Ind. Eng. Chem. Res. 1994,33,2209-2214
2209
Crack Initiation Mechanism on the Glass Beads Used as Grinding Media in an Agitation Bead Mill Yoko Hashi' Ashizawa Ltd., 4-2, Akanehama 1 -chome, Narashino, Chiba 275, Japan
Mamoru Senna Faculty of Science and Technology, Keio University, 14-1, Hiyoshi 3-chome, Kohoku-ku, Yokohama 223, Japan
Wear of glass beads used in an agitation bead mill as grinding media was observed in detail with varying amount and hardness of the powders to be ground. Wear and surface damage of the beads were examined by a weight loss during grinding, scanning electron microscopic observation, and three-dimensional profilograms of the bead surface before and after etching by a n aqueous solution of potassium hydroxide. T h e amount of weight loss and the feature of surface damage varied significantly with the material to be ground, even under the same operating condition of the mill. Observed microcracks after etching revealed the difference in the loading conditions during collision or compression of two beads and subsequent microcrack initiation depending on the hardness of the powders to be ground. 1. Introduction An agitation bead mill is frequently used for the finest grinding of powders below several microns. Its operation, however, is always accompanied by wear of beads used as grinding media. Wear of grinding media causes many annoying effects, e.g., contamination of the product and running up of the cost due to exchange of worn media. Studies on the ball wear with tumbling ball mills have been carried out for many years (Suzuki, 1964,1971;Austin and Klimpel, 1985; Vermeulen, 1986; Menacho and Concha, 1986,1987; Howat and Vermeulen, 1988). Wear of beads was studied with vibration ball mills with beads smaller than 3 mm and under high-energy input (Rose and Jimbo, 1963; Jimbo, 1964; Nishitake and Matsuda, 1967; Suzuki et al., 1989; Yokoyama et al., 1992). Similar study with regard to a centrifugal ball mill was also carried out (Yamauchi and Nishiyama, 1964). With agitation bead mills, Stanley et al. (1974) studied the contamination of the product on barium ferrite. Nishida et al. (1990) reported the weight loss of four kinds of beads, i.e., PSZ (partially stabilized zirconia), alumina, zircon, and titania on piezoelectric ceramics powders. Kusunoki (1990) observed the surface of damaged beads with a scanning electron microscope (SEM) and measured the weight loss of beads in blank operation without powder. All the papers mentioned above dealt with the wear of the beads from their weight loss in connection with the operating conditions and the bead material. In an actual mill, however, the surface of the beads is subjected to the impact, compressive, or shearing force during operation. Consequently, its chemical reactivity may be enhanced by the mechanochemical effect. In such a case, a solution of beads which does not occur under normal condition may promote wear as well as mechanical damage. Wear of beads is caused by the interactions among beads, powder, and dispersing liquid. The surface of the beads is damaged namely by (i) the collision and the attrition among the beads; (ii) the interaction between beads and machine elements, e.g., agitator disks and a vessel wall; and (iii) the interaction between beads and the powder. The interaction between the beads and the machine elements can be disregarded, since the surface area of the machine elements is negligibly OSSS-5SS5/94/2633-2209$04.50/0
Table 1. Operating Conditions machine type disk type number of disks disk diameter grinding vessel diameter grinding vessel capacity rotating speed filling degree flow rate
horizontal perforated disk 5 75 mm 100 mm 0.978 dm3 1750 rpm 0.8 0.2 dmalmin
small compared with that of beads or powder. Most of the damage is caused by the interaction among the beads and between the beads and the powder. The purpose of the present study is to examine the difference in the interaction among beads with varying amount and hardness of the powder. The differences in the interaction were discussed from morphological observation and chemical activity of the bead surface. 