DEM study of the mechanical strength of iron ore compacts

International Journal of Mineral Processing 142 (2015) 73–81

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International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro

DEM study of the mechanical strength of iron ore compacts Y. He a, Z. Wang a, T.J. Evans b, A.B. Yu a,c, R.Y. Yang a,⁎ a b c

School of Materials Science and Engineering, University of New South Wales, Sydney 2052, Australia Rio Tinto Iron Ore Group, Australia Department of Chemical Engineering, Monash University, Clayton 3900, Australia

a r t i c l e

i n f o

Article history: Received 3 October 2014 Received in revised form 7 April 2015 Accepted 28 May 2015 Available online 31 May 2015 Keywords: Compaction Iron ore fines Discrete element method Interparticle bonding

a b s t r a c t Numerical simulations based on the discrete element method (DEM) were conducted to study the die compaction of iron ore fines and the mechanical strength of formed compacts under the uniaxial unconfined compression. To mimic the strength gained after the die compaction and brittle behaviour of compacts under compression, a bonded particle model was introduced between contacting particles. The simulated stress–strain responses were comparable with those observed from the physical experiments, confirming the validity of the model. The analyses of the evolutions of the structure and force during the die compaction indicated that the consolidation was initiated from the upper moving punch and gradually propagated to the lower stationary punch. The inhomogeneity of density and force trees was also observed. In the unconfined compression, the main characteristics of the stress–strain response, i.e., the linear increasing part, peak value and residual stress state, were captured in the simulations. The brittle failure of the compact was due to the broken inter-particle bonds by shear and tensile stress. The compressive strength of compacts increased with the consolidation pressure, bond thickness and bond strength. This work indicated that the DEM model with a proper interparticle bond model is able to study the mechanical strength of compacts. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Iron ore fines are created as a result of mining, crushing and processing large iron ore particles, and may account for 50% of the total ore mined. For many processes (e.g. iron-making), lump ores (size larger than 10 mm) are preferred since fines not only increase the cost of handling but also suppress the air flow in a blast furnace (Dwarapudi et al., 2007). Therefore, ore fines have to be processed first to increase their sizes. Compaction is a method to compress iron ore fines into a denser compact using pressure (Kim et al., 2000; Pizette et al., 2010). Water is added as a binding agent to increase compact strength. Comparing with other size enlargement methods, such as pelletising and sintering, compaction is a cold bonding process and consequently less capital intensive, and does not need milling materials to a very small size. The mechanical strength of a compact is critical to maintaining geometrical and mechanical integrity of the compact in the downstream operations (Alderborn et al., 1988; Darvell, 1990; Fell and Newton, 1970; Podczeck, 2012). It is strongly affected by the interparticle bonding (Rumpf, 1962) and internal structure (Nystrom et al., 1993; Shotton and Ganderton, 1961). Experimental characterization of these microscopic information, however, is difficult (Adolfsson et al., 1999; Olsson and Nystrom, 2001). On the other hand, the discrete element method ⁎ Corresponding author. E-mail address: [email protected] (R.Y. Yang).

http://dx.doi.org/10.1016/j.minpro.2015.05.005 0301-7516/© 2015 Elsevier B.V. All rights reserved.

(DEM) is an effective way to investigate particle behaviour under compaction as it treats particle individually and explicitly considers the particle characteristics, material properties and the interparticle forces. The DEM simulations have been conducted to investigate the various issues in particle compaction, such as mechanical properties of single particle (Hassanpour and Ghadiri, 2004; Samimi et al., 2005), particle-wall friction induced inhomogeneity (Foo et al., 2004), evolution of compact structure (Sheng et al., 2004) and the effects of moisture, particle shape and particle size (Skrinjar and Larsson, 2004, 2012; Thakur et al., 2014). Recently, the DEM has also been extended to simulate compaction of powders with large deformation (Jerier et al., 2011). Under compression, different failure patterns, such as crack/ breaking lines and shear bands, have been observed (Iwashita and Oda, 2000; Nguyen et al., 2013; Wu et al., 2005, 2008). While various theories based on fracture mechanics (Mashadi and Newton, 1987) and bonding mechanisms (Nystrom et al., 1993) have been proposed, so far the bulk response of compacts under strength testing is not yet well understood. To investigate these phenomena using the DEM, various techniques have been proposed. Iwashita and Oda (2000) highlighted the role of rolling resistance in forming share bands. Hu and Molinari (2004) identified the role of initial imperfection in the shear banding formation in the biaxial compression. It is understood that brittle behaviour of a compact under unconfined compression is caused by mechanical interlocking between irregularly shaped particles but also solid bridges due to high level of

