*3.1. Material Characteristics*

A summary of the characteristics of the samples is presented in Table 1. The Carajás sample has the lowest values of density, whereas Brucutu and Itabira have the highest. Details about the composition of the samples may be found elsewhere [41].


**Table 1.** Summary of physical characteristics of the samples.

#### *3.2. Force–Displacement Profiles*

In order to analyze bed response in compressive bed breakage in greater detail, force–deformation profiles are analyzed as follows. Figure 2 presents force–displacement curves for different compressive forces, highlighting the load and unload (relief) curves. It is evident that, when the bed is compressed up to relatively small loads, namely below 100 kN (80 MPa), no elastic recovery appears, with no recoil of the bed. Mütze [17] observed that, in this case, all energy applied to the bed is either dissipated in rearranging the particles or in producing particle breakage. Under such conditions, the thickness of the bed after unloading progressively reduces as loads increase. Beyond this point, as loads increase, the force–displacement curves become steeper. In this case, unloading exhibits progressively more

elastic response, with the bed presenting ever more elastic recovery, which becomes evident from the lower slopes of the unloading curves.

**Figure 2.** Load and unload force-displacement curves in tests up to different applied compressive forces for the Itabira sample contained in the size range of 150–125 μm.

Force-deformation curves such as those in Figure 2 may be presented more suitably on the basis of the relationship between the packing density (ratio between apparent density of the bed and specific gravity) and the vertical stress applied. Results are presented in Figure 3 for the Itabira and Carajás samples contained in the narrow particle size range of 150–125 μm. For a vertical stress of 800 MPa (1000 kN), the Itabira sample presented a maximum packing density of around 0.88, whereas a maximum of 0.95 was reached for the Carajás sample. The reasonable difference in the curves indicates a softer response for the Carajás sample under compressive loads. In addition, both results are able to show that, even though different vertical stresses were applied, the final packing density after total relief was nearly constant for each material, being equal to around 0.70 for the Itabira and 0.75 for the Carajás samples.

**Figure 3.** Relationship between the vertical stress and the packing density for different compressive forces applied for the (**a**) Itabira and (**b**) Carajás samples in the narrow size range of 150–125 μm.

A more detailed examination of the results is possible by calculating the areas below the curves. The input energy is given by numerical integration of the curves up to the maximum vertical stress, whereas the elastic energy is given by the area corresponding to the unloading of the piston. The inelastic or dissipated energy is simply given by the difference between the two. Results are presented in Figure 4,

which shows the rapid increase in elastic energy with the increment in vertical stress. The results also show that for low compressive forces the elastic energy is almost negligible, whereas it corresponds to around 60% of the input energy for the highest compressive forces analyzed.

**Figure 4.** Variation of the input, elastic, and dissipated energy in the particle bed as a function of vertical stress for the Itabira sample for the narrow size range of 150–125 μm.

In order to assess the particle bed behavior under multiple pressing cycles, Figure 5 shows the relationship between the packing density with the vertical stress applied in seven repeated pressing stages. For a vertical stress of up to 160 MPa (200 kN), the different pressing stages showed a great distinction in the initial bed configuration with the packing density reaching a maximum value of around 0.7 for the last stage. This result is consistent with the maximum packing density found after the single-stage pressing process presented in Figure 3a for the Itabira sample. Indeed, there is a marked relationship between the initial feed size distribution and the progressive change in packing density of the material. The results from Figure 5 indicate that, for the fine feed size distributions used, there is an increment in packing density caused by the reduction in the voids fraction within the particle bed. As the multiple stages of pressing were applied, the force–displacement profile started to superimpose, with this effect being potentially associated with the high particle bed packing. The dispersion of the material following each pressing cycle, coupled with the application of a relatively low vertical stress in each cycle, allowed to prevent particle bed saturation.

**Figure 5.** Relationship between vertical stress and packing density for different stages of pressing for the Itabira sample in a narrow size range of 106–75 μm.

