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Measuring the strength of irregularly-shaped fine particles in a microcompression tester
Minerals Engineering 65 (2014) 149–155
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Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
Measuring the strength of irregularly-shaped fine particles in a microcompression tester Luciane Ribas a, Guilherme C. Cordeiro a,b, Romildo D. Toledo Filho a, Luís Marcelo Tavares c,⇑ a
Department of Civil Engineering, Universidade Federal do Rio de Janeiro – COPPE/UFRJ, Rio de Janeiro, RJ, Brazil Laboratory of Civil Engineering, Universidade Estadual do Norte Fluminense Darcy Ribeiro – UENF, Campos dos Goytacazes, RJ, Brazil c Department of Metallurgical and Materials Engineering, Universidade Federal do Rio de Janeiro – COPPE/UFRJ, Rio de Janeiro, RJ, Brazil b
a r t i c l e
i n f o
Article history: Received 17 August 2013 Accepted 25 May 2014 Available online 1 July 2014 Keywords: Fracture Particle strength Planetary mill Modeling
a b s t r a c t Characterizing the response of individual particles to stresses is of great relevance in a number of fields. In the field of grinding, important advances in mill modeling by decoupling material from machine contributions to the outcome of the process have been made in recent years that require direct information on the distribution of strengths of particles being ground. Although a number of methods and experimental devices have been proposed to measure the breakage strength of individual particles, only recently alternatives have become commercially available for testing particles in the fine size range. The paper demonstrates that a micro compression testing machine allows measuring the distribution of strengths and fracture energies of non-spherical fine particles, although great care should be taken while doing the measurements. It then shows that the mean strength of particles contained in a narrow size range is closely related to the rate of breakage of particles in the same size range in a planetary ball mill, thus demonstrating the validity of the measurements. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Characterizing the response of individual particles to stresses is of great relevance in a number of fields. In the case of chemical and pharmaceutical powders, as well as lump ores and pellets it is of relevance to understand their likelihood to lose physical integrity or fines due to abrasion during pneumatic or mechanical handling and transport (Yan et al., 2009; Nguyen et al., 2009; Rahmanian and Ghadiri, 2013). In the case of aggregates and cement constituents it is of interest to understand their behavior in pavements, mortars and concrete (McDowell and Bolton, 1998), whereas for a number of materials, including ores and cement clinker, it is of relevance to understand the material contribution to the effort required in mechanical size reduction (Schönert, 1991; Tavares, 2007). In the field of grinding, important advances in mill modeling by decoupling material from machine contributions to the outcome of the process have been made in recent years (Tavares and Carvalho, 2009; Crespo, 2011; Breitung-Faes and Kwade, 2013) that require direct information on the distribution of strengths of particles being ground to predict the performance of different mill types. ⇑ Corresponding author. Tel.: +55 2139382538. E-mail address: [email protected] (L.M. Tavares). http://dx.doi.org/10.1016/j.mineng.2014.05.021 0892-6875/Ó 2014 Elsevier Ltd. All rights reserved.
A number of methods and experimental devices have been proposed to measure the breakage strength of individual particles, varying in size range that can be treated and in the rate of application of stresses (Steier and Schönert, 1972; Yashima et al., 1979; Schönert, 1991; Tavares and King, 1998; Unland and Szczelina, 2004; Antonyuk et al., 2005). In the context of comminution, probably the most challenging and important within these is testing of fine and ultrafine particles, since these are the sizes in which energy consumption in size reduction is the highest. In the past, the breakage strength of particles contained in these size ranges could only be measured using special custom-made presses (Steier and Schönert, 1972; Yashima et al., 1979; Sikong et al., 1990). More recently, with the development of a number of micro compression testing machines it became possible to determine the strength of nearly-spherical individual particles loaded under slow compression (Antonyuk et al., 2005; Nguyen et al., 2009; Yan et al., 2009). The present work demonstrates that a commercial micro compression testing machine allows measuring the distribution of strengths and fracture energies of non-spherical fine particles. It then shows that the mean strength of particles contained in a given size range is closely related to the rate of breakage of particles in that same size range in a planetary ball mill, thus demonstrating the validity of the measurements.
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2. Experimental 2.1. Materials Six materials were chosen for the investigation, given their widely different mechanical properties: silicon carbide, quartz, blast-furnace slag, limestone, coal shale and rice husk ash. Their chemical compositions was measured using an X-ray fluorescence spectrometer (EDX-720 from Shimadzu) and results are presented in Table 1. The specific gravity of the samples was determined using a Helium pycnometer (AccuPyc 1340 from Micromeritics). Indentation hardness and Young´s modulus measurements were carried out using an Ultra-micro Hardness Tester (DUH-21 from Shimadzu) using a Vickers indenter, at a loading rate of 44 mN/s, holding at the maximum load for 5 s. A summary of the results is presented in Table 2. Samples were previously ground dry in a tumbling ball mill and wet-sieved in the 45 37 lm size range for the tests, having a maximum allowance of 5% of out-of-size material, which corresponded in its majority to the material passing 37 lm. After sieving, samples were oven-dried for testing. The fracture strength of particles contained in the 37–45 lm was measured using a Micro Compression Testing Machine (MCT-W Series 500 from Shimadzu). This high-resolution press uses a 50 lm-diameter flat-ended indenter that is capable of applying loads that range from as low as 10 mN to about 5 N, measuring displacements that range from 100 lm to 10 lm with 0.01 lm and 0.001 lm of resolution, respectively. The device is equipped with a camera installed sideways, which allows observing the specimen status during the entire compression event. The procedure used in single-particle testing consisted of first dispersing a small amount of material in ethyl alcohol and letting a drop of the suspension fall on the lower compression plate, which is fixed to the equipment table. After evaporation, particles were
appropriately dispersed, allowing the selection of individual ones for testing. Particle size (average of length and width) was measured using the specimen dimension measurement function which is used at 50 times magnification. From these two measurements, the aspect ratio of each material was estimated. The rate used in compression of the particles was 8.3 mN/s for quartz, rice husk ash, silicon carbide and blast-furnace slag. A lower rate of 1.5 mN/s was required for coal and limestone, given their lower strength. The machine applies loads at a constant rate using an electromagnetic system, in which the force is proportional to the intensity of the electric current, whereas deformations are measured. Fracture of the particle under loading is identified as a plateau in the force–displacement profile (Fig. 1), which results from a rapid increase in displacement at a constant load. From this load the particle compressive strength rp is calculated by (Hiramatsu and Oka, 1966; Tavares, 2007):
rp ¼
2:8F c
ð1Þ
p d2
where d is the particle size and Fc is the load at failure. For each material 50 particles contained in each size range were tested. The mass-specific particle fracture energy Em was calculated by integrating the force–deformation response
Em ¼
1 mp
Z
ec
F de
ð2Þ
0
where ec is the deformation at failure, mp is the particle mass, esti3 mated using bq d , so that q is the specific gravity of the material and b the shape factor. In the present work, given the difficulty of measuring shape factors of particles in such fine ranges, it was assumed that their value was equal to 0.43, which is equivalent to the average value found for a number of materials (Tavares and King, 1998).
