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The tensile strength of moist limestone powder. Measurements by different apparatuses
Powder
0
Technology.
15 (19i6)
Elsevier Sequoia S-A.,
-The
TensileStrength
G. A. TURNER, Department
November
9’7
Printed in the Netheriands
ofMoistLhnestonePowder_
&I_ BAL4SUBR_LLIANIAN*
of Chemical
(Received
97 - 105
Lausanne -
Engineering.
3, 1975;
Results
are presented
by Different
Apparatuses
and L_ O’ITEN**
University
of Waterloo.
Waterloo.
Ontario
(Canada)
in revised form March 22, 19’76)
SUMMARY
The tensile strength of stone was measured with of Shinohara and Tanaka Spring Laboratory sliding
Measurements
finely divided limethe compaction cell and the Warren plate apparatus_
in terms
of the void
fraction of the sample and moisture content. Comparison of the two sets of results showed that the measured tensile strength depends on the particular properties of the apparatus. The observed discrepancies reinforce Schubert’s conclusion that the sliding plate apparatus is only suitable &hen the tensile strength can be extrapolated to zero sample height_
INTRODUCTION
A number of methods and devices have been developed to give some measure of the cohesion of solid particles, each, in general, being applied to a specific situation and a particular type of cohesive force. Tlhis situation arises from the limited understanding of the behaviour of bulk powders and the problems encountered in obtaining their fundamental properties. In consequence it is very difficulttodevelopamethodordevice which will give quantitative and reproducible results, especially for a variety of conditions. The methods reported in the literature may be divided into three main groups according to the type of cohesive force measured. An indirect estimate of the extent of cohesion of
*Present address: Department of Chemical Engineering, The University of British Columbia, Vancouver, British Columbia, Canada. **Present address: School of Engineering, University of Guelph, Guelph, Ontario, Canada.
powders in certain processes is obtained in one of the groups. It includes, for esample, a pneumatic shear test method (Shinohara ef al. ]I] ), the angle of repose method (Craik and Miller [2], Carr ]3] ), flowability measurements (Neumann [4] j, a method using a modified Brookfield viscometer and a fluidized bed (Chong [5] ), and a method of measuring dustability (Neumann [ 41) or dispersability (Irani et al. [S] )_ The second group measures the cohesive or adhesive force between two particles or between a particle and a plane surface. Examples of this group are the weighing methods (Corn [7] ) which make use of a spring or torsion balance, the pendulum method (MC Farlane and Tabor 181) in which the adhesion between a spherical particle and a flat plate is obtained by measuring the masimum deflection angle of the pendulum particle from the vertical, and a centrifugal method (Kordecki and Orr [9], Zimon and Deryagin [lo] ) in which a particle is separated from a plane by centrifugal action. These processes all measure the cohesive or adhesive properties of an individual particle rather than the properties of an agglomeration of particles. The third group consists of methods which measure cohesive forces by breaking a consolidated or agglomerated powder mass_ In this group is the tilting or split plate method developed by Tideswell and Tolleyfield (unpublished) and quoted by Dawes [ll] . Here, the tensile breaking strength of a prepared bed of powder was measured by observing the angle with the horizontal at which the powder deposit on the split glass plate broke in two. Improved reproducibility of the measurements was obtained by certain modifications which were described in detail by Thouzeau and Taylor [ 123 _ The improved apparatus was further
Fis.
I_ Schematic
diagram
of the Shinohara
and Tanaka
used by Eisner e; al. [ 131 and Shotton and Harb [ 14]_ X similar method was the inclinedplane or friction method (Bowden and Tabor [ 151, Cremer and co-workers [ 16 j j in \vhizh the angle was measured at which a consolidated block sta:red to slide down the inclined plane. Patat and Schmidt 1171 made a detailed investigation into Cremer’s method and they concluded that the results appeared to be inconsistent with the model and the physics of the system_ A cohesive shear strength can be obtained by extrapolating shear strength measurements to zero normal load. The required data is obtained from such apparatus as the Jenike flowfactor tester [IS] which is a direct-shear, constant rate of s-b-ah machineX similar apparatus is the annuku shear ceIL for granular materials developed by Carr and Walker 1191; it can be used to measure the shear and the tensile strength of granular materials- Umeya et al. [ 201 developed a twodimensional shear apparatus to measure the overah stress-strain relationship for beds of model powders. A break-off’method by Tanaka et al. i21] allowed calculation of the cohesive strength from the weight of a broken coiumn of horizontally extruded, packed powder mass. It is ba=ed on the idea that when the packed column’s strength and its extruded weight are in equihbrium, a portion of the column breaks off. Finally, there are a number of tensile test methods which because of their simple mechanism are of considerable interest_ That of Bumpf 1223 measures the strength of agglomerates obtained from a disc pelietizer.
compaction
cell apparatus
(S & T cell)_
A 25 mm diam. green pellet was first glued to a special adaptor and then turned in a lathe down to a cylinder, 18 mm diam., with rounded-off edges_ After properly positioning a second adaptor, the specimen was subjected to a vertically applied tensile force in the same direction as the cylindrical axis of the pellet. In 1966, Nakajima et al. [23] presented an experimental apparatus for testing the tensile force required to fracture horizontally a consolidated bed of particles. Basically, the apparatus consists of a balance, consolidation test cell, calibrated spring, cyhndrical water container, and a differential transformer with recording equipment. However, Shinohara and Tanaka 1241 have recently modified this equipment and they report having obtained more accurate and reproducible data. Another apparatus used in measuring the tensile strength of powder compacts is the Warren Spring Laboratory tensile strength tester (WSLT). A complete description of this split-plate apparatus and method of operation may be found in the original paper by Ashton et al. [25] _ In a recent publication Schubert [SS] reported on the use of a similar splitplate apparatus with two movable plates and one fixed plate in conjunction with Griffith’s capillary pressure method [27] _ The fiit part of this paper reports the work 1261 on moist limestone powder in a replica of Shinohara and Tanaka’s compaction cell, while the second part deals with the results of an earlier study 1271 on the same powder using the WSLT.
