# An innovative setup to study the breakage of SiO2 agglomerates under shear stress

Hanin Atwi, Guillaume Dumazer, Sylvain Martin, Guilhem Kauric, Thomas Genevès, Olivier Bonnefoy

► To cite this version:

Hanin Atwi, Guillaume Dumazer, Sylvain Martin, Guilhem Kauric, Thomas Genevès, et al. An innovative setup to study the breakage of SiO2 agglomerates under shear stress. Powder Technology, 2026, 468, pp.121598. 10.1016/j.powtec.2025.121598. emse-05262792

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Submitted on 16 Sep 2025

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# An innovative setup to study the breakage of SiO₂ agglomerates under shear stress

Hanin Atwi<sup>a</sup>, Guillaume Dumazer<sup>aID,*</sup>, Sylvain Martin<sup>aID</sup>, Guilhem Kauric<sup>b</sup>, Thomas Geneves<sup>c</sup>, Olivier Bonnefoy<sup>aID</sup>

## HIGHLIGHTS

* Innovative device for characterizing controlled sheared granular materials.

* Particle Size Distribution mode decomposition analysis.

* Scanning Electron Microscopy.

* Tribological in situ force measurements.

* Fragmentation and reagglomeration of SiO₂ powder.

## GRAPHICAL ABSTRACT

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**
Agglomerate
Breakage
Shear stress
Shear test bench

## ABSTRACT

Granular materials are involved in many industrial processes such as mixing, compaction, etc. When the granular material is in the form of agglomerates, i.e. an assembly of aggregates, particle fragmentation might occur under shear stress. This can either be a benefit for the process and should be controlled, or an issue which must be avoided. This paper focuses on the study of agglomerate breakage under shear stress, presenting a new experimental set-up designed for industrial contexts. The stress range selected lead to two distinct regimes: at

<footnote><sup>a</sup> Mines Saint-Etienne, Univ Lyon, CNRS, UMR 5307 LGF, Centre SPIN, F-42023 Saint-Etienne, France</footnote>

<footnote><sup>b</sup> Orano Support, Direction R&D, 125 Avenue de Paris, 92320 Chatillon, France</footnote>

<footnote><sup>c</sup> Orano Etablissement MELOX - B.P. 93124 - 30203 Bagnols-sur-Cèze CEDEX, France</footnote>

<footnote>* Corresponding author.
E-mail address: guillaume.dumazer@emse.fr (G. Dumazer).</footnote>
low stresses, agglomerates break into individualized fragments, while high stresses fines agglomeration leads to the formation of flakes. These observations contribute to quantify the breakage stress of initial agglomerates, showing agreement with findings in the existing literature.

# 1. Introduction

Powder manufacturing processes can produce three different particle forms: primary particle, aggregates, and agglomerates. Primary particle is described as the smallest discrete entity. In cristalline materials, this entity is usually a single crystal. An aggregate is defined as primary particles held together by strong bonds, and can vary in size from the nanoscale to the microscale [1]. An agglomerate is a collection of weakly bounded primary particles, or aggregates or a mixture of the two. Therefore, unlike aggregates, agglomerates can be broken easily down into their constituents [2].

Agglomerates are processed in industrial equipments such as reactors, pneumatic conveying systems [3,4], atomizers [5], presses and grinders. The agglomerates can be exposed to high mechanical stresses, and therefore, be fragmented into smaller particles or agglomerated to form larger entities. Kelley and Spottiswood [6], Redner [7], Austin [8], Gao and Forssberg [9], and King [10], have described the main fragmentation mechanisms as a function of the energy applied to the particles and the particle size distribution (PSD). Each fragmentation mechanism was associated to a specific change in the PSD [10–12]. Two types of mechanisms can be identified: surface fragmentation (abrasion and attrition) and volume fragmentation (disintegration and rupture). Surface fragmentation generally produces limited particle damage, while volume fragmentation can significantly affect particle morphology. Fragmentation mechanisms depend on material characteristics and applied stress. Surface fragmentation are observed at low levels of stress on the particle, while disintegration and rupture are associated with higher levels.

