Failure function from shear tests

Jenike (1964, 1970) has published a fundamental and widely used definition and shear testing protocol on the flowabiUty of powders. The failure properties of powders and thus flow are measured and calculated from a family of yield loci obtained from a number of shear tests. 

The two parameters determined experimentally from the yield loci are as follows. 

2 Major consolidation stress a ) This is the principal normal stress (cti) under which the sample has been consolidated in the principal stress plane. The major consolidation stress should not be confused with the initial compaction stress, which is the stress that compacts the powder bed. Each different compaction stress, (7c, leads to a different yield locus and becomes one of a family of yield loci at different densifications. The major consolidation stress is obtained by drawing a Mohr semi-circle through the equilibrium or end point of the yield locus and tangential to the yield locus. 

This equilibrium stress is found when there is no volume change occurring in the powdered sample when stressed. The Mohr semi-circle, tangential to the locus, then cuts the normal stress axis to give a.  

3 Jenike failure function (Jf) This is the reiationship between the unconfined yield strength (fa) and the major consoiidation stress (cti ). A plot of the values fa versus cti shows the possible relationship of the rate of flow of powdered material out of hopper orifices. Jenike could classify the flowability of powders from selected ratios of these values. 

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Direct and indirect shear stress equipment is usually limited to research projects because of the expense, the skill and time evolved to determine the yield loci and failure functions of particulate materials from bi- and ffi-axial shear testers. The designation of which type of shear tester has been used may be defined by the location of the shear failure zone. With direct shear testers - Jenike type - the major principal stress rotates during shear (Figure 1.35), whilst with indirect shear testers - tri- and bi-axial - the directions of the principal stresses are fixed and orientated in either three or two dimensions, respectively, and remain constant during the test. 

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