99
EXPERIhIENTAL
The compaction cell of Shinohara and Tanaka The apparatus is shown schematically in Fig- 1 and comprised a compaction cell, a fiied platform, a balancing weight, permanent magnet and coil assembly and an electrical unit to vary the current in a desired mannerIn the cell a powder was compressed between the upper and lower pistons in a threaded housing. The gap between them can be adjusted by turning the top and bottom half cells by hand- Thus, the compaction occurs by shear and compressive loading during this process- A powder bed 18 mm in diameter and 10 mm in height was formed in this manner_ The void fraction of the bed was varied by changing the mass of sample over the range 2.6 X 10m3 kg to 3.4 X 10e3 kg. As suggested by Shinohara and Tanaka, corrected void fractions of the bed in the plane of failure were determined for different overall void dictions- The corrected values were higher than the overall void fraction values. The force necessary to rupture the bed was applied using a permanent magnet suspended in a coil assembly- The electric current in this coil came from a d-c. power supply controlled by a function generator. In this way the tensile force was applied at any desired rate. The Warren Spring Laboratory Tester (WSLT) The Warren Spring Laboratory tensile strength tester is a version of the tilting plate apparatus- The apparatus has been used by its designers and other investigators in-a number of studies on powders. For instance, in 1965 Ashton et al. 1301 used it along with the Jenike flowfactor tester to show that for a number of powders the yield loci at constant bulk density follow power law relationships with the applied compressive stress. Similarly, Williams and Birks 1311 and Jimbo et al. [32] used the tester to measure the ultimate tensile stress as part of a study of failure measurements of powders. Cheng et al. [ 331, Farley and Valentin [34], Cheng [35], Kocova and Pilpel [36] and York and Pilpel [37] have reported experimental and theoretical investigations in which the WSLT played an important partThe apparatus used in the present work was essentially a replica of the one described by Ashton et al. [25]. The basic parts of the tester are the split sample cell, the calibrated
spring system and the motor-driven rack and pinion_ The sample cell was a shallow, cylindrical, stainless-steel dish, 52 mm i- d. and 11 mm deep. The cell was split diametrically into a fixed and a movable half- In order to increase the stability of the movable half, 32 precision stainless-steel_ ball bearings were used in four V-shaped, highly polished grooves in the base- After each test the grooves and ball bearings were examined to ensure that no deformation of the contact area had occurred. The original WSLT used the time required to split the powder compact to calculate the spring extension required and hence the applied force. In our initial tests both time measurements and direct extension measurements (using a dial gauge) were used- The latter method was found to be more direct and less prone to experimental error. An electronic trigger, consisting of a light source and photocell, stopped the timer and motor when the bed broke. This trigger mechanism replaced the proximity probe used by Ashton et al. ; there was no interference with the sample cell and the loading spring did not have to supply the force required to trigger the proximity switch_ In order to obtain a reliable tensile strength measurement with the tester it is necessary to prepare a sample which is isotropic in strength and of uniform density- To obtain isotropy the sample must contain a sufficient number of all sizes of particles present in the powder and must be randomly arrauged in the split cell. This condition is extremely difficult to obtain, as different sizes will segregate very easily. In order to reduce this segregation, the powder was spooned rather than poured into the cell. The cell walls were temporarily raised by means of a ring placed on the cell and a load was applied vertically on a consolidation plate. This consolidation load could be varied from 4.5 to 33 N. Different bulk densities were obtained by varying both the amount of powder and the load while keeping the consolidated powder surface first below the top of the cell. The average sample depth was 10.46 mm, with a standard deviation of 0.63 mm. The powder was consolidated by twisting the consolidation plate ten times back and forth through about 150” followed by two complete revolutions_ The ring and consolidation plate were then removed and
100 the
clampingscrewonthemovablehalfof thesplitcellwasreleasedBulk densitiesofthesample andhencethe pcrosity weredirectlydeterminedfrom the weightofpowderinthe ceiland the corre-
900
‘\’
I
x
MOISTURE ’
’
CONTENT ’
’
75% ’
i’
sponding volume- The latter, as well as the area of fracture, were determined from the cell dimensions and the height of the sample after splitting. Experimen tai material Some of the physical properties of the limestone used were determined by Chong 151, who reported that 54.2% of the particles were less than 1 pm, 80% were less than 2.5 pm, 95_1% were less than 5 I.trn and 98.4% were less than 10 pm. Its size distribution obeyed a log-normal distribution law and the median size was 0.8 pm while the mean particle diameter was 1.55 pm. Its density was 2-7 X lo3 kg/m3_ lMoist powder samples for the tests were prepared by first wetting the powder compietely to form a paste and then drying it in an oven at SO “C for different intervals of time. The samples were then put through a screen to have the final sample devoid of lumps. Moist powder thus prepared was then stored in tightly sealed bottles until testing.
1. Shinohara and Tanaka compaction cell resu Its A. Tensile strength versus void fraction (Figs_ 2 and 3) The experimental observations for samples of moisture content of 7.5% are shown in Fig. 2, while Fig. 3 presents the mean curves for experiments involving moisture contents of 2.3%, 7_5%, 12.5% and 14.7%. The considerable scatter in the data observed in this study is similar to that reported by other investigators [35,38,41433 _ The spread may be taken into account in analyzing the results in various ways. For example, Eaves and Jones [3S] used a double log regression line between tensile strength and p/p, by themethodofleastsquaresto
interprettheeffectofmoisturecontenton tensilestrength.Simiiarly, Farley [39] reported
that while for cohesive
060
powders
the
OS?
-
\
,
064
VO ID
ObB
o-66
FRACTION
Fig. 2. Tensiie strength U.S.void fraction at ‘7.5% moisture contctnt (S & T ceil).
for limestone
4
JO0
RESULTS _4ND DISCUSSION
,x
100
- 14-7x
-
060
062
0 64
VOID
066
06E
FRACTION
Fig_ 3. Mean curves of the tensile strength us void fraction for limestone at 2.3%, T-590, 12.5% ar.d l&i% moisture content (S & T cell).
scatterof the resultswassufficiently
small to draw a line through the data by eye, in the case of freer flowing powders a double regression technique was used. This assumed errors in both tensile strength and bulk density (or void fraction) measurements. The computer
edtorejectpointsbutsidethe wasprogramm 95%confidencelimitsofthedata_Inthe presentworkthe ohservedtensilestrength values were related to the void fractionvalues bythefollowingequation:
101
1
TABLE
of the parameters 81 and 82 at different moisture contents of powder. 131 and 02 were obtained linear least-squares method for estimation of parameters to equation: CT,= 8x(1 - E)‘=
by non-
VaIues
Moisture
content
01
02
Observed no. of points
Standard error in 0,
(%) Shinohara and Tanaka cell 2.2 7.5 12s 14.7
19.47 14-42 72-83 12.08
x
x
105 lo6 lo5 105
8.606 10.238 9.517 8.008
20 29 19 21
104.3 S6.0 105.6 77.5
13.78
X lo3
4.529
29
55.7
X x
WSLT
0.5
I
3
I 6
t 9
I
IZ
LIQUID
Fig_ 4. Effect (S & T cell).