Table 1 Chemical composition of the materials.
a
Oxides
Blast furnace slag
Coal shale
Limestone
Quartz
Rice husk ash
Silicon carbide
SiO2 Al2O3 SO3 CaO K2O SrO P2O P2O5 MnO Fe2O3 MgO CuO Rb2O TiO2 BaO ZrO2 L.O.I.a
18.79 9.29 1.73 27.64 0.28 0.11 – – 0.51 0.29 2.60 – – 0.33 0.10 – 38.31
47.68 26.77 4.94 0.67 1.49 0.03 – 0.43 – 1.08 – 0.02 0.02 1.28 0.25 0.05 15.28
0.55 0.25 – 55.43 0.05 – – – – 0.25 0.29 – – – – – 42.8
99.27 0.13 – 0.03 – – – – – 0.07 –
77.96 – 1.97 0.91 1.66 – 1.23 – 0.29 0.15 – – – – – – 15.80
96.45 2.19 1.03 – – – – – – – – – – – – – 0.30
– 0.01 – – 0.26
Loss on ignition.
Table 2 Summary of data from additional characterization testing (mean values, with standard deviations from 10 measurements in parentheses). Material
Specific gravity (g/cm3)
Young0 s modulus (GPa)
Blast furnace slag Coal shale Limestone Quartz Rice husk ash Silicon carbide
2.04 2.28 2.67 2.67 2.29 3.21
37.7 16.4 12.2 64.1 8.3 210.3
Vickers hardness (GPa) (16.2) (5.2) (3.1) (5.7) (1.6) (48.8)
539.8 70.9 117.9 1306.2 22.4 3283.3
(154.3) (31.4) (45.1) (138.5) (3.5) (649.7)
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After each grinding time the mill load was discharged, separating the balls and the material, which was then oven dried at 60 °C. From the dried material, a sample was collected for wet sieving at 37 lm, from which the amount of material retained was measured after drying. 3. Results and discussion 3.1. Breakage characterization
Fig. 1. Schematic diagram of a force–displacement profile measured using the micro compression machine.
Milling experiments were performed in a laboratory-scale planetary mill (Retsch PM-4) powered by a 750 W motor. The mill uses two 500 ml agate pots with equivalent rotation speeds (1:1) around their axis (counterclockwise) and around the arm of rotation (clockwise), being equivalent to 75% of critical speed. The revolution radius of each pot center was 300 mm and the internal diameter of the pots was 100 mm. Stainless steel balls measuring 6.3 mm of diameter were used in the experiments, which were all conducted with a constant mill filling of 30% (1170 g of balls) and a powder voids filling ratio of 80% at a constant rotation frequency of 200 RPM. Experiments were conducted wet at 25 % solids by volume, using deionized water (86.4 ml). Grinding times were varied typically from 1 to 8 min, but for selected materials they were varied from 0.5 min to 20 min, given their particularly high and low breakage rates, respectively.
One challenge in the micro compression test is to measure breakage characteristics of irregularly-shaped particles. Unlike in the case of spherical or nearly-spherical particles, primary breakage of these particles often follows minor breakage events, which go from minor surface breakage to removal of large chips (Schubert, 1987). In the case of the present work, this may be illustrated in Fig. 2, which shows the measured force–deformation profile and images depicting the initial contact (1), the breakage of a large chip (2) and the final disintegration of the particle (3). Fig. 3 illustrates the variety of force–displacement profiles found for the different materials studied. In nearly all curves, the section before fracture shows a series of elastic deformations and small fractures that result in surface abrasion and chipping. When the fracture load is reached, which is identified by an arrow in each profile, the particle shatters. The lateral camera, available in the device, was particularly useful to help identify this condition throughout the experimental work. The force–displacement profiles presented in Fig. 3 for the various materials studied allow identifying additional material-specific differences in breakage response.
500
Force (mN)
400
300
200
100
0 0
10
20
30
40
50
Displacement (µm)
Fig. 2. Typical force–deformation profile of a blast furnace slag particle with images depicting different events during compression.