### *3.3. Size Analyses*

Figure 6 presents the product size distributions for the Brucutu and Carajás samples at different stressing conditions. They demonstrate the increase in fineness as compressive forces increase, as well as the onset of the breakage saturation that is associated with the application of compressive forces higher than about 300 kN (240 MPa). The higher propensity of the Carajás sample to breakage in the piston-and-die test is evident from the larger proportion of fines produced.

**Figure 6.** Product size distributions for different maximum compressive forces for the (**a**) Brucutu and (**b**) Carajás samples contained in the size range of 150–125 μm in piston-and-die tests.

#### *3.4. Breakage of Top Size Particles*

After each piston-and-die test, the proportion passing the original narrow size range was recorded by sieving. The proportion broken was then plotted as a function of specific energy in Figure 7, following the approach used by Liu and Schönert [18] and Dundar et al. [21].

**Figure 7.** Proportion broken out of the original size for (**a**) Brucutu and (**b**) Carajás samples for different specific energies and feed particle sizes.

The figure shows that the proportion of particles broken increases significantly at low specific input energies, but reaches a maximum value, which becomes nearly constant with increasing input energies. Beyond this point, increasing the input energy does not lead to more breakage of particles contained in the original size range, as they become stabilized by neighboring particles. Tavares [42] observed that, whereas little or no additional breakage occurred at these higher energy inputs in HPGR experiments, particles may become progressively weaker. Furthermore, as observed by Liu and Schönert [18], it is evident that this maximum proportion broken varies with size, reducing significantly for the finer size range studied. Indeed, in the finest size range studied (53–45 μm), less than half of the particles broke for the Carajás sample (Figure 7b), in spite of the energy applied, showing the significant size effect on particle stabilization in confined bed breakage. The figure also shows that, at specific energies in the order of 2 kWh/t, saturation is reached on the maximum proportion of particles broken. This specific energy corresponds to a maximum load in the order of 200 kN (159 MPa), coinciding with the conditions in which the bed starts to recoil partially elastically (Figure 3) and also the condition under which the multiple stage pressings (Figure 5) were carried out.

Figure 8 compares results on the proportion broken for the Itabira sample as a function of input energy in individual pressings at progressively higher vertical stresses and results from multistage pressings. It shows that the sequential pressing and dispersion of the material prior to another pressing stage allowed the additional breakage of particles contained in the top size fraction, preventing saturation.

**Figure 8.** Proportion broken out of the original size for the Itabira sample in the narrow particle size range of 106–75 μm for single-stage pressing and multistage pressing. Line fits data from single-stage pressing.

#### *3.5. Blaine Specific Surface Area*

The Blaine specific surface area (BSA), an important parameter used to characterize the fineness of powdered materials, is commonly used to control pellet feed quality in iron ore pelletizing plants [43]. Figure 9 shows the relationship between the BSA increase from the feed BSA and the specific energy applied for all samples in piston-and-die tests. It is evident that the BSA increase is nearly proportional to the input specific energy up to a point, beyond which the slope of the line reduces. As such, in analogy to Figure 7, the data approach a maximum value, but in this case only at specific energy inputs above about 6 kWh/t. Such a value corresponds to maximum vertical loads in the order of 600 kN (480 MPa).

As already reported by Schönert [14] and recently observed by Zhou et al. [38] using DEM simulations, the main cause for the drop in energy efficiency in particle bed breakage is the reduction in the voids that are caused by fine debris relocating themselves as a result of the application of high normal applied stresses. Such a drop in energy efficiency in compressed bed breakage is also evident in Figure 9 for specific energies higher than about 6 kWh/t.

With the aim of analyzing in greater detail the issue of saturation in compressed bed breakage, a comparison between single and multiple pressing results for the Itabira sample is presented in Figure 9b. It compares the results from piston-and-die tests carried out at different maximum pressures to results from multiple compressive cycles at a constant maximum loading force of 200 kN (159 MPa). Dispersion of the material after each pressing cycle allowed reaching significantly higher BSA values

than those obtained in a single pass at higher pressures, since the dispersion prevented particles from stabilizing in the bed. This effect becomes noticeable at specific energies above about 3 kWh/t. These results demonstrate the value, for iron ore concentrates, of using multiple passes as a way of increasing the specific surface area of the product, in contrast to a single pass.