0,
I 1s
SATURATION.
of the percentage
saturation
I
I
1
I
18
21
24
27
S (%I
on the tensile
=el(l--e)@:
This equation
(1) was used
previously
by Ashton
and Farley and Valentine 1343, among others. In the case of limestone (which could be classified as &e-flowing), both 8 1 and 0 2 were obtained from non-linear least-squares estimates of the parameters, assuming that only the tensile strength measurements were subject to error. Although it is conceded that the void fraction values were very much subject to errors, it was felt that for the purpose of comparing our data it was not necessary to go to the high degree of sophistication resulting from a double regression analysis. Examination of Figs. 2 and 7 et al.
[30],
strength
of moist
limestone,
at constant
void
fraction
shows that the least-squares curves do indeed describe the trend of the results. A summary of the least squares results is presented in Table 1. B_ Tensile strength (Fig_ 4)
versus moisture
content
Figure 4 is a cross plot of Fig. 3 and it illustrates the variations in tensile strength with percentage saturation of voids with water at constant void fraction. The percent liquid saturation is defined as: 6 = (PJPL) (1 - e)/e (100
WLlrv,)
(2)
show a maximum with percentage saturation. However, for a void fraction value equal to 0.625 the tensile strength All
curves
-I
0 44
5s
*
50
VOID
Consolidation limestone (\VSLT)_ -zig.
6.
52
55
56
FRACTION
pressure cs void fraction for dry
increased by 50% and then decreased 28%_ The probable explanation for this is that the number of pendular bonds of water between the particles increases up to a certain percentage saturation of voids After this point the size of liquid bridges increases, leading to a decrease in the attractive force between particles as the radius of curvature of the liquid increases (Newitt and Conway-Jones C401)On the other hand, for a void fraction of 0.66 there was a much smaller change in the tensile strength with increasing percentage saturation. It is possible that any effect of an increase in the number of pendular bonds of moisture was counteracted by the increase in the size of pendular bridges, and hence of their radii of curvature_ 2. Warren Spring Laboratory Tester results A. Consolidated pressure versus void fraction (Fig. 5) The consolidation plate was twisted at a constant angular velocity without jarring the apparatus. The result of ‘he process is that the powder was initially loosels; packed and then compressed by the consolidation load. Twisting of the consolidation plate at constant load resulted in a further decrease in the void fraction, becaluse during this operation work was done on the system to reorientate the particles. The consolidation process was completed when no further decrease in the sample vohume was observed_ Therefore, at least theoreticaIly, it was possible to obtain reproducible compaction of a powder by
-4c
-44
5.3
-48
VOID
-52
-56
FRACTION
Fig. 6. Tensile strength of dry limestone fraction (WSLT).
us. void
using the same compressive load and procedure. However, the results for dry limestone (moisture content ~0.5% or S = 0.06) clearly showed a considerable amount of scatter, which indicates that in practice it was difficult to reproduce compacts of the same average void fraction. One reason for this may be that no useful work is done when the consolidation lid slides over the powder surface, and hence no reorientation of the particles takes place. Presumably this happens when the consolidation process is completed; however, it may occur before completion. in which case the powder is no longer consolidated. It appears that one method of preventing such sliding is to roughen the lid, thus increasing the coefficient of friction between the lid and the powder. Furthermore, it has been shown by Lenczner [41] that fine powders behave quite differently from granular materials in the transmission of pressure to the base of the containing cell_ Hence it is possible that the void fraction of certain fine powders in the cell may vary from high values near the base to Icw values near the lid where most of the reorientation took place. Regardless of the scatter, the experimental results indicated a definite trend as shown by the curve. This curve was obtained by a nonlinear lea&squares fit of the data to a power law model. ‘The equation of the curve was thus found to be M = 3.95
e-iQ*
103
information was supplied about the limestone and the experimental technique_ On the other hand, comparison of the results for E = 0.56 with Schubert’s [ZS] results for dry limestone and a bed height of 10 mm shows that our results are about a factor of two to three times smaller than his. In other words, our results fall approximately halfway between those of Ashton et al. and Schubert_ It appears that variability in limestone samples in addition to variations in equipment and/or techniques may be responsible for the differences in the results.
cu
2 1500 -
LiPUlD
SATURATION.
Fig. 7. Tensile strength of moist limestone liquid saturation (WSLT).
S (%I
us. percent
1303 reported a similar power law type relationship between bulk density and the compressive normal load. For example, for lithopone M’ = 31.6 p’-% and for sodium bicarbonate M’ = 11.3 p384 (where M’ = g/cm2 and p = g/cm3). Ashton
ef aZ_
B. Tensile strength (Fig. 6)
versus void fraction
The experiments covered a range of void fractions varying from about 0.44 to 0.56. Figure 6 clearly shows that the tensile strength decreased significantly with a small increase in void fraction. This trend was as expected and is readily explained in terms of void fraction as a measure of the degree of consolidation. The experimenti results may be described by the same relationship as those obtained in the Shinohara and Tanaka cell, ie. *z = 1.38 X lo4 (1 -E)~= The results may also be examined in terms of bulk density rather than void fraction values. This means that the tensile strength increased from 340 to 940 N/m2 with a corresponding density increase from 1.19 X lo3 to l-48 X 1C3 kg/m3. In comparison, Ashton et al. 1301 reported a range of about 63 - 240 N/m2 for limestone dust with a corresponding bulk density range of 0.92 X lo3 to 1.35 X lo3 kg/m3. From Fig. 6, the tensile strength at a bulk density of 1.35 X lo3 kg/m3 was approximately equal to 600 N/m=, i.e. higher than Ashton et aZ_‘s value of 240. Unfortunately, Ashton ef al. obtained the reported results from some undisclosed outside source, and no
C. Tensile strength saturation (Fig_ 7)
versus percentage
liquid