Therefore, evaluating the mechanical strength of agglomerates holds significant importance. In existing literature, there are both experimental and numerical studies dedicated to characterizing the mechanical resistance of agglomerates under various stress conditions [13,14]. A characterization of uranium dioxide agglomerates by in-situ nanoindentation in the scanning electron microscope (SEM) was carried out by Iltis [15]. This study involved powders of uranium dioxide from different manufacturing processes, revealing distinct crushing behaviours. Dumas [16] investigated the fragmentation of silica in water by ultrasounds. The mean diameter of the silica agglomerates decreased over time, following an exponential law. Boudimbou [17] explored the fragmentation of silica, focusing on a single agglomerate confined in a sheared elastomer matrix. The study revealed that the breakage stress follows a decreasing linear function of the particle size, on the tested particle's size range. In a numerical study, Wang et al. [18] employed the discrete element method and incorporated a fragmentation model (fragment replacement model) to simulate a sheared granular geological fault. The analysis of the influence of grain breakage on stick-slip dynamics indicated that particle fragmentation results in reduced grain size, increased macroscopic friction, and fault gouge compaction.

However, a significant research gap exists, where there is a need for a fragmentation characterization tool capable of applying compression and shear stress to the bulk powder. While shear and compression devices are commercially available like the FT4 powder rheometer, they have limitations, such as a restricted normal stress range (e.g., 77 kPa for a 25 mm cell) and, more crucially, a bed thickness above 20 mm is generally required. This requirement results in a non-uniform deformation, with the sheared bed undergoing deformation within a plane spanning over a thickness of 5 to 30 times the diameter of a grain, while the rest moves as a solid [19].

This paper aims to introduce a new breakage experimental setup for a large population of particles of SiO₂ under shear stress. Section 2

<table><caption>**Table 1**
Physical properties of silica Z1165MP measured or taken from [16].</caption><thead><tr><td>Properties</td><td>Silica</td></tr></thead><tbody><tr><td>Agglomerate diameter d[4, 3] (μm)</td><td>277 ± 10</td></tr><tr><td>Primary particle diameter (μm)</td><td>0.017</td></tr><tr><td>Density (g/cm³)</td><td>2.18 ± 0.004</td></tr><tr><td>Specific surface area (m²/g)</td><td>158 ± 1.9</td></tr></tbody></table>

gives a complete description of the experimental setup. In Section 3 several observations and experimental characterizations of the powder after shearing are presented and a transition in the fragmentation mechanism is put in evidence. A fragmentation mechanism determined by the imposed shear stress is proposed and confirmed by local shear stress measurements. The conclusion in Section 4 summarizes the content of this study. The objective is to explore the specific role that shear stress plays in the fragmentation of agglomerates within a compressed granular bulk thanks to this new apparatus, and if results already known from the literature can be recovered.

# 2. Materials and methods

## 2.1. Silica powder

The amorphous silica used in this study (Zeosil 1165MP, Solvay) has an average diameter $d_{[4,3]}$ of 277 ± 10 µm, see the (PSD) in Fig. 1(a) obtained with a Malvern Mastersizer 3000 Granulometer using dry method of operation. Regarding the morphology of the silica granules, they are mostly spherical as depicted in Fig. 1(b) from a SEM imaging. The SEM picture present a large number of silica granules with diameters smaller than 200 µm which provides an information about the particle size distribution in numbers, opposed to the particle size distribution in volume provided in Fig. 1(a). The volume of the powder is concentrated on particles fraction with large diameters, whereas the number of the finest particles is larger.

Table 1 gives some physical properties of the silica powder taken from [16] or measured for this study. According to [17], the breakage stress for the silica embedded in a sheared elastomer matrix decreases linearly from 280 to 140 kPa as the grain diameter varies from 100 to 200 µm.

## 2.2. Experimental devices

### 2.2.1. Shear test bench

A novel shear test bench has been developed, as shown in Fig. 2. This experimental setup is designed to apply a controlled shear stress to a uniform powder bed located on a horizontal substrate, see schematics in Fig. 2. The bed width is 30 mm, the height is precisely controlled with a value between 1 and 5 mm, and its length covers almost entirely the 1 m long substrate. It is deposited on a layer of abrasive paper covering the substrate. The horizontal shear stress is applied onto the bed by an inclined blade with a self adjusting angle $α$ of around 2°. The vertical compressive component of the stress applied to the powder bed is controlled by a variable mass $M$ (1.6 to 10 kg) applying a vertical weight force on the blade. The system composed of the inclined blade and the applied weight is attached to a four-wheel trolley pulled horizontally along the bed with a constant speed of 5 mm s⁻¹ by a highly stiff string (a load of 50 N gives a relative elongation of 0.67%), over a distance of approximately 1 m.

