1 Introduction

The steel industry has been a valuable asset for the development of societies. The slag is a residue from metallurgical industrial processes that allows the removal of impurities during steel production by forming oxides and also allowing reaction exchanges with liquid metal, among some other roles. The worldwide production of crude steel has had a growing trend since the early twentieth century with an annual production of 1951 million tons during 2021 [1]. Within the production of crude steel, pyrometallurgical processes produce slags in rates of 0.25–0.30 tons per ton of crude iron for typical ore grades and 1.0–1.2 tons for low-value grades from iron blast furnaces (BF), while typically 0.2 tons from steel furnaces [2]. The figures are high: the total production of steel furnace slags in 2018 in Europe was 16.3 million tons, and blast furnace slags was 20.7 million tons [3]. The composition of the slag depends highly on the metal being produced, and therefore, certain slags are considered potentially hazardous wastes, or simply, the uncontrolled disposal can represent a critical environmental risk for populations living and working in the vicinity. With this in mind and following the sustainability principles reflected by the World Steel Association, incorporating pyrometallurgical by-products in a circular economy framework is of great interest in order to maximize the efficient use of resources throughout the life cycle of the steel products and help in the reduction of CO2 emissions [4].

The current practice for the management of steel slag includes the re-use of slag for different product applications such as infrastructure construction, fillers, binders, and soil stabilization, among others [5], due to its mechanical properties. It is considered to be a valuable and low-cost resource to be used for industries with a significant carbon footprint [6, 7]. Thus, it has a great potential to be introduced in the production line to reduce the carbon emissions and keep large productions. Within this scope and to illustrate the value of this material, ground granulated blast furnace slag (GGBS) can be used instead of ordinary Portland cement (OPC) in concrete production: slags become a cement substitute that improves durability [8]. GGBS is obtained by quenching molten iron slag from a blast furnace in water or steam, to produce a glassy, granular product that is then dehydrated and ground into a fine powder. Furthermore, GGBS is a by-product of the iron-making industry that can be used in a concrete mix, offering a good alternative to traditional Portland cement. As GGBS is a by-product of current industrial processes, GGBS is even more sustainable than other cement substitutes. GGBS offers great durability, and it improves concrete resistance to damage from alkali-silica reaction, sulfates, and chlorides and reduces the likelihood of concrete thermal cracking [9].

Silico-manganese slag derived from the production of alloy steels is a special kind of by-product that comes from carbothermic reductions of raw material in arc furnaces [10]. Typically, the production of silico-manganese alloy produces 1.2–1.4 tons of slag for every ton of SiMn alloy for a total of 8.9–10.4 million tons per year. SiMn slags consist mainly of oxides such as SiO2, CaO, Al2O3, and MgO and are glassy in nature. Due to its constituents, manganese slag is a potential raw material for alkali-activated binders in cement production [11]. In general, the applicability of the slag depends on refinement processes where certain particle sizes are needed to increase the binding properties of the granulated material.

It is known that the efficiencies of a plant-scale comminution process are often evaluated according to indexes such as the bond work index (\(W_i\)) and measures of the size reduction which can tell more about the efficiency in downstream processes such as flotation responses and mineral recovery [12]. Following the same principle of geometallurgical modeling (known as Bond \(W_i\)), which aims to better understand the ore and its properties to predict more accurate behavior and thus improve extraction operations in the mine [13], the increase of knowledge of the mechanical response of the slags becomes important in the process of valorization of secondary raw materials. The mechanical response and fracture patterns give information of the material under mechanical loads that can be used further on, e.g., modeling applications for the upscaling and evaluation of industrial-scale recycling processes.

The split Hopkinson pressure bar (SHPB) is a technique widely used for the dynamic characterization of materials to obtain the stress–strain response of materials at high strain rates (\(10^2-10^5\) s\(^{-1}\)). It has been adapted to test brittle materials such as ceramics and rocks to obtain information about high strain rate responses in terms of primarily strengths [14,15,16,17,18,19], but to the authors knowledge, there is no information of tests on manganese slags. Previous experimental compressive analyses describing the stress–strain behavior of mercury slags have shown time-dependent mechanical behavior reflected as variations of the stability and strength of the material [20]. On the other hand, dynamic mechanical experiments on copper slag reinforced concrete (having an inherent heterogeneous micro-structure) with a 50-mm SHPB test [21] resulted in irregular fragmented pieces after the impact failure. A strong dependency of, not only the dynamic compressive strain rate, but also of the weighted value of inclusions of slag within the matrix, on the stress–strain curve has been observed for recycled concrete with ferro-nickel slag aggregates [22]. Further characterization has described a proportional effect of the strain rate on the mechanism of fracture [23, 24], resulting in higher degrees of destruction and fragmentation by the increase of the strain rate. Different morphologies and slag content of concrete mortars have been studied, reasoning on the effect of the structure on the development of the damage. Although investigations of the effect of slag aggregates on the mechanical behavior matrices made from structural material are inconclusive, the content of slag aggregate can impact positively or negatively the peak stress, elastic modulus, and energy absorption (toughness) depending on the type of slag and nature of the matrix as shown for ash/slag-based geopolymeric concrete and coal-fired slag concrete [25, 26]. Overall, slag inclusions have a significant effect on the mechanical properties of the materials and fracture behavior.

