1. Measuring and Modeling Density Distributions in Pharmaceutical Tablets Katherine Doyle Advisor: Dr. Zavaliangos Mentor: Wenhai Wang

2. Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Background  Die compaction: loose powder pressed in a die by upper and lower punch  Wide range of tablet densities possible by varying compressive force and die shape  Physical analysis coupled with FEA modeling How do we describe the mechanics of die compaction? Schematic of a die/ punch assembly 4

3. Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Background Hydrostatic and Mises Equivalent Stresses (First and Second Invariants) Principle Stresses on a Differential Element

4. Background Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Simple Tension: Shear: Diametrical Compression: Simple Compression: Simple tests for strength properties 3 Mohr-Coulomb Shear Failure line from simple tension, shear, diametrical compression, and simple compression:

5. Die Compaction Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Drucker-Prager/cap Model for powder die compaction  Widely used model because accounts for:  Stronger compact in compression than tension  Cohesion, internal friction angle, and their dependence on relative density (RD)  Shear failure and cap surfaces Drucker-Prager/cap model showing two failure surfaces and various RD values on P-Q plane 1

6. Tablet Formation Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Method for tablet formation  Equipment:  Carbide steel die and punches (flat and convex circular, convex oval)  INSTRON mechanical testing machine  Materials:  Microcrystalline cellulose  Magnesium stearate (die/punch lubricant)  Specimen preparation:  Compacted to 10-120 MPa  Clean or lubricated die/punch  Sliced to show cross section INSTRON model 1127 General testing machine 5

7. Current Work Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Experiments:  Calibration curves: compaction pressure versus RD and RD versus hardness  Microhardness testing and x-ray computerized tomography to map density distribution in tablet slices  Diametrical compression tests Clean and lubricated tablets after diametrical compression 2 Clean and lubricated tablets after diametrical compression. Experiments by K. Doyle.

8. Current Work Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Modeling:  Learning ABAQUS FEA software  Graphical interface, coded input files, setting up problem, analysis  Gurson model (simple), Drucker-Prager/cap model  Previous results:  Physical experiment, clean die  ABAQUS simulation, clean die Density distributions on 4mm slice of convex tablet 2

9. Future Work Agenda Introduction Die Compaction Tablet Formation Current Work Future Work Future Experiments and Modeling:  Map density distributions of circular and oval convex tablets (verify previous experiments)  Compare manual results to x-ray tomography and simulation  Repeat and continue diametrical compression testing for wide range of RD  Continue to learn how to model with ABAQUS  Complete die compaction model of 3D oval convex tablet

10. References 1. Cunningham, J.C, Sinka, I.C., Zavaliangos, A. 2004. Analysis of Tablet Compaction. I. Characterization of Mechanical Behavior of Powder and Powder/Tooling Friction. Journal of Pharmaceutical Science, Vol. 93, No. 8, August 2004: 2022-2039. 2. Cunningham, J.C, Sinka, I.C., Zavaliangos, A. 2004. Analysis of Tablet Compaction. II. Finite Element Analysis of Density Distributions in Convex Tablets. Journal of Pharmaceutical Science, Vol. 93, No. 8, August 2004: 2040- 2053. 3. A.T. Procopio, J.C. Cunningham, A. Zavaliangos. 2003. Analysis of the Diametrical Compression Test and the Applicability to Plastically Deforming Materials. Journal of Materials Science. 38, pp. 3629 – 3639, 2003. 4. “Powder Forming Research.” Department of Mechanical Engineering at University of Wales Swansea. http://www.swan.ac.uk/nfa/powdercompaction.htm. 5. “Tensile and Compression Testing.” ETS, North Tower Technologies. http://www.equiptechonline.com/PDetail.cfm?pid=1591&catID=75&subID=38 &sid=6

11. Drucker-Prager/cap Model for powder die compaction Cap Surface: Shear Surface: cohesion internal friction angle no physical meaning determined from experiments Die Compaction Agenda Introduction Die Compaction Tablet Formation Current Work Future Work