L. Ribas et al. / Minerals Engineering 65 (2014) 149–155
1400
35
1200
30
1000
25
Test force (mN)
Test force (mN)
152
800 600 400 200
20 15 10 5
0
0 0
2
4
6
8
0
10
2
4
Displacement (µm)
6
8
10
12
14
16
18
20
Displacement (µm)
(b) Coal Shale
(a) Silicon Carbide 600
450 400
500
Test force (mN)
Test force (mN)
350 300 250 200 150
400 300 200
100 100 50 0
0 0
2
4
6
8
0
10
2
Displacement (µm)
4
6
8
10
Displacement (µm)
(c) Quartz
(d) Blast-firnace slag
50
35
45
30
35
Test force (mN)
Test force (mN)
40
30 25 20 15
25 20 15 10
10 5
5 0
0 0
2
4
6
8
10
0
2
4
6
8
10
12
14
Displacement (µm)
Displacement (µm)
(e) Residual Rice husk ash
(f) Limestone
16
18
20
Fig. 3. Typical force–displacement results for the materials tested.
Whereas in the case of brittle materials such as quartz, silicon carbide and coal, fracture is reasonably well identified by a horizontal line following a fairly steep loading line, in the case of other materials, such as rice husk ash and, to a lesser extent, blast furnace slag, fracture is often not as clearly identified from the graph. The force–deformation profile of these materials seem to demonstrate a strain-softening response, probably associated to the highly porous internal structure of, at least, a fraction of the particles. Fig. 3 also demonstrates the variability of the data for a given material, which is typically found in the breakage response of
brittle solids. A summary of the results is presented in Fig. 4, where the data are presented in log-linear axes as order statistics. The greatest variability of the particle strength among the materials studied has been found for limestone and quartz, whereas the greatest uniformity was found for coal shale. Attempts have been made to describe the data with standard statistical distributions and it became clear that data for silicon carbide and rice husk ash could be well described using the lognormal distribution (Fig. 4) (Tavares, 2007), whereas the Weibull or the uppertruncated lognormal distribution could describe well fracture data
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Table 4 Replicate analyzes of quartz samples (mean values, with standard deviations in parentheses).
1.0 Quartz
0.9
Cumulative distribution
Blast furnace slag
0.8
Silicon carbide
0.7
Limestone
0.6
Rice husk ash
0.5
Coal shale
0.4
Lot number
Number of particles
Particle strength, r (MPa)
Particle fracture energy (J/g)
1 2 3
50 50 50
118.6 (62.1) 117.4 (65.4) 133.8 (70.4)
2.75 (3.09) 2.45 (2.91) 3.01 (3.06)
123.3
2.74
Average
0.3 0.2 0.1 0.0
1
10
100
1000
Particle strength (MPa) Fig. 4. Distribution of particle strengths for the materials tested (solid lines represent fit to the lognormal distribution).
of the remaining materials, although the model fit is not included in the graphs for clarity. A summary of the statistics of the data is presented in Table 3, with coal shale presenting the lowest average particle strength and silicon carbide the highest. A comparison between data from the irregularly-shaped quartz particles in the present study and nearly-round quartz particles tested by Sikong et al. (1990) of nearly the same size (50 lm) shows that the later presented over three times the strength (about 500 MPa). The comparatively lower values found for quartz in the present investigation may be explained by the irregular shapes of the particles tested, which has also been found previously when testing coarse particles of different shapes (Tavares and King, 1998; Antonyuk et al., 2005), besides their different geological origin. Indeed, measured fracture strengths are in reasonable agreement with values reported by Schönert (1991) (with the appropriate correction, since a different expression was used by the author to calculate the values), who obtained values of about 70 MPa and 25 MPa for quartz and limestone, respectively. In principle, Eq. (2) suggests that fracture energies could be calculated from direct integration of each force–displacement profile. However, the mode of operation of the microcompression tester in which forces are not directly measured and do not drop during the entire test, even when contact between the particle and the indenter is lost, could result in unrealistically high values of fracture energies every time a plateau is found in the force–deformation profile. In these cases the area below the graph corresponding to a period of constant force is subtracted from the total work of deformation until fracture. These results are presented in Table 3, which show values of particle fracture energies that vary significantly for the different materials studied. A point that is often raised in single-particle fracture studies is the minimum number of particles required for testing (Tavares, 2007). This is due to the large variability of the data contained in the distributions (Fig. 4), particularly when considering the distributions of particle fracture energies (Table 3). In order to
analyze if the number of particles tested in each lot in the present work (50) was sufficiently large, two additional lots were tested of a given material (quartz) and the average values were compared. These results are summarized in Table 4, which shows that differences between the average values from each lot and the estimate of the average for the material were not greater than 10 MPa for the particle strength and 0.3 J/g for the particle fracture energies. If it is considered that each 50-particle lot yields a single estimate of the mean, and that three lots were tested, then the coefficients of variation for these average particle strengths and particle fracture energies for the repeated tests were 7.4% and 10.2%, respectively. This means that it is not possible to state in Table 3 that the average strength of quartz is higher than that of blast furnace slag and neither that the average fracture energy of quartz is higher than that of rice husk ash. It is possible, however, to discriminate all other differences in respect to quartz, in spite of the very large variability that is found for individual measures.
3.2. Batch grinding Results from a grinding operation are codetermined by the contributions of the mechanical environment inside the mill and of the powder breakage properties. This is particularly evident in the quantitative description of tumbling mills using the population balance model, in which the breakage rates of particles are influenced by both the grinding conditions and the material. Unfortunately, data are scarce that demonstrate the nature of the relationship that exists between the breakage strength of particles and the rates of breakage in the mill, particularly in ultrafine grinding. As such, in order to establish the validity of the results obtained from the micro compression tests in the present work, batch grinding tests have been conducted for the same materials with particles contained in the same size range as tested previously and the results compared. Assuming a first-order rate of breakage, the population balance model predicts that material contained in the coarsest size fraction disappears according to the relationship (Austin et al., 1984)
dw1 ðtÞ ¼ S1 w1 ðtÞ dt
ð3Þ
where w1(t) is the weight fraction of material contained in the top size range, S1 is their specific breakage rate and t is the grinding
Table 3 Summary of data from micro compression tests (mean values, with standard deviations in parentheses).
a
Material
Particle size – d (lm)
Aspect ratioa
Particle strength, r (MPa)
Particle compression at fracture (lm)
Particle fracture energy (J/g)
Blast furnace slag Coal shale Limestone Quartz Rice husk ash Silicon carbide
46.1 44.6 45.2 44.7 44.6 45.2
0.83 0.80 0.80 0.88 0.87 0.83
116.1 (47.9) 10.0 (3.10) 17.7 (16.5) 123.3 (66.1) 13.4 (3.6) 327.8 (209.9)
6.4 4.8 9.5 3.3 3.5 5.3
4.54 (3.31) 4.12 (2.52) 1.50 (1.57) 2.75 (3.01) 3.14 (2.50) 11.48 (22.20)
(2.3) (4.0) (3.2) (3.3) (3.4) (2.9)
Ratio between width and length of each particle.