Full-field displacements and strain measurements are of great interest when studying the mechanical response of heterogeneous material to time-dependent loads for the development of constitutive models and validation of numerical simulations. Digital image correlation (DIC) techniques have become attractive since they are independent of the geometry, size, material, and deformation rate. Besides, this technique is useful for the analysis of heterogeneous materials when heterogeneous deformations and strain localization are present during dynamic testing [27]. By combining these techniques, the history of full-field deformations can be obtained. Previous studies have shown information using a frequency up to 200,000 fps of axially compressed specimens [28], Brazilian disc [29], and notched specimens [30, 31], although, due to the brittle nature of the materials, even higher frequencies are desired to minimize aliasing problems.

The focus of this work is to understand and evaluate the macro-mechanical response and damage of manganese slag under compressive and indirect tensile loading from a meso-scale point of view. This is to increase the knowledge on the fracture of complex material and the value of material data for, e.g., modeling of the breakage required in external applications such as concrete binders. Therefore, the mechanical behavior of manganese slag from steel production is studied under dynamic loading conditions using a SHPB machine and ultra-high speed digital image correlation (DIC) to obtain information of the displacements and strains, as well as crack initiation, fracture process, and energy dissipation.

2 Materials and Methods

This section presents the procedure followed in this study. It consisted of manufacturing the slag specimens, calibrating the system, and acquiring and post-processing data from unconfined compression tests and indirect tensile tests (Brazilian disc) under dynamic conditions.

2.1 Slag

2.1.1 Description of the Material

Air-cooled MnSiFe-slags from electric arc furnace (EAF) manganese steel production in Norway were studied. Due to segregation processes during uncontrolled cooling, the material presents a high level of heterogeneity. A total of 14 different phases were determined in previous studies performed by Bravo et al. [32]. These phases were classified into groups according to their texture: a group of fine phases defined as a crystalline-amorphous matrix consisting mainly of a silicate phase of Ca-Al-Mg (85% of the total volume of the samples) and a group defined as inclusions corresponding to spherical phases of MnSiFe, where 95% of the total iron is concentrated.

2.1.2 Specimen Preparation

Brazilian disc and unconfined compression tests specimens were taken from a batch material (see Fig. 1) showing the following features: layered material with dissolved phases of MnSiFe\(_{x}\), silicate phases of Ca-Al-Mg, and high amounts of spherical inclusions of different sizes distributed randomly within a highly porous matrix [32, 33].

Fig. 1
figure 1

Cross-sections from X-ray microtomography of four representative samples of manganese slags. a shows layered material with dissolves phases of MnSiFe\(_{x}\) distributed randomly within the matrix, b shows a crystalline-amorphous matrix containing large amounts of CaSiAlMgMnO, c shows the high porous appearance of the crystalline-amorphous matrix with heterogeneous distributions of dissolved phases of CaMgFeMnSiO and CaFeAlSiO, and d contains high amounts of MnSiFe\(_{x}\) spherical inclusions of different sizes distributed randomly. Reprinted with permission from [33]

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Cylindrical specimens were drilled with a diamond core drill bit and then machined to obtain parallel and flat ends. The diameter was selected according to information presented in a previous study on similar material where most of the inclusions had a size ranging from 80 to 400 \(\mu \)m [33]. Based on ASTM standards (ASTM \(D7012-14^{\varepsilon ^1}\); ASTM \(D3967-16\)), it is recommended to have a diameter ten times larger than the largest grain size (in this case, the inclusions were considered instead) to minimize errors. Brazilian disc specimens of \(25.5 \pm 0.3\) mm diameter with a thickness of \(10.2 \pm 0.6\) mm and axially loaded specimens of \(25.3 \pm 0.6\) mm diameter with a length of \(23.9 \pm 2.5\) mm were prepared. The specimens were sandblasted and sprayed with black and white boron nitride aerosol paint to obtain a clear and well-adhered stochastic pattern on the surface to enable DIC measurements.

