Mechanics of 21st Century - ICTAM04 Proceedings
XXI ICTAM, 15-21 August 2004, Warsaw, Poland
EXPERIMENTAL CHARACTERISATION AND NUMERICAL MODELLING OF DENSITY
DISTRIBUTION IN TABLETS
I.C. Sinka*, J.C. Cunningham** and A. Zavaliangos***
Merck, Sharp and Dohme Ltd., Hertford Road, Hoddesdon, Hertfordshire EN11 9BU, UK
**
Merck and Co., Inc., West Point, PA 19486, USA
***
Department of Materials Engineering, Drexel University, Philadelphia, PA19104, USA
*
INTRODUCTION
Density gradients in pharmaceutical tablets are important for they affect the local properties of the material which in
turn influence the mechanical response of the tablet during post-compaction operations, such as coating, packaging,
transport, storage or use.
Experimental density maps obtained using techniques such as indentation hardness and X-ray computed tomography
(CT) are presented.
Constitutive models have been developed to describe the compaction behaviour of the powder and the friction
interaction between powder and die wall. The models were calibrated for microcrystalline cellulose using data from a
compaction simulator and a die instrumented with radial stress sensors. The results are implemented in the finite
element program ABAQUS/Standard. The predictions of the model for a selection of tablet images and given die wall
lubrication conditions are compared with the experimental density maps generated for various stages during
compaction.
The agreement between the experimental data and simulation results gives confidence in the predictive capabilities of
the model. The applicability of the technique to formulation design, process development, tablet image and tool design
is discussed.
The experimental and numerical methodologies presented are applicable for any powder system in general.
EXPERIMENTAL METHODS
Indentation tests
Indentation hardness tests were carried out on cross-sections of tablets manufactured under controlled die wall
lubrication conditions. Density distribution maps were obtained using an empirical relationship [1] between indentation
hardness and density.
X-ray CT
For a given material the X-ray attenuation energy is approximately proportional to the density. X-ray CT density maps
obtained using a 250 kV X-ray cabinet (X-Tek Systems) with TOMOHAWK CT [2] (AEA Technology) are presented
for two capsule shaped tablets having different curvatures, break-line and embossing.
0.6 0.57 0.55
0.62
0.556 0.544 0.544 0.539
0.64
0.562 0.556
0.559
0.589
0.5660.582
0.66
0.575 0.562 0.562 0.575 0.575
0.647
0.604
0.601
0.7
0.593 0.586
0.601
0.597
0.579 0.566 0.572
0.625
0.562
0.575
0.6330.6160.597
0.712 0.689
0.572 0.559 0.586 0.579
0.572 0.572
0.647
0.6160.579
0.667
0.556 0.566 0.556 0.569
0.604
0.575 0.569
0.569
0.6040.566
0.547 0.544
0.484?0.5150.472? 0.474?0.482?0.530
0.643
(a)
0.657
0.689
0.662
0.700
0.694
0.597 0.612
0.662
0.575
0.620
0.586
0.556
0.643
0.5970.608
(c)
0.620
5 mm
(b)
0.64
0.65
0.64
0.66
0.66
0.65
0.64
0.643
0.6
0.620
0.53
0.612 0.643 0.6200.647
0.625 0.638
0.638
0.638 0.638 0.657 0.652 0.6520.643 0.647
0.657
0.643
0.616
0.629
0.633
0.633
0.6290.638
0.652 0.6470.657
0.672 0.662
0.525
0.647
0.638
0.629
0.625
0.652
0.652
0.652
0.638
0.657
0.633 0.662 0.647
0.647
0.539
0.643
0.608
0.643 0.647 0.647
0.633 0.647
0.643 0.643 0.652
0.633
0.633
0.6290.638
0.638
0.633
0.625 0.616 0.625 0.629 0.633
0.61
0.53
0.63
0.652
0.550
0.643 0.643
0.643
0.647 0.547
0.652 0.643
0.652
0.652
0.667
5 mm
(d)
Figure 1 Indentation hardness density maps for tablets compacted in unlubricated (a) and lubricated (c) die, respectively
and the corresponding numerical predictions (b) and (d), respectively.
Mechanics of 21st Century - ICTAM04 Proceedings
XXI ICTAM, 15-21 August 2004, Warsaw, Poland
RESULTS AND DISCUSSION
Indentation hardness
Experimental and numerical results presented in Figure 1 indicate that by manipulating the die wall friction conditions
opposite density distribution trends are induced.
X-ray CT
X-ray CT for capsule shape tablets with different curvatures and break-line geometry (Figure 2) indicate the importance
of the details of the tablet geometry.
Quantitative and qualitative results from friability, abrasion and disintegration tests indicate that the low density zones
around the lettering (at the bottom of the tablets) or close to the break-line are prone to erosion.
2 mm
2 mm
(a)
(b)
Figure 2 X-ray CT density images
FACTORS INFLUENCING TABLET COMPACTION
Numerical analysis of tablet compaction [3] require detailed knowledge of:
• Constitutive behaviour of powder
• Friction between powder and die wall
• Geometry of die and punches
• Sequence of punch motions
• Initial conditions from die fill
CONCLUSIONS
The factors influencing tablet compaction were characterised experimentally and numerical analysis was carried out.
The model predictions are in good agreement with the experimental data.
It is shown that different die wall lubrication conditions induce opposite density distribution trends in identical tablets
(weight, height and material) and this affects the break force, failure mode and friability: it is then demonstrated that for
a given average tablet density the break force and failure mode are not unique [4]. Also, tablet regions having lower
density locally have higher propensity for damage.
The application of numerical analysis for optimising tablet formulation, process development and tablet image is
discussed.
References
[1] Sinka, I.C., Cunningham, J.C. and Zavaliangos, A.: The effect of wall friction in the compaction of pharmaceutical
tablets with curved faces: A validation study of the Drucker-Prager Cap model. Powder Technology, 133: 33-43, 2003.
[2] Sinka I.C., Burch S.F., Tweed J.H. and Cunningham J.C.: Measurement of density variations in tablets using X-ray
computed tomography; International Journal of Pharmaceutics, In press, available online 14 January 2004.
[3] Cunningham, J.C., Sinka, I.C. and Zavaliangos, A.: Analysis of tablet compaction. Part 1 – Characterisation of
mechanical behaviour of powder and powder/tooling friction. Journal of Pharmaceutical Sciences. To appear.
[4] Sinka, I.C., Cunningham, J.C. and Zavaliangos, A.: Analysis of tablet compaction. Part 2 – Finite element analysis of
density distribution in convex tablets. Journal of Pharmaceutical Sciences. To appear.
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