An experimental study of the impact breakage of wet granules

Chemical Engineering Science 60 (2005) 4005 – 4018 www.elsevier.com/locate/ces An experimental study of the impact breakage of wet granules Jinsheng Fua , Gavin K. Reynoldsa , Michael J. Adamsb , Michael J. Hounslowa , Agba D. Salmana,∗ a Department of Chemical and Process Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK b Centre for Formulation Engineering, Department of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK Available online 1 April 2005 Abstract The breakage behaviour of wet granules produced in a high-shear mixer was investigated experimentally using single granule impact tests and the results are described in terms of the critical impact velocity, breakage pattern, and extent of breakage. The failure patterns of these wet granules have a number of common features that have been observed for dry granules including the formation of debris with a conical geometry. A more quantitative description is presented of the factors that control the volume of these conical regions. The granules were produced with negligible air voidage and there were unusual strength characteristics with varying binder content. Most previous studies have involved a reduction in the air voidage of granules as the binder content is increased, which leads to a maximum in the strength at some critical binder content. For the granules studied in the current work, the strength either showed a minimum value or decreased monotonically with increasing binder content depending on the size of the primary particles. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Wet granule; Impact; Strength; Granule age; Breakage 1. Introduction Granule breakage has been identified as one of the main processes that occurs during granulation (Iveson et al., 2001). Two principal approaches have been adopted for measuring the strength of granules under impact conditions: multi-particle and single particle tests. Bemrose and Bridgwater (1987) concluded in their review of attrition that the results from multi-particle tests are more closely related to the type of conditions found in most powder handling and processing equipment, but these tests are primarily empirical in nature and could not reveal the nature of detailed breakage mechanisms. Although arguably less representative of practical conditions, single particle impact tests can provide enhanced detail of the breakage behaviour that is useful for understanding failure processes and mechanisms. One of the key aims of performing such tests is to obtain an insight into the different ways in which impacts can ∗ Corresponding author. Tel.: +44 114 222 7560; fax: +44 114 222 7566. E-mail address: a.d.salman@shef.ac.uk (A.D. Salman). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.02.037 generate damage with respect to the failure patterns and the extent of the damage. The damage ratio (see Section 2) is defined as the mass ratio of the impact debris and the mother granules (Ning et al., 1997) and this parameter provides a direct and simple measure of the extent of breakage for multi-particle tests. However, it has limited value when the failure patterns and breakage processes are of more interest for understanding the mechanisms involved, which is the case for granulation, for example. There are relatively few studies of the breakage behaviour of granules using single particle impact tests. They include the work of Subero and Ghadiri (2001) who described experimental data for agglomerates formed from small glass spheres and an expoxy resin. Definitive work on ‘dry’ agglomerates was undertaken by Arbiter et al. (1969), which involved free fall and double impact measurements on sand-cement spheres. Computer simulations have also been employed for ‘dry’ agglomerates (Thornton et al., 1999, 2004; Potapov and Campbell, 2001). Moreover, there is an extensive literature concerning experimental work based on diametric compression rather than impact, e.g., Kapur and 4006 J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 Fuerstenau (1967), Wynnyckyj (1985), Adams et al. (1994) and Sheng et al. (2004). For typical brittle materials the failure mechanisms associated with impact and diametric compression are quite similar as there is a weak rate dependence of the mechanical properties. However, in the cases of polymer and granular materials, especially those having a viscous liquid binder, the failure mechanisms are strain rate dependent. This aspect will be discussed later in more detail. In a granulation process, the failure characteristics of the agglomerates in the ‘wet’ rather than the ‘dry’ state are more important. Experimental impact studies have been limited to a velocity range in which only plastic deformation occurs (Iveson and Litster, 1998; Fu et al., 2004a). Continuum computer simulations (finite element analysis) involving elastoplastic and elasto-viscoplastic deformation have also been conducted in order to understand the rebound behaviour of wet agglomerates (Thornton and Ning, 1998; Adams et al., 2004). More severe impact damage of ‘wet’ agglomerates involving interparticle bond rupture has been examined by Lian et al. (1998) who used a discrete simulation procedure (distinct element analysis). In contrast to agglomerates, there is a much greater understanding of the failure behaviour, for both impact and diametric compression, of spherical particles made from a continuous material. A wide range of such particles have been investigated experimentally by Salman et al. (2004) and it was possible to classify the failure patterns in terms of low, intermediate and high velocity regimes. Shipway and Hutchings (1993) found that metallic and ceramic spheres displayed similar fracture behaviour under impact and compression loadings. This was because only elastic deformation was involved such that the stress distributions were essentially similar under the two loading conditions for equivalent axial deformations. However, in the case of spheres made from a glassy