Fig. 2
figure 2

Split Hopkinson pressure bar (SHPB) setup, where \(d_i = 700~mm\) and \(d_t=420~mm\)

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The heterogeneity of the composition and structure of the material affected the final axial dimensions. As a consequence, obtained specimens display variation of the thickness (t) of Brazilian discs and length (L) of uniaxial compression specimens. Although the suggested length/diameter ratio for metals is \(L/D = \sqrt{3\nu _s/4}\) in SHPB tests, modified tests for brittle material use a thickness ratio of \(t/D \approx 0.5\) for Brazilian discs and length ratio \(L/D \le 1\) for axial compression specimens. This is to avoid premature failure due to frictional and inertial effects and allow a larger displacement of the bar end before failure [34].

2.2 Experimental Setup

The experimental setup of modified Brazilian disc (BD) and the unconfined compression tests (UCT) included a split Hopkinson pressure bar (SHPB) complemented with a high-speed camera for evaluation of deformation fields utilizing DIC (see Fig. 2).

The SHPB is a technique widely used for the dynamic characterization of materials. Kolsky (1949) [35] was the first to extend the original Hopkinson bar technique to measure stress–strain response of materials at high strain rates. It works under the theory of wave propagation through a material sandwiched between an incident and transmission bar. A compressive pulse is generated to reach a specimen with lower impedance, and so a reflected tensile pulse travels back along the incident bar. The setup consists of 25.4 mm diameter maraging steel (\(E=210 \) GPa, hardness 58 HRC) bars with a length of 3 m and 2 m for the incident bar and transmitted bar, respectively. A cylindrical projectile of 140 mm length and 25 mm diameter is accelerated by an air gun and impacts the incident bar, generating a compressive stress wave. The waves propagate through the incident bar finding a difference of impedance when reaching the specimen. The wave is partially transmitted through the specimen and partially reflected along the incident bar. Strain gauges (Measurements group CEA-06-250UW-350, 6.35 mm) are mounted on each of the bars to obtain information about the strain histories of the incident \(\varepsilon _i(t)\), reflected \(\varepsilon _r(t)\), and transmitted \(\varepsilon _t(t)\) waves. The signals are amplified (Measurements group 2210A bandwidth 100 kHz) and sampled at a frequency of 1 MHz. The time resolution of the wave measurements is around 1 \(\mu \)s based on the length of the strain gauges and the speed wave of the bars.

The cylindrical specimens were placed between the incident and transmitted bars so that they were loaded diametrically for the case of BD or axially, for UCT specimens (see Fig. 3). A lubricant was applied on the surface of contact, between the specimen and the bar, to reduce the friction on the interface that might hinder the free deformation of the specimen along the radial direction of the bars [34, 36, 37]. Another reason to use lubricant is to improve the contact by filling irregularities on the surface due to wear and difference of the roughness between the specimen and the bars, and minimize the effects due to a possible difference of impedance.

Fig. 3
figure 3

Setup for Brazilian disc specimens (left), showing the region of interest (ROI) as the dotted line and highlighted area used for deformation analyses, and unconfined compression specimens (right) on the split Hopkinson pressure bar machine

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SHPB tests of metals are usually performed with a rectangular incident wave, characterized by sharp arising edges and oscillations at the plateau region. Although, when working with brittle materials, it is necessary to take into account small failure strains considering that the specimen might fail immediately after being impacted by the incident bar. Pulse shaping techniques were used not only to minimize effects of dispersion and reach dynamic stress equilibrium, which favors minimal inertial effects induced by the stress wave [38], but also to decrease high-frequency oscillations. A thin ductile material was placed between the striker and the incident bar to make it easier to keep the specimen deforming at a nearly constant strain rate.

Two sets of experiments were performed: a total of 9 specimens were tested under a Brazilian disc configuration and 8 specimens under unconfined axial compression. BD specimens were subjected to an impact velocity rounding 5 m/s together with a thin lead shim placed at the interface between the incident bar and the projectile, while UCT specimens at 24 m/s with an aluminum foil.