**Figure 9.** Relationship between Blaine specific surface area (BSA) increase and specific input energy for (**a**) Brucutu, (**b**) Itabira, (**c**) Timbopeba, and (**d**) Carajás samples.

Given the various effects observed, including that of the mean particle size, the size distribution of the original material, the degree of its dispersion, and the observed trends towards saturation at higher pressures, a parameter, called pressing factor κ, is proposed to capture the bed propensity to pressing in a test. It is given by the following:

$$\kappa = (\phi\_p - \phi\_o)(1 - \phi\_o) \tag{1}$$

where φ*<sup>o</sup>* is the packing density of the originally pressed material and φ*<sup>p</sup>* is the final packing density of the bed after unloading the piston, that is, of the permanently deformed bed. φ*<sup>o</sup>* varies as a function of particle size and size distribution, degree of dispersion, if previously in loose form or preloaded. In the experiments in the present work, it was estimated from the value corresponding to a preload of 20 MPa, in order to remove any bias due to uneven bed surface in the beginning of the test (Figure 3).

The higher the value of κ, the greater the expected size reduction for a given material. As such, it increases with the increase in pressure and stressing energy applied to the bed, the maximum achievable packing density, whereas it decreases with an increase in initial bed packing density. As such, it acknowledges that pressing results change if the bed was previously loose or preloaded in the beginning of a test.

Figure 10 presents the results from Figure 9, now as a function of the parameter κ. It shows that the increase in Blaine specific surface area varies as a function of parameter κ, relatively independently of initial particle size and final pressure. It demonstrates that it is possible to represent data not only from single but also from multiple pressings (Figure 10b) in the same curve. As such, it suggests that κ is a parameter that may be used to characterize the potential of a material to undergo breakage under confined conditions.

**Figure 10.** Relationship between BSA increase and pressing factor κ for the (**a**) Brucutu, (**b**) Itabira, (**c**) Timbopeba, and (**d**) Carajás samples.

Since data included experiments with narrow size beds that presented the lowest initial packing density φ*<sup>o</sup>* and that were subjected to pressures beyond those responsible for breakage saturation (Figure 9), a maximum achievable value of Blaine specific surface area increase in a single loading stage could also be identified, as shown in Figure 10. Such a value corresponded to the maximum achievable magnitude of pressing factor. It varied according to material, being about 0.10–0.11 for Brucutu and Itabira and about 0.11–0.13 for Timbopeba and Carajás, identifying the greater pressing propensity of the latter in comparison to the former (Figure 10).

Figure 11 then shows the variation of the pressing factor as a function of the input energy in pressing for one of the samples. It demonstrates that the data, including those from multiple pressings, follow approximately the same general trend, with a maximum pressing factor reached with specific energies above about 6 kWh/t, varying only marginally with initial particle size. Alternatively, the relationship between the pressing factor κ and the input energy could be estimated by a model describing the force–displacement profile for both loading and unloading of the bed [17], which would make the method suitable for predicting results in the piston-and-die apparatus.

**Figure 11.** Relationship between the factor κ and specific input energy for the Itabira sample, including data for single and multiple pressings (106–75 μm).

#### *3.6. Energy Utilization*

Assuming the validity of Rittinger's law, Rumpf [44] proposed a definition of energy utilization as the ratio between the increment in surface area from the feed and the energy spent in comminution. This definition has been used by Campos et al. [12] with a minor modification presented in Equation (2), from the ratio between the BSA increase and the specific energy spent on the process:

$$\text{Energy utilization} = \frac{BSA\_{product} - BSA\_{fuel}}{\text{Specific energy consumption}} \tag{2}$$

For iron ore pelletizing operations, this relationship is commonly used as a metric for characterizing the comminution process efficiency [12,41].

