The standard measurement of the yield locus is taken over from the classic soil mechanics. This yield locus contains a number of points consolidated with the same pressure and sheared under different load. That means that such yield locus represents the shear resistance for the same consolidation.
A bulk material is composed of many individual particles which, for bulk material characterization, must be considered as a continuum. Many influencing factors such as moisture, temperature, particle size, particle shape, surface structure, mechanical properties such as elastic, viscoelastic, plastic or brittle behavior as well as the chemical composition, gravitational force and interparticle and electrostatic Van der Waals forces, have influence of the physical behavior of the bulk material. It is not possible to determine all these data individually and make conclusions about the flow behavior. The shear test should simulate the circumstances in which the powder behave in an handling equipment. Qualitative physical properties are obtained which are used for further calculations.
The powder changes his packaging density depending on the load and movement and therefore has a yield point dependent on the tension condition. The tension condition descried the yield point where the powder starts to move on the gliding area under influence of the shear stress(t). It starts to flow.
By transfers the tensions into a (normal loasd(σ) – shear stress(τ) – diagram) you will receives a geometrical representation of the steadystate conditions in arbitrary cutting planes in one of socalled Mohr’s tension circles. Each (σ,τ) combination, lies on the straights, lead to the flowing of the powder, tension conditions below the straights are stable, above is physically not possible.
The circle of Mohr describes all stresses at an point of the powder mass. The minor an mayor principal stress are on the σaxes. The midpoint of the Mohr circle represents the average stress between mayor and minor principal stress. The stresses can only grow only until the shear stress reaches the value of plastic deformation. Stresses above this value are not possible.
The major principal stress cause the consolidation to the corresponding density. Therefore it is also the base parameter for functions.
If another Mohr circle with the smallest principal stress = 0 is constructed, which also touch the yield locus, then the compressive strength (σd) of the bulk material results at the major principal stress. The ratio of compressive strength to the largest principal stress is used to classify the flowability of a bulk material. Compressive strength is also important for determining bridging in a silo.
The measurements and evaluation provide us with basic physical parameter that can be used further technological calculations.
Such:
file name  YL250a.yl  
date  05 May 2016  
material  validation powder  
client  SHEARTEST  
operator  MB  
humidity  12.47 % Moisture  
note  


device  ST200AUTO  
shear cell  RSL ST30.cel  
Δσ  + 0 Pa  
ΔΤ  + 0 Pa  
use prorating 
SHEAR STRESSES  MEASUREMENT ACCORDING ASTM D668201  
σ_{r}  Τ_{rm}  Τ_{rs}  σ_{N}  Τ_{m}  Τ_{s}  
[Pa]  [Pa]  [Pa]  [Pa]  [Pa]  [Pa]  
24612  16859  15315  24612  16134  15275  
...  
24612  16134  15275  4999  4739 
ρ_{b0} =  0.479  g/cm³  bulk density  
ρ_{br} =  0.7382  g/cm³  density σ_{r}  
YIELD LOCUS EVALUATION RESULTS  
φ_{e} =  33.6  deg  effective angle of friction DIN10556, DIN EN 19914  
φ_{i} =  29.9  deg  angle of internal friction (linear approximation)  
Τ_{c} =  1245  Pa  cohesion  
σ_{1} =  49866  Pa  major principal stress  
σ_{2} =  14356  Pa  minor principal stress  
σ_{c} =  4943  Pa  unconfined compressive strength  
σ_{t} =  1255  Pa  tensile strength  
...  
FL =  7.04  flowability factor = ffc = σ_{1} / σ_{c}  
R =  0.999  coefficient of correlation  

It is important that the location of the flow site is dependent on the packing density of the sample. For each initial density, there is a corresponding flow location. As it is not known exactly which load will occur in the application case, several loci with different reference stresses(σ_{r}) are measured in order to be able to interpolate the results afterwards. The effective friction angle(φ_{e}) is a function which is tangent to the large Mohr circles. Using the function of the effective friction angle, the horizontal load ratio (λ) can be calculated for any stress state between the measured flow locations.
Three yield loci (blue) of the same material at different reference stresses (σr)
effective flow function (red)