Stress concentration sensitivity of pharmaceutical tablets: The concept of an equivalent crack and microstructural...

The sensitivity of the strength of powder compacts to presence of a hole as a stress concentrator has been explored in the past as a parameter that may provide insight to the propensity of these materials to develop defects during the compaction/ejection sequence. In recent work it was shown that the ratio of the strength in side pressing of two specimens of the same overall size with and without a hole depends on the size of the hole and the variation is varied for different materials. Yet the mechanistic explanation of the stress concentration sensitivity has been lacking. In this work we present the concept of an equivalent crack which represents the microstructural effects on the fracture of these materials, and we connect the stress concentration sensitivity with the equivalent crack size. This new approach shows that the stress concentration sensitivity is independent of the fracture toughness of the material and is only a function of geometric characteristics of the specimens and the equivalent crack size. This observation allows us to numerically derive the size of the equivalent crack from the experimental measurement of ratio of strengths of two specimens. In this way we can explain the reduction of the apparent stress concentration sensitivity as the size of the hole is reduced and we prove that the equivalent crack size and the strength ratio scale with the powder size. This new understanding can provide insight into the response of powder compacts in situations where stress concentrations are present.