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stress concentration (Adolfsson et al., 1999; Morris, 1983). Several interparticle bonding models have also been proposed in the DEM models to mimic the brittle behaviour of compacts. Jiang et al. (2005, 2006) introduced rigid bond elements and rolling resistance in the DEM model and they found that the bond thickness affects the bond failure criterion significantly (Jiang et al., 2014). Based on the beam theory, Potyondy and Cundall (2004) proposed a bonded particle model (BPM) in which the bond can transmit both force and moment. These bonds were treated as a type of cement of finite size that acted in parallel with particle–particle interaction. More recently, Brown et al. (2014) proposed a bonded-contact model based on the Timoshenko beam theory, in which the bond can be broken either by compression, tension or by shear. Little work, however, has been conducted to link the die compaction with the strength and failure pattern of the compact under the uniaxial unconfined compression. This work is thus to develop a DEM model to establish such relation. The BPM model proposed by Potyondy and Cundall (2004) is included to account for the effect of interparticle bonding. The parameters in the model are calibrated from the data from experiments. The evolutions of compact structure and forces are analysed. The effects of bond parameters are also studied. 2. Model description In the DEM model, the translational and rotational motions of a particle with radius Ri and mass mi are given by,

mi

Ii

 dvi X  n ¼ Fi j þ Fti j þ Fcap þ Fbij þ mi g i j dt j

dωi ¼ dt

X

Mti j þ Mrij þ Mbij



ð1Þ

ð2Þ

j

where vi, ωi, and Ii are, respectively, the translational and angular velocities, and moment of inertial of particle i. The interparticle forces include normal contact force Fnij, tangential contact force Ftij, the capillary force Fcap for wet particles and the bonding forces Fbij ij when a bond is present between the two particles. Mtij (= Ri × Fnij) is the moment caused by tangential force, Mrij(= − μrRi|Fnij|ωi/|ωi|) is the moment due to particle rolling friction caused by the elastic hysteresis losses or viscous dissipation (Zhou et al., 1999), and μr is the rolling friction coefficient. Mbij is the moment induced by the tangential bonding force and bond bending/torsion. In the following, the forces will be described in details.

The tangential force is described by Mindlin and Deresiewicz (1953) theory, given by,  h    3=2 i Fsij ¼ − sgnðξs Þμ s  Fnij j 1− 1− min ξs ; ξs; max =ξs; max

ð4Þ

where μs is the sliding friction coefficient, ξs the total tangential displacement of particles during contact. ξs,max is the threshold value determining the onset of gross sliding and given by ξs,max = 3μs|Fnij|/ (16G*a), where a is the radius of the contact area and G* is the effective shear modulus defined as G* = E*(1 − ν)/(4 − 2ν). 2.2. Capillary force The capillary force used in our previous study (Liu et al., 2011) was adopted in this work, given by:

Fcap ¼ ik

8 2πR γcosθc > > ^ ik ðP−P Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi >  ffi n > > > < 1 þ 1= 1 þ 2VL = πR S2 −S > > > > > > :

4πR γcosθc ^ ik pffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1 þ S= πR=VL

ð5Þ

ðP−W Þ

where γ is the surface tension of liquid. The solid–liquid contact angle θc and the interparticle separation S are defined as indicated in Fig. 1. A minimum separation Smin is adopted to take into account surface roughness. The rupture distance is given as Srup = (1 + 0.5θc)V1/3 L . 2.3. Bonding force The BPM model proposed by Potyondy and Cundall (2004) was adopted to describe the interparticle bonding forces and moments. The model has a simple, linear form (similar to the linear spring model for the contact forces) and can be efficiently implemented into the DEM. More importantly, the model has been demonstrated to be able to reproduce the brittle fracture observed in the experiments (Cho et al., 2007; Yoon, 2007). In the model, the forces and moments are calculated incrementally and can be expressed in a matrix form as, fΔFg ¼ −fKgfΔxg

ð6Þ

2.1. Contact forces An elastic-perfectly plastic contact model proposed by Thornton and Ning (1998) was adopted to describe the normal contact force, given by,

Fnij

¼

f

  4  1=2 3=2 ^ E R δ n δbδy 3 ij h  i   ^ δ ≥δy Fy þ πpy R δ−δy n

ð3Þ

ij

where δ is the overlap between particle i and particle j. py is the yield pressure beyond which the particle deforms plastically. δv and Fy are the corresponding overlap and force at the onset of the plastic deforma    ^ ij ¼ Ri −R j =Ri −R j  and E* = EiEj/(Ei + Ej), tion. R* = RiRj/(Ri + Rj), n 2 where E = Y/(1 − ν ). Y and v are, respectively, Young's modulus and Poisson's ratio. The unloading and reloading processes are assumed to be elastic.