Except for position and magnitude, the shape of the tensile strength curve is similar to the one obtained by Pietsch et al. [42] for a limestone sample having a mean particle diameter of 185.4 pm. The latter authors also obtained a maximum at S =5% while their minimum was at S =40%. In terms of the theoretical model described by Pie&h and Rumpf [43], the initial rise and drop (0 < S < 12.5%) may be cosidered to occur in the pendular state of liquid saturation, while the linear increase occurs in the funicular state. The point S = 12.5% would correspond to the critical percentage liquid saturation at which the liquid bridges touched and coalesced. The observed linear increase in tensile strength, starting at the critical percentage liquid saturation, was in agreement with Rumpf’s iinearity proposal [22] for the funicular state. Extrapolation to the capillary state at S = 100% gave a tensile strength of about 1900 N/m2, thus illustrati ing the fact that the capillary state results in the highest possible tensile strength of an agglomerate bound by liquid only. Due to experimental difficulties in handling the powder, the percentage saturation had to be kept below 43%. 3. Comparison of the results A comparison of the tensile strength values obtained using Shinohara and Tanaka’s compaction cell with those using the WSLT on limestone samples having the lowest moisture content show that both sets of results are of the same order of magnitude_ However, the tensile strengths corresponding to a given void fraction of the bed were quite
10-l
different. In fact, the entire void diction range is different for each piece of equipment. It is felt that the difference is attributable to the method of packing the powder as well as the dimensions of the bed. There is no doubt that preparation of the bed is the single most important step in testing the tensile strength of a powder, but unfortunately its status is not characterized solely by its void fraction, especially when the results of two different testers are compared. In addition to the differences in preparing the specimen, the two testers are also different in the way sample failure is caused. In the Shinohara and Tanaka cell the tensile stress is in the same direction as the consolidating stress, while in the WSLT the tensile stress is at right-angles to the consolidating stress The presence of any anisotropy in the sample will obviously result in a different tensile strength measurement for both testersThe two sets of results appear to substantiate Zimon’s statement 1441 that the preliminary compressive force brirlging macroscopic bodies into contact :vith one another determines the true contact area, and therefore the force of interaction between the particles differs for different methods (although generally remaining constant for any particular set of esperiment conditions). We, therefore, conclude with Schubert [ 263 that the measured tensile strength depends on the particular properties of the apparatus. A more important observation reported by Schubert was that for a split-plate apparatus the tensile strength is a function of sample height and that extrapolation to zero height is necessary for correct tensile strength valuesSchubert also pointid out that extrapolation of his dry limestone results was questionable because the tensile strength-sample height relationship became very non-linear at heights less than 10 mm. His conclusion was, therefore, that for powders where extrapolation is not reasonable, the split-plate method is not suitable. Since all our experiments were run at a sample height of about 10.5 mm it is not pcssible to verify this conch&on; however, if the conclusion is correct, it wouId account for the observed discrepancy between the results obtained with the Tanaka and Shinohara cell and the WSLT. Repeated trials to produce compacts of the same void fraction but different percent liquid
saturation in the WSLT were unsuccessful. Consequently it is not possible to compare Figs. 4 and 7.
ACKNOWLEDGEMENTS
We wish to express our gratitude to Dr. R. Farley and the Warren Spring Laboratory for providing us with plans of their apparatus. Our thanks are also due to the National Research Council of Canada for grants supporting this research and for providing L. Otten with a research schoIarship_
LIST OF SYhIBOLS
consolidation pressure (N/m*) percent saturation of voids (%) weight of liquid in specimen (kg) weight of powder in specimen (kg) porosity or void fraction of the bed (dimensionless) parameters in eqn. (1) bulk density of sample (kg/m3) true density of powder (kg/m3) density of liquid (kg/m3) tensile strength (N/m*)
REFERENCES K. Shinohara, K. Tamura. K_ Gotoh and T. Tanaka, Kagaku Kogaku, 31(1967) 267. D. J. Craik and B. F_ Miller, The flow properties of powders under humid conditions, J_ Pharm. Pharmacol_. 10 (1958) 136T_ R_ L C&-r, Particle behaviour, storage and flow, ASME Symp. on Flow of Solids, Boston, Oct. 1968, Paper No. 68-MH-6. B. S. Neumann_ in J. J. Hermanns (Ed.). Flow Properties of Disperse Systems, Ndrth-Holland Publ. Co., Amsterdam, 1953, p_ 382. S. P. Chong, Flow properties of fine powders, M.kSc_ Thesis, Univ. of Waterloo, 1966. R. R. Irani, C. F_ Callis and T. Liu, Flow conditioning and anticaking agents, Ind. Eng. Chem., 51(1959) 1285. M. Corn, The adhesion of solid particles to solid surfaces, J. Air. Poliut Control Asoc_, 11 .(1961) 528. 8 J. S. McFarlane and D. Tabor, Relation between friction and adhesion, Proc. Roy. Sot_, A202 (1950) 244. 9 hl. C. Kordecki and C. Orr, Adhesion of solid particles to solid surfaces, Arch. Environ. Health, l(l960) 1.
105 LO A. D. Zimon and B. V_ Deryagin, Colloid J_ USSR, 25 (1963) 135. 11 J. G_ Dawes. Dispersion of dust deposits by blasts of air, Part 1, Saf. Mines Res. l&tab. Res. Rep. 36, HMSC, London, 1952. 12 G. Thouzeau and T. W. Taylor, The physical properties of colliery stone dust. Saf_ hlines Res. l%.tab_ Rep. 19’7, HMSO, London, 1962. 13 H. S. Eisner, G. Fogg and T. W_ Taylor, Cohesion of powders and the effect of atmospheric moisture, 3rd Int. Congr. on Surface Activity, 2 (1960) 378. 14 E. Shotton and N. Harb, The effect of humidity and temperature on the cohesion of powders, J. Pharm. Pharmacol., 18 (1966) 175. 15 F. Bowden and D. Tabor, The Friction and Lubrication of Solids. Oxford Univ. Press, London, 1949, p_ 98. 16 E. Cremer, F. Conrad and T_ H. Draus, Use of adhesion of powders in particle size determination, Angew_ Chem_, 64 (1952) 10. 17 F. Patat and W. Schmidt, Adhesion of powders, Chem. Ing. Tech., 32 (1960) 8. 18 A_ IV_ Jenike, Gravity flow of bulk solids, Utah Univ. Eng. Exp_ Stn Bull 108 (1961)_ 19 J. F. Carr and D. h1. Walker, An annular shear cell for granular materials, Powder Technol., 1 (1967I 68) 369 - 373. 20 K. Umeya, Ryuichi Ham and Junichi Kikuta, On two-dimensional shear tests by model powders, J. Chem. Eng. Jpn., 8 (1975) 56. 21 T_ Tanaka, K. Gotoh and K. Shinohara, Cohesion of fine particles, hliner. Process., (Mar. 1966) 32. 22 H. Rumpf, in W. A. Knepper (Ed.). Agglomeration, Wiley, New York, 1961, pp_ 379 - 418_ 23 H. Nakajima, K Gotoh and T_ Tanaka, hleasurement of the cohesive force of packed fine particles, Kagaku Kogaku, 30 (1966) 946. 21 K. Shinohara and T. Tanaka, A device for evaluating cohesiveness of powders by tersile test. J. Chem. Eng. Jpn., 8 (1975) 46. 25 M. D. Ashton, R. Farley and F. H. H. Valentin, An improved apparatus for measuring the tensile strength of powders, J. Sci. Instrum., 41 (1964) 763. 26 H. Schubert, Tensile strength of agglomerates, Powder Technol., 11 (1975) 107 - 119. 27 R. M_ Griffith, Chem. Eng. Sci., 20 (1965) 1015 1019. 28 M. Balasubramanian, Contribution of electrical and other forces to the cohesive strength of powders, Ph. D. Thesis, Univ. of Waterloo, Ontario, 1973.