To measure the normal stress, a vertical force sensor is located under a vertically mobile T-shaped piece with a thickness of 5 mm, as
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Particle size distribution (PSD) in volume (%) of the initial silica powder with a dry dispersion pressure $\Delta p$ = 0.1 bar. (b) SEM image of the amorphous silica agglomerates used.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Schematical side view of the setup with components leading to the overall functionality, and a close-up of the normal force sensor under the T-shaped piece (yellow colour). The abrasive paper is represented by the bold black line sticking the steel bar (grey colour). The silica powder bed is represented by the patterned texture right above the abrasive paper. The inset shows a picture of the trolley on the shear test bench.</figcaption></figure>

illustrated in Fig. 2. This piece is placed in series between the two metal bars and is covered by the abrasive paper. A narrow gap is maintained between bars and the vertically moving T-shaped piece transferring the normal component of the force in such a way to minimize losses due to vertical solid friction. In the absence of any granular bed, when the inclined blade reaches the position of the T-shaped piece, the sensor records a peak for the normal force $F_N$ = Mg. To measure the horizontal shear stress, a tangential sensor is attached to the tensile cable pulling the trolley forward. The tangential force $F_T$ is measured continuously throughout the displacement.

## 2.3. Methods

The powder used in this study is delivered in large 20–30 dm³ containers. To avoid segregation-induced error measurements, a rotary sample splitter with a vibratory feeder is used to accurately divide and distribute the powder in small 10 cm³ samples each with identical particle size distribution.

### 2.3.1. Shear test bench protocol

The first step is the coating of the substrate surface with abrasive paper (2000 grains/cm²) to control the roughness. Following that, a

powder bed with a thickness of 2 mm is prepared approximately 20 cm after the beginning of the abrasive paper, marked as point A on Fig. 2. Then, a mass M is positioned on the vertically sliding plate to generate a compressive stress applied on the inclined blade. The experiment starts when the trolley is pulled by the highly stiff string along the substrate at a constant speed v = 5 mm/s, and an approximate shear rate of 2.5 s⁻¹, thereby applying the shear stress. In this setup, the grains forming the granular bed are exposed to deformation and rearrangement.

### 2.3.2. Characterization of fragmentation

The method used to characterize the fragmentation involves comparing the particle size distribution (PSD) before and after the fragmentation phenomena, see [11]. In this study, the macroscopic characterization of the powder is performed using a laser diffraction analyser equipped with a dry powder disperser (Malvern Analytics, Mastersizer 3000-Aero S) with a low pressure difference of 0.1 bar. This setting is chosen to minimize potential damages to the agglomerates during measurement. The optical principles employed by the Malvern apparatus are commonly used to establish PSD measurements of non-transparent particles [20].

The curve-fitting and data-analysis software Fityk was used to interpret the evolution of the particle size distribution. In this case, the PSDs
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** PSD decomposition of (a) initial silica and (b) fragmented silica under a shear stress of 270 kPa. The three classes L, M, and S are obtained with the Fityk software decomposition algorithm.</figcaption></figure>

<table><caption>**Table 2**

Investigated experimental parameter values and conducted analyses.</caption><thead><tr><th>Mass load (kg)</th><th>Shear stress (kPa)</th><th>Analyses</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>PSD, SEM</td></tr><tr><td>0.6</td><td>40</td><td>Normal and tangential force, PSD</td></tr><tr><td>1</td><td>66</td><td>Normal and tangential force, PSD</td></tr><tr><td>1.6</td><td>105</td><td>Normal and tangential force, PSD, SEM, visual aspect</td></tr><tr><td>2</td><td>131</td><td>Normal and tangential force, PSD</td></tr><tr><td>2.6</td><td>170</td><td>Normal and tangential force, PSD</td></tr><tr><td>3</td><td>197</td><td>Normal and tangential force, PSD</td></tr><tr><td>3.6</td><td>235</td><td>Normal and tangential force, PSD, SEM, visual aspect</td></tr><tr><td>4</td><td>261</td><td>Normal and tangential force, PSD</td></tr><tr><td>4.6</td><td>300</td><td>Normal and tangential force</td></tr><tr><td>5</td><td>326</td><td>Normal and tangential force</td></tr><tr><td>5.6</td><td>366</td><td>Normal and tangential force, SEM, visual aspect</td></tr></tbody></table>