Fig. 1. Schematic of the forces acting on particle i from contacting particle j and pendular liquid-bridge linked particle k.

Y. He et al. / International Journal of Mineral Processing 142 (2015) 73–81 n t n bt bn bt T where {ΔF} (={ΔFbn ij , ΔFij , ΔMij , ΔMij } ) and {Δx} (={Δδ , Δδ , Δθ , Δθt}T) are, respectively, the incremental force vector and the incremental displacement vector. {K} (={knA, ktA, ktJ, knI}T) is the stiffness matrix, in which kn (=Yb/Lb) and kt (=kn/ψ) are the bond normal and tangential stiffness. Yb is the bond Young's modulus and ψ the bond stiffness ratio. For a bond with radius Rb and length Lb, its bonding area A = πR2b, moment of inertia I = πR4b/4 and polar moment of inertia J = πR4b/ 2. In the present work, the bond radius is proportional to the contact radius Rc of two particles and a bonding radius multiplier λ is defined as (λ = Rb/Rc). The bonds can be broken either by tension or by shear and the criteria for bond failure are given by,

      0  bt     bn  1 M i j Rb  F bt Mi j Rb −F bn ij  i j A ≥ σb þ ; þ min@ A I J A

ð7Þ

where σb is the strength of the bonds. Once broken, these bonds can no longer be restored. 3. Simulations and physical experiments

Table 1 Parameters used for simulation. Parameter

Value

Container diameter, D (m) Particle number, N Particle diameter, d (μm) Particle density, ρ (kg·m−3) Young's modulus, Y (GPa) Yield pressure, py (MPa) Poisson ratio, ν Sliding friction coefficient, P-P Sliding friction coefficient, P-W Rolling fiction coefficient, μr Surface tension, γ (N/m) Volumetric liquid content, VL (%) Bond-area multiplier, λ Young's modulus of bond, Yb (MPa) Bond stiffness ratio, kn/kt Bond strength, σb (MPa)

1.0 × 10−3 10,000 25–75 5.17 × 103 9 300 0.29 0.3 0.1 0.2 0.073 5.0 0.68 200 1.0 15

Table 2 Consolidation force, pressure and packing fraction in the die compaction.

3.1. Simulation conditions The die compaction of particles followed by unconfined compression were simulated in this work. As shown in Fig. 2, a simulation included four stages: die filling, die compaction, unloading/relaxation and unconfined compression. The simulation started with feeding particles into a cylindrical die by generating particles inside the die and allowing the particles fall down under gravity to form a packed bed (Fig. 2a). Once the packing was formed, the upper punch moved downward at a constant velocity to compress the particles till the compact reached a prescribed packing fraction (Fig. 2b). The upper punch then stopped and moved upward until it was separated from the compact (Fig. 2c). After the unloading process, the side wall was removed directly from the model and the compact was given a short period of relaxation to remove the residual stress while the interparticle bonding was introduced between the contacting particles. Finally, the punch moved downward to perform the unconfined compression (Fig. 2d). The current work included both capillary force and bond force. In the packing and die compaction stages, the capillary force played an important role as there was no formation of bonds. Once the bond forces were added at the end of unloading, the bond force dominated the behaviour of unconfined compression and compact strength. For consistence the capillary force was present for all the stages. To ensure quasi-static compaction, a strain rate smaller than 10−5 s−1 was selected. This, however, resulted in extremely long simulation time

(a)

75

(b)

Consolidation force (KN) Consolidation pressure (MPa) Mean packing fraction

Case 1

Case 2

Case 3

4 31.60 0.702

3 23.62 0.678

2 15.77 0.649

for the die compaction process. To reduce simulation time, a mass scaling scheme was adopted during the die compaction to increase time step. This scheme is particularly suitable to simulations of a quasi-static process in which the accelerations and velocities are not important (Persson and Frenning, 2012; Sheng et al., 2004; Thornton and Antony, 2000). A scaling factor of 1010 was selected and no effect on the pressure-packing fraction response was noticed. The mass scaling scheme was not adopted during the unconfined compression. Table 1 lists the values of parameters used in the simulations. The particle size has a uniform distribution between 25 μm and 75 μm. A cylindrical container of 20 mean particle size was used in this work. We have examined the effect of container size on the compaction behaviour by varying container diameter from 20 to 70 particle diameter and found the difference is less than 2%. To reduce simulation time, the container of 20d was therefore adopted. Also since only spherical particles were used in the current work, a large rolling friction coefficient was adopted to include the effect of particle shape. Note some parameters were calibrated using the experimental data as described below.