organic polymer, it has been found that impact resulted in more brittle failure compared with compression for which failure was predominantly plastic under the conditions examined (Gorham et al., 2003). This behaviour was attributed to the high strain rate sensitivity of the mechanical properties of such polymers that allows plastic flow to occur when the characteristic time of the experiment is long compared with the relaxation time, which is more likely to be the case for diametric compression. The general failure patterns for brittle spheres were first established by Arbiter et al. (1969) and they have been confirmed by subsequent experimental studies involving a wider range of materials, e.g., Shipway and Hutchings (1993), Majzoub and Chaudhri (2000) and Salman et al. (2004). ‘Brittle failure’ may be considered as corresponding to the initiation and propagation of cracks under primarily an elastic tensile stress field, i.e., with only limited plastic deformation at the crack tip. Practically this means that the fragments may be fitted together to reconstitute the original geometry of the cracked body. The results of these studies on the impact and diametric fracture of brittle spheres may be summarised as follows. At small impact velocities (or small diametric compressive strains), a flattened circular contact region(s) forms due to elastic Hertzian deformation (Johnson, 1985). The corresponding hoop (circumferential) stress is compressive within the volume adjacent to the contact region. There is a maximum radial tensile stress at the edge of the contact circle that may result in Hertzian ring cracking, which is observed as the formation of surface fragments with the so-called ‘angels wings’ geometry. The maximum shear stress occurs at a depth of about half the contact radius. Initial sub-surface yielding occurs when this stress is approximately equal to the uniaxial yield value. With increasing impact velocity, the plastic zone will grow until it reaches the contact interface; the mean contact pressure is then equal to the hardness of the material, which is a factor of about three times the uniaxial yield stress. At this stage, there is a specific impact velocity (defined in the current paper as the ‘critical impact velocity’) at which the hoop stress becomes sufficiently tensile, at and just outside the contact circle, that a primary meridian crack starts to propagate. It should be noted that fracture may occur during unloading but this case is not relevant for the current purpose. Either just before or just after the formation of this primary meridian crack, photoelastic measurements reveal (Arbiter et al., 1969) that an intense shear stress field extends from the contact circle, which results in the formation of a cone due to a ductile fracture process that will be discussed more fully in Section 4.2. The primary meridian crack grows along the surface and interior of the body but does not penetrate the cone, demonstrating that at this stage the hoop stresses are compressive in this region. The crack may also branch when it reaches the load axis and the resulting secondary meridian cracks cause orange-segment shaped fragments or lunes to be formed rather than the body simply splitting into equalsized fragments. At greater impact velocities, oblique cracks propagate in fan-like pattern from the conical zone along the trajectories of maximum compression. The final fragment size will depend on a number of tertiary processes such as the formation of cracks normal to the load axis, intersections of meridian and oblique cracks, which may also cause a second conical region to be formed above the initial impact cone, and multiple crack branching. The cone itself may be highly fragmented possibly because cracks are able to penetrate this region when the compressive hoop stresses unload or simply due to a more uniform disintegration process. The sand–cement spheres studied by Arbiter et al. (1969) are arguably not conventional agglomerates. However, this is not the case for the sand agglomerates examined by Newitt and Conway-Jones (1958), for which a similar pattern of failure was observed, and also some subsequent experimental studies such as that of Kapur and Fuerstenau (1967) and the discrete computer simulation work described by Thornton et al. (2004). However, more porous agglomerates may be sufficiently weak that they fail by disintegration (Subero and Ghadiri, 2001; Thornton et al., 2004). As was mentioned earlier the failure characteristics of ‘wet’ agglomerates, in which the binder is in liquid state, J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 has not been studied previously and this was the aim of the current work. The agglomerates were made by a specially developed process that results in highly reproducible properties and spherical geometries (Fu et al., 2004b). A major advantage of the process is that a range of packing densities of the primary granules may be obtained by varying the granulation time or the amount of liquid binder while maintaining a relatively low air voidage. This allows the mechanical properties of the agglomerates to be varied widely from highly plastic to relatively brittle as the packing density of the primary particles is increased. The failure mechanisms were monitored using high-speed photography and the extent of failure was quantified in terms of the critical impact velocity, the size of the impact cone and that of the largest non-conical fragment using the survival ratio. 