2.3 Dynamic Testing

The SHPB consists of three main components: a loading device, impact components, and an acquisition system. The loading device should be designed in such a way that the loading is performed in a controlled, stable, and repeatable way. The most common method to launch a striker is by the use of a gas gun that suddenly releases pressured air and accelerates the striker along a closed channel towards the incident bar. When the striker impacts its target with a certain speed, it induces a mechanical wave into the input bar (incident pulse). The wave travels along the bar until it reaches the first interface (between the incident bar and the specimen), generating a reflected wave (reflected pulse) which travels back along the incident bar and a transmitted wave (transmitted pulse). The strain pulse signals are captured by strain gauges on both the incident and transmitted bars. The signals are analyzed by accounting for the propagation of a single one-dimensional elastic wave through the bar, as well as stress equilibrium and continuity equations.

The force (P), at the front end (sub-index 1) and rear end (sub-index 2), is given as follows:

$$\begin{aligned} P_1=A_s\sigma _1=A_0 E_0 (\varepsilon _i+\varepsilon _r) \end{aligned}$$
(1a)
$$\begin{aligned} P_2=A_s\sigma _2=A_0 E_0 (\varepsilon _t) \end{aligned}$$
(1b)

where \(A_0\) and \(E_0\) are the sectional area and elastic modulus of the bars, and \(A_s\) is the sectional area of the specimen. \(\varepsilon _i\) and \(\varepsilon _r\) are the incident and reflected strains, respectively, recorded at the incident bar.

Assuming force balance on both interfaces (\(P_1 = P_2\)), Eqs. (1a) and (1b) give \(\varepsilon _i+\varepsilon _r = \varepsilon _t\). As a consequence, the strain rate (\(\dot{\varepsilon }\)), strain (\(\varepsilon \)) and stress (\(\sigma \)) of the specimens are given as follows [39]:

$$\begin{aligned} \dot{\varepsilon }_s (t) = \frac{2C_0}{L_s}\varepsilon _r(t) \end{aligned}$$
(2a)
$$\begin{aligned} \varepsilon _s = \int _0^t\dot{\varepsilon }_s(t)dt \end{aligned}$$
(2b)
$$\begin{aligned} \sigma _s(t)=\frac{A_0 E_0}{A_s}\varepsilon _t(t) \end{aligned}$$
(2c)

where \(\varepsilon _t\) is the strain recorded at the transmitted bar and \(C_0\) is the wave propagation speed of the bar. It is important to note that Eqs. (2a)–(2c) are applicable to axially loaded specimens, but not to diametrically loaded specimens due to geometrical reasons. For Brazilian disc specimens, it is necessary to implement other techniques to estimate the history of strains, such as DIC.

The incident energy (\(U_i\)), reflected energy (\(U_r\)), and transmitted energy (\(U_t\)) can be calculated from the strain signals as follows [40, 41], where \(n=i,r,t\):

$$\begin{aligned} U_n=A_0 E_0 C_0 \int _0^t(\varepsilon _n(t)^2)dt \end{aligned}$$
(3)

In SHPB tests, the energy absorbed by the material is the same as the energy dissipated during the impact, i.e., energy used for the creation of new surfaces, crack branching, and deformation, just to mention some. The dissipated energy (\(U_d\)) is calculated by

$$\begin{aligned} U_{d} = U_i- (U_r + U_t) \end{aligned}$$
(4)

2.4 Ultra-High Speed Digital Image Correlation

Due to the rapid crack initiation and propagation within the slag specimens, ultra-high speed imaging is crucial. A high frame rate is beneficial when it comes to detecting the actual crack initiation. The frame rate is therefore maximized with a trade-off in image resolution due to the maximum pixel transfer rate of the camera. A high-speed camera, Phantom Vision v2512, equipped with a microscopic lens was therefore selected.

The region of interest (ROI), i.e., the photographed area of diametrically loaded specimens, was chosen considering the theory of a Brazilian disc presented by Hondros [42] as a baseline, in which the specimen experiences a tensile condition [43, 44]. The ROI is shown in Fig. 3. It can be seen that the physical size or, more specifically, the height (vertical direction) of the ROI for the Brazilian disc specimens is approximately half of the size compared to the ROI if considering a full-sized specimen. The image resolution (pixels) could thereby be reduced for the Brazilian discs without lowering the spatial resolution (pixels/mm). By reducing the image resolution, the frame rate could thereby be increased. The frame rates for the UCT and BD were set to 380,000 and 663,200 fps, respectively. A pair of external LED illumination system (Constellation 120E15 with 22,000 lm) was used to light up the specimens in order to keep short exposure times.