29
30
31
32
33
34
35 36
37
38
39 40
41
42
13
44
L. Otten, Tensile strength of finely divided limestone, hl. A. SC. Thesis, Univ. of Waterloo, Ontario, 1969. hl. D. Ashton, D. C. H. Cheng, R. Farley and F.H.H_ Valentin, Some investigations into the strength and flow properties of powders, Rheol. Acta, 4 (1965) 206. J. C. Williams and A. H. Birks, The comparison of the failure measurements of powder with theory, Powder Technol., 1 (196’7) 199. G. Jimbo, S. Asakawa and N. Saga, Measurement of adhesion of powder particles by powder bed tensile strength method, J. Sot. Mater. Sci. Jpn., 17 (1968) 540 - 544. D. C. H. Cheng, R. Farley and F. H. H. Valentin, The effect of particle size and inter-particle forces on the flow properties of powders, Paper to Tripartite Chem. Engineers hleeting, Montreal, 1968, 18. R_ Farley and F. H. K Valentin, Effect of particle size upon the strength of powders, Powder Technol., 1 (1968) 34% D. C. H. Cheng, The tensile strength of powders, Chem. Eng. Sci.. 23 (1968) 1405. S. Kocova and N. Pilpel, The tensile properties of mixtures of cohesive powders, Powder Technol., i (1973) 51. P. York and N. Pilpel, The effect of temperature on the frictional, cohesive and eIectrical conducting properties of powders, BIater. Sci. Eng_, 9 (1972) 2Sl. T. Eaves and T_ hl. Jones, Effect of moisture on tensile streng:h of bulk solids. L Sodium chloride and effect of particle size, J. Pharm. Sci., 61 (1972)256. R. Farley, personal communication, 1968. D. hI. Newitt and J. h1. Conway-Jones, A contribution to the theory and practice of granulation, Trars. Inst. Chem. Eng., 36 (1958) 422. D. Lenczner, An investigation into the behaviour of sand in a model silo, Struct. Eng., 41 (1963) 369. W. Pietsch, E. Hoffmann and H. Rumpf, Tensile strength of moist agglomerates, Ind. Eng. Chem. Prod. Res. Dev., 8 (1969) 58. W_ Pietsch and H. Rumpf, Haftkraft, Kapillardruck. Fliissigkeitsvolumen und Grenzwinkel einer Fliissigkeitsbrucke zwischen zwei Kugein, Chem. Ing. Tech., 39 (1967) 885. k D. Zimon, in h1. Corn (Ed.), Adhesion of Dust and Powder, Plenum Press, New York: 1969, p_ 53.
0
Technology.
15 (19i6)
Elsevier Sequoia S-A.,
-The
TensileStrength
G. A. TURNER, Department
November
9’7
Printed in the Netheriands
ofMoistLhnestonePowder_
&I_ BAL4SUBR_LLIANIAN*
of Chemical
(Received
97 - 105
Lausanne -
Engineering.
3, 1975;
Results
are presented
by Different
Apparatuses
and L_ O’ITEN**
University
of Waterloo.
Waterloo.
Ontario
(Canada)
in revised form March 22, 19’76)
SUMMARY
The tensile strength of stone was measured with of Shinohara and Tanaka Spring Laboratory sliding
Measurements
finely divided limethe compaction cell and the Warren plate apparatus_
in terms
of the void
fraction of the sample and moisture content. Comparison of the two sets of results showed that the measured tensile strength depends on the particular properties of the apparatus. The observed discrepancies reinforce Schubert’s conclusion that the sliding plate apparatus is only suitable &hen the tensile strength can be extrapolated to zero sample height_
INTRODUCTION
A number of methods and devices have been developed to give some measure of the cohesion of solid particles, each, in general, being applied to a specific situation and a particular type of cohesive force. Tlhis situation arises from the limited understanding of the behaviour of bulk powders and the problems encountered in obtaining their fundamental properties. In consequence it is very difficulttodevelopamethodordevice which will give quantitative and reproducible results, especially for a variety of conditions. The methods reported in the literature may be divided into three main groups according to the type of cohesive force measured. An indirect estimate of the extent of cohesion of
*Present address: Department of Chemical Engineering, The University of British Columbia, Vancouver, British Columbia, Canada. **Present address: School of Engineering, University of Guelph, Guelph, Ontario, Canada.
powders in certain processes is obtained in one of the groups. It includes, for esample, a pneumatic shear test method (Shinohara ef al. ]I] ), the angle of repose method (Craik and Miller [2], Carr ]3] ), flowability measurements (Neumann [4] j, a method using a modified Brookfield viscometer and a fluidized bed (Chong [5] ), and a method of measuring dustability (Neumann [ 41) or dispersability (Irani et al. [S] )_ The second group measures the cohesive or adhesive force between two particles or between a particle and a plane surface. Examples of this group are the weighing methods (Corn [7] ) which make use of a spring or torsion balance, the pendulum method (MC Farlane and Tabor 181) in which the adhesion between a spherical particle and a flat plate is obtained by measuring the masimum deflection angle of the pendulum particle from the vertical, and a centrifugal method (Kordecki and Orr [9], Zimon and Deryagin [lo] ) in which a particle is separated from a plane by centrifugal action. These processes all measure the cohesive or adhesive properties of an individual particle rather than the properties of an agglomeration of particles. The third group consists of methods which measure cohesive forces by breaking a consolidated or agglomerated powder mass_ In this group is the tilting or split plate method developed by Tideswell and Tolleyfield (unpublished) and quoted by Dawes [ll] . Here, the tensile breaking strength of a prepared bed of powder was measured by observing the angle with the horizontal at which the powder deposit on the split glass plate broke in two. Improved reproducibility of the measurements was obtained by certain modifications which were described in detail by Thouzeau and Taylor [ 123 _ The improved apparatus was further
Fis.
