experiments, these assumptions are not satisfied automatically, which requires further efforts in experiment design. The valid testing conditions and necessary approaches to achieve specified conditions in the Kolsky-bar experiments are presented in this Chapter.

Many brittle materials deform in a manner of nearly linear elasticity until failure at small strains. As specimens in Kolsky-bar experiments, these materials are extremely sensitive to stress concentrations due to bar misalignment or non-parallel loading surfaces. To deform a linear elastic specimen at a constant strain rate, a loading pulse with constant stress rate is needed. This chapter describes the characteristics of brittle specimens, introduces the modifications to Kolsky bar necessary to achieve the desired and valid testing conditions on the specimen, and outlines the design of Kolsky compression bar experiments on brittle materials with step-by-step examples.

In this chapter, we present Kolsky-bar techniques modified for soft material characterization in compression. Soft materials typically have low strength, stiffness, and wave impedance, which make it challenging to obtain accurate stress-strain responses at high strain rates. The challenges in characterizing soft materials are introduced in this chapter. Solutions in regard to achieving stress equilibrium, generating proper pulse shapes and sensing low-amplitude forces are then presented. Experimental design for soft material characterization is illustrated with example materials that include PMMA, rubber and rubber-like polymers, brittle and elastic-plastic polymeric foams, and biological tissues.

Ductile materials initially deform elastically and then plastically to large strains. The material stiffness is quite different in elasticity and plasticity. Experiment design may be focused on the response in either elasticity or plasticity, but mostly in the latter. This chapter describes the distinct characteristics of ductile materials, introduces a compound pulse shaper to maintain constant plastic strain rates. Examples are then given with the specimen materials being metals, a shape-memory alloy, an alumina particle- filled epoxy, and a lead-free solder.

Triaxial experiments are commonly performed under quasi-static loading conditions on pressure-sensitive materials. In such an experiment, a cylindrical specimen is placed inside a pressure chamber where hydrostatic pressure is applied. Further axial pressure is then applied to measure the material response in terms of principal stress difference verses pressure or axial strain. A compression Kolsky bar can be modified through integration of pressure chambers such that further axial load is applied dynamically after hydrostatic pressure on the specimen. This chapter describes the design principle of a dynamic triaxial test system consisting of a Kolsky bar and two pressure vessels, the instrumentation for pressure and specimen deformation measurement inside a pressure chamber, and an example of using such a system to characterize the dynamic compressive response of sand under various hydrostatic pressures. In addition to the pressure boundary conditions on the lateral surface of the specimen, snug-fit sleeve can be used to supply dynamic triaxial load through displacement boundary conditions during a Kolsky compression bar experiment. Examples are given to determine the mechanical responses of an EPDM rubber and an epoxy syntactic foam under such dynamic lateral confinement.

When the specimen temperature differs from the room temperature, timing of mechanical load becomes a variable due to heat conduction. There are two approaches to conduct experiments with the specimens heated or cooled. One is to heat/cool the specimen with the bars attached. The other is to bring the bars in contact with the specimen after it reaches a desired temperature. The latter is preferred particularly at very high temperatures since temperature gradient in the bars affects wave propagation, which must be corrected. This chapter describes methods for high/low temperature Kolsky-bar experiments. The design of a computer- controlled automated system for high temperature experiments is presented. Examples are given with specimen materials including a stainless steel, a shape memory alloy, a syntactic epoxy foam, and PMDI foams with different densities.

In addition to the compression version of the Kolsky bar, there are bars that subject the specimen under tension, torsion, and combined torsion/ axial loading conditions to explore the high-rate response of materials under more diversified stress states. The work principles of these bars are similar to that of Kolsky compression bar. However, the loading mechanisms are more complicated than the simple bar-to-bar impact seen in compression experiments. The specimens in both tension and torsion experiments must be attached to the bar ends, which brings in the complication of gage-section identification in strain-rate calculations. This chapter describes various designs of Kolsky bars to conduct dynamic experiments for the specimen stress-strain response under uniaxial tension, pure torsion, combined tension/torsion, or compression/torsion. The designs of specimens will also be described. Examples of high-rate uniaxial tension experiments on polymers, bones, and high-performance fibers are provided.

Most Kolsky bars characterize dynamic material properties at strain rates between 5×0² and 1×10⁴ s^-1. On the other hand, quasi-static material testing machines operate under closed-loop control at strain rates below 1 s^-1. However, many applications require stress-strain data around the intermediate strain-rate range of 5×10¹ - 5×10² s^-1, where data is scarce for any material. This chapter describes designs of Kolsky bars to conduct dynamic experiments at strain rates below 10² s^-1, which is the upper limit of modified quasi-static methods. The overlap in strain rates achieved by the modified Kolsky bar and quasi-static techniques bridges the gap in the intermediate strain-rate range, which also facilitates the system-error examination between the quasi-static and dynamic testing methods.

Kolsky bars rely on stress wave propagation in elastic bars to apply dynamic load on a specimen and to measure the loading and deformation histories in the specimen. This principle of using stress waves to supply dynamic loading and to remotely detect mechanical events can be equally employed to characterize the dynamic response of various structures. In this chapter, we review some of the recent applications of different versions of the Kolsky bars including (1) determination of dynamic fracture behaviors of notched specimens, (2) determination of the biaxial flexural strength of thin brittle sheets, (3) examination of the dynamic response of micro-machined structures, and (4) low-speed penetration.