2D images were captured for both BD and UCT, although only data from diametrically loaded samples (BD) was used to quantify strain fields. Due to the out-of-plane curved surface of the compression specimens, 2D imaging is insufficient for the evaluation of strain fields of axially loaded samples. Images from UCT were taken as a reference to identify the stages of fracture and not to obtain local values of strain on the surface. The information was processed with an integrated software of an Aramis v6.3.1 Digital Correlation System (GOM mbH, Germany). Global information was obtained for each time step by averaging local information. Figure 3 shows the area from BD specimens taken into account for these analyses.

3 Results

The following section presents the results obtained for both BD and UCT of manganese slag material. Tables 1 and 2 show both the physical and mechanical properties of the specimens tested under unconfined axial compression and Brazilian disc configurations, respectively. The mechanical properties for axially loaded specimens are presented in terms of the first visible crack and the ultimate compressive strength (UCS), which describes the maximum value of stress before the structure collapses. The strain rate was estimated at the point of maximum stress in order to discard post-fracture effects. The loading rate (\(\dot{P}_{max}\)) at the point of maximum load is presented for diametrically loaded specimens.

Table 1 Physical and mechanical properties of manganese slag specimens tested under unconfined axial compression. D is the mean diameter, L is the length of the specimen, and \(\rho \) is the apparent density. The strain rate at the UCS point is presented, where UCS refers to the ultimate compressive strength. The stress where the first visible crack is perceived is presented as a percentage of the UCS under the acronym f.v.c. \(U_{peak}\) refers to the dissipated energy up to peak load, and it is presented as a percentage of the total dissipated energy (\(U_d\))
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Table 2 Physical and mechanical properties of manganese slag specimens tested under Brazilian disc configuration. D is the mean diameter, t the thickness of the specimen, \(\rho \) is the apparent density, and \(\dot{P}\) denotes the loading rate
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Fig. 4
figure 4

Example of the incident, reflected, and transmitted pulses of the split Hopkinson pressure bar tests for specimens a, b UCT-06 tested under unconfined axial compression and c, d BD-06 under the Brazilian disc configuration

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Figure 4 shows representative data of the behavior of the correlated pulses (incident, reflected, and transmitted) from axially and diametrically loaded specimens, respectively. Stress equilibrium was evaluated to identify the different stages of fracture. The dotted line represents the stress history at the front end face, while the transmitted pulse equals to the rear end face (see Eq. (1)). In general, a good correlation of the pulses was obtained ensuring equilibrium. Information from the pulses, together with high-speed images, indicated that deformation and damage occurred within the first impact pulse.

Results of the signals obtained from axial compression and Brazilian disc tests are presented in Fig. 4.

3.1 Unconfined Compression Tests

Dynamic compressive stress–strain histories of an axially loaded specimen are presented in Fig. 5. Although the UCS of specimens UCT-01 to UCT-04 are similar with a value of \(248 \pm 13\) MPa, there is a great variability of the overall behavior among all the specimens. Specimens UCT-01 and UCT-02 showed a lower stiffness compared to specimens UCT-03 and UCT-04, reaching higher values of both, UCS by 4%, and average strain at the fracture point by 24%. The average stress where the first visible crack is perceived for specimens UCT-03 and UCT-04 is 23% higher compared to the lowest average value of specimens UCT-01 and UCT-02.

Fig. 5
figure 5

Dynamic compressive stress as a function of the axial strain for specimens tested under unconfined axial compression and. Yellow square markers present the first visible crack of each specimen

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Results from specimens UCT-05 to UCT-08 seem to have a larger variability where, particularly, specimen UCT-08 presents the maximum value of stress and smallest deformation from the whole batch of material. On the contrary, specimen UCT-06 reaches larger deformations and overall lower values of stress. Figure 6 shows that the UCS of specimens UCT-01, UCT-02, and UCT-05 to UCT-08 decreases with an increased strain rate, while specimens UCT-03 and UCT-04 seem to be more stable to time-dependent loads in general.

Fig. 6
figure 6

Maximum stress (MPa) as a function of the strain rate (1/s)

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Fig. 7
figure 7

Incident energy (\(U_i\)) (gray), total dissipated energy (\(U_d\)) (orange), and dissipated energy up to peak load (\(U_{peak}\)) (green) as a function of the strain rate for axial compression samples

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Although the UCS is an important mechanical property for the analysis of fracture, it is relevant to study the dissipation of energy during dynamic loading processes as well. The results of the dissipated energy up to peak load are presented as a percentage of the total dissipated energy during impact in Table 1. The tests were executed accordingly so that an average incident energy of 78 J was obtained. From Fig. 7, it is clear that specimen UCT-08 has the lowest dissipated energy together with the lowest strain rate. As the strain rate increases, the total dissipated energy becomes more stable with an average value of 29 J. Specimens showing a strain rate below 450 \(s^{-1}\) present a similar dissipated energy to peak load \(U_{peak}\) of approximately 10.5 J which corresponds to 35% of the total dissipated energy (\(U_d\)) in average. For specimens, reaching strain rates higher than 450 \(s^{-1}\), \(U_{peak}\) averages a value of 15 J which corresponds in average to 54% of the total dissipated energy. This information shows a trend where specimens reaching higher strain rates dissipate a great part of the total dissipated energy before reaching peak load.