2. Experimental 2.1. Granule impact measurements The impact breakage behaviour of wet granules was measured using a compressed gas gun that could project a single well-characterised granule onto a rigid transparent target; the details are described elsewhere (Fu et al., 2004a). Two high-speed video cameras with an image capture rate of 40,500 fps (Kodak HS4540, Japan) were used to determine the impact velocity and also to record the impact events so that the detailed breakage process could be identified. One was positioned horizontally to the target in order to record the failure process and the other was positioned at the rear of the target to measure the radius of the contact zone. In order to minimise the associated errors and uncertainties in determining the mode of breakage, due to any variability of the granules, typically 20 granules were tested at each impact velocity. This number of repeat measurements also allowed the mean critical impact velocity to be obtained more accurately. The critical impact velocity was defined in the current work as the minimum impact velocity at which one or more visible cracks in the granule was observed. This parameter was obtained by optical examination of the impacted granules using a microscope in order to determine whether or not a meridian crack had started to form. There was some difficulty in making an accurate determination of this velocity because of the tendency for cracks to heal after their initial formation, which arose from the elasto-plastic nature of the granules during relaxation. At relatively high impact velocities, the formation of a cone-like fragment at the contact zone is generally an important feature of the granule breakage as discussed in Section 1. Despite their fragility, with great care it was possible to collect and weigh the conical fragments from the impact debris. The ratio of the mass of the cone, mc , and that of the mother granule, mg , was termed the ‘cone mass ratio’,
c (=mc /mg ). 4007 Table 1 Primary particle size data Calcium carbonate grade Characteristics of volume based size distribution (
m) D10 Durcal Durcal Durcal Durcal 5 15 40 65 2.8 5.9 7.8 10.2 D50 6 15 23 38 Span D90 23 52.7 86 103.3 3.36 3.25 3.4 2.66 The mass of the largest fragment of the impact debris provides a useful measure of the extent of the breakage (see Section 1). In this case, the term fragment excludes from consideration the principal cone-like fragment. The ‘survival ratio’,
f , was defined as the mass ratio of the largest fragment, mf , and the mother granule, thus
f = mf /mg . For both the survival ratio and cone mass ratio, the results presented in the current work are the average of 20 impacted well-characterised individual granules and are expressed as a percentage. 2.2. Granule preparation Four different grades of Durcal powder (Omya, France), which were produced from white marble by comminution and classification, were used as the primary particles for making the wet granules. The grades are termed Durcal 5, Durcal 15, Durcal 40 and Durcal 65 and the particle size distributions were measured using a laser light scattering instrument (Sympatec). Characteristic values of the particle sizes of the powders are presented in Table 1. The span is calculated as the difference between the diameters at the 10th and 90th percentiles relative to the median diameter, D(v; 0.5). The true density of the solid particles is approximately 2750 kg/m3 (Johansen and Schaefer, 2001). Polyethylene glycol (PEG 400 supplied by Surfachem Ltd) was used as the main liquid binder. It behaves as a Newtonian fluid and has a viscosity of 134 mPa s and a density of 1127 kgm−3 at 25 ◦ C. The viscosity was measured using a Contraves Rheomat 115 viscometer. In addition, aqueous solutions of glycerol were employed to obtain binders with a range of viscosities having a relatively constant liquid surface tension (63–70 mN/m). The granules were manufactured in a 2 l bench-scale highshear mixer as described in detail by Fu et al. (2004b). The binder content of a single granule was determined from the loss in weight after heating for 2 h at 600 ◦ C. This thermo-gravimetric analysis assumed that the binder may be removed completely at the elevated temperature without causing a reduction in the mass of the calcium carbonate (Knight et al., 1998). For a given granule type, a mean value of the binder content was calculated from 20 individual measurements to ensure that the distribution was uniform across different granules. The measured binder content was J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 0.18 0.06 Binder ratio 0.05 Air fraction 0.16 0.04 0.14 0.03 Air fraction represented using the term ‘binder ratio’, S, which is the ratio of the mass of the binder to that of the primary particles. The average air voidage (pore volume fraction of air) of a group of granules was determined from the measured apparent density of a collection of granules and the true density of the granules. The apparent density of the granules was measured by using the liquid displacement technique, which is similar to the method described by Iveson et al. (1996). The details of the determination of the average air voidage have been described elsewhere (Fu et al., 2004b). Binder ratio 4008 0.02 0.12 0.01 3. Results 0.1 0 20 40 60 80 100 0.00 120 Granulation time (min) Fig. 1. The variation of the binder ratio and air voidage with the granulation time for granules with a mean diameter of 4.5 mm prepared with PEG 400 and Durcal 40. 16 Critical impact velocity (m/s) The variation of the binder ratio and air voidage with the granulation time is shown in Fig. 1 and the corresponding plot for the critical impact velocity is shown in Fig. 2. These data are for granules prepared with PEG 400 and Durcal 40; the mean diameter and mass of the granules at the end of the granulation process were in the range of 4.0–4.75 mm and 0.12–0.16 g. During the granulation period of 110 min, there is a large reduction in the binder ratio from the initial value of about 0.18 decreasing to 0.135 for this size range. There is also a concomitant reduction in the air voidage. This densification of the primary particle packing in granulation processes due to mechanical agitation is a well established phenomenon, e.g., Newitt and Conway-Jones (1958), and causes the granules to appear wet towards the end of the process as the binder is squeezed to the surface. The main point to be made here is that the air voidage for the granules studied in the current work is negligible (<1%) in most of the cases. In