(c)

(d)

Fig. 2. Schematic of the whole process: (a) filling; (b) loading; (c) unloading and relaxation; and (d) unconfined compression.

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the die compaction and unconfined compression of iron ore powders were tested using a Universal Testing Machine (Instron 5566). At the beginning of the test, the iron ore powders were sieved and the powders of size 25–75 μm were selected. The powders were dried in an oven for 24 h and then mixed with water of 0.5% volumetric content. The wet particles were then added into a stainless steel die of inner diameter of 12.5 mm. The inner surface of the die was treated with silicon oil to reduce wall friction. The sample was then compacted using the machine with different forces ranging from 2KN–4KN. After the compaction, the compact was then carefully ejected from the die and then compressed again using the machine to test its strength. Each experiment was repeated three times to obtain the mean value and the varying range. Table 2 shows the three cases carried out with different consolidation forces. The compaction curves and final results in the experiments were used to calibrate the parameters in the simulations.

Fig. 3. Comparisons of the evolution of axial pressure with packing fraction between the experiments and simulations during the die compaction.

3.2. Physical experiments To calibrate and validate the numerical model, physical experiments under comparable conditions were also conducted. In the experiments,

4. Results and discussion 4.1. Die compaction Fig. 3 shows the compaction curves of the three cases obtained from the simulations and the experiments. Similar trends are observed for all the cases, showing non-linear increases in pressure with density during the loading process and a near linear decrease of pressure at unloading

Packing fraction

Stage A

Stage B

Stage C

Stage D

(a)

(b) Fig. 4. (a) Spatial distributions of density; and (b) axial density distribution of different stages in Case 1 (consolidation pressure 31.6 MPa) as marked in Fig. 3.

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77

and propagates to the lower punch, which is comparable with the experimental observations by Kong and Lannutti (2000) on alumina granules. The compaction process can be further understood by analysing the evolution of internal forces (Cates et al., 1998; Yang et al., 2008). Fig. 5a shows the spatial distributions of normalized normal contact forces within the compact at the corresponding stages, in which all the individual normal contact forces Fn are normalized by the averaged value bFnN within the compact. At stage A, only a small portion of contacts near the punch carry larger forces. The contact force branches are sparser and thinner at the bottom part. This demonstrates that the applied pressure is transmitted from the top to the bottom with vertically aligned pathway and clearly showing force gradients along the axial direction, similar to the results obtained by (Radjai et al., 1998). With larger pressure, the force networks at stages B and C become denser and more uniform, indicating a strong force-chain network with smaller force clusters embedded among them. It is clear that the network of force path is developed and the applied load is largely transmitted by heavily stressed chains of particles forming a relatively sparse network (Thornton and Antony, 1998). In terms of the orientation pattern, large forces are more vertically aligned while small forces show an isotropic distribution. Unlike the loading process, the force distribution at stage D varies significantly. The network of larger forces becomes more horizontally oriented. Fig. 5b shows the log-linear plots of distribution of the normalized normal contact forces. A normalized parameter f is defined as

except for the last stage of the unloading. The simulation results are comparable with experiments except for the discrepancy at the initial stage of compression. This is because densification at this stage is mainly due to particle rearrangement with little deformation of the particles (Sheng et al., 2004). Factors such as particle shape and particle surface properties may affect particle rearrangement. As only spheres were used in the DEM, the simulations may not be able to capture the effect of particle shape (Wiacek et al., 2012). It is important to understand the evolution of internal structure and stress during the compaction process. Four different stages therefore have been selected from Case 1, corresponding the beginning, middle and end of the loading process and the end of unloading process. As shown in Fig. 3, stages A–D corresponds to D = 0.525, 0.648, 0.702 and 0.671, respectively. Fig. 4a shows the spatial distributions of density at different stages. The density shows an inhomogeneous distribution with higher density at the top and lower density at the bottom due to the friction force preventing the motion of particles. This is consistent with the previous experimental results on ceramics (Kim et al., 2000) and pharmaceutical powders (Han et al., 2008), indicating a variation of density distribution along compression direction. Fig. 4b shows the density variation along the compaction direction at different stages. At stage A (D = 0.525), the density distribution is largely inhomogeneous. With further densification, the density distribution shifts to the right with reduced variation along the height. It clearly shows that the densification is localized at the top of the sample, suggesting that the densification process is initiated at the upper punch

0.0 3.0 6.0

9.0

12.0

15.0

Stage A

Stage B

Stage C

Stage D

(a)

(b) Fig. 5. (a) Spatial distributions of normalized normal contact force; and (b) the distribution of normalized normal contact force at different stages of Case 1 with consolidation pressure 31.6 MPa.