(2.8) (3.1) (8.9) (3.1) (3.3) (6.6)
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L. Ribas et al. / Minerals Engineering 65 (2014) 149–155
time. The solution of the equation, subjected to the initial condition w1(0) = w1,0, is given by
w1 ðtÞ ¼ expðS1 tÞ w1;0
ð4Þ
A summary of the batch grinding results is presented in Fig. 5, which shows the variation of the fraction of material remaining in the top size fraction as a result of grinding time. Data from fractions remaining below 0.01 or 1% are not included in computing the breakage rates. It shows that the data may be reasonably well described considering first-order breakage kinetics, which is what is typically found for wet milling (Austin et al., 1984), in which the slope of the curves represents the rate of breakage (Eq. (1)). As mentioned, the specific breakage rates are codetermined by the material strength and the grinding environment, being significantly influenced by particle size (Austin et al., 1984). There have been some attempts to establish a relationship between the strength of particles and breakage rates in grinding (Tavares and Carvalho, 2009; Crespo, 2011; Breitung-Faes and Kwade, 2013). One of the authors recently (Tavares and Carvalho, 2009) proposed expressions in which the strengths or the fracture energies of particles, besides their energy-specific breakage function, are related to the breakage rates in ball milling, so that it is expected that it will be possible to predict the rates of breakage in mills from the knowledge of particle properties.
1
Fig. 6 compares the median particle strength and the breakage rates of particles contained in the size range 37–45 lm in the planetary ball mill. It shows a reasonable agreement between the two, with the exception of the data point for rice husk ash, which is a material that is characterized with exceptionally low values of Vickers hardness and Young´s modulus (Table 2) and high porosity. Breakage rates were also found to correlate with particle fracture energies (mass- and volume-specific), although the results are not presented for shortness. In the latter case, however, the scatter in the graph was larger, which may be associated to a number of factors, that include the uncertainty in the measurement of particle weight. Besides the reasonably good correlation, Fig. 6 shows that a significant change in particle strength of the material results in a more modest change in rate of breakage in a mill. Such behavior is consistent with the well-known low energy efficiency of ball mills, in which a significant fraction of the collisions that occur is not capable of producing size reduction, being dissipated as heat, besides a mismatch between the strength of the particle and the intensities of the stresses involved in each collision. The analysis of milling processes on the basis of particle fracture strength information such as the one provided by tests using the micro compression machine and appropriate mathematical models can serve as the basis for a deeper understanding of comminution, opening the way to improve the process that occurs in different mill types. Evidently, in that case, it would be required to measure fracture strengths over a range of particle sizes, which is beyond the scope of the present work.
Coal shale
4. Conclusions
Limestone Blast furnace slag
W1(t)/W1(0)
Rice husk ash Silicon carbide Quartz
0.1
0.01
0
2
4
6
8
10
Grinding time - t (min) Fig. 5. First-order disappearance plot from batch grinding of the materials tested in size range 45 37 lm in a planetary mill.
2
Breakage rate (1/min)
Breakage rate (1/min) = 2.05 - 0.273 ln[σ (MPa)] 1.5
Testing of irregularly-shaped particles of size 37–45 lm in a micro compression testing machine allowed measurement of the distributions of particle strength and particle fracture energies. Besides presenting values which are reasonably lower than those found for spherical particles, testing of irregularly-shaped particles also differs in the sense that minor fracture events occur prior to the main catastrophic event that is responsible for failure of the particle. In spite of that, results show that the test can discriminate among materials, and that the variability in their fracture strengths is significant. However, this was only possible by analyzing the force–deformation profiles synchronized with the recordings from the side view camera that was installed in the device. The rate of breakage in wet grinding of the materials in a planetary mill was well described by first-order breakage kinetics. A comparison between the breakage rates and the average particles strength for the different materials demonstrated that a logarithmic relationship exists between the two, so that the higher the particle strength, the lower the rate of breakage. However, the logarithmic relationship demonstrated that significant changes in material strength are not followed by comparable changes in the rates of breakage in a planetary mill for the particle size studied. Acknowledgements
1
The authors would like to acknowledge the financial support from CNPq, CAPES and FAPEAM from Brazil to this investigation, as well as from Petrobrás S.A.
0.5
References
0 1
10
100
1000
Particle strength (MPa) Fig. 6. Comparison between median particle fracture energy and breakage rates of particles contained in size range 45 37 lm in the planetary mill. The arrow identifies the data point for rice husk ash.