addition, it may be seen that there is a large increase in the critical impact velocity from about 7–14 m/s for these granules, corresponding to the increase in the effective binder ratio. This aspect of the data will be considered in more detail later. Images of the impact of granules made from PEG 400 and Durcal 40 with a binder ratio of 0.15, an air voidage of 0.009, a diameter range of 4.00–4.75 mm and a mass range of 0.12–0.16 g are shown in Fig. 3. For an impact velocity of 16 m/s, it may be observed that plastic deformation has occurred initially. A meridian crack has formed at some time less than the image captured at 0.17 ms and this crack has extended in the subsequent image at 0.19 ms (Fig. 3(b)). In the interval 0.19–0.24 ms, the granule has rebounded and, subsequently, it is evident that a conical fragment has adhered to the target and became detached from the mother granule. The behaviour for the impact velocity of 12 m/s is similar except that there is no evidence of a cone being formed; this could be because a cone was not formed or because one did but it did not adhere to the target. The images obtained at 20 and 28 m/s show that the extent of the initial plastic deformation increases with increasing impact velocity at comparable times, as would be expected. It is difficult from the images to determine accurately the time, and hence the deformation, at which a meridian crack starts to form 12 8 4 0 20 40 60 80 Granulation time (min) 100 120 Fig. 2. The variation of the critical impact velocity with the granulation time for granules with a mean diameter of 4.5 mm prepared with PEG 400 and Durcal 40. because of their limited resolution in time and because only one-half of the granules is observable. However, it is clear that the gross deformation and break up of the granules, in terms of the number and the opening of the cracks, increases with increasing impact velocity. Photographs showing the final failure patterns of the granules used to obtain the results in Fig. 2 are displayed in Fig. 4 for a wider range of impact velocities. There are 5 failure patterns that exemplify the general trends described in Section 1 and which are shown schematically in Fig. 5. At a low impact velocity (<8.0 m/s), significant plastic deformation has occurred without observable breakage (Pattern 1). With an increase in the impact velocity (8–12 m/s), meridian cracks, which propagate from the impact zone, are visible (Pattern 2). Cracking has occurred gradually rather J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 4009 Fig. 3. Images of the impact of granules made from PEG 400 and Durcal 40 with a binder ratio of 0.15, a air voidage of 0.009, a diameter range of 4.00–4.75 mm and a mass range of 0.12–0.16 g. They correspond to impact velocities of (a) 12, (b) 16, (c) 20 and (d) 28 m/s; the times (ms) for each frame are also given in the figure where 0 ms refers to first contact of a granule with the target. Fig. 4. Photographs showing the failure patterns of the granules referred to in Fig. 3 corresponding to the impact velocities shown in the figure. The white dashed circles enclose conical fragments. than as a rapid propagation through the granule body. This is termed stable crack propagation and is typical of plastically deforming materials while brittle materials usually exhibit unstable fracture; the growth of a stable crack will cease when the load is removed because excess strain energy has not been stored in the bulk of the body during loading. The number of the cracks increases with increasing impact velocity but none of them extend throughout the granule so that it remains coherent after impact. With a further increase in the impact velocity (16 m/s), a fragment is formed by a failure plane that extends from the contact circle to form an approximately conical shape (Pattern 3). Generally, the residue of a granule either forms a single intact cup-like region or splits into a few large fragments without any fines. With increasing impact velocity (20 and 28 m/s), the size of the conical fragment increased and the residue started to break up into increasingly smaller fragments (Patterns 4 and 5). It should be noted that the cones formed during impact were completely different from the initial state of the mother 4010 J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 Fig. 5. A schematic diagram of the failure patterns shown in Fig. 4. Table 2 The binder ratios and air voidage of the granules used to investigate the influence of binder content; they were made with PEG 400 and Durcal 15 and Durcal 40 with diameters in the range 4.00–4.75 mm Binder ratio, S Air voidage Durcal 15 Durcal 40 0.115 0.13 0.15 0.17 0.19 0.0021 0.052 0.013 0.044 0.009 0.025 0.009 0.012 0.007 0.014 80 80 S = 0.19 S = 0.17 Cone mass ratio (%) S = 0.15 60 Cone mass (%) S = 0.13 S = 0.115 40 70 28 m/s 60 21.5 m/s 15 m/s 50 40 30 20 20 10 0 0 10 15 20 25 30 Impact velocity (m/s) 0.1 0.12 0.14 0.16 0.18 0.2 Binder ratio Fig. 6. The cone mass ratio for the granules referred to in Table 2 as a function of the impact velocity and for the range of binder ratios given in the figure. Fig. 7. The cone mass ratio for the granules referred to in Table 2 as a function of the binder ratio for the range of impact velocities given in the figure. granules. Relatively loose and small powdery fragments were observed to cover their surface, while a denser structure was found particularly near the impact plane. However, the fragments arising from the residues were visually similar to the initial state of the mother granules even at the highest impact velocity employed of 28 m/s. Moreover, at this velocity, the smallest daughter fragments were observed to be a cluster of primary particles rather than individual primary particles. The cone mass ratios for the granules described in Table 2 were found to increase linearly with increasing impact velocity as shown in Fig. 6. There is clearly a critical velocity at a given binder ratio below which a cone cannot be formed provided the data can be linearly extrapolated to small values of the binder mass ratio. These ratios also increase asymptotically with increasing binder ratio; the dependence is shown more clearly in Fig. 7 for which the data in Fig. 6 have been re-plotted. These results show that the cone mass ratio increases with increasing deformation either as a result of increasing the impact velocity or as a result of decreasing the hardness of the granules by increasing the binder ratio. The cone mass ratio as a function of the primary particle size for the granules described in Table 3 is shown in Fig. 8. There seems to be an increasing J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 Table 3 The primary particle size and air voidage of the granules used to investigate the influence of primary particle size; they were made with PEG 400 with a binder ratio of 0.15±0.01 and with diameters in the range 4.00–4.75 mm Primary particle size (
m) Air voidage 6 0.036 15 0.019 23 0.025 38 0.008 60 4011 Table 4 The binder ratios and air voidage of granules to investigate the influence of granule size; they were made with PEG 400 and Durcal 40 Granule size (mm) Binder ratio, S Air voidage 1.55 3.07 4.35 6.7 8.0 0.130 0.137 0.132 0.138 0.139 0.022 0.025 0.024 0.026 0.025 20 40 30 20 10 0 0 10 20 30 40 Critical impact velocity (m/s) Cone mass ratio (%) 50 16 12 8 4 Primary particle size (µm) 0 Fig. 8. The cone mass ratio as a function of the primary particle size at an impact velocity of 28 m/s for granules made with PEG 400 at a binder ratio of 0.15 and a range of Durcal powders as described in Table 3. 400 800 1200 1600 Binder viscosity (mPa s) Fig. 10. The critical impact velocity as a function of the binder viscosity for the granules described in Table 5. 12 Critical impact velocity (m/s) 0 Table 5 The binder composition, binder viscosity and granule air voidage of the sample granules used for examining the effect of binder viscosity; the granules were made with Durcal 40 with a binder ratio of 0.168±0.01 and they had a size range of 4.00–4.75 mm. 9 6 Glycerol (% w/w) Viscosity (mPa s) Air voidage 50 85 95 98 100 6 112 545 975 1499 0.035 0.023 0.018 0.011 0.008 3 0 2 4 6 Granule size (mm) 8 10 Fig. 9. The critical impact ratio as a function of the granule size for the granules described in Table 4. linear dependence, which again suggests that the granules became more deformable with increasing primary particle size. The critical impact velocity decreases approximately linearly as a function of the granule size as shown in Fig. 9 for the granules described in Table 4. Clearly, the linear relationship is a result of the limited range of granule sizes investigated since physically the rate of decay will have to gradually decrease at larger granule sizes. The corresponding data for the influence of the binder viscosity are shown in Fig. 10 for the granules described in Table 5. Given that the viscosity was increased by more than two orders of magnitude, the increase of about a factor of four in the critical impact velocity is relatively modest. Fig. 11 shows the effect of the fractional interstitial volume on the critical impact velocity, which was calculated from the data given in Fig. 1. Here, the interstitial volume is the total value that is mainly occupied by the binder since the air voidage of the granules is negligible as discussed earlier. The rate of increase of the strength of the granules with decreasing interstitial volume becomes very much greater at fractional interstitial volumes 4012 J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 80 16 S = 0.13 S = 0.15 60 12 Survival ratio (%) Critical impact velocity (m/s) S = 0.115 14 10 8 6 4 S = 0.17 S = 0.19 40 20 2 0 0.24 0 0.26 0.28 0.30 0.32 0.34 12 14 16 18 20 22 24 Impact velocity (m/s) Fractional interstitial voidage Fig. 11. The critical impact velocity as a function of the fractional interstitial volume calculated from the data shown in Fig. 1. Fig. 13. The survival velocity as a function of the binder ratio for the granules described in Table 2. 4. Discussion 14 Durcal 15 4.1. Introduction Critical impact velocity (m/s) Durcal 40 12 10 8 6 4 0.1 0.12 0.14 0.16 0.18 0.2 Binder ratio Fig. 12. The critical impact velocity as a function of the binder ratio for the granules described in Table 2. In many respects, the current work shows that the impact behaviour of wet agglomerates has a number of features in common with typical dry agglomerates and nonagglomerated particles, which were described in Section 1. There are two aspects that are worth discussing in more detail here. Firstly, it seems that there is a relationship between the mass of the cones formed and the extent of deformation of the mother granule. A more quantitative description of this behaviour will be presented together with some consideration of the origin of the cones. Secondly, it was observed that the agglomerates made with Durcal 15 displayed a minimum strength at some intermediate binder content, unlike the more conventional behaviour with the coarser Durcal 40 granules. In order to provide an interpretation of this observation, it will be necessary to consider more strictly what is meant by the term ‘strength’. 