In order to analyze the energy utilization in greater detail, Equation (2) is used considering both the total specific energy consumption and also only the inelastic energy, that is, the result of subtracting the elastic recovery from the input specific energy, as shown in Figure 4. These results are presented in Figure 12, which shows that energy utilization was maximum when the bed was subjected to the lowest pressures. Such high energy utilization at the lowest pressures may be explained by the fact that stressing energy is used to break the most brittle particles contained in the original size range. Figure 12, however, shows that beyond the minimum energy applied, energy utilization decreased, in particular for pressures above 150 MPa, even when the elastic restitution was subtracted from the input stressing energy. This is evidence of the progressively lower energy efficiency in size reduction as beds approach saturation.

**Figure 12.** Comparison of energy utilization for different applied vertical stresses for the Itabira sample for the narrow size range of 150–125 μm, considering both the input and the inelastic energy.

#### **4. Discussion**

From the various analyses, it becomes feasible to describe the main features observed during the pressing of confined beds containing fine iron ore concentrates. This is illustrated in Figure 13, which shows that the first step in compression of the particle bed corresponds to a rearrangement of the particles, which occurs up to about point A. This key feature can be observed in Figure 3 for the different materials tested and, as already reported by Mütze [23], is associated predominantly with low stress levels (below about 40 MPa), when particles rearrange themselves within the bed by rotating and sliding in respect to each other. This is associated with very low energy inputs but is responsible for reasonable increases in the packing density of the bed.

**Figure 13.** Schematic summarizing the main features of the particle bed pressing behavior of fine iron ore particles.

After initial rearrangement of the bed and within the interval from points A to B in Figure 13, the stress chains connecting the particles are formed, with stresses increasing significantly with deformation. As the critical force or stressing energy required to fracture each of the particles is reached, the weakest particles are progressively broken, leading to a rearrangement of the stress field, which is transmitted by the skeleton formed by the remaining unbroken particles. Point B in the figure corresponds to the saturation in breakage of particles contained in the top size. This occurs at pressures of around 180 MPa (2 kWh/t), as already shown in Figure 7. Such stresses and specific energies would have been sufficient to break all particles contained in the original size, if stressed individually in a micro compression tester [41]. Beyond this point, a proportion of particles contained in the top size, which varied from about 10% for the coarsest sizes tested to about 50% for the finest, remained unbroken, even as stressing energies increased. This is associated with the well-known phenomenon in confined particle bed breakage where the finer debris from breakage of the coarser particles are able to prevent the remaining coarser particles from further breaking [18,23]. The larger proportion of finer particles remaining in comparison to the coarser ones demonstrates the greater ability of the finer particles to dissipate the stresses. Until this point, the bed behaves perfectly inelastically, with all energy applied dissipated in either bed rearrangement or breakage.

The interval from point B to C in Figure 13 corresponds to further breakage of the debris from the initial breakage of the top size material in the case of narrow size beds, with additional increase in fines generation and specific surface area, as is evident in Figures 6 and 9, without additional breakage of particles contained in the top size class. The same effect of saturation in breakage of the top size then appears to happen with progressively finer sizes, as the increase in applied pressures results in only the progressive generation of finer particles.

In the interval from point B to C, deformations start to show an elastic component, with the bed recoiling partially after reaching the maximum stress during loading. As stresses are progressively increased, bed breakage reaches complete saturation at about point D, with no measurable increase in fines generation or specific surface area as a result of applying higher loads. At pressure beyond point D, a substantial increase in the elastic energy stored in the bed, which can correspond to over half of the energy input (Figure 4), is observed. Unlike the interval from A to B, in this interval the increasing inelastic energy is progressively used less in breakage, but more in dissipative phenomena, such as friction, plastic deformation, and interlocking and cold-welding of the particles, forming a tough final agglomerate, quite familiar in tableting studies [30–33] and consistent with final compaction.