I_ Schematic
diagram
of the Shinohara
and Tanaka
used by Eisner e; al. [ 131 and Shotton and Harb [ 14]_ X similar method was the inclinedplane or friction method (Bowden and Tabor [ 151, Cremer and co-workers [ 16 j j in \vhizh the angle was measured at which a consolidated block sta:red to slide down the inclined plane. Patat and Schmidt 1171 made a detailed investigation into Cremer’s method and they concluded that the results appeared to be inconsistent with the model and the physics of the system_ A cohesive shear strength can be obtained by extrapolating shear strength measurements to zero normal load. The required data is obtained from such apparatus as the Jenike flowfactor tester [IS] which is a direct-shear, constant rate of s-b-ah machineX similar apparatus is the annuku shear ceIL for granular materials developed by Carr and Walker 1191; it can be used to measure the shear and the tensile strength of granular materials- Umeya et al. [ 201 developed a twodimensional shear apparatus to measure the overah stress-strain relationship for beds of model powders. A break-off’method by Tanaka et al. i21] allowed calculation of the cohesive strength from the weight of a broken coiumn of horizontally extruded, packed powder mass. It is ba=ed on the idea that when the packed column’s strength and its extruded weight are in equihbrium, a portion of the column breaks off. Finally, there are a number of tensile test methods which because of their simple mechanism are of considerable interest_ That of Bumpf 1223 measures the strength of agglomerates obtained from a disc pelietizer.
compaction
cell apparatus
(S & T cell)_
A 25 mm diam. green pellet was first glued to a special adaptor and then turned in a lathe down to a cylinder, 18 mm diam., with rounded-off edges_ After properly positioning a second adaptor, the specimen was subjected to a vertically applied tensile force in the same direction as the cylindrical axis of the pellet. In 1966, Nakajima et al. [23] presented an experimental apparatus for testing the tensile force required to fracture horizontally a consolidated bed of particles. Basically, the apparatus consists of a balance, consolidation test cell, calibrated spring, cyhndrical water container, and a differential transformer with recording equipment. However, Shinohara and Tanaka 1241 have recently modified this equipment and they report having obtained more accurate and reproducible data. Another apparatus used in measuring the tensile strength of powder compacts is the Warren Spring Laboratory tensile strength tester (WSLT). A complete description of this split-plate apparatus and method of operation may be found in the original paper by Ashton et al. [25] _ In a recent publication Schubert [SS] reported on the use of a similar splitplate apparatus with two movable plates and one fixed plate in conjunction with Griffith’s capillary pressure method [27] _ The fiit part of this paper reports the work 1261 on moist limestone powder in a replica of Shinohara and Tanaka’s compaction cell, while the second part deals with the results of an earlier study 1271 on the same powder using the WSLT.
99
EXPERIhIENTAL
The compaction cell of Shinohara and Tanaka The apparatus is shown schematically in Fig- 1 and comprised a compaction cell, a fiied platform, a balancing weight, permanent magnet and coil assembly and an electrical unit to vary the current in a desired mannerIn the cell a powder was compressed between the upper and lower pistons in a threaded housing. The gap between them can be adjusted by turning the top and bottom half cells by hand- Thus, the compaction occurs by shear and compressive loading during this process- A powder bed 18 mm in diameter and 10 mm in height was formed in this manner_ The void fraction of the bed was varied by changing the mass of sample over the range 2.6 X 10m3 kg to 3.4 X 10e3 kg. As suggested by Shinohara and Tanaka, corrected void fractions of the bed in the plane of failure were determined for different overall void dictions- The corrected values were higher than the overall void fraction values. The force necessary to rupture the bed was applied using a permanent magnet suspended in a coil assembly- The electric current in this coil came from a d-c. power supply controlled by a function generator. In this way the tensile force was applied at any desired rate. The Warren Spring Laboratory Tester (WSLT) The Warren Spring Laboratory tensile strength tester is a version of the tilting plate apparatus- The apparatus has been used by its designers and other investigators in-a number of studies on powders. For instance, in 1965 Ashton et al. 1301 used it along with the Jenike flowfactor tester to show that for a number of powders the yield loci at constant bulk density follow power law relationships with the applied compressive stress. Similarly, Williams and Birks 1311 and Jimbo et al. [32] used the tester to measure the ultimate tensile stress as part of a study of failure measurements of powders. Cheng et al. [ 331, Farley and Valentin [34], Cheng [35], Kocova and Pilpel [36] and York and Pilpel [37] have reported experimental and theoretical investigations in which the WSLT played an important partThe apparatus used in the present work was essentially a replica of the one described by Ashton et al. [25]. The basic parts of the tester are the split sample cell, the calibrated
spring system and the motor-driven rack and pinion_ The sample cell was a shallow, cylindrical, stainless-steel dish, 52 mm i- d. and 11 mm deep. The cell was split diametrically into a fixed and a movable half- In order to increase the stability of the movable half, 32 precision stainless-steel_ ball bearings were used in four V-shaped, highly polished grooves in the base- After each test the grooves and ball bearings were examined to ensure that no deformation of the contact area had occurred. The original WSLT used the time required to split the powder compact to calculate the spring extension required and hence the applied force. In our initial tests both time measurements and direct extension measurements (using a dial gauge) were used- The latter method was found to be more direct and less prone to experimental error. An electronic trigger, consisting of a light source and photocell, stopped the timer and motor when the bed broke. This trigger mechanism replaced the proximity probe used by Ashton et al. ; there was no interference with the sample cell and the loading spring did not have to supply the force required to trigger the proximity switch_ In order to obtain a reliable tensile strength measurement with the tester it is necessary to prepare a sample which is isotropic in strength and of uniform density- To obtain isotropy the sample must contain a sufficient number of all sizes of particles present in the powder and must be randomly arrauged in the split cell. This condition is extremely difficult to obtain, as different sizes will segregate very easily. In order to reduce this segregation, the powder was spooned rather than poured into the cell. The cell walls were temporarily raised by means of a ring placed on the cell and a load was applied vertically on a consolidation plate. This consolidation load could be varied from 4.5 to 33 N. Different bulk densities were obtained by varying both the amount of powder and the load while keeping the consolidated powder surface first below the top of the cell. The average sample depth was 10.46 mm, with a standard deviation of 0.63 mm. The powder was consolidated by twisting the consolidation plate ten times back and forth through about 150” followed by two complete revolutions_ The ring and consolidation plate were then removed and
100 the
clampingscrewonthemovablehalfof thesplitcellwasreleasedBulk densitiesofthesample andhencethe pcrosity weredirectlydeterminedfrom the weightofpowderinthe ceiland the corre-
900
‘\’
I
x
MOISTURE ’
’
CONTENT ’
’
75% ’
i’
sponding volume- The latter, as well as the area of fracture, were determined from the cell dimensions and the height of the sample after splitting. Experimen tai material Some of the physical properties of the limestone used were determined by Chong 151, who reported that 54.2% of the particles were less than 1 pm, 80% were less than 2.5 pm, 95_1% were less than 5 I.trn and 98.4% were less than 10 pm. Its size distribution obeyed a log-normal distribution law and the median size was 0.8 pm while the mean particle diameter was 1.55 pm. Its density was 2-7 X lo3 kg/m3_ lMoist powder samples for the tests were prepared by first wetting the powder compietely to form a paste and then drying it in an oven at SO “C for different intervals of time. The samples were then put through a screen to have the final sample devoid of lumps. Moist powder thus prepared was then stored in tightly sealed bottles until testing.
