(T1330-09-62) Mechanistic Determination of Tensile Strength of Shaped Tablets

Purpose: During early drug product development, methods for characterization of mechanical attributes are developed for flat, round tablets. However, there is a lack of understanding on how to compute the tensile strength of shaped tablets, which makes determination of the tabletability and compressibility impossible. This presentation has two main objectives. The first objective is to compare existing models for tensile strength prediction of biconvex-round and capsule shaped (elongated) tablets. The effect of dimensional parameters, such as tablet diameter, thickness, and cup depth, were investigated for three existing models [1,2,3]. The second objective is to introduce a simplified FEM model to compute the tensile strength of oval shaped tablets.

Methods: The sensitivity of the mathematical models for the tensile strength of biconvex-round tablets were investigated by varying the dimensions of the tablets. The sensitivity analysis was done for the shape factors (Q), where Q is proportional to the tensile stress, by changing width, diameter, and thickness of the tablet independently, which represent changes in thickness of tablet, size of die, and shape of punch, respectively. In addition, the sensitivity of the models was investigated by changing W and t, simultaneously. The latter investigation represents changing the shape of a tablet from flat, round to a biconvex shape while keeping the volume of the tablet constant. To determine the tensile strength of oval tablets, we developed an FEM model using Abaqus 2018 software (Dassault Systèmes, Vélizy- Villacoublay, France). Since the purpose of these FEM simulations is to develop the relationship between the maximum tensile stress and the applied force on the tablet, there is no need to apply large forces that may cause breakage or large deformations of the tablet. In the current study, the tablets are assumed to be purely elastic. To further simplify the simulation, a static scheme was used in the Abaqus solver and only 1/8 of the tablet is required for the simulation due to symmetry of the tablet.

Results: Existing models for biconvex-round and capsule shaped (elongated) tablets were analyzed. As shown in Figure 1, it was found that the model by Shang et al. (2013) for biconvex tablets is consistent over a wide range of dimensions including flat, round tablet. A hybrid model was proposed for capsule shaped tablets based on models by Shang et al. and Pitt et al. (2013). However, models developed for capsule shaped tablets may under predict or over predict the tensile strength of oval tablets; for the evaluated shapes the difference was up to 160% (Figure 2). As shown in Figure 2, for the oval shapes evaluated in this study, it was found that the tensile strength was found to have a power-law type relationship with the thickness of the tablet. Furthermore, the FEM results for oval tablets show that curvatures along all directions can significantly affect the tensile strength of the tablets (Figure 3).

Conclusion: All existing models for calculating the tensile strength of biconvex-round tablet yield a reasonable result. Any of these models can be used in drug product development activity. However, to get a fair comparison for all sizes and shapes of biconvex-round tablets, we recommend scientists to pick one model and consistently apply it to all biconvex-round tablets. On the other hand, the tensile strength of oval tablets should be determined on a case-by-case approach rather than using a universal equation as in the case of biconvex-round and capsule shaped tablets.

References: [1] C. Shang, I. Sinka, B. Jayaraman, J. Pan, Break force and tensile strength relationships for curved faced tablets subject to diametrical compression, Int. J. Pharm. 442 (2013) 57–64.
[2] K.G. Pitt, M.G. Heasley, Determination of the tensile strength of elongated tablets, Powder Technol. 238 (2013) 169–175.
[3] F. Podczeck, K.R. Drake, J.M. Newton, Investigations into the tensile failure of doubly-convex cylindrical tablets under diametral loading using finite element methodology, Int. J. Pharm. 454 (2013) 412–424.

Acknowledgements: We thank Dr. Omar Sprockel and Dr. Faranak Nikfar for very helpful discussions and feedback.

Comparison of tensile strength models developed by Shang et al. [1], Pitt et al. [2], and Podzeck et al. [3] for biconvex tablets.

Tensile stress in oval tablets computed using finite element method. a) Distribution of tensile stress in oval tablets with varying thicknesses and b) maximum tensile stress as a function of thickness for oval and capsule shaped tablets.

Shape factors (which is directly proportional to maximum tensile stress) for various dimensions and curvatures of oval and capsule shaped tablets.