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L. Ribas et al. / Minerals Engineering 65 (2014) 149–155 Crespo, E.F., 2011. Application of particle fracture energy distributions to ball milling kinetics. Powder Technol. 210 (3), 281–287. Hiramatsu, Y., Oka, Y., 1966. Determination of the tensile strength of rock by a compression test on an irregular test piece. Int. J. Rock Mech. Min. Sci. 3, 89–99. McDowell, G.R., Bolton, M.D., 1998. On the micromechanics of crushable aggregates. Geotechnique 48 (5), 667–679. Nguyen, V.B., Wang, C.X., Zhang, Z., 2009. Mechanical properties of single alginate microspheres determined by microcompression and finite element modelling. Chem. Eng. Sci. 64, 821–829. Rahmanian, N., Ghadiri, M., 2013. Strength and structure of granules produced in continuous granulators. Powder Technol. 233, 227–233. Schönert, K., 1991. Advances in comminution fundamentals and impacts on technology. Aufbereitungs-Technik 32, 487–494. Schubert, H., 1987. On the microprocesses of comminution. Aufbereitungs-Technik 5, 237–246. Sikong, L., Hashimoto, H., Yashima, S., 1990. Breakage behavior of fine particles of brittle minerals and coals. Powder Technol. 61, 51–57.
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Contents lists available at ScienceDirect
Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
Measuring the strength of irregularly-shaped fine particles in a microcompression tester Luciane Ribas a, Guilherme C. Cordeiro a,b, Romildo D. Toledo Filho a, Luís Marcelo Tavares c,⇑ a
Department of Civil Engineering, Universidade Federal do Rio de Janeiro – COPPE/UFRJ, Rio de Janeiro, RJ, Brazil Laboratory of Civil Engineering, Universidade Estadual do Norte Fluminense Darcy Ribeiro – UENF, Campos dos Goytacazes, RJ, Brazil c Department of Metallurgical and Materials Engineering, Universidade Federal do Rio de Janeiro – COPPE/UFRJ, Rio de Janeiro, RJ, Brazil b
a r t i c l e
i n f o
Article history: Received 17 August 2013 Accepted 25 May 2014 Available online 1 July 2014 Keywords: Fracture Particle strength Planetary mill Modeling
a b s t r a c t Characterizing the response of individual particles to stresses is of great relevance in a number of fields. In the field of grinding, important advances in mill modeling by decoupling material from machine contributions to the outcome of the process have been made in recent years that require direct information on the distribution of strengths of particles being ground. Although a number of methods and experimental devices have been proposed to measure the breakage strength of individual particles, only recently alternatives have become commercially available for testing particles in the fine size range. The paper demonstrates that a micro compression testing machine allows measuring the distribution of strengths and fracture energies of non-spherical fine particles, although great care should be taken while doing the measurements. It then shows that the mean strength of particles contained in a narrow size range is closely related to the rate of breakage of particles in the same size range in a planetary ball mill, thus demonstrating the validity of the measurements. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Characterizing the response of individual particles to stresses is of great relevance in a number of fields. In the case of chemical and pharmaceutical powders, as well as lump ores and pellets it is of relevance to understand their likelihood to lose physical integrity or fines due to abrasion during pneumatic or mechanical handling and transport (Yan et al., 2009; Nguyen et al., 2009; Rahmanian and Ghadiri, 2013). In the case of aggregates and cement constituents it is of interest to understand their behavior in pavements, mortars and concrete (McDowell and Bolton, 1998), whereas for a number of materials, including ores and cement clinker, it is of relevance to understand the material contribution to the effort required in mechanical size reduction (Schönert, 1991; Tavares, 2007). In the field of grinding, important advances in mill modeling by decoupling material from machine contributions to the outcome of the process have been made in recent years (Tavares and Carvalho, 2009; Crespo, 2011; Breitung-Faes and Kwade, 2013) that require direct information on the distribution of strengths of particles being ground to predict the performance of different mill types. ⇑ Corresponding author. Tel.: +55 2139382538. E-mail address: [email protected] (L.M. Tavares). http://dx.doi.org/10.1016/j.mineng.2014.05.021 0892-6875/Ó 2014 Elsevier Ltd. All rights reserved.
A number of methods and experimental devices have been proposed to measure the breakage strength of individual particles, varying in size range that can be treated and in the rate of application of stresses (Steier and Schönert, 1972; Yashima et al., 1979; Schönert, 1991; Tavares and King, 1998; Unland and Szczelina, 2004; Antonyuk et al., 2005). In the context of comminution, probably the most challenging and important within these is testing of fine and ultrafine particles, since these are the sizes in which energy consumption in size reduction is the highest. In the past, the breakage strength of particles contained in these size ranges could only be measured using special custom-made presses (Steier and Schönert, 1972; Yashima et al., 1979; Sikong et al., 1990). More recently, with the development of a number of micro compression testing machines it became possible to determine the strength of nearly-spherical individual particles loaded under slow compression (Antonyuk et al., 2005; Nguyen et al., 2009; Yan et al., 2009). The present work demonstrates that a commercial micro compression testing machine allows measuring the distribution of strengths and fracture energies of non-spherical fine particles. It then shows that the mean strength of particles contained in a given size range is closely related to the rate of breakage of particles in that same size range in a planetary ball mill, thus demonstrating the validity of the measurements.
