(144e) Understanding Die Compaction of Hollow Spheres Using the Multi-Particle Finite Element Method (MPFEM)

Powder compaction is a complex manufacturing process. Although the procedure follows four presumably simple steps: (i) die filling, (ii) compaction, (iii) unloading, and (iv) ejection, it is a very challenging process to understand due to its complex nonlinear micromechanical and statistical nature. It is especially challenging for empirical studies to investigate particle-level interactions. Thus, computational analyses are required for particle-level understanding. A wide range of computational methods has been developed, grouped based on the macromechanical approach (continuum approach) and based on the micromechanical approach (discrete element methods). Although the continuum approach can provide information on the evolution of tablet density and stress upon compaction, unloading, and ejection, it ignores the problem's discrete nature. The discrete element method (DEM) and the multi-particle finite element method (MPFEM) were developed to understand the discrete behavior and the global behavior of the powder compaction.

DEM technique successfully represents the particle level interactions; however, it cannot compensate for the deformed particle surfaces during compaction, which plays an essential role in determining the contact pressure between contact pairs (particle-particle and particle-tooling). Although new approaches were developed in recent studies to address the issues, these approaches require particular calibration methods, which increase the computational cost. MPFEM addresses the challenges associated with DEM and other macromechanical techniques by incorporating the characteristics of both methods. Although MPFEM helps to identify the particle level interactions, the computational load is heavy. Due to the computational limitations, a limited number of studies in the literature have analyzed the powder compaction using a 3D MPFEM. Historically, these studies focus on solid particles.

In this study, hollow spheres' compaction behavior, common to pharmaceutical spray drying, was investigated both computationally and experimentally. In the computational analysis, two different particle sizes with three different shell-thickness levels were examined using the 3D MPFEM via a commercially available FEM software Abaqus (Version 2019, Simulia, Providence, RI). Particles were grouped into two based on their size: (i) Large particles with a unit radius (r_L) and (ii) small particles with a 25% smaller radius (r_s). The initial particle coordinates were generated randomly using a simple DEM particle generator simulation, which was only allowed to generate one type of particle at a given time. DEM simulations run until the first 2000 particles were settled in the die, i.e., the average displacement in all particles reached a plateau. Keeping the particle numbers under 2000 allowed to keep wall clock time for the simulations to <60hrs. Additionally, the total mass of models was kept constant for consistency. The models were divided into groups based on the outer particle radius and by the particle diameter (d): shell-thickness (w) ratio. In this study, the thick shell, medium shell, and thin shell particles were represented with a d/w of 2.5, 5, and 10, respectively (Table 1). The particles were designed as elastic-perfectly plastic with of 100 and Poisson's ratio () of 0.3, where E and are Young's modulus and the uniaxial yield stress, respectively. Since material property selection directly influences the stable time increment the accuracy of the results, an optimized selection must be made on material properties. All simulations run up to approximately 0.9 RD. The punch velocity was set to complete the compaction stage in 5 seconds.

The spray-dried intermediate (SDI) used for the experimental portion of this study was produced on a Mobile Minorâ„¢ spray dryer (GEA Niro A/S, Denmark). The polymer used was hydroxypropyl methylcellulose acetate succinate (HPMCAS) M-grade from Ashland (Wilmington, DE). Compaction experiments were performed using a Huxley-Bertram (Cambridge, U.K.) hydraulic compaction simulator with round flat-faced punches with 2mm punches. Each tablet was compressed after weighing approximately 4-4.5 mg of powder. The powder was manually fed into the die. The die fill height was set to 16 mm to allow for the greatest volume for powder fill. The compaction process was completed in 10 seconds, including 5 seconds for compression, 5 seconds for unloading, and 2 seconds for ejection starting after unloading was complete. The compaction requirements were satisfied with a single action movement until the total punch separation between the upper and lower punch was 1 mm. Following the tablet formation process, weight, thickness, and diameter measurements were executed immediately. Each tablet was weighted using a Mettler Toledo balance with a 0.1 mg resolution, and the thickness and diameter were measured with a Mitituyo thickness gauge with a resolution of 1 µm modified with a flat contact surface for the measurement probe. Uncompressed SDI particles and tablets were scanned with a high-resolution XRadia Versa 500 (White Plains, NY, USA) x-ray tomography. Surface characterization of SDI particles and tablets was performed on an FEI Quanta FEG 250 (FEI Corporate, Hillsboro, OR, USA) environmental scanning electron microscope.