2. Experimental Procedure The test apparatus was a horizontal agitation bead mill witha 2.2-kW electric motor, equipped with a strain gauge torque meter on its drive shaft. The principal dimensions of the grinding chamber and operating conditions are listed in Table 1. Glass beads (Toshiba-Ballotini, EGB503) were used as the grinding media, comprising soda-lime glass with a diameter of 1.4-2.0 mm. The Mohs hardness was 5. A batch contained 1197 g of the beads, which corresponded to a filling degree of 0.8. Two kinds of powders with hardness above and below that of the soda-lime glass were used; i.e., synthetic mullite (Naigai Ceramics, MMS325, Mohs hardness 7) and heavy calcium carbonate (calcite; Nitto-Funka, "200, Mohs hardness 3) were ground in water. The slurry was fed into the chamber from a hopper by means of a pump. The discharged slurry was returned to the hopper and recycled. Running time was kept constant at 4 h except for mullite. Mullite was ground by a short batch running. For the blank operation without powder, water was renewed every 15 min to remove small debris from the beads. The energy input was calculated from the observed torque, the rate of rotation of the agitator shaft, and the running time. The surface damage of beads was examined from the changes in the surface morphology and the chemical 0 1994 American Chemical Society
2210 Ind. Eng. Chem. Res., Vol. 33. No.9, 1994
Table 2. Runnini Conditions and Wekht Less of Beads grinding medium h a t a d water mullit@ CaCW 8011-
grinding condition
median particle a h of powder bra) Mob hardness of d e r running time (rnin) total energy input (MJ) weight less during running (%) weight losalenergy input (g/MJ) weirht losa dwine etchine (%) surkce area ratio-before &hing surface area ratio after etching
15 0
0 0
0.05 2.1 2.6
7 2 4 0 5 1.67 0.036 0.38 1.40 2.7 466 0.16 0.35 8.5 53 15 67
20 3
deformation on the bead surface. These beads were subsequently observed by SEM and subjected to threedimensional surface profilometry. The cross sections of beads were also etched after embedding into a resin and polishing.
240 2.49 0.18 0.88 0.22 16
24
Volume fraction 0.1.
properties. The microstructure on the surface and the cross section wasobserved by aSEM. Surfacemorphology wasalsod~bedfromtheviewpointofsurfaceroughneas, expressed by a three-dimensional profilogram for the area 0.1 mm x 0.1 mm on the bead surface. The profilogram was obtained from the three-dimensional surface roughness analyzer (Mitsutoyo, Surftest SV-9500 3D). The surface area ratio was defined by dividing the area of the rugged surface from the above-mentioned roughness analysis by the geometrically swept one. The curvature of the head surface was corrected by eliminating a waviness larger than 25 pm. Though glass is macroscopically brittle, it also deforms plastically on a microscopic scale, particularly in the vicinity of cracks. As the plastically deformed part of silicates including soda-lime glass has a higher solubility to alkali (Chida et al., 1990), beads were etched by a 0.1 N aqueous solution of potassium hydroxide at 60 "C for 6 h to examine the distribution and intensity of local plastic
3. Results and Discussion 3.1. SEM Micrographs of Bead Surface. The characteristics of powders and operating conditions are summarizedinTable2. Figures 1-4areSEMmicrographs of beads. Parts a and b of each figure show the surface of beads before and after etching, while (e) and (d) are the corresponding cross sections. Figure 1shows the virgin beads. As shown in Figure l a c , nontreated beads have a smooth surface with a maximum roughness of 0.5 pm with a small number of cracks or voids. Shallow etch grooves on the bead surface can be seen in Figure l b (indicated by arrows A). As these etch grooves were not clearly observed on the cross-sectional view, their depth must be not much larger than their width, Le., at most 0.2 pm. The beads used in the operation without powder are shown in Figure 2. As shown in Figure 28, the surface was chipped to give holes after fragments of the beads fell out, asindicated by A. Theotherpart, indicatedby B, however, remained smooth. In Figure 2b, deep etch grooves were observed all over the surface. As can be seen in Figure 2d, these grooves were developed perpendicular to the bead surface as indicated by C, and their depth was about 5 rm. In general, the part of the beads nearer the surface was etched more intensively. The maximum etch depth was about 20 pm from the top surface.
F h r e 1. SEM micrographs of nontreated beads: (a) surface before etching; (b)surface after etching; (e) CIOBB section before etching, (d) e r o aection ~ ~ after
etching.
Ind. Eng. Chem. Res., VoL 33, No.9,1994 2211
Fimre 2. SEM micrograph of beads used in blank operation without powder: (a) surface before etching; (b) surface after etching; (e) aaa m i o n before etching; (d) cross section after etching.