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f = Fn/bFnN. It can be observed that P(f) at stage A exhibits an exponential decay at large forces and a peak for f b 1, consistent with previous results on the packing of cohesive fine particle (Yang et al., 2008). With increasing compaction pressure, the distribution falls off more quickly as indicated in the stages B and C, indicating that the applied force made the forces more uniform by reducing the number of larger forces. The force distributions for stage B and stage C are similar, both showing a well-defined peak at f = 0.5 and a “dip” at small forces, suggesting that the stress-transmission path has been fully developed. At stage D, the force distribution exhibits significant changes and is similar to stage A except that the largest value occurs at 0 as a result of capillary forces.

4.2. Unconfined compression The mechanical strength of the compacts is tested by the unconfined compression. Fig. 6a compares the stress–strain responses from the experiments and the simulations. The overall comparisons are reasonable, although the rate of increase is slightly overestimated in the simulations at larger consolidation pressures. In particular, three main characteristics of the stress–strain response observed in the experiment are captured by the simulations, the stress increasing part, peak value and stress softening state (Han et al., 2008; Thakur et al., 2014). The prepeak behaviour is consistent with the results obtained by others using

Fig. 6. Comparisons of (a) stress–strain response; and (b) compressive strength versus packing fraction from experiments and simulations.

the bond models for cemented sands (Jiang et al., 2005, 2006) and concrete (Brown et al., 2014). When the axial strain reaches around 4%, the stress reaches its peaks and starts to decrease. Increasing consolidation pressure resulted in larger axial strain at the failure and sharper decrease after the failure, indicating increasing brittleness of the compacts. These trends are in good agreement with the experimental observations obtained by other researchers (Korachkin et al., 2008). However, it is worth noting that the stress builds up more slowly and drops down more quickly in the experiments than in the simulations. These behaviours might be related to the particle shape but also the linear elastic behaviour of bond in response and the single value of bond strength is chosen to be responsible for bond failure. The distribution of bond strength (Potyondy and Cundall, 2004) and progressive bond failure model (Ergenzinger et al., 2011) could be incorporated in bond behaviour to improve the model. Fig. 6b compares the relationship between compressive strength and consolidation pressure of the compacts from the experiments and simulations. The error bars in the experimental data represent the varying ranges. The results indicate that the compressive strength increases linearly with consolidation pressure of the compacts. A similar relation was also observed in a previous study (Moreno-Atanasio et al., 2005). While the result seems to contradict to the nonlinear relationship from experiments, this is because the consolidation pressures in this work were relatively small and the packing fractions of the final compacts were around 0.7. At this early stage of compaction, the pressure–strength relation is relatively linear. Similar to the die compaction, different stages are selected to study the evolution of the compact structure. As shown in Fig. 6, four stages A–D have been selected in Case 1, corresponding to the axial strain of 1.1%, 2.51%, 4.56% and 6.13%, respectively. Fig. 7 presents the failure patterns of the compact at different stages. At stage A, the axial compression dominates the deformation as there is no clear sign of distortion on the surface of the compact. The compact keeps its integrity as a result of relative intact internal structure. At stage B with increasing compression pressure, the particles located at the bottom part of the compact start to squeeze out in the horizontal direction. At stage C, the macroscopic breakage pattern starts to show after the peak stress point in which the fracture propagates through the compact due to the reduction of load bearing capacity. With further increasing axial strain, the fragmentation becomes more distinct, indicating an increased bond breakage in the shear band (stage D). The principal shear band that cuts across the compact generated over a relatively small strain interval during the decreasing of macroscopic stress. The shear band concentrates within the bottom part of the compact, in which the local density is relatively lower. As a result, the interparticle bonding becomes weaker in the bottom part. This phenomenon is consistent with the findings of Hu and Molinari (2004) that the shear bands is an instability triggered by the initial imperfections. Fig. 8 compares the percentage of the broken bonds at different stages. At stage A, very few bonds are broken, indicating a relative intact internal structure. This is followed by more bond breakage at stage B while keeping the geometrical integrity. At stage C which is the onset of the failure, the ratio of broken bonds is only 6.2%, suggesting that the macroscopic failure of compact is caused by a very small proportion of broken bonds. During the stress softening, the bonds continue to break as the reduction of load bearing capacity. Comparing the bonds broken by tension and those by shear, it is observed that the primary failure mode at all stages is by shear. This is different from the results reported by other researchers (Brown et al., 2014) in which tension is the dominating bond failure mode. However, the dominating mechanism of bond failure is dependent on the bond property. For example, bonds of different stiffness ratio may have different failure mechanisms. Fig. 9 shows the angular distribution of broken bonds at stage C. The angle θb is defined as the angle between the bond and the vertical direction with θb ∈ [0°, 90°]. It clearly illustrates the anisotropy of the