are decomposed into a sum of two or three lognormal distributions: $f_V(D) = \sum_i f_{\mu_i, \sigma_i}(D)$. The different distributions' maxima must be selected manually, based on the subjective observation of the measured total distribution. Then, the software Fityk adjusts the chosen functions to fit the experimental curves as closely as possible. Fig. 3(a) shows the PSD of the initial silica powder. This bimodal curve is decomposed into a sum of two lognormal distributions. The first distribution represents large particles, designated as Class L (Large), while the second distribution represents finer particles, designated as Class S (Small). Each distribution is characterized by two parameters: the mode $D_{Class} = a_0 \exp(\mu_i - \sigma_i^2)$ indicates the maximum and therefore the most probable diameter of that class (with a chosen measurement unit $a_0$, µm here), and $A_{Class}$ represents the area under the class distribution curve, corresponding to the volume fraction of that class. Fig. 3(b) shows the PSD of fragmented silica under a shear stress produced with a mass $M = 4$ kg. In this case, the distribution is trimodal and an intermediate M (Medium) class is formed.

Also, in this study, the Scanning Electron Microscope (SEM) imaging is used to qualitatively assess the morphology of some grains, both in their initial and final states.

# 3. Results and interpretation

## 3.1. Fragmentation with shear and compression test bench

A series of experiments have been conducted for various load in order to vary the intensity of the shear stress imposed to the powder bed. The Table 2 summarizes the various analyses conducted for various loadings.

### 3.1.1. Visual characterization of sheared powder

The appearance of the granular bed after shearing depends on the level of stress applied, as observed in Fig. 4. The global stress $\sigma$ is defined by the weight force ($F_g = Mg$) applied by the mass through the inclined blade divided by the T-shaped piece surface area in contact with the abrasive paper ($A = 30 \text{ mm} \times 5 \text{ mm}$). Fig. 4 illustrates the visual aspect of the powder bed surface after the passage of the trolley. The existence of two distinct regimes is noticed as stress increases:

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Appearance of the sheared silica granular bed with three different mass values $M = 1.6$ (top), $3.6$ (middle) and $5.6$ kg (bottom) applying respectively the following global shear stress values $\sigma = 105, 235$ and $366$ kPa.</figcaption></figure>

1. The first regime is characterized by a powder bed where the grains remain individualized, though sometimes plastically deformed and entangled.

2. The second regime is characterized by the appearance of continuous macroscopic objects designated as “flakes”.

A transitional regime can also be identified for intermediate stress values, where the powder becomes cohesive. A reduced flowability has been observed when the powder is collected with visible clusters of particles.

The (SEM) images presented in Fig. 5 show the initial powder (a), the powder after different levels of stress (b and c) and the flake structure (d). In Fig. 5(a), the initial powder shows $SiO_2$ agglomerates as grains characterized by smooth spherical surfaces. Intact grains are still visible after shearing and emphasized with red circles, as shown in Fig. 5(b) and (c). Additionally, as stress increases, fine particles become more dominant. Fig. 5(d) shows the detail of micrometer scale flakes formed from silica powder. The formation of a dense, rough, continuous structure, with some embedded grains still intact is observed.

The first regime is obtained up to a stress of 105 kPa. Above this value, the empty spaces between particles begin to shrink, marking the start of the transition phase, which continues up to a stress value of 235 kPa. Beyond this value, flakes begin to form, involving fines particles produced during the shearing.

