Introduction & Context

The yield locus construction from shear-cell data is a fundamental step in powder characterization for process engineering. It quantifies how a bulk solid transitions from elastic to plastic deformation under combined normal and shear loading. The resulting locus, together with the flow function ffc and the wall friction angle φ, is used to design reliable hoppers, silos, pneumatic conveyors, and tablet dies. Without these parameters, equipment may suffer from arching, ratholing, segregation, or unacceptable shear on contact surfaces.

A yield locus is a line or curve that separates stress states at which powder will flow from those at which it will remain stationary. Constructing it from shear cell data lets you determine critical parameters such as cohesion, unconfined yield strength, and flow functions—information essential for hopper design, mixer scale-up, and troubleshooting flow issues.

Use at least three pre-shear points that bracket the major principal stress you expect in your process. For each pre-shear, shear to failure at three lower normal stresses. Plot all failure points (σ, τ) and fit a straight line or slight curve; R² ≥ 0.98 is usually sufficient for engineering work.

Draw a Mohr circle tangent to the locus through your pre-shear point to obtain the major consolidation stress σ1.
Draw a second Mohr circle tangent to the locus and passing through the origin to obtain the unconfined yield strength σc.
Repeat for several consolidation levels to generate pairs (σ1, σc) and plot σ1 vs σc—this is your flow function.

No. Many cohesive powders show curvature. Fit a minor arc or use the Warren-Spring equation τ = c + σ tan(φi) where φi is the angle of internal friction at each stress level. Retain the curve; forcing a straight line underestimates σc and can lead to undersized hopper outlets.

Both variables shift the locus: higher moisture increases cohesion and σc; higher temperature can reduce cohesion but may increase electrostatic effects. If your process sees >5 °C or >1 % RH variation, generate separate loci at the extremes and use the most conservative σc for design.

Worked Example – Yield Locus Construction from Shear Cell Data

A small-scale food plant needs to characterise a new breakfast-cereal powder before it is stored in a 2 m diameter silo. A ring-shear tester is used to obtain the consolidation and wall points required to build the yield locus and calculate the flow factor (ffc).

Knowns

Atmospheric pressure: 101.325 kPa
Consolidation normal stress, σ_consol: 8.0 kPa
Consolidation shear stress, τ_consol: 3.8 kPa
Major principal stress, σ₁ (from test): 2.2 kPa
Wall normal stress, σ_wall: 4.0 kPa
Wall shear stress, τ_wall: 1.5 kPa

Step-by-Step Calculation

Convert consolidation stresses to absolute values (gauge + atmospheric): \[ \sigma_{\text{consol,abs}} = 8.0 + 101.325 = 109.325\ \text{kPa} \] \[ \tau_{\text{consol,abs}} = 3.8\ \text{kPa (unchanged)} \]
Compute the flow factor ffc: \[ \text{ffc} = \frac{\sigma_{\text{consol,abs}}}{\sigma_1} = \frac{109.325}{2.2} = 49.693 \rightarrow 3.636\ \text{(rounded to 3 decimal places)} \]
Determine the effective angle of internal friction φ from the slope of the yield locus: \[ \phi = \arctan\left(\frac{\tau_{\text{consol}}}{\sigma_{\text{consol}}}\right) = \arctan\left(\frac{3.8}{8.0}\right) = 0.359\ \text{rad} = 20.556^\circ \]

Final Answer

The powder has a flow factor ffc = 3.636 and an effective angle of internal friction φ = 20.6°. These values indicate moderate flowability and are now ready for silo design calculations.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle