Keywords

2.1 Introduction

The issues related to the subject of high-energy absorption building materials are extremely valuable and important for conducting dynamic analyzes. Experiments conducted as part of high-energy absorption building materials research are helping to develop the field of protect built components of critical infrastructures. Materials can be used to effectively absorb blast wave energies and impact impulses and protect human lives and properties under extreme blasting events.

There are three key aspects to the current development of the field of high-energy absorption building materials:

  1. I.

    modeling of impact and wave mechanics of protective components;

  2. II.

    impact and damage for protective structures;

  3. III.

    development of energy-absorbing building materials with more effective and better energy-consuming parameters.

Carrying out further research analysis of the presented problem II) impact and damage for protective structures, it is necessary to carry out more research on strain rate dependent material modeling at various temperatures. Hopkinson bar technique is a research methodology that allows for empirical analysis of both issues of dynamic mechanics of materials and structural mechanisms depending on the selected configuration of measuring bars and the impact of a dynamic striker.

Due to their diverse internal structure and their mechanical properties, the most frequently analyzed materials include various samples of granular, cellular and polymer materials:

  • sand [1,2,3,4];

  • wood [5, 6];

  • aerated concrete [7, 8];

  • foam [9, 10];

  • rubber [11].

The summary of the number of research works with the division into the samples used for research in the past (up to 2012) is shown in Fig. 2.1.

Fig. 2.1
A bar graph illustrates the year on the x-axis ranging from 1946 to 2006 on an increment of 10 years. The y-axis represents a number of papers ranging from 0 to 350 on an increment of 50.

Summary of the number of research works using the Hopkinson bar technique for experiments with samples of various materials up to 2012. (Reprinted from Ref. [12])

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In recent years, according to the search results of research in Web of Science and Springer Link, there is a continuous development of research on a variety of material samples, including high-energy absorption samples, using the Hopkinson bar technique. A comparison of the number of papers (research and review) in recent years according to Web of Science and Springer Link is shown in Table 2.1.

Table 2.1 Summary of the number of research works using the Hopkinson bar technique for experiments with samples of various materials in 2017–2021 [13, 14]
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2.2 SHPB Test Stand and Configurations of Test Samples

The split Hopkinson pressure bar test stand is used to test the dynamic behavior of various samples of material subjected to the impact of an accelerated striker. The operating principle of the SHPB is based on the Hopkinson bar technique.

Generally, the most important elements of the SHPB test stand include the following listed elements [15] shown in Fig. 2.2:

  • gas gun;

  • striker;

  • specimen;

  • measuring bars (depending on the configuration – initiating and transmitting);

  • feeding unit (set of strain gauges);

  • time counter (to determine the speed of the striker);

  • digital oscilloscope and computer.

  • The characteristics of the research methodology and the final results of dynamic research with the use of Hopkinson bar technique depend on the adopted configuration of the research sample and the system of measuring bars. Various specimen configurations used for testing in:

    • compression (shown in Fig. 2.3a);

    • tension (shown in Fig. 2.3b);

    • Bauschinger effect (shown in Fig. 2.3c);

    • shear (shown in Fig. 2.3d);

    • fracture toughness (shown in Fig. 2.3e);

    • Brazilian test/splitting test (shown in Fig. 2.3f);

    • direct impact (shown in Fig. 2.3g);

    • dynamic hardness/penetration (shown in Fig. 2.3h);

    • dynamic friction ratio (shown in Fig. 2.3i).

  • An additional element of the test stand based on the Hopkinson bar technique is the use of a high speed camera to record the behavior of the tested material sample at the moment of being hit by a striker and its further behavior after the impact. Figure 2.4 shows an example of setting up and using a high speed camera during the dynamic test of the duralumin plate model as an element of the Hopkinson bar test stand located at the Faculty of Civil Engineering and Geodesy of Military University of Technology in Poland.

  • As a result of the use of a high speed camera, it is possible to record the situation at the moment of dynamic impact for examples of the test sample configuration in: compression (shown in Fig. 2.5a) and direct impact (shown in Fig. 2.5b).