On the heads used in the blank operation, etch grooves appeared from the smooth surface with no appreciable change in the surface morphology on the micrograph. This is an indication of the existence of the microcracks, which were not visible on the micrograph before etching. The plasticallydeformed zone developed alongthe microcracks. The etching rate was, therefore, correspondingly higher than the other parts. These microcracks became broader after etching, and turned visible under the microscope. It istobeconcludedthatthesmoothsurfacewithnoappa~ent flaw was also damaged, actually during running. Figure 3 shows SEM micrographs of heads used for grinding calcium carbonate. In Figure 3a, the bead surface waspartlychippedasindicated byA,while theotherpart, indicated by B, was still smooth, similar to the beads used in the operation without powder. However, in Figure 3b, no etch groove was observed on the smooth surface corresponding to B in Figure 3a. This indicates that no microcracks were formed on the surface of the heads on grinding calcium carbonate, in contrast to the blank operation. SEM micrographs of beads used in grinding mullite are shown in Figure 4. In Figure 4a, beads were chipped all over the surface and no smooth surface remained. Deep etch grooves were observed, as shown in Figure 4h. The density of grooves was, however, lower than that of the heads used in the blank operation. 3.2. Surface Profile. Representative three-dimensional profilograms are shown in Figure 5. The values of the surface area ratio are listed in Table 2. The surface area ratio of the beads after etching was higher than that of beads before etching on each sample. As the three-
dimensiondsurfaceroughnessanalyzerdidnotdetectthe zigzag plane with an angle higher than 1 5 O from the plane to be observed surface, steep etch grooves and holes were automatically excluded from Figure 5. The surface of nontreated beads was relatively smooth, whereas those used in the blankoperationconsistedofsmooth(indicated by B)and rough (indicated by A) regions. The surface of the beads used for grinding mullite was rough all over the surface. These features of the surface profile were consistent with SEM observation. 3.3. Crack Initiation Mechanism. In the case of a solid volume fraction, = 0.Le., operating without any powder, two beads come directly into contact as shown in Figure 6a. The problem of two elastic spheres pressed together was studied by Hertz (1881). When twospheres are identical, the surface of contact becomes a plane. The radius a of the surface of contact is given by
where P is a compressive force, R is a radius of spheres, and v and E are Poisson's ratio and Young's modulus of spheres, respectively. The maximum tensile stress occura at the circular boundary of the surface of contact in the radial direction as shown in Figure 6b. The magnitude of the tensile stress ur is 1-2v a,=-2
P 102
Taking or= 1 X 10 Pa as tensile strength, E = 8 X 10'O Pa, v = 0.22 (Band and Doremus, 1986).and R = 1X 1 P
2212 Ind. Eng. Chem. Res., Vol. 33, No. 9,1994
Pigum 3. SEM micrograph of beads used in grinding calcium earborlate: (a) surface before etching; (b) surface after etching; (e) croea U o n before etching; (d) cross section after etching.
m, the value of a when a crack occurs is calculated as 5.9 pm from eqs 1and 2. In the case of a brittle material like soda-lime glass, failure is produced by maximum tensile stress. The cracks perpendicular to thesurface,observed in Figure 2b,d, were considered to be produced by the tensile stress by the direct contact of two beads. In the case of the beads used in grinding calcium carbonate, two beads do not always come into contact because the powder particles are captured between them. Fracture characteristica of various single particles including fine calcium carbonate were studied by Hess (1980). He reported that fine particles did not show a brittle fracture but deformed plastically, irrespective of the material. Microplastic deformation began with a particle size of 5-9 r m on calcium carbonate. In the present study, the final median particle diameter of calcium carbonate was 0.81 pm and, accordingly, well in the size region of microplastic deformation. When powder particles are plastically deformed, the kinetic energy of the beads is partly dissipated for plastic deformation. A t the eame time, the contacting condition of two beads changes as shown in Figure 6c. It is assumed that the calcium carbonate particles begin to be captured between two beads when the particle becomes as small as the clearance between two beads (within a circle of a solid line in Figure 6c). The state of capture ends up with the direct contact of the two beads (a circle of a dash-dotted line). TheparticleslocatedinregionsAandBaresupposed to be caught by the beads. The particles in region A are plastically deformed to fill region C. The total volume of all the particles in the region A, VA, based on the concentration, and the volume of region C,
VC,are expressed as VA= rR2 sin' 0 +pd
vc = (*R3/2)$
(3)
(4)
whereBistheanglebetareenthestraightlinethatconnecta the centers of two spheres and the straight line that conneds a point on the circumference and the centpr of sphere. If the volume VAis .qual to Vc, eqs 3 and 4 give
*R2 sin*B +pd = (d?/2)@
(5)
which is approximated as a, = (2+&W2
(6)
under the assumption, 01, a2