Particularly, specimen UCT-04 uses 66% of the total dissipated energy before reaching peak load. The correlation of the deformation and fracture process of this specimen is presented in Fig. 8. Different stages are presented on the graph as markers of visible failure and UCS points, as well as the corresponding stress, where the maximum value of strain rate is reached, and an additional fully developed fracture point. The strain history shows a rapid increase of the stress within a short deformation up to a first plateau zone that lasts for 0.22% in strain until a total deformation of 0.38% in strain is achieved. This event happens before the first visible crack while the specimen is still been loaded. This points to micro-cracking and weakening of the structure, hence reducing the stiffness of the material.

Fig. 8
figure 8

Results from axial compression test of specimen UCT-04. Left: SHPB output signals. Right: compressive stress (solid line) and strain rate (dotted line) as a function of the axial strain. Correlated points (a) the first visible crack, (b) failure point, and (c-d) stages of unstable propagation of the cracks. The shaded area on both images highlights a plateau zone of stress during loading

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3.2 Brazilian Disc

Dynamic results of diametrically loaded specimens are presented in Fig. 9. The mechanical response of BD specimens is presented in terms of load and strain due to the complexity of the texture of the material. Thus, the theoretical solution presented by Hondros [42], where the crack should initiate in the center of the specimen, does not apply to manganese slag. Load-strain curves were reconstructed following the procedure defined in Sect. 2.4. It presents greater similarity among the specimens compared to results presented in Sect. 3.1 for unconfined axially loaded specimens. Despite the fact that weak areas of the structure cause non-central crack initiation, the overall behavior of the material is similar: a rapid increase at lower values of strain followed by a transition towards a plateau zone where the unstable crack propagation rules the macroscopic response. Previous studies on manganese slag carried out by Suarez et al. [33] under quasi-static monotonic and cyclic loading exposed a greater dispersion of the mechanical response, where several maximum values of load and stiffness were found. Contrarily, the evolution of damage from dynamic tests exhibits unrecoverable dissipated energy resulting in splitting and fragmentation of the material when a critical strain above approximately 0.2% is attained.

Fig. 9
figure 9

Force-strain relation for Brazilian disc specimens

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From the results in Table 2, it is possible to comment on the increasing response of the tensile stress along with the increase of the loading rate. Specimens BD-01 and BD-02 display the lowest values of stress, while specimens BD-03 to BD-05 and BD-07 appear to have the highest values. Specimen BD-06 presents a similar macro-behavior to BD-08 despite the difference of the amount of spherical inclusions embedded within the matrix (see Fig. 10).

Fig. 10
figure 10

Post fracture images of two manganese slag BD samples. a shows BD-08, and b shows BD-06. Visual examination allows to qualitatively compare the amount, shape, and size of inclusions embedded within the matrix

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Fig. 11
figure 11

Correlated DIC images of of specimen BD-08. Force vs. vertical strain curves correlated to (i) the first visible crack, (ii) fracture, and at (iii) propagation points. DIC images present localized events happening at each state of deformation

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Figure 11 shows correlated DIC images of one of the specimens containing a high amount of inclusions. Considering the post-fracture split pattern and its composition featured by high amount of embedded spherical inclusions, information suggests that the energy has been consumed during the creation of new surfaces, as well as crack branching and friction due to relative motion between crack surfaces.

From Fig. 12, it is clearly visible the path of the propagating crack during loading. Results are correlated to its corresponding force vs. time curve so that different stages of fracture are captured. This particular specimen made it possible to identify a central crack initiation at the maximum force. The unloading behavior happens progressively: after failure, the specimen seems to recover at around 70 \(\mu \)s to then fall again thereafter. From Fig. 12e and f, it is seen that the cracks “avoid” the inclusions while propagating towards the rear end of the specimen. Secondary cracks are created at the back side of the inclusions suggesting that (1) the matrix is more sensitive to tensile stresses compared to the inclusions and (2) grain boundaries are weaker (see Fig. 12f).