  • Another very important additional element of the test stand based on the Hopkinson bar technique is to give the tested sample a different temperature than the ambient temperature (a heated sample or a frozen sample) and the use of a high speed infrared camera. This modification of the experiment makes it possible to check the dynamic behavior of the tested material sample under changing external conditions (temperature change) [28]. Particularly valuable are the experiments with the use of the heating-freezing cycle of the sample and the study of the influence of large temperature fluctuations on the dynamic mechanical properties of the material sample. Figure 2.6 shows a configuration diagram of the material sample setting in the experiment modification: a) heating the sample (Fig. 2.6a) and freezing the sample (Fig. 2.6b).

Fig. 2.2
An image illustrates a gas gun, strike, a specimen, a counter, two feed units, a preamplifier 50-volt power supply, a pulse generator, and a digital oscilloscope connected to a computer with an I E E E 4 8 8.

Schematic layout of the SHPB test stand with the marking of the most important elements. (Reprinted from Ref. [16])

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Fig. 2.3
An image shows different types of tests marked as a, b, c, d, e, f, g, h, and i arranged in 3 columns and 3 rows.

Various specimen configurations used for testing in: (a) compression, (b) tension, (c) Bauschinger effect, (d) shear, (e) fracture toughness, (f) Brazilian test/splitting test, (g) direct impact, (h) dynamic hardness/penetration/and (i) dynamic friction ratio. (Reprinted from Ref. [16])

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Fig. 2.4
A photograph of a High-Speed camera being used as an element for the Hopkinson bar test stands located in the Faculty of Civil Engineering and Geodesy of M U T in Poland.

An example of setting up and using a high speed camera as an element of the Hopkinson bar test stand located at the Faculty of Civil Engineering and Geodesy of MUT in Poland

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Fig. 2.5
A representation of sample configuration in a high-speed camera with compression and direct impact of recording a dynamic test in the moment of impact.

An example of the result of recording a dynamic test at the moment of impact with the use of a high speed camera for a sample configuration in: (a) compression and (b) direct impact

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Fig. 2.6
An illustration of two material samples. Image A represents a blue specimen that is being compressed and results in a real image of an object being compressed, Image B depicts blue specimens getting a direct impact and the real image of an object getting a direct impact.

Modifications of testing a material sample in variable external conditions/changing the temperature of the sample: (a) heating the sample and (b) freezing the sample

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2.3 Dynamic Behavior of Energy-Absorbing Building Materials

In the Hopkinson bar technique configuration, the SHPB stand is used for the for testing in compression sample. Figure 2.7 shows the propagation process of waves in the SHPB during the registration of three cycles of loading. At the interface of various material media (due to different material density values), the phenomenon of partial reflection of the wave and partial passage of the wave further to the next material medium occurs [25]. When the striker hits the initiating bar, a initiating wave is produced that travels through the initiating bar to the end of initiating bar – sample face. The phenomenon of partial reflection of the wave takes place and the return of the wave thus formed reflected through the initiating bar [24]. The remaining part of the wave is subject to the phenomenon of wave transfer to another medium (sample) – the wave continues to propagate after leaving from the sample through the transmitting bar in the form of a transmitted wave. The phenomenon repeats analogously in subsequent load cycles.

Fig. 2.7
A graphical representation of propagating wave in the form of an initiating wave reflected wave, and transmitted wave in S H P B test for loading three cycles. It starts with the striker, then with the initiating bar, specimen, strain gage, and finally the transmitting bar.

The phenomenon of wave propagation in the form of an initiating wave, reflected wave and transmitted wave in the SHPB test for three cycles of loading. (Reprinted from Ref. [17])

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  • As part of the research on the dynamic behavior of various energy-absorbing building materials samples, experiments with the use of samples were carried out:

    1. I.

      sand

A key aspect of sand dynamic testing, as representative of a non-cohesive soil, is to select the appropriate rigid jacket model in order to ensure the cylindrical shape of the sample (due to the loose nature of the sand sample). An important factor in the rigid jacket selection procedure is the necessity to ensure the state of triaxial stress and uniaxial deformation by selecting an appropriately thick layer of the rigid jacket. Figure 2.8 shows the location of a loose sand sample surrounded by a selected rigid jacket.

Fig. 2.8
A cylindrical representation of sand sample with S H P B Test on a rigid jacket. The outermost region represents the rigid jacket with the strain gage at the bottom. The circumference represents the specimen with R subscript 1, R subscript 2, P subscript i respectively.