### 3.1.2. Particle size distribution (PSD)

Fig. 6(a) shows the particle size distributions obtained after shearing the powder at different stress levels. After shearing, an evolution of the initial bimodal distribution, with fractions of large particles with a mode $D_L > 100 \mu m$ and medium particles with a mode $10 < D_M < 100 \mu m$, can be observed towards trimodal distributions with the rise of a third population of fine particles with mode $D_S < 10 \mu m$. The modes emerging in the PSD after shearing corresponds to particles whose sizes >1 µm fit aggregates rather than primary particles
<figure><img src="image_8.png" /><figcaption>Fig. 5. (SEM) images: (a) Initial powder, (b) Powder sheared under 105 kPa, (c) Powder sheared under 235 kPa showing intact grains highlighted in red circles, and (d) Powder sheared under 366 kPa: Formation of flakes observed.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. (a) Particle size distribution (PSD) in volume (%), (b) 3D representation as a function of applied stress, and (c) corresponding contour lines.</figcaption></figure>

($\epsilon$ [10–40] nm) [17]. The 3D representation shown in Fig. 6(b) shows the decrease in the fraction of large-sized particles, accompanied by an increase in medium- and small-sized fractions, as shear stress increases. The PSD in Fig. 6(a) and contour lines in Fig. 6(c) show the appearance of particles smaller than 10 µm above an applied stress of 50 kPa. The size of fine particles decreases significantly before stabilizing at 100 kPa. Fractions of medium-sized particles, with diameters $D$ between 10 and 100 µm, increase progressively with increasing stress. Above 200 kPa, a second maximum appears between 10 and 30 µm.

In order to investigate the fragmentation mechanisms that take place during these shear tests, particle size distribution curves are decomposed into a sum of log-normal distributions. Thus, the initial

powder is decomposed into two classes: large (L) and small (S), whereas after shearing all the silica powders can be decomposed into three classes : large (L), medium (M) and small (S). Fig. 7(a) shows the decrease in the diameter of the largest particles mode $D_L$ after applying stress to the powder bed, where $D_L$ falls from 280 µm to 160 µm. The medium particles mode $D_M$ of sheared powders decreases from 85 µm at 39 kPa to 25 µm at 235–261 kPa. For the diameter of the smallest particles mode $D_S$, the reduction goes from 10 µm under a global stress of 39 kPa to 4 µm under stresses of 235–261 kPa. This evolution of the PSD with the applied shear stress is more pronounced below 100 kPa.

Fig. 7(b) gives the areas of three classes as a function of applied global stress $\sigma$. The areas under the curves corresponds to the volume
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Characteristic parameters of the PSD particle size distribution, small, medium and large (a) class' modes $D_S$, $D_M$, and $D_L$, and (b) classes area $A_S$, $A_M$ and $A_L$, versus applied global stress $\sigma$. The error bars are obtained from the standard error.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Evolution of the centres (diameters of each class) of the lognormal functions of silica for each case: (a) initial powder, (b) under 1.6 kg and (c) under 4 kg. The right-hand column illustrates the proposed fragmentation mechanisms for two initial particles of sizes L and M.</figcaption></figure>

fraction and the class L covers a fraction of particles >99% by volume in the initial powder. As stress increases, this volume proportion falls from 99.5% to 78%, while the areas $A_M$ and $A_S$ increase from 11% to 19% and from 0.4% to 3% respectively. This observation points towards a transfer of volume going from large class towards medium and small classes. This transfer is more effective at stress values below 100 kPa.

### 3.1.3. Fragmentation mechanisms

Based on the particle size distribution data and the decomposition of PSD curves into a sum of log-normal distributions with Fityk, potential rupture mechanisms can be suggested. The initial powder is composed of two populations of grains: large particles with a modal diameter of 282 µm and fine particles with a modal diameter of 46 µm (see Fig. 8(a)).

After shearing with a global shear stress controlled by the mass carried by the trolley, the large particles of the initial powder fragment

into three populations: L, M and S, suggesting a combination of erosion into fines and disintegration of larger particles [10]. On the one hand, fines (<10 µm) may detach from the surface of the larger particles, together with fragments (<200 µm) resulting from the splitting of large particles present in the initial distribution and reflecting the size of the particles initially present in the powder. Other medium-sized fragments ([20–40] µm) can be seen in Fig. 8(b) and (c). On the other hand, it is expected that the medium-sized particles from the initial powder, with a diameter of 46 µm, appear to undergo erosion to transform into finer particles, belonging to the [20–40] µm and <10 µm classes.