Another example where it is possible to identify the pattern of propagating cracks by the naked eye is given in Fig. 13. Figure 13b displays a crack that has started close to the center of the specimen suggesting that the effect of the inclusions does not have a major impact on the macro-response and the specimen holds high tensile stresses in a zone around its geometrical center. Figure 13c and d highlight the fracture process of an inclusion on the right end, while Fig. 13e and f evidence the evolution of damage displayed as secondary cracks behind the inclusions. As a general comparison, it is evident that the crack propagation path tends to avoid the inclusions unless they are loaded directly and subjected to high strain rates.

4 Discussion

Comminution is an expensive process energetically speaking as the resistance to create new surfaces tends to increase as the particle size diminishes. The knowledge on the dynamics of the fracture of material is of great interest since it can be applied to improving the energy efficiency of breaking operations, such as crushing, by obtaining information about valid failure criteria for the promotion of fracture [45]. Hence, an opportunity to develop constitutive equations and feed numerical models where mechanical properties, such as maximum strength and onset of fracture points, are used for damage and failure models, as well as the history of strains and deformation rates [46, 47].

The mechanical characterization of manganese slag is essential for increasing the knowledge of the mechanical behavior, from a macroscopic point of view, of secondary raw materials under time-dependent loading conditions. The rich portfolio of crushers available on the market, which offer special characteristics of the end product, makes dynamic tests become important for optimization processes such as modeling. Dominant loading mechanisms such as compression and impact [48] must be considered as they act as influencing factors on the fracture behavior and efficiency of the overall process.

The manufacturing of the specimens was a demanding job and special care needed to be taken into account considering the brittleness of the material. The separation of the phases and interfacial tension of slag specimens generated during the cooling process [49] had a great influence on the structure and, hence, the behavior of the material. As a consequence, specimens with a similar apparent density (some of them containing a high amount of randomly distributed inclusions and some others with a predominant glassy phase) were obtained. This dynamic study used a SHPB machine and ultra-high speed digital image correlation to obtain information of the deformation and development of damage under high strain rates. An open system worked in favor of supervising the response of the specimens under dynamic compressive pulses.

Fig. 12
figure 12

Stages of fracture of specimen BD-09 with high amount of inclusions randomly distributed: a contact point, b first visible crack, c failure point, d visible superficial damage, and e, f unstable propagation of the cracks along the specimen

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Fig. 13
figure 13

Stages of fracture of specimen BD-08 with high amount of inclusions randomly distributed

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Diametrical and axial compressive tests were set to obtain strain histories (\(\varepsilon \)) during impact. The UCS, first visible crack, and strain rate were estimated for axially loaded specimens, while the maximum load and loading rate were for Brazilian disc specimens. Additional information was given regarding the crack propagation path of specimens with a high amount of inclusions embedded within the matrix and dissipation of energy during impact.

Slight differences between the front and rear end faces point out non-uniform deformation of the matrix due to internal and localized events, which might be related as well to the unstable propagation of internal cracks. Results from both axially and diametrically loaded specimens exhibited a staggered progress that starts with an initial pre-loading, seen as a delayed increasing signal, followed by evolving internal damage and, finally, ending up in failure. In the case of axially loaded tests, information suggests that a critical source of error is the parallelism of the specimens. The nature of the initial contact point for BD specimens implies that the material exhibits chipping at the beginning, jumping from a tangential contact point to a cross-sectional area, where the structure is able to balance the forces at the front end of the specimen. Further analyses excluded the first stages of fracture.

It is important to notice that although the stress finds a plateau, the strain rate increases (see Fig. 8). Superficial cracks were visualized from the high-speed images suggesting that internal effects might have taken place. This points to compression-expansion transitions within the porous and heterogeneous matrix resulting in possible volumetric effects and progression to unstable crack propagation.

Stress gradients observed as variations of stress histories at the front and rear end faces of the specimen are a consequence of dissipative processes which lead to non-uniform deformations. SHPB signals give evidence of a global macroscopic behavior by averaging local information in time. Internal events such as micro-cracking and unstable propagation of cracks are not captured individually. It is also necessary to mention the strong dependence of the macro-behavior to inertial effects during the rapid rise of the strain rate at the beginning of the test. The findings of this study suggest that the variability of the points where the first visible crack was perceived might be strongly related to loss of cohesion during the compression of the specimen. The localization of micro-cracks and formation of shear planes are predominant factors of the failure process of brittle materials [50].