4.2. Cone formation less than about 0.26, which is presumably associated with the approach to the maximum packing density. The effect of the binder ratio on the critical impact velocity is shown in Fig. 12 for the granules described in Table 2. There appears to be a minimum value of the critical impact velocity at intermediate velocities for granules made from Durcal 15. This arguably unexpected behaviour for the granules prepared from Durcal 15 compared with those from Durcal 40 (see Figs. 1 and 2) is also displayed by the survival ratios of similar granules as shown in Fig. 13. The ratio decreases with increasing impact velocity as might be expected. However, for a given impact velocity, the ratio first decreases and then increases with increasing binder ratio. The mass of the cones increased with increasing impact velocity and binder ratio (Figs. 6 and 7). In previous work (Fu et al., 2004a,b), the contact ratio, Ã∗ , as a function of the impact velocity, V , was measured for similar granules; the contact ratio was defined as A∗ /A0 where A∗ and A0 are the final contact area and the initial cross-sectional area of the agglomerate. These data were obtained for a range of impact velocities that corresponded to plastic deformation rather than fracture and, consequently, it should be possible to calculate their dynamic yield stresses and thus provide a more quantitative dependence of the mass of the cone on the deformability of the agglomerates. Provided that a wet agglomerate does not fracture, the kinetic energy at impact J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 Table 6 The yield stresses, yield velocities and Young’s moduli calculated for different binder ratios from the slopes of Fig. 14 0.24 S=0.135 S=0.15 S=0.175 0.2 Binder ratio, S Yield stress, Y (MPa) Yield velocity, Vp (m/s) Young’s modulus, E (MPa) 0.16 Ã *2 (m4) 4013 0.135 3.9 8.0 40.4 0.150 2.9 6.2 31.8 0.175 2.1 4.0 26.6 0.12 0.08 0.04 0 0 100 200 300 400 V 2 (m2/s2) Fig. 14. The contact ratio as a function of the impact velocity for the granules described in Table 2. is dissipated by elastic, elastoplastic and plastic deformation (see Li et al., 2002), thus
∗ 1 1 2 2 mg V = mg V p + F d, (1) 2 2 p where Vp is the velocity at which full plastic deformation occurs (viz., below which deformation is either elastic or elastoplastic) and p is the corresponding compression, ∗ is the maximum compression and F is the contact force under full plastic deformation. The fully plastic condition corresponds to the mean contact pressure being equal to about 3Y as discussed in Section 1, where Y is the dynamic uniaxial yield stress. The integral in (1) may be written in the following form (see Johnson, 1985):
a∗ 3a 3 Y 1 1 2 2 mg V = mg V p + da, (2) 2 2 4R ap where R is the undeformed radius of the agglomerate, ap is the contact radius at the full plastic yield velocity and a ∗ is the final value. If it is assumed that the dynamic yield stress is constant for a given agglomerate, it is possible to integrate (2) as follows: Ã∗2 − Ã2p = 8 2 (V − Vp2 ), 9Y (3) where Ãp is the contact ratio at the full plastic yield velocity and  is the granule density. Thus a plot of Ã∗2 as a function of V 2 should be linear for V 2 > Vp2 with a slope that is inversely related to the uniaxial yield stress. This is approximately the case as shown in Fig. 14. At smaller impact velocities the contact area ratio will tend to zero at a zero impact velocity with a slower rate corresponding to elastic and elastoplastic deformation. The yield stresses calculated from the slopes are given in Table 6 and show that increasing the binder ratio from 0.135 to 0.175 results in a reduction by a factor of about two. That the behaviour is approximately linear also suggests that the granules behave as simple elastoplastic, rather than as elasto-viscoplastic, bodies. However, there is evidence of rate dependence for wet agglomerates (see Adams et al., 2004) and the yield stresses calculated here probably represent mean values in the velocity range considered. It is also worth pointing out that the limiting value of a ∗ /R for the application of contact mechanics, and thus the strict validity of Eq. (3), is generally taken as ∼0.4 whereas the maximum value for the data in Fig. 14 is ∼0.6. However, a previous numerical study has found that the errors in the predicted contact areas are relatively small at this higher limit (Adams et al., 2004). The linearity of the data in Fig. 14 extends to small values of Ã∗2 , which suggests that Ãp is relatively small. On this basis it is possible to make an estimate of the yield velocity, Vp , from the intercepts on the x-axis. The values are given in Table 6 and decrease with increasing binder content as would be expected. The yield velocity may be estimated by inspection of the coefficients of restitution as a function of impact velocity for similar granules (Fu et al., 2004a) since the maxima for these adhesive granules correspond approximately to the transition from elastic to plastic deformation. On this basis, the values estimated here may be up to a factor of two too large for the smallest binder content and approximately correct for the largest binder content. The initial yield velocity is related to the effective Young’s modulus, E + =E/(1− 2 ), of the granules as follows (Johnson, 1985): 0.5  pY5 , (4) VY = 1.56 E +4  where pY is the contact pressure at first yield (=1.1Y ) and also E and  are the Young’s modulus and Poisson’s ratio. It is now clear from the work of Thornton and co-workers (e.g., Mishra and Thornton, 2001) that this relationship is valid up to full yield provided that pY is set to 3Y when VY ≈ Vp . Thus the Young’s modulus may be obtained from  0.25 Y5 E = 4.93 . (5) Vp2  The calculated values of E are also given in Table 6 and show the expected trend of decreasing with increasing binder content to an extent that is comparable with the change in the calculated yield stresses. In summary, the increase in the cone mass with increasing binder ratio reflects the decreasing trend of the yield 4014 J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 40 S=0.13 S=0.15 S=0.17 Vcone / Vgranule (%) 30 20 10 0 20 30 40 50 a*/R (%) 60 70 80 Fig. 15. The ratio of the volumes of the cone and mother granules as a function of a ∗ /R; the data were obtained at different impact velocities (see Figs. 6 and 7). 