1. Shinohara and Tanaka compaction cell resu Its A. Tensile strength versus void fraction (Figs_ 2 and 3) The experimental observations for samples of moisture content of 7.5% are shown in Fig. 2, while Fig. 3 presents the mean curves for experiments involving moisture contents of 2.3%, 7_5%, 12.5% and 14.7%. The considerable scatter in the data observed in this study is similar to that reported by other investigators [35,38,41433 _ The spread may be taken into account in analyzing the results in various ways. For example, Eaves and Jones [3S] used a double log regression line between tensile strength and p/p, by themethodofleastsquaresto
interprettheeffectofmoisturecontenton tensilestrength.Simiiarly, Farley [39] reported
that while for cohesive
060
powders
the
OS?
-
\
,
064
VO ID
ObB
o-66
FRACTION
Fig. 2. Tensiie strength U.S.void fraction at ‘7.5% moisture contctnt (S & T ceil).
for limestone
4
JO0
RESULTS _4ND DISCUSSION
,x
100
- 14-7x
-
060
062
0 64
VOID
066
06E
FRACTION
Fig_ 3. Mean curves of the tensile strength us void fraction for limestone at 2.3%, T-590, 12.5% ar.d l&i% moisture content (S & T cell).
scatterof the resultswassufficiently
small to draw a line through the data by eye, in the case of freer flowing powders a double regression technique was used. This assumed errors in both tensile strength and bulk density (or void fraction) measurements. The computer
edtorejectpointsbutsidethe wasprogramm 95%confidencelimitsofthedata_Inthe presentworkthe ohservedtensilestrength values were related to the void fractionvalues bythefollowingequation:
101
1
TABLE
of the parameters 81 and 82 at different moisture contents of powder. 131 and 02 were obtained linear least-squares method for estimation of parameters to equation: CT,= 8x(1 - E)‘=
by non-
VaIues
Moisture
content
01
02
Observed no. of points
Standard error in 0,
(%) Shinohara and Tanaka cell 2.2 7.5 12s 14.7
19.47 14-42 72-83 12.08
x
x
105 lo6 lo5 105
8.606 10.238 9.517 8.008
20 29 19 21
104.3 S6.0 105.6 77.5
13.78
X lo3
4.529
29
55.7
X x
WSLT
0.5
I
3
I 6
t 9
I
IZ
LIQUID
Fig_ 4. Effect (S & T cell).
0,
I 1s
SATURATION.
of the percentage
saturation
I
I
1
I
18
21
24
27
S (%I
on the tensile
=el(l--e)@:
This equation
(1) was used
previously
by Ashton
and Farley and Valentine 1343, among others. In the case of limestone (which could be classified as &e-flowing), both 8 1 and 0 2 were obtained from non-linear least-squares estimates of the parameters, assuming that only the tensile strength measurements were subject to error. Although it is conceded that the void fraction values were very much subject to errors, it was felt that for the purpose of comparing our data it was not necessary to go to the high degree of sophistication resulting from a double regression analysis. Examination of Figs. 2 and 7 et al.
[30],
strength
of moist
limestone,
at constant
void
fraction
shows that the least-squares curves do indeed describe the trend of the results. A summary of the least squares results is presented in Table 1. B_ Tensile strength (Fig_ 4)
versus moisture
content
Figure 4 is a cross plot of Fig. 3 and it illustrates the variations in tensile strength with percentage saturation of voids with water at constant void fraction. The percent liquid saturation is defined as: 6 = (PJPL) (1 - e)/e (100
WLlrv,)
(2)
show a maximum with percentage saturation. However, for a void fraction value equal to 0.625 the tensile strength All
curves
-I
0 44
5s
*
50
VOID
Consolidation limestone (\VSLT)_ -zig.
6.
52
55
56
FRACTION
pressure cs void fraction for dry
increased by 50% and then decreased 28%_ The probable explanation for this is that the number of pendular bonds of water between the particles increases up to a certain percentage saturation of voids After this point the size of liquid bridges increases, leading to a decrease in the attractive force between particles as the radius of curvature of the liquid increases (Newitt and Conway-Jones C401)On the other hand, for a void fraction of 0.66 there was a much smaller change in the tensile strength with increasing percentage saturation. It is possible that any effect of an increase in the number of pendular bonds of moisture was counteracted by the increase in the size of pendular bridges, and hence of their radii of curvature_ 2. Warren Spring Laboratory Tester results A. Consolidated pressure versus void fraction (Fig. 5) The consolidation plate was twisted at a constant angular velocity without jarring the apparatus. The result of ‘he process is that the powder was initially loosels; packed and then compressed by the consolidation load. Twisting of the consolidation plate at constant load resulted in a further decrease in the void fraction, becaluse during this operation work was done on the system to reorientate the particles. The consolidation process was completed when no further decrease in the sample vohume was observed_ Therefore, at least theoreticaIly, it was possible to obtain reproducible compaction of a powder by
-4c
-44
5.3
-48
VOID
-52
-56
FRACTION
Fig. 6. Tensile strength of dry limestone fraction (WSLT).