Following the first law of thermodynamics for SHPB experiments, it is possible to recognize three main conversion mechanisms of the absorbed energy. Internally, this energy is mainly used for the creation of new surfaces, fragmentation processes, and heat and acoustic emission [51]. From a macroscopic point of view, dynamic tests might result in two different kinds of fracture categories: class I, described by slight splits, and class II by fragmentation of the material. Manganese slag specimens have shown that depending on their composition, not only the creation of new surfaces and crack branching play an important role, but also pulverized material due to fragmentation [52]. Differences in the values of dissipated energy are related to the amount of energy consumed after failure where further crack branching and unstable propagation of cracks weaken the structure showing a softening effect after peak point. Qualitatively, post-fracture material illustrated that specimens with high amounts of phases of MnSiFe\(_{1}\) and MnSiFe\(_{2}\) are more susceptible to splitting, whereas specimens with a crystalline-amorphous matrix containing small amounts of Si, SiO, and silicate-bearing material, to fragmentation. The probability of the defect activation within the matrix increases due to a high driving energy during a short period of time becoming dominant all over when the highly packed material is loaded, so that localized crack rupturing results in an increase of macro failure strength [52]. Analysis on inertial effects of dynamic tests found in literature states that the main contribution to the difference between the front and rear end faces of the specimen is related to the change of strain rate in time (\(\ddot{\varepsilon }\)) as a function of the length and density of the specimen [53]. Manganese slag, being highly heterogeneous, behaves similarly to a composite-like material in which multiple cracks are gradually developed and enhanced due to mutual restriction [54], in this case, among phases and inclusions.

In hindsight, the manufacturing process plays an important role for the experiments due to the nature of the SHPB. Pulse shaping techniques allow to control the dispersion of the input pulses as they travel along the bars. The main challenge when working with slag is its high dependency on the metal being produced and the external conditions during cooling. As a result, randomized compositions and structures among the batch are obtained impacting the reproducibility of the experiments. Even though manganese slag material was drilled, cut, and polished to obtain the highest possible level of similarity, it is highly likely that induced irregularities entailed radial effects on the interfaces. The manufacturing process could be automatized in order to minimize any misalignment.

5 Conclusion

The methodology implemented for this study consisted of dynamic compression tests of manganese slag specimens loaded axially and diametrically (indirect tension) for an open system. Pulse shaping techniques, used to reduce the dispersion of the incoming pulses, were implemented together with ultra-high speed photography for the identification of the different stages of fracture. The following are the main observations:

  • The stress related to UCT seems to be a good indicator of the macro-behavior of the specimen, but it should be taken with precaution as stress gradients might indicate further internal events of heterogeneous materials.

  • Strain histories of UCT give a good indication of the fracture initiation point, although it is recommended to consider the behavior of the strain rate to estimate the contribution of inertial effects of non-uniform deformations.

  • Dynamic BD tests of manganese slag revealed two types of fracture: splitting and fragmentation. These seem to be, somehow, dependent on the composition and structure of the specimen. Specimens with a crystalline-amorphous matrix containing small amounts of Si are more susceptible to fragmentation, while specimens with high amounts of phases MnSiFe\(_{x}\) are more susceptible to splitting.

  • Axial compression tests showed a threshold of the energy dissipated during impact up to a peak load of 17 J.

  • UCT specimens presenting strain rates over 450 \(s^{-1}\) use in average 54% of the total dissipated energy up to peak load, while specimens presenting lower strain rates use 35% in average. The total absorbed energy was in average 37% of the incident energy except from UCT-08. This specimen presented a packed crystalline-amorphous matrix and a small amount of inclusions, which absorbed 18% of the incident energy instead.

  • The high variability of the mechanical response becomes a challenge for the increase of the energy efficiency of comminution processes. It was found that both splitting and fragmentation might be present, so staged comminution processes are recommended for mineral liberation applications.

  • Dynamics are important in comminution processes, and therefore, mechanical characterization of slags requires not only information about ultimate strength but also dissipated energy during impact.

  • High-speed imaging is highly recommended when testing heterogeneous material as it gives local information that could be used for calibration and post-processing investigations.

Manganese slag is a complex material in texture, composition, and mechanical response, but still has a great potential for crushing using equipment already installed at steel production facilities (and mines, if the market wants to open up even more). Results can be useful, as well, for the calibration and validation of numerical models to optimize the energy consumption of comminution processes. The increase of knowledge of the fracture process of material unfolds great opportunities to introduce by-products into a circular economy and contribute to the reduction of CO2 emissions.