With a larger value for the global applied shear stress of 261 kPa this combination between splitting and erosion mechanism still holds. These mechanisms seem to be even more marked with this higher stress, resulting in a greater production of fine particles (see Fig. 8(c)).
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Tangential force measurements as a function of the position of the trolley for masses ranging from (a) 0.6 kg to 3 kg and (b) 3.6 kg to 5.6 kg. The shaded area represents the region without powder.</figcaption></figure>

### 3.1.4. Tangential force

The tangential force recorded during the passage of the inclined blade along the thin granular bed prepared on the substrate is given in Fig. 9. Fig. 9(a) shows a decrease in the tangential force measurement once the blade enters the region covered with silica, leaving behind the region without powder located at the left-end side of the blade's displacement (shaded area). This effect may be due to grains' rolling and to the powder bed rearrangement which reduces friction. Fig. 9(b) represents the effect of larger masses, where a slight decrease in tangential force is observed with significant fluctuations' magnitude compared to the area without powder. These fluctuations are attributed to local dynamic instabilities due to formation and collapse of force chains, particle fragmentation, etc. [21].

Using this data, a friction coefficient $\mu = F_T/F_g$ can be calculated by dividing the shear force by the gravitational force $F_g$ exerted on the inclined blade. Fig. 10 depicts the variation of the friction coefficient $\mu$ as a function of $F_g$, showcasing that in the absence of grains, $\mu$ decreases with increasing global stress before stabilizing. When abrasive papers rub against each other, abrasive particles wear leads to a reduction in friction. By adding a powder between the two abrasive surfaces, the coefficient is lowered due to a solid lubrication effect, as the spherical particles are generally good lubricants. As the force $F_g$ increases, there is a tendency for the coefficient calculated with silica powder to rise. Particle breakage produces an increase in the friction coefficient as the dissipation of energy goes into both particle-particle friction and particle breakage [18]. After breakage, particles may lose their sphericity and therefore their ability to roll which contributes to the effective friction coefficient rise. Fragmented particles have higher surface roughness and angularity, leading to a strengthening of the granular bed [18,22]. Above 40 N, the coefficient of friction stabilizes, becoming almost similar to that observed in the absence of powder, as the majority of grains undergo fragmentation.

The coefficient of friction in the presence of silica powder is determined by the shear mechanism within the powder bed. In the Coulomb model, the friction coefficient is considered independent of the normal force. However, in the presence of a third body between two surfaces in relative shear motion, this relation changes. Numerical works in the literature exhibit cases where a third body made of deformable elastic grains leads to a decreasing friction coefficient with the normal stress [21,23]. In our study, an opposite tendency is observed and may correspond to the rearrangement of non-smooth particle fragments. A similar observation can be found in the experimental work of [24], where they studied the frictional response of faults to changes in normal stress.

### 3.1.5. Normal force

Fig. 11 shows the vertical force transmitted through the powder bed by the blade as it moves, for various global stress intensities. In terms of curve shape, for small masses, a slightly asymmetrical peak is observed

<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Friction coefficient versus normal force $F_g$ in two cases. The first case (black) depicts a thin bed of powder between two abrasive papers, while the second case (red) involves the shearing of abrasive papers against each other.</figcaption></figure>

(see Fig. 11(a)), while for higher masses the curve expands into two distinct phases separated by an inflection point (see Fig. 11(b)): from the left, while the blade approaches the sensor's location, the force increases in an exponential manner with a positive convexity, then reaches an inflection point, followed by a peak. The inflection point is visible in the [15–20] N range.

These observations are consistent with the two distinct behaviours described in Section 3.1.1 for small and large masses. Fig. 11(a), representing small masses' effect, corresponds to the first and second regimes, where grains are individualized and begin to cohere. On the other hand, Fig. 11(b), representing larger masses' effect above 3.6 kg, corresponds to the third regime, where flakes are forming. In these cases, the inflection point seems to mark the transition from the first fragmentation phase when the blade approaches, and the second cohesion phase producing the flakes.

