title: The bending strength of tablets with a breaking line--Comparison of the results of an elastic and a "brittle cracking" finite element model with experimental findings.
abstract: The aim of this work was to ascertain the influence of the position of the breaking line of bevel-edged tablets in a three-point bending test. Two different brands of commercially available, flat-round, bevel-edged tablets with a single central breaking line were studied. Breaking line positions tested, relative to the upper loading roll, were 0°, 22.5°, 45°, 67.5° and 90°. The breaking line faced either up- or downwards during the test. The practical results were compared with FEM results simulating similar test configurations. Tablets failed mainly across the failure plane, resulting in two tablet halves. An exception to this was found for tablets where the breaking line faced down and was positioned at an angle of 22.5° relative to the loading plane. Here the crack followed the breaking line in the centre of the tablets and only diverged towards the loading plane position at the edges of the tablets. The breaking line facing upwards resulted in a significantly higher tensile strength of the tablets compared to it facing downwards. However, with one exception, the orientation of the breaking line relative to the loading plane appeared not to affect the tensile strength values. A fully elastic FEM model indicated that both the position of the breaking line relative to the loading plane and as to whether the breaking line faced up- or downwards during the bending test would result in considerably different failure loads during practical experiments. The results also suggested that regardless of the breaking line position, when it is facing down crack propagation should start at the outer edges propagating towards the midpoint of the discs until failure occurs. Failure should hence always result in equal tablet halves, whereby the failure plane should coincide with the loading plane. Neither predictions fully reflected the practical behaviour of the tablets. Using a brittle cracking FEM model significantly larger tensile stresses for tablets with the breaking line positioned downwards at 0° or 22.5° relative to the loading plane were still predicted, but the differences between model and experimental values was greatly reduced. The remaining differences are more likely due to the inadequacy of the equation available to calculate the experimental tensile strength values. This equation cannot account for the presence of a breaking line and overestimates the thickness of the loading plane by the depth of the breaking line when in 0° or 22.5° position. If the depth of the breaking line is taken into account, the model predictions and the experimental findings are comparable. Also, in the brittle cracking FEM simulations the predicted crack propagation patterns were similar to those found in the experiments, and the model stress distributions across the lower surfaces were much more homogeneous and streamlined parallel to the loading plane. The brittle cracking model hence reflected the practicalities of the bending test more closely. The findings suggested that with the breaking line facing down fracture should always start in the centre of a tablet at its lower surface, initiated by the breaking line. Due to simultaneous development of larger stresses along the y-axis the tablet should still break into two equal halves along the loading plane, unless the position of the breaking line relative to the loading plane was 22.5°. In this case the tablet would fail by a mixed process, whereby failure would occur mainly along the breaking line, but due to simultaneous crack formation at the lower surface close to the bevel edge parallel to the loading plane the final breaking pattern would deviate from the breaking line about half-way from its centre, as seen in the practical experiments.
authors.affiliation: University College London, Department of Mechanical Engineering, Torrington Place, London WC1E 7JE, UK. Electronic address: f.podczeck@ucl.ac.uk.
authors.forename: Fridrun
authors.initials: F
authors.lastname: Podczeck
authors.affiliation: University College London, Department of Mechanical Engineering, Torrington Place, London WC1E 7JE, UK.
authors.forename: J Michael
authors.initials: JM
authors.lastname: Newton
authors.affiliation: University College London, Department of Mechanical Engineering, Torrington Place, London WC1E 7JE, UK.
authors.forename: Paul
authors.initials: P
authors.lastname: Fromme
mesh_terms: D020342:Finite Element Analysis; D013314:Stress, Mechanical; D013607:Tablets / Q000737:chemistry*; D013678:Technology, Pharmaceutical / Q000379:methods*; D013718:Tensile Strength
chemical_list: D013607:Tablets
keywords: Bevel-edge; Breaking line; Brittle cracking; Finite element method (FEM); Tablet tensile strength; Three-point bending