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2. Experimental 2.1. Materials Six materials were chosen for the investigation, given their widely different mechanical properties: silicon carbide, quartz, blast-furnace slag, limestone, coal shale and rice husk ash. Their chemical compositions was measured using an X-ray fluorescence spectrometer (EDX-720 from Shimadzu) and results are presented in Table 1. The specific gravity of the samples was determined using a Helium pycnometer (AccuPyc 1340 from Micromeritics). Indentation hardness and Young´s modulus measurements were carried out using an Ultra-micro Hardness Tester (DUH-21 from Shimadzu) using a Vickers indenter, at a loading rate of 44 mN/s, holding at the maximum load for 5 s. A summary of the results is presented in Table 2. Samples were previously ground dry in a tumbling ball mill and wet-sieved in the 45 37 lm size range for the tests, having a maximum allowance of 5% of out-of-size material, which corresponded in its majority to the material passing 37 lm. After sieving, samples were oven-dried for testing. The fracture strength of particles contained in the 37–45 lm was measured using a Micro Compression Testing Machine (MCT-W Series 500 from Shimadzu). This high-resolution press uses a 50 lm-diameter flat-ended indenter that is capable of applying loads that range from as low as 10 mN to about 5 N, measuring displacements that range from 100 lm to 10 lm with 0.01 lm and 0.001 lm of resolution, respectively. The device is equipped with a camera installed sideways, which allows observing the specimen status during the entire compression event. The procedure used in single-particle testing consisted of first dispersing a small amount of material in ethyl alcohol and letting a drop of the suspension fall on the lower compression plate, which is fixed to the equipment table. After evaporation, particles were
appropriately dispersed, allowing the selection of individual ones for testing. Particle size (average of length and width) was measured using the specimen dimension measurement function which is used at 50 times magnification. From these two measurements, the aspect ratio of each material was estimated. The rate used in compression of the particles was 8.3 mN/s for quartz, rice husk ash, silicon carbide and blast-furnace slag. A lower rate of 1.5 mN/s was required for coal and limestone, given their lower strength. The machine applies loads at a constant rate using an electromagnetic system, in which the force is proportional to the intensity of the electric current, whereas deformations are measured. Fracture of the particle under loading is identified as a plateau in the force–displacement profile (Fig. 1), which results from a rapid increase in displacement at a constant load. From this load the particle compressive strength rp is calculated by (Hiramatsu and Oka, 1966; Tavares, 2007):
rp ¼
2:8F c
ð1Þ
p d2
where d is the particle size and Fc is the load at failure. For each material 50 particles contained in each size range were tested. The mass-specific particle fracture energy Em was calculated by integrating the force–deformation response
Em ¼
1 mp
Z
ec
F de
ð2Þ
0
where ec is the deformation at failure, mp is the particle mass, esti3 mated using bq d , so that q is the specific gravity of the material and b the shape factor. In the present work, given the difficulty of measuring shape factors of particles in such fine ranges, it was assumed that their value was equal to 0.43, which is equivalent to the average value found for a number of materials (Tavares and King, 1998).
Table 1 Chemical composition of the materials.
a
Oxides
Blast furnace slag
Coal shale
Limestone
Quartz
Rice husk ash
Silicon carbide
SiO2 Al2O3 SO3 CaO K2O SrO P2O P2O5 MnO Fe2O3 MgO CuO Rb2O TiO2 BaO ZrO2 L.O.I.a
18.79 9.29 1.73 27.64 0.28 0.11 – – 0.51 0.29 2.60 – – 0.33 0.10 – 38.31
47.68 26.77 4.94 0.67 1.49 0.03 – 0.43 – 1.08 – 0.02 0.02 1.28 0.25 0.05 15.28
0.55 0.25 – 55.43 0.05 – – – – 0.25 0.29 – – – – – 42.8
99.27 0.13 – 0.03 – – – – – 0.07 –
77.96 – 1.97 0.91 1.66 – 1.23 – 0.29 0.15 – – – – – – 15.80
96.45 2.19 1.03 – – – – – – – – – – – – – 0.30
– 0.01 – – 0.26
Loss on ignition.
Table 2 Summary of data from additional characterization testing (mean values, with standard deviations from 10 measurements in parentheses). Material
Specific gravity (g/cm3)
Young0 s modulus (GPa)
Blast furnace slag Coal shale Limestone Quartz Rice husk ash Silicon carbide
2.04 2.28 2.67 2.67 2.29 3.21
37.7 16.4 12.2 64.1 8.3 210.3
Vickers hardness (GPa) (16.2) (5.2) (3.1) (5.7) (1.6) (48.8)
539.8 70.9 117.9 1306.2 22.4 3283.3
(154.3) (31.4) (45.1) (138.5) (3.5) (649.7)
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After each grinding time the mill load was discharged, separating the balls and the material, which was then oven dried at 60 °C. From the dried material, a sample was collected for wet sieving at 37 lm, from which the amount of material retained was measured after drying. 3. Results and discussion 3.1. Breakage characterization
Fig. 1. Schematic diagram of a force–displacement profile measured using the micro compression machine.
Milling experiments were performed in a laboratory-scale planetary mill (Retsch PM-4) powered by a 750 W motor. The mill uses two 500 ml agate pots with equivalent rotation speeds (1:1) around their axis (counterclockwise) and around the arm of rotation (clockwise), being equivalent to 75% of critical speed. The revolution radius of each pot center was 300 mm and the internal diameter of the pots was 100 mm. Stainless steel balls measuring 6.3 mm of diameter were used in the experiments, which were all conducted with a constant mill filling of 30% (1170 g of balls) and a powder voids filling ratio of 80% at a constant rotation frequency of 200 RPM. Experiments were conducted wet at 25 % solids by volume, using deionized water (86.4 ml). Grinding times were varied typically from 1 to 8 min, but for selected materials they were varied from 0.5 min to 20 min, given their particularly high and low breakage rates, respectively.
One challenge in the micro compression test is to measure breakage characteristics of irregularly-shaped particles. Unlike in the case of spherical or nearly-spherical particles, primary breakage of these particles often follows minor breakage events, which go from minor surface breakage to removal of large chips (Schubert, 1987). In the case of the present work, this may be illustrated in Fig. 2, which shows the measured force–deformation profile and images depicting the initial contact (1), the breakage of a large chip (2) and the final disintegration of the particle (3). Fig. 3 illustrates the variety of force–displacement profiles found for the different materials studied. In nearly all curves, the section before fracture shows a series of elastic deformations and small fractures that result in surface abrasion and chipping. When the fracture load is reached, which is identified by an arrow in each profile, the particle shatters. The lateral camera, available in the device, was particularly useful to help identify this condition throughout the experimental work. The force–displacement profiles presented in Fig. 3 for the various materials studied allow identifying additional material-specific differences in breakage response.
500
Force (mN)
400
300
200
100
0 0
10
20
30
40
50
Displacement (µm)
Fig. 2. Typical force–deformation profile of a blast furnace slag particle with images depicting different events during compression.