The shape of the normal force curves is related to the mechanical strength and intrinsic characteristics of the powder, such as the granular particle stress resistance to fragmentation or the stress redirection within the granular assembly. In particular, under high-stress conditions, it can be characterized using two parameters $L$ and $\sigma_N^p$, as illustrated in Fig. 11(c). The first parameter, $L$, represents the distance between the sensor and the measurement starting point, when the sensor detects the powder accumulation. In other words, this parameter corresponds to the length of powder displaced by the inclined blade (see Fig. 11(d)). The second parameter, $\sigma_N^p$, represents the stress reached at the inflection point on the curve. The normal stress applied
<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Normal force measurements as a function of the position of the trolley for masses ranging from: (a) 0.6 kg to 3 kg and (b) 3.6 kg to 5.6 kg. (c) Parameters of the normal stress $F_N^P/A$ curves: L and $\sigma_N^P$. (d) Illustration of L in the system.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 12.** (a) L as a function of imposed mass M, and (b) $\sigma_N^P$ as a function of added mass.</figcaption></figure>

to the grains can be obtained using the normal force divided by the surface $A = W \times l$ of the T-shaped piece, of width W (=5 mm) and length l (=30 mm). Fig. 12(a) shows the evolution of the first parameter, L, as a function of the imposed mass M. The value of L increases quasi-linearly with increasing mass M. Fig. 12(b) represents the stress $\sigma_N^P$ as a function of mass M, varying in the range 80 to 140 kPa.

Referring back to the literature [17], the breaking strength for a single grain varies from 140 to 280 kPa, for diameters ranging from 200 to 100 µm. A power-law particle size dependency of the breakage strength of the form [25]: $\sigma_{br} = kd_{grain}^{-3/m}$, would fit these data with $k = 2.8 \times 10^6$ Pa m, and m = 3. The inflection point observed in the normal stress profile $\sigma_N^P$ lies within the same range of values reported in the literature [17]. The initial powder PSD showing a significant fraction of large particles with diameter larger than 200 µm is consistent with an average breaking stress given by the measured inflection point shear stress values.

### 3.2. *Suggested restructuring mechanism under shear*

These observations allow us to propose the following restructuring mechanism of the granular bed under normal and shear stresses. Before the inclined blade passes over the thin powder bed, and without any applied force, the system is in a state of moderate and disordered compaction. When a normal and shear stresses is applied, the particles undergo initial rearrangement, resulting in an increase in powder compaction [26]. When no further relative movement is possible, any increase in force results in deformation or fragmentation, depending on the characteristics of the particles. For a sufficiently large applied stress, the PSD evolves beyond any asymptotic ultimate PSD [27] since the powder bulldozing produces a continuous mixing of the particles. Based on the analysis of local normal force measurement, see Fig. 11, two regimes can be distinguished as a function of the global stress applied and are illustrated on Fig. 13. In the first regime where grains fragmentation is observed below a certain global stress threshold approximately
<figure><img src="image_17.png" /><figcaption>Fig. 13. Illustration of two distinct regimes based on the shape of the curves, considering the inclined blade as the reference point.</figcaption></figure>

equal to 235 kPa, the solid particles remain individualized and the curve generally presents two distinct phases: phase I corresponds to a rearrangement of the grains, leading to an exponential increase in stress $\sigma$; during phase II, a stress maximum $\sigma_{max} \le \sigma_{br}$ is reached indicating partial fragmentation of the grains and rearrangement. In the second regime, obtained for a global stress exceeding a specific threshold ([80–135] kPa) and for which the formation of flakes can be observed, the curve presents now three distinct phases: phase I corresponds once again to grain rearrangement with an increase of the local stress $\sigma$; phase II is marked by the inflection point at $\sigma = \sigma_{br}$, indicating that the breakage stress has been reached; phase III is marked by a steep stress gradient, leading to a sharp peak, indicating high compression corresponding to the formation of flakes.

It has been shown that a polydisperse granular material under stress hosts a force chains network with a long-tailed asymmetrical statistical distribution of force intensities [28,29]. The largest force intensities carried by the solid particles are then concentrated over a minority of particles. However, as the imposed stress increases, the amount of particles exposed to forces exceeding the breakage load increases quickly. This could explain the progressive fracturing observed with increasing applied global stress until the mixed regime is reached (individualized grains and flakes).