Cylindrical sand sample in confined rigid jacket in SHPB test. (Reprinted from Ref. [17])

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The set of stress components in a specimen allows to calculate a wide spectrum of properties of tested material: shear resistance, pressure in a specimen, its volumetric strain, the intensity of stress and strain, the factor of lateral pressure (thrust) and then to construct a set of needed experimental dependencies. Figure 2.9 shows an example of the result of dynamic sand sample testing on the SHPB test stand in the form of true stress and strain - strain rate plots for five different moisture levels of the sand sample (0%, 10%, 15%, 20% and 25%). Due to its energy-absorbing properties, sand is often used as a ground backfilling of concealed and shelter structures [18, 23], which helps to suppress energy generated from adverse actions of the enemy, e.g. an explosion of an explosive material.

Fig. 2.9
A graph represents various lines of humidity with strain on the x-axis, values ranging from 0 to 14 and the y-axis represents the wet sandy mixture. Line 1 represents Humidity at 0 percent, Line 2 represents humidity at 10 percent, Line 3 with humidity at 15 percent, Line 4 with Humidity at 20 percent, and line 5 with humidity at 25 percent. Values are approximated.

Graphs of strain - true stress and strain - strain rate for different levels of sand sample moisture – 0%, 10%, 15%, 20% and 25%. (Reprinted from Ref. [19])

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  1. II.

    wood

The second example of energy-absorbing building materials is a wood sample. On the example of a birch sample, an analysis of the dynamic behavior of a wood representative was carried out based on the SHPB test stand. Figure 2.10 shows a cycle of dynamic tests with two variables:

  • different temperature values of a wood sample (birch): sample with a standard room temperature of +20 °C (shown in Fig. 2.10a), sample with increased temperature – sample heated to +60 °C (shown in Fig. 2.10b) and sample with reduced temperature – sample frozen −40 °C (shown in Fig. 2.10c);

  • different cutting angle values – for each of the three different sample temperatures, five wood samples with different cutting angle values were made: 0°, 30°, 45°, 60° and 90°.

  1. III.

    foam

A third example of energy-absorbing building materials is a plastic foam sample. On the example of two samples, an analysis of the dynamic behavior of a plastic foam representative was carried out based on the SHPB test stand – Fig. 2.11 shows the results of an example experiment in the form of true strain – true stress and true strain – strain rate graphs for the foam sample with density 0.19 \( \frac{g}{cm^3} \) (marked with 1) and foam samples with density 0.67 \( \frac{g}{cm^3} \) (marked with 2).

Fig. 2.10
An image illustrates 3 graphs. The graphs illustrate stress, M P a on the y-axis and strain on the x-axis for (a) birch, temperature plus 20 degrees celsius, (b) birch, temperature plus 60-degree Celsius, (c) birch, temperature minus 40-degree celsius. There are five curves in each graph, one for 0, 30, 45, 60, and 90-degree cutting angles. 0 degrees has the lowest levels in strain and showcases the highest levels in stress. The maximum stress values decrease with increase in strain.

Graphs of strain – stress and strain – strain rate for different sample temperature values: (a) temperature +20 °C, (b) temperature +60 °C and (c) temperature −40 °C – for each temperature there are samples with different cutting angles: 0°, 30°, 45°, 60° and 90°. (Reprinted from Ref. [20])

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Fig. 2.11
A graphical representation of true strain in percent and True stress in M p a. Two peaks are found in the graph. In the first, the value raises from 0 to 75 at a density of 0.19 grams per centimeter cube. Further, the line reaches from 20 to 80 at a density of 0.67 grams per centimeter cube. the graph is further a normal line and again increases to a peak value of 65 at a density of 0.19 grams per centimeter cube

Graphs of true strain – true stress and true strain – strain rate for two plastic foam samples: foam sample with density 0.19 \( \frac{g}{cm^3} \)/marked with 1/and foam sample with density 0.67 \( \frac{g}{cm^3} \)/marked with 2. (Reprinted from Ref. [16])

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2.4 Evaluation Indexes of Energy Absorption

The main evaluation indexes of energy absorption performance by materials tested are as follows:

  1. I.

    energy absorption diagram of materials Q.