L. Ribas et al. / Minerals Engineering 65 (2014) 149–155
1400
35
1200
30
1000
25
Test force (mN)
Test force (mN)
152
800 600 400 200
20 15 10 5
0
0 0
2
4
6
8
0
10
2
4
Displacement (µm)
6
8
10
12
14
16
18
20
Displacement (µm)
(b) Coal Shale
(a) Silicon Carbide 600
450 400
500
Test force (mN)
Test force (mN)
350 300 250 200 150
400 300 200
100 100 50 0
0 0
2
4
6
8
0
10
2
Displacement (µm)
4
6
8
10
Displacement (µm)
(c) Quartz
(d) Blast-firnace slag
50
35
45
30
35
Test force (mN)
Test force (mN)
40
30 25 20 15
25 20 15 10
10 5
5 0
0 0
2
4
6
8
10
0
2
4
6
8
10
12
14
Displacement (µm)
Displacement (µm)
(e) Residual Rice husk ash
(f) Limestone
16
18
20
Fig. 3. Typical force–displacement results for the materials tested.
Whereas in the case of brittle materials such as quartz, silicon carbide and coal, fracture is reasonably well identified by a horizontal line following a fairly steep loading line, in the case of other materials, such as rice husk ash and, to a lesser extent, blast furnace slag, fracture is often not as clearly identified from the graph. The force–deformation profile of these materials seem to demonstrate a strain-softening response, probably associated to the highly porous internal structure of, at least, a fraction of the particles. Fig. 3 also demonstrates the variability of the data for a given material, which is typically found in the breakage response of
brittle solids. A summary of the results is presented in Fig. 4, where the data are presented in log-linear axes as order statistics. The greatest variability of the particle strength among the materials studied has been found for limestone and quartz, whereas the greatest uniformity was found for coal shale. Attempts have been made to describe the data with standard statistical distributions and it became clear that data for silicon carbide and rice husk ash could be well described using the lognormal distribution (Fig. 4) (Tavares, 2007), whereas the Weibull or the uppertruncated lognormal distribution could describe well fracture data
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Table 4 Replicate analyzes of quartz samples (mean values, with standard deviations in parentheses).
1.0 Quartz
0.9
Cumulative distribution
Blast furnace slag
0.8
Silicon carbide
0.7
Limestone
0.6
Rice husk ash
0.5
Coal shale
0.4
Lot number
Number of particles
Particle strength, r (MPa)
Particle fracture energy (J/g)
1 2 3
50 50 50
118.6 (62.1) 117.4 (65.4) 133.8 (70.4)
2.75 (3.09) 2.45 (2.91) 3.01 (3.06)
123.3
2.74
Average
0.3 0.2 0.1 0.0
1
10
100
1000
Particle strength (MPa) Fig. 4. Distribution of particle strengths for the materials tested (solid lines represent fit to the lognormal distribution).
of the remaining materials, although the model fit is not included in the graphs for clarity. A summary of the statistics of the data is presented in Table 3, with coal shale presenting the lowest average particle strength and silicon carbide the highest. A comparison between data from the irregularly-shaped quartz particles in the present study and nearly-round quartz particles tested by Sikong et al. (1990) of nearly the same size (50 lm) shows that the later presented over three times the strength (about 500 MPa). The comparatively lower values found for quartz in the present investigation may be explained by the irregular shapes of the particles tested, which has also been found previously when testing coarse particles of different shapes (Tavares and King, 1998; Antonyuk et al., 2005), besides their different geological origin. Indeed, measured fracture strengths are in reasonable agreement with values reported by Schönert (1991) (with the appropriate correction, since a different expression was used by the author to calculate the values), who obtained values of about 70 MPa and 25 MPa for quartz and limestone, respectively. In principle, Eq. (2) suggests that fracture energies could be calculated from direct integration of each force–displacement profile. However, the mode of operation of the microcompression tester in which forces are not directly measured and do not drop during the entire test, even when contact between the particle and the indenter is lost, could result in unrealistically high values of fracture energies every time a plateau is found in the force–deformation profile. In these cases the area below the graph corresponding to a period of constant force is subtracted from the total work of deformation until fracture. These results are presented in Table 3, which show values of particle fracture energies that vary significantly for the different materials studied. A point that is often raised in single-particle fracture studies is the minimum number of particles required for testing (Tavares, 2007). This is due to the large variability of the data contained in the distributions (Fig. 4), particularly when considering the distributions of particle fracture energies (Table 3). In order to
analyze if the number of particles tested in each lot in the present work (50) was sufficiently large, two additional lots were tested of a given material (quartz) and the average values were compared. These results are summarized in Table 4, which shows that differences between the average values from each lot and the estimate of the average for the material were not greater than 10 MPa for the particle strength and 0.3 J/g for the particle fracture energies. If it is considered that each 50-particle lot yields a single estimate of the mean, and that three lots were tested, then the coefficients of variation for these average particle strengths and particle fracture energies for the repeated tests were 7.4% and 10.2%, respectively. This means that it is not possible to state in Table 3 that the average strength of quartz is higher than that of blast furnace slag and neither that the average fracture energy of quartz is higher than that of rice husk ash. It is possible, however, to discriminate all other differences in respect to quartz, in spite of the very large variability that is found for individual measures.