us. void
using the same compressive load and procedure. However, the results for dry limestone (moisture content ~0.5% or S = 0.06) clearly showed a considerable amount of scatter, which indicates that in practice it was difficult to reproduce compacts of the same average void fraction. One reason for this may be that no useful work is done when the consolidation lid slides over the powder surface, and hence no reorientation of the particles takes place. Presumably this happens when the consolidation process is completed; however, it may occur before completion. in which case the powder is no longer consolidated. It appears that one method of preventing such sliding is to roughen the lid, thus increasing the coefficient of friction between the lid and the powder. Furthermore, it has been shown by Lenczner [41] that fine powders behave quite differently from granular materials in the transmission of pressure to the base of the containing cell_ Hence it is possible that the void fraction of certain fine powders in the cell may vary from high values near the base to Icw values near the lid where most of the reorientation took place. Regardless of the scatter, the experimental results indicated a definite trend as shown by the curve. This curve was obtained by a nonlinear lea&squares fit of the data to a power law model. ‘The equation of the curve was thus found to be M = 3.95
e-iQ*
103
information was supplied about the limestone and the experimental technique_ On the other hand, comparison of the results for E = 0.56 with Schubert’s [ZS] results for dry limestone and a bed height of 10 mm shows that our results are about a factor of two to three times smaller than his. In other words, our results fall approximately halfway between those of Ashton et al. and Schubert_ It appears that variability in limestone samples in addition to variations in equipment and/or techniques may be responsible for the differences in the results.
cu
2 1500 -
LiPUlD
SATURATION.
Fig. 7. Tensile strength of moist limestone liquid saturation (WSLT).
S (%I
us. percent
1303 reported a similar power law type relationship between bulk density and the compressive normal load. For example, for lithopone M’ = 31.6 p’-% and for sodium bicarbonate M’ = 11.3 p384 (where M’ = g/cm2 and p = g/cm3). Ashton
ef aZ_
B. Tensile strength (Fig. 6)
versus void fraction
The experiments covered a range of void fractions varying from about 0.44 to 0.56. Figure 6 clearly shows that the tensile strength decreased significantly with a small increase in void fraction. This trend was as expected and is readily explained in terms of void fraction as a measure of the degree of consolidation. The experimenti results may be described by the same relationship as those obtained in the Shinohara and Tanaka cell, ie. *z = 1.38 X lo4 (1 -E)~= The results may also be examined in terms of bulk density rather than void fraction values. This means that the tensile strength increased from 340 to 940 N/m2 with a corresponding density increase from 1.19 X lo3 to l-48 X 1C3 kg/m3. In comparison, Ashton et al. 1301 reported a range of about 63 - 240 N/m2 for limestone dust with a corresponding bulk density range of 0.92 X lo3 to 1.35 X lo3 kg/m3. From Fig. 6, the tensile strength at a bulk density of 1.35 X lo3 kg/m3 was approximately equal to 600 N/m=, i.e. higher than Ashton et aZ_‘s value of 240. Unfortunately, Ashton ef al. obtained the reported results from some undisclosed outside source, and no
C. Tensile strength saturation (Fig_ 7)
versus percentage
liquid
Except for position and magnitude, the shape of the tensile strength curve is similar to the one obtained by Pietsch et al. [42] for a limestone sample having a mean particle diameter of 185.4 pm. The latter authors also obtained a maximum at S =5% while their minimum was at S =40%. In terms of the theoretical model described by Pie&h and Rumpf [43], the initial rise and drop (0 < S < 12.5%) may be cosidered to occur in the pendular state of liquid saturation, while the linear increase occurs in the funicular state. The point S = 12.5% would correspond to the critical percentage liquid saturation at which the liquid bridges touched and coalesced. The observed linear increase in tensile strength, starting at the critical percentage liquid saturation, was in agreement with Rumpf’s iinearity proposal [22] for the funicular state. Extrapolation to the capillary state at S = 100% gave a tensile strength of about 1900 N/m2, thus illustrati ing the fact that the capillary state results in the highest possible tensile strength of an agglomerate bound by liquid only. Due to experimental difficulties in handling the powder, the percentage saturation had to be kept below 43%. 3. Comparison of the results A comparison of the tensile strength values obtained using Shinohara and Tanaka’s compaction cell with those using the WSLT on limestone samples having the lowest moisture content show that both sets of results are of the same order of magnitude_ However, the tensile strengths corresponding to a given void fraction of the bed were quite
10-l
different. In fact, the entire void diction range is different for each piece of equipment. It is felt that the difference is attributable to the method of packing the powder as well as the dimensions of the bed. There is no doubt that preparation of the bed is the single most important step in testing the tensile strength of a powder, but unfortunately its status is not characterized solely by its void fraction, especially when the results of two different testers are compared. In addition to the differences in preparing the specimen, the two testers are also different in the way sample failure is caused. In the Shinohara and Tanaka cell the tensile stress is in the same direction as the consolidating stress, while in the WSLT the tensile stress is at right-angles to the consolidating stress The presence of any anisotropy in the sample will obviously result in a different tensile strength measurement for both testersThe two sets of results appear to substantiate Zimon’s statement 1441 that the preliminary compressive force brirlging macroscopic bodies into contact :vith one another determines the true contact area, and therefore the force of interaction between the particles differs for different methods (although generally remaining constant for any particular set of esperiment conditions). We, therefore, conclude with Schubert [ 263 that the measured tensile strength depends on the particular properties of the apparatus. A more important observation reported by Schubert was that for a split-plate apparatus the tensile strength is a function of sample height and that extrapolation to zero height is necessary for correct tensile strength valuesSchubert also pointid out that extrapolation of his dry limestone results was questionable because the tensile strength-sample height relationship became very non-linear at heights less than 10 mm. His conclusion was, therefore, that for powders where extrapolation is not reasonable, the split-plate method is not suitable. Since all our experiments were run at a sample height of about 10.5 mm it is not pcssible to verify this conch&on; however, if the conclusion is correct, it wouId account for the observed discrepancy between the results obtained with the Tanaka and Shinohara cell and the WSLT. Repeated trials to produce compacts of the same void fraction but different percent liquid
saturation in the WSLT were unsuccessful. Consequently it is not possible to compare Figs. 4 and 7.
ACKNOWLEDGEMENTS
We wish to express our gratitude to Dr. R. Farley and the Warren Spring Laboratory for providing us with plans of their apparatus. Our thanks are also due to the National Research Council of Canada for grants supporting this research and for providing L. Otten with a research schoIarship_
LIST OF SYhIBOLS
consolidation pressure (N/m*) percent saturation of voids (%) weight of liquid in specimen (kg) weight of powder in specimen (kg) porosity or void fraction of the bed (dimensionless) parameters in eqn. (1) bulk density of sample (kg/m3) true density of powder (kg/m3) density of liquid (kg/m3) tensile strength (N/m*)
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44
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