50 S=0.15 S=0.17 Contact ratio (%) 40 30 20 10 0 0 10 20 30 40 Primary particle size (µm) Fig. 16. The contact area ratio as a function of the primary particle size for two binder ratios that were measured for the granules described in Table 3. stresses. Fig. 15 is a plot of the ratio of the volumes of the cone and mother granules as a function of a ∗ /R obtained at different impact velocities (see Figs. 5 and 6). Interestingly, the data approximately superimpose to a single line (for a ∗ /R < 0.6), which shows that the cone volume is linearly related to the contact area; the contact area during plastic deformation is proportional to the reciprocal of the yield stress. The linearity of the data indicates that the cones are self-similar. There also appears to be a minimum value of a ∗ /R for a cone to be formed, so that smaller values will correspond to homogeneous plastic deformation. The influence of the primary particle size on the contact area, for agglomerates of the type described in Table 3 has also been studied previously (Fu et al., 2004a). Fig. 16 shows a plot of the maximum contact area ratio as a function of the primary particle size for two binder ratios. It is evident that the granules become more deformable with increasing primary particle size, which is consistent with the trend in the cone mass ratios shown in Fig. 8. This could arise from improved lubrication between the particles. It has been shown that the coefficient of friction between smooth hydrodynamically lubricated spherical particles is inversely related to the radius of the particles (Adams and Edmondson, 1987). Such lubrication is possible given the relatively large viscosity of PEG 400 and the potentially large interparticle displacement velocities induced during impact. It is also the case that there will be a reduced number density of contacts with increasing particle size, which will be important if boundary or mixed lubrication was operating between the particles. Newitt and Conway-Jones (1958) first described the formation of conical fragments from wet granules under diametric compression. They also correctly recognised that such fragments are initiated by localised plastic deformation of the internal cylindrical volume between the contact zones. It is well established that a critical factor in controlling the directions of these shear bands is the lubrication of the platens. If a cylindrical sample is compressed along its axis and the platens are well lubricated, then it will undergo pure compression, which will result in homogeneous plastic flattening or alternatively splitting along the loading axis for brittle materials. However, in the case of a high platen friction, a plastic material such as a soil or metal will display shear bands at angles of approximately ±(/4 + /2) to the loading axis, where  is the angle of internal friction. For example, in the triaxial testing of soils, lubrication of the platens tends to reduce the probability that shear bands will form (Rowe and Barden, 1964). The factors controlling the initiation, growth, direction and thickness of shear bands are extremely complex and not completely understood. For example, a study of the shear band formation in a model paste (‘Plasticine’) has been carried out in which the friction of the platens was progressively reduced by heating them to a maximum temperature of 80 ◦ C (Adams et al., 1998). Shear bands were only produced at intermediate temperatures. In granular media, shear bands usually occur in the overconsolidated state. It has been argued that the resulting dilatancy arising in these band is caused by a combination of buckling and rolling of chains of load bearing particles (Oda and Kazama, 1998). In this latter work, X-ray analysis and optical microscopy of thin sections of sand revealed that large voids were formed along a shear band resulting in a large local void ratio. This is typical of the conditions that may be expected for Mode II (in-plane shear) ductile fracture to occur in plastically deforming materials such as metals. That is, such fracture is initiated by the formation, growth and coalescence of voids; in metals, for example, the voids are formed as a result of inclusions and coalescence occurs by plastic necking (Beeson et al., 2003). In the case of wet agglomerates, it is reasonable to assume that the voids in shear bands form by cavitation during impact due to the dilatancy. J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 4015 Fig. 17. Images of the impact of granules made from PEG 400 and Durcal 15 at a velocity of 12 m/s showing the effect of binder ratio. The times in ms are shown under the figure, where 0 ms refers to first contact of a granule with the target. The above process of shear banding, strain softening and ductile fracture is quite different from the Mode I (crack opening) mechanism for the formation of the meridian cracks. In this case, fracture occurs in a relatively homogeneous strain field as a result of a stress concentration induced at a particular flaw. However, ductile fractures are not associated with high stress concentrations and may occur by a co-operative process involving void coalescence (net section rupture) rather than by the propagation of a crack. The differences in the two processes are likely to account for the markedly different appearance of the conical and residue fragments. 4.3. Critical impact velocity The experimental data showed that the critical impact velocity decreased with increasing agglomerate size (see Fig. 9). As discussed in the previous sub-section, meridian cracks most likely form by a Mode I mechanism and such fracture is usually associated with a critical strain. The plastic strain in spherical bodies scales with a/R, which is the square root of the contact ratio, Ãp , and which is an increasing function of the impact velocity. However, this function is independent of the size of the spherical body as demonstrated by Eq. (3). That is, for a given impact velocity, the kinetic energy scales linearly with the size but so does the volumetric plastic work or strain energy. Thus the data in Fig. 9 cannot be interpreted on this simple basis. Possibly, a more plausible explanation is the well-known phenomenon that the number of critical flaws scales with increasing body size. It was certainly observed that the damage to the larger granules at impact velocities just exceeding the critical value displayed multiple micro-cracks just outside of the contact zone while the smaller granules generally showed a single crack leading