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Fig. 9. Angular distribution of broken bonds at stage C for Case 1 with consolidation pressure of 31.6 MPa.

4.3. Effects of bond parameters With the implementation of interparticle bonding in this work, the macroscopic bulk response and mechanical strength of compact is

Fig. 7. Failure pattern at different stages for Case 1 (consolidation pressure 31.6 MPa). The particles are coloured by velocity magnitude in the horizontal direction.

bond breakage. Most of the tension-induced broken bonds are horizontally aligned. In contrast, the shear-induced broken bonds have a peak between 60° and 70°. Due to the dominant role of shear-induced bond failure, the angular distribution of total broken bonds is similar to that of shear-induced broken bonds. Therefore, the angle of shear band is determined by the most likely angle of the broken bonds, as shown by the failure pattern in Fig. 7.

Fig. 8. Broken bond number at various stages during unconfined compression of Case 1 with consolidation pressure of 31.6 MPa.

Fig. 10. Effects of bond parameters on axial stress–strain responses: (a) bonding thickness in terms of radius multiplier; (b) bond strength.

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contrast, the bending and twist moment shows non-linear response with varying interparticle bonding area. 5. Summary The compaction behaviour and mechanical strength of compacts were investigated using the DEM simulations. By introducing the interparticle bonding between contacting particles, the predicted bulk response showed good agreements with experiments in terms of pressure–density relationship and stress–strain response. The analyses of the compact structure and forces showed the following. • In the die compaction, the densification was initiated at the moving punch and propagates to the stationary punch. A clear inhomogeneity in density distribution along the compression direction is observed. A network of axially-aligned stress path was developed during loading stage and the applied load was largely transmitted by heavily stressed chains of particles. • In the unconfined compression, three main characteristics of the stress–strain response, namely the stress increasing part, peak value and stress softening state, were captured in the simulations. A shear-dominated bond failure mode was obtained, forming localized shear banding concentrates within the bottom part of the compact. • Consolidation pressure, bond thickness and bond strength increased the compressive strength of formed compact but had no influence on the dominating bond failure mode.

Acknowledgement The authors are grateful to the Australian Research Council and Rio Tinto Iron Ore group for financial support of this work through an ARC Linkage project (LP110201157). References Fig. 11. Effects of bond parameters on the compressive strength: (a) bond thickness in terms of radius multiplier; and (b) bond strength.

directly linked to the properties of these bonds. Therefore, it would be interesting to investigate how the bond parameters affect the behaviour of compact under unconfined compression. Two bonding parameters have been varied: bonding thickness characterized in terms of radius multiplier and bond strength. Fig. 10 shows the effects of the two parameters on the stress–strain response of the unconfined compression of the Case 1 compact. Fig. 10a shows that with increasing bond thickness, larger forces are required to break these bonds, resulting in the increase in bulk stiffness. However, the strain at failure is almost unchanged due to the stress-controlled bond failure criterion. Interparticle bond strength characterizes the bond failure criterion. As a result, bond strength significantly contributes to the compressive strength of compact, as shown in Fig. 10b. However, it has no noticeable impact on both the pre-peak and post-peak stress response. This is due to the fact that a single value of bond strength is chosen to be responsible for different failure modes. Thus, neither the tension-induced bond failure nor the shear-induced bond failure is suppressed (Potyondy and Cundall, 2004). Fig. 11 shows the effect of bond parameters on the compressive strength. The compressive strength shows a non-linear effect on the interparticle bond thickness and an approximately linear effect on bond strength. The difference in the rate of strength increase can be explained by recalling the bond failure criterion that the bonding forces are proportion to the interparticle bonding area and bond strength. In

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