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MEASUREMENT OF YIELD LOCI

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 steady-state conditions in arbitrary cutting planes in one of so-called 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.

 

Fließort

The circle of Mohr describes all stresses at an point of the powder mass. The minor an mayor principal stress are on the σ-axes. 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.

 

Spannungen im SchüttgutThe 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:

  • internal friction angle (φi),
  • effective angle of friction (φe),
  • cohesion (Τc),
  • compressive strength (σ c ),
  • flowability factor (FL or ffc),
  • Bulk density after consolidation
  • ...

 

file name YL-250-a.yl
date 05 May 2016
material validation powder
client SHEAR-TEST
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 D6682-01
σr Τrm Τrs   σN Τm Τs  
[Pa] [Pa] [Pa]   [Pa] [Pa] [Pa]  

24612 16859 15315   24612 16134 15275  
           
...          
           
24612 16134 15275   4999 4739

ρb0 = 0.479 g/cm³ bulk density
ρbr = 0.7382 g/cm³ density σr
       
YIELD LOCUS EVALUATION RESULTS
φe = 33.6 deg effective angle of friction DIN1055-6, DIN EN 1991-4
φi = 29.9 deg angle of internal friction (linear approximation)
Τc = 1245 Pa cohesion
σ1 = 49866 Pa major principal stress
σ2 = 14356 Pa minor principal stress
σc = 4943 Pa unconfined compressive strength
σt = -1255 Pa tensile strength
...    
FL = 7.04 flowability factor = ffc = σ1 / σc
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(σr) are measured in order to be able to interpolate the results afterwards. The effective friction angle(φe) 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.


Auswertung mehrerer Fließorte


Three yield loci (blue) of the same material at different reference stresses (σr)
effective flow function (red)

 

 

Berechnung der Spannungen im Silo DIN 1055-6, EN 1991-4 - Messwerte yield locus effective angele of friction flow function