to the agglomerate splitting in half at greater velocities. The minimum in the critical impact velocity for the Durcal 15 agglomerates is most graphically demonstrated by the images shown in Fig. 17. The impact velocity was 12 m/s with t = 0 corresponding approximately to the time at which they first contacted the target and t = 760 ms being shorter than that corresponding to restitution. This velocity is equal or greater than the critical impact velocities for these granules (see Fig. 12) but cracks are not obviously visible in the photographs for the binder contents of 0.115, 0.130 and 0.190, which is for the reasons discussed in Section 3. However, a relative large meridian crack may be observed for the agglomerate with a binder content of 0.150 while there is a smaller crack for the binder content of 0.170. While the above images are supporting evidence for a minimum in the strength at an intermediate binder content, they do not provide any indication of the mechanistic origin. Fig. 18 shows images of the agglomerates with binder ratios of 0.115, 0.150 and 0.190 at impact velocities in the 4016 J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 Fig. 18. Images of the impact of granules made from PEG 400 and Durcal 15 at velocities in the range 18–20 m/s showing the effect of binder ratio. Fig. 19. Images of the impact at 12 m/s of granules made from PEG 400 and Durcal 40 and different binder contents. range 18–20 m/s. Severe fragmentation is evident for the intermediate binder content. For the smallest binder ratio, the formation of a cone together with a meridian crack may be observed. The meridian crack is indicative of brittle failure as discussed earlier. It is reasonable to expect the fracture toughness to decrease with increasing binder content as the packing density decreases. However, it appears from the images for the largest binder content that the agglomerate deforms plastically. That is, it becomes harder to initiate a crack and hence the critical impact velocity increases with increasing binder content in this regime as the agglomerate becomes increasingly deformable. In this case, smaller primary particle and lower binder content leads to more compacted structure, i.e., high contact number, hence resulting J. Fu et al. / Chemical Engineering Science 60 (2005) 4005 – 4018 in stronger granule, while with higher binder content (ratio >0.15) the pores are full and liquid will easily flow through pores and act as a lubricant for particle movement, thus giving high deformability and critical impact velocity. It is interesting to note that this transition to a highly deformable paste-like response was not observed for the Durcal 40 (Fig. 11). In this case there was a monotonic decrease in the critical impact velocity with increasing binder content. This is also exemplified by the photographs in Fig. 19 showing the increasing break-up of the granules with increasing binder for an impact velocity of 12 m/s. It is common experience that it becomes more difficult to make deformable paste-like materials as the primary particle size becomes greater. In practice, such mixtures are often quite friable. The criteria for forming a paste are not well understood but clearly the particle size and interparticle forces are critical. 5. Conclusions It has been found that there are a number of common features between the impact failure mechanisms of wet granules and those that have already been established for granules in the dry state. At small impact velocities (and times), they display homogeneous elastic, elastoplastic and plastic deformation. At some critical strain, stable meridian cracks propagate from the impact zone. At larger strains, a conical fragment is formed and the residue increasingly fragments with increasing velocity. The volume of the cone scales with the maximum contact area during impact and thus depends on the impact velocity and the deformability of the granules. The critical impact velocity for the formation of observable cracks is a measure of granule strength and this parameter increases with decreasing granule size and increasing binder viscosity. For very fine primary particles sizes, there is a minimum value of the critical impact velocity with increasing binder strength. This may be ascribed to the binder content at which there is a transition in the failure mechanism from crack propagation to gross plastic flow. Granules made with relatively coarse primary particles are generally more friable, thus the critical impact velocity decreases monotonically with increasing binder because of the reduction in the fracture strength. The velocities of powder particles in a high shear mixer have been reported previously (Nilpawar et al., 2005). It was reported that corresponding to impeller tip speeds in the range 1.5–9.0 m/s (impeller speeds of 100–600 rpm), the bed velocity was measured to be in the range 0.7–1.35 m/s, indicating that the relative velocity of the particles is in the range of 0.8–7.75 m/s. The critical impact velocities measured here exceed this range and are thus consistent with the idea that there is only limited granule breakage at the long granulation times used to make the granules in the current work. The general concepts established using such non-porous granules will undoubtedly apply at greater porosities. However, it 4017 is considerably more difficult to obtain granules with nominally constant properties for more porous granules. Acknowledgements The authors would like to thank EPSRC for funding this project and providing the high-speed cameras, and Unilever Port Sunlight, UK, for funding this project and providing materials. We would also like to acknowledge the excellent technical support provided by C. Turner and S. Richards. References Adams, M.J., Edmondson, B., 1987. Forces between particles in continuous and discrete liquid media. In: Brsicoe, B.J., Adams, M.J. (Eds.), Tribology in Particulate Technology. Adam Hilger, Bristol, pp. 154–172. 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