The results showed that particle diameter/shell-thickness (d/w) plays an essential role in powder compaction behavior. The initial relative density, the relative density after die filling but prior to compression, and the fill depth varied with respect to the particle diameter and d/w ratio. During the initial stage of compaction, the punches remained stress-free, or the stress was negligible, despite the non-zero velocity of the upper punch at this early stage of compression. Once the stress levels are not negligible, a steady stress increase was observed in all models (Figure 1a). As compression continues, the rate at which stress increases is highly dependent on the particle's d/w ratio. The d/w ratio 2.5 models show the steepest increase in compaction stress. The d/w 5 particles show a softer response up to the point at which the relative density equals that of the d/w 2.5 particles at a =0.58 and RD=0.78 (Figure 1a). At this point, the two particles begin to behave similarly up through the end of compression, where the d/w 5 particles show slightly lower peak stress. The response of the thin-shelled particles, d/w 10, shows drastically different results across the entire compaction range. Upon final compression, the d/w 10 particles do not reach the same stress as achieved by the d/w of 5 and 2.5 despite reaching the same final RD. However, based on the stress trajectory of the d/w 10 models, it is expected to reach stresses equivalent to the other models but not until an RD higher than 0.9 is achieved. It was also found that shell-thickness is the dominant factor in particle yielding (Figure 1b). The yielded volume was calculated by summing the total volume of the elements within all particles that exhibited non-zero equivalent plastic strain. Since the selected material property is elastic-perfectly plastic, plastic strains on deformed elements do not increase local particle stresses. The total yield volume (YV) was normalized by the total particle volume (TV) showing yield density in a model, e.g. if the ratio (YV/TV) is equal to 1, all the particles in the model passed the yield point. Although the particle size is shown to alter the global yielding behavior, the influence is not as dominant as the shell-thickness. The results show that thin-shell models tend to reach total yielding at much lower macroscopic stress than the thick- and medium-shell models. Also, small particles require slightly higher forces to have the same amount of yield before reaching complete yielding because of the larger contributions of inter-particle friction per unit volume (Figure 1b).

Experimental compaction studies were performed using the two different SDI particles produced. The particles generated with the higher outlet temperature were larger in diameter and thinner in wall thickness than the particles generated with the lower outlet temperature. The larger particles with thinner shells (SDI-80 ^oC) initially build stress upon consolidation greater than smaller thicker shelled particles (SDI-45 ^oC) (Figure 1c). This is a direct result of the difference in particle packing between the two SDI particles. However, the smaller, thicker shelled particles result in a stress value greater than that of the larger thinner particles for equivalent RD upon further compression. This trend is consistent with that of the MPFEM model (Figure 1c-d). As the compression event continues, the thinner shelled particles start to show a softened response, as was observed experimentally. This is likely due to the buckling phenomenon of the thinner shell larger particles. Upon compression to an RD approaching 0.9, the MPFEM simulation stresses continue to show agreement with the experimental results. As was captured in MPFEM, the required stress to reach the final compression level (RD= 0.9) was higher for the thick-shell particles than the thin-shell particles. Due to the lack of cohesive elements used in this work's modeling portion, the MPFEM analysis was only performed through the compaction and unloading event. Even though the final MPFEM tablet upon ejection could not be compared, there are interesting similarities between the unloaded MPFEM models and the physical tablets (Figure 1e-f).

In summary, this study provides new information on how powder compaction behavior was influenced by particle size and particle shell-thickness. The approach used in this study helps to understand the complexity involved in the powder compaction process and may be used to identify the additional mechanisms during the compaction process.