Distinct element analysis and experimental evaluation of the Heckel analysis of bulk powder compression

In a number of powder processing operations such as dosing, compaction and tabletting, the behaviour of bulk powders subjected to compression is of great interest. Single particle mechanical properties obviously affect the bulk behaviour and there have been a number of attempts to establish relationships between the two scales of single particle and bulk deformation. A widely used approach, particularly in the pharmaceutical industries, is the Heckel analysis where the applied load and bulk deformation are used to infer the yield stress of individual particles. However, it is difficult to analyse this process rigorously and to ascribe any significance to the parameters quantified in the Heckel analysis because the individual particles are not loaded uniformly in the bed. It is therefore of great interest to elucidate what exactly the Heckel analysis does provide. The most appropriate approach for this purpose is the use of the Distinct Element Method (DEM) to simulate the bulk deformation based on single particle properties. Our analysis shows that there is a critical ratio of Youngʹs modulus to the yield stress of individual particles (E/σy)c, above which the Heckel analysis does reflect the effect of the yield stress, but below which it in fact reflects the effect of Youngʹs modulus. Heckelʹs parameter is numerically equal to the yield stress of particles only for a certain value of E/σy. For ratios higher than this value, Heckelʹs parameter can even exceed the yield stress of the individual particles. Therefore the Heckel analysis does not have general validity and should be used with caution.