## 4. Conclusion

A new experimental setup has been developed with a linear geometry to study the fragmentation mechanisms that occur when powder samples are simultaneously exposed to compressive and tangential stresses. Measurements of tangential and normal forces undergone by a powder sample forming a 2 mm horizontal powder bed are performed. A trolley carrying a mass controlling the applied stress to the granular bed through an inclined blade is displaced horizontally at a constant speed. Tangential and normal force sensors are recording respectively the force applied to displace horizontally the trolley and the force transmitted vertically across the granular bed on a 5 × 30 mm² surface. In addition, the effect of increasing shearing intensity controlled by adjusting masses is assessed through PSD measurements. To the authors' knowledge this setup has a unique capability to characterize the frictional and restructuring behaviour of a granular bed under shear and normal stresses ranging typically from 30 to 600 kPa, and shear rate ranging from 0 to 10 s⁻¹ which is not covered by commercially available instruments.

The fragmentation of particles forming the sheared granular bed leads to the evolution of the PSD with a shift of the largest modes towards smaller sizes, accounting for the disintegration of large particles, and the rise of a population of small and medium particle sizes, denoting an erosion mechanism. These observations are confirmed with a quantitative analysis based on a decomposition of the measured PSD in a sum of three log-normal distributions, corresponding to three classes of large, medium and small particles. A decrease of the modes with the imposed stress has been observed, as well as a transfer of volume from large classes to small and medium classes. The slight change in behaviour noted at 100 kPa might be related to the breakage stress reported by [17]. Some light could be shed on this evolution of the PSD by applying a population balance approach with a breakage kernel consistent with the observed breakage stress evolution with the particle size.

As the stress increases various regimes were observed, including an agglomeration transition. The agglomeration regime is characterized by the formation of flakes composed of small silica particles fragments. These fragments correspond to cohesive flat structures integrating some intact grains according to SEM imaging. Flakes appear above a threshold load, and may be the results of an ultimate energy dissipation mechanism by re-agglomeration taking place once the energy dissipation through a series of fragmentation processes is completed. Further comminution would probably require more energy than flakes formation.

The measurement of the tangential forces put in evidence the well known lubrication effect produced by the dry grains, as well as a slight increase of the friction coefficient with the applied normal force. Moreover, enabling the measurement of local normal stress at the bottom of the sheared thin granular bed helped to observe the transition between the fragmentation below a critical stress, and the reagglomeration regime above it. The fragmentation and erosion processes result in an asymmetrical normal stress profile, and the reagglomeration regime is characterized by an inflection point and a peaked value below the tip of the blade.

The present setup with its instrumentation giving access to the local normal stress below the sheared granular bed, complemented by PSD analysis and SEM imaging, have the capability to provide enough data so that fragmentation mechanisms featuring a combination of surface breakage erosion and bulk breakage partial disintegration, as well as a restructuring of the sheared and fragmented granular material can
be clearly explained. A discrepancy between various definitions of the applied stress still remains. The global normal stress applied due to the mass carried by the trolley gives a 235 kPa threshold for the transition towards the agglomeration regime. After looking at the stress value given by the normal force sensor located below the granular thin bed, the threshold value becomes 115 kPa. This surprisingly low value seems to contradict higher reported fragmentation stress values available in the literature [17]. Further studies at a granular particle scale such as provided by the DEM numerical simulation approach [30,31] can describe the force chains network developing in a granular assembly under stress. The force chains network is responsible for the stress redistribution as described at a first order by the Janssen's model [32]. The fluctuations in the force chains branching [33] may explain this anomalously low normal stress measurement which is averaged on a 5 m × 30 mm area, whereas the fragmentation stress threshold can be reached locally at a single particle scale.

## CRediT authorship contribution statement

**Hanin Atwi:** Writing – original draft. **Guillaume Dumazer:** Writing – review & editing. **Sylvain Martin:** Writing – review & editing. **Guilhem Kauric:** Writing – review & editing. **Thomas Geneves:** Writing – review & editing. **Olivier Bonnefoy:** Writing – review & editing.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.

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