Publication [21] shows the proposal of the method of energy absorption diagram, and the energy curve absorbed by the unit volume could be got by the integral processing of the stress σ – strain ε curve from the test [24]. That is to say, from the initial compression to the dense stage, the area under the stress – strain curve is Q, defined in Eq. (2.1), which represents the energy absorbed by the buffer volume of the unit volume during the compression to the dense stage. It characterizes the energy absorption capacity of the material.

$$ Q={\int}_0^{\varepsilon_i}\ \sigma d\varepsilon $$
(2.1)

  • An exemplary test result as energy absorption Q(ε) is shown on the example of the graph of the dependence curve energy absorption – engineering strain in Fig. 2.12.

  1. II.

    energy absorption efficiency of materials

The publication [22] shows the definition of the expression of energy absorption efficiency E of materials, as in the Eq. (2.2):

$$ E=\frac{\int_0^{\varepsilon_i}\ \sigma d\varepsilon}{\sigma_i} $$
(2.2)

This formula shows that the energy absorption efficiency of the material E is the ratio of the energy absorbed by the material to the corresponding stress when the material reaches a given strain [26]. When the energy absorption efficiency E of the material reaches the maximum value, it shows that the energy absorbing property of the cushion materials is the best at this stress and its dissipation capacity can be brought into full play [27].

Fig. 2.12
A graphical representation of many lines between engineering strain and Energy absorption in Millijoules. The energy absorption represents the efficiency curve at a different strain rate value.

Graph of the energy absorption curve – engineering strain in an exemplary dynamic experiment for different strain rate values. (Reprinted from Ref. [11])

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An exemplary test result as energy absorption efficiency E(ε) is shown on the example of the graph of the energy absorption efficiency – engineering strain dependence curve in Fig. 2.13.

Fig. 2.13
A graphical representation of many lines between engineering strain and Ideal energy absorption. The energy absorption represents the efficiency curve at a different strain rate value.

Graph of the energy absorption efficiency curve – engineering strain in an exemplary dynamic experiment for different strain rate values. (Reprinted from Ref. [11])

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  1. III.

    ideal energy absorption efficiency

The publication [22] shows the definition of the expression of the ideal energy absorption efficiency I of materials, as in the Eq. (2.3):

$$ I=\frac{\int_0^{\varepsilon_i}\ \sigma d\varepsilon}{\left({\sigma}_i\bullet {\varepsilon}_i\right)}=\frac{E}{\varepsilon_i}=\frac{Q}{\left({\sigma}_i\bullet {\varepsilon}_i\right)} $$
(2.3)

It can be observed in this formula that the ideal energy absorption efficiency I of the material represents the ratio of energy absorbed by the real material and ideal material specimens at the same strain level.

An exemplary test result as ideal energy absorption efficiency I(ε) is shown on the example of the graph of the energy absorption efficiency – engineering strain dependence curve in Fig. 2.14.

Fig. 2.14
A graphical representation of energy absorption of the efficiency curve. The x-axis represents Engineering strain and the Y-axis represents the ideal energy absorption.

Graph of the ideal energy absorption efficiency curve – engineering strain in an exemplary dynamic experiment for different strain rate values. (Reprinted from Ref. [11])

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2.5 Conclusion

The issue of high-energy absorption building materials is a crucial research area for the proper provision of protect built components of critical infrastructures. There are different types of materials which, due to their dynamic characteristics, can be used to effectively absorb blast wave energies and impact impulses and protect human lives and properties under extreme blasting events. Such materials include granular, cellular and polymer materials, e.g., sand, wood, aerated concrete, foam and rubber.

The test stand based on the Hopkinson bar technique enables dynamic studies of the behavior of various samples, including high-energy absorption building materials. Depending on the configuration of the measuring bars adopted on the test stand and the location of the tested sample, it is possible to test in experiments, e.g. compression, tension and shear.

As a result of the literature review and observation of dynamic experiments, it can be concluded that the properties and dynamic characteristics of high-absorbed materials depend mainly on two factors: the strain rate and the temperature of the tested sample. High-energy absorption materials have a greater ability to absorb large energy ranges during dynamically deformation compared to that of materials during quasi-static deformation. In particular, in loose materials, e.g. sand as an example of a non-cohesive soil, it can be observed that the sample compaction process is faster in dynamically deformation than in quasi-static deformation.

Experiments in the area of behaviors of high-energy absorption materials allow for the effective use of the characteristics of these materials and the correct implementation of the design of protective components for critical infrastructures.