3.2. Batch grinding Results from a grinding operation are codetermined by the contributions of the mechanical environment inside the mill and of the powder breakage properties. This is particularly evident in the quantitative description of tumbling mills using the population balance model, in which the breakage rates of particles are influenced by both the grinding conditions and the material. Unfortunately, data are scarce that demonstrate the nature of the relationship that exists between the breakage strength of particles and the rates of breakage in the mill, particularly in ultrafine grinding. As such, in order to establish the validity of the results obtained from the micro compression tests in the present work, batch grinding tests have been conducted for the same materials with particles contained in the same size range as tested previously and the results compared. Assuming a first-order rate of breakage, the population balance model predicts that material contained in the coarsest size fraction disappears according to the relationship (Austin et al., 1984)
dw1 ðtÞ ¼ S1 w1 ðtÞ dt
ð3Þ
where w1(t) is the weight fraction of material contained in the top size range, S1 is their specific breakage rate and t is the grinding
Table 3 Summary of data from micro compression tests (mean values, with standard deviations in parentheses).
a
Material
Particle size – d (lm)
Aspect ratioa
Particle strength, r (MPa)
Particle compression at fracture (lm)
Particle fracture energy (J/g)
Blast furnace slag Coal shale Limestone Quartz Rice husk ash Silicon carbide
46.1 44.6 45.2 44.7 44.6 45.2
0.83 0.80 0.80 0.88 0.87 0.83
116.1 (47.9) 10.0 (3.10) 17.7 (16.5) 123.3 (66.1) 13.4 (3.6) 327.8 (209.9)
6.4 4.8 9.5 3.3 3.5 5.3
4.54 (3.31) 4.12 (2.52) 1.50 (1.57) 2.75 (3.01) 3.14 (2.50) 11.48 (22.20)
(2.3) (4.0) (3.2) (3.3) (3.4) (2.9)
Ratio between width and length of each particle.
(2.8) (3.1) (8.9) (3.1) (3.3) (6.6)
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L. Ribas et al. / Minerals Engineering 65 (2014) 149–155
time. The solution of the equation, subjected to the initial condition w1(0) = w1,0, is given by
w1 ðtÞ ¼ expðS1 tÞ w1;0
ð4Þ
A summary of the batch grinding results is presented in Fig. 5, which shows the variation of the fraction of material remaining in the top size fraction as a result of grinding time. Data from fractions remaining below 0.01 or 1% are not included in computing the breakage rates. It shows that the data may be reasonably well described considering first-order breakage kinetics, which is what is typically found for wet milling (Austin et al., 1984), in which the slope of the curves represents the rate of breakage (Eq. (1)). As mentioned, the specific breakage rates are codetermined by the material strength and the grinding environment, being significantly influenced by particle size (Austin et al., 1984). There have been some attempts to establish a relationship between the strength of particles and breakage rates in grinding (Tavares and Carvalho, 2009; Crespo, 2011; Breitung-Faes and Kwade, 2013). One of the authors recently (Tavares and Carvalho, 2009) proposed expressions in which the strengths or the fracture energies of particles, besides their energy-specific breakage function, are related to the breakage rates in ball milling, so that it is expected that it will be possible to predict the rates of breakage in mills from the knowledge of particle properties.
1
Fig. 6 compares the median particle strength and the breakage rates of particles contained in the size range 37–45 lm in the planetary ball mill. It shows a reasonable agreement between the two, with the exception of the data point for rice husk ash, which is a material that is characterized with exceptionally low values of Vickers hardness and Young´s modulus (Table 2) and high porosity. Breakage rates were also found to correlate with particle fracture energies (mass- and volume-specific), although the results are not presented for shortness. In the latter case, however, the scatter in the graph was larger, which may be associated to a number of factors, that include the uncertainty in the measurement of particle weight. Besides the reasonably good correlation, Fig. 6 shows that a significant change in particle strength of the material results in a more modest change in rate of breakage in a mill. Such behavior is consistent with the well-known low energy efficiency of ball mills, in which a significant fraction of the collisions that occur is not capable of producing size reduction, being dissipated as heat, besides a mismatch between the strength of the particle and the intensities of the stresses involved in each collision. The analysis of milling processes on the basis of particle fracture strength information such as the one provided by tests using the micro compression machine and appropriate mathematical models can serve as the basis for a deeper understanding of comminution, opening the way to improve the process that occurs in different mill types. Evidently, in that case, it would be required to measure fracture strengths over a range of particle sizes, which is beyond the scope of the present work.
Coal shale
4. Conclusions
Limestone Blast furnace slag
W1(t)/W1(0)
Rice husk ash Silicon carbide Quartz
0.1
0.01
0
2
4
6
8
10
Grinding time - t (min) Fig. 5. First-order disappearance plot from batch grinding of the materials tested in size range 45 37 lm in a planetary mill.
2
Breakage rate (1/min)
Breakage rate (1/min) = 2.05 - 0.273 ln[σ (MPa)] 1.5
Testing of irregularly-shaped particles of size 37–45 lm in a micro compression testing machine allowed measurement of the distributions of particle strength and particle fracture energies. Besides presenting values which are reasonably lower than those found for spherical particles, testing of irregularly-shaped particles also differs in the sense that minor fracture events occur prior to the main catastrophic event that is responsible for failure of the particle. In spite of that, results show that the test can discriminate among materials, and that the variability in their fracture strengths is significant. However, this was only possible by analyzing the force–deformation profiles synchronized with the recordings from the side view camera that was installed in the device. The rate of breakage in wet grinding of the materials in a planetary mill was well described by first-order breakage kinetics. A comparison between the breakage rates and the average particles strength for the different materials demonstrated that a logarithmic relationship exists between the two, so that the higher the particle strength, the lower the rate of breakage. However, the logarithmic relationship demonstrated that significant changes in material strength are not followed by comparable changes in the rates of breakage in a planetary mill for the particle size studied. Acknowledgements
1
The authors would like to acknowledge the financial support from CNPq, CAPES and FAPEAM from Brazil to this investigation, as well as from Petrobrás S.A.
0.5
References
0 1
10
100
1000
Particle strength (MPa) Fig. 6. Comparison between median particle fracture energy and breakage rates of particles contained in size range 45 37 lm in the planetary mill. The arrow identifies the data point for rice husk ash.
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