Flow point and yield point

The flow point is a single point on the flow limit. It describes the specific stress state (σ, τ) at which the bulk material fails in the shear test and begins to flow. A series of flow points for different pre-compactions results in the flow curve or flow limit of the material. For many applications, the flow limit is approximately described by a Coulomb straight line.

τ=c + σ · tan(φ_i)

• τ: shear stress
• σ: Normal stress
• c: Cohesion of the bulk material
• φ_i: internal friction angle

For free-flowing, non-cohesive bulk solids, c = 0 is often set. This simplifies the relationship to:

τ  =  σ · tan(φ_i)

• Flow function and flow factor ff

Both the yield point and the flow function are derived from the shear tests. It describes the dependence of the bulk strength σ_c on the consolidation stress σ₁. From this, a dimensionless flow factor f_(fc) is formed.

ffc = σ_1 / σ_c

• ffc: Flowability index
• σ_1: consolidation stress
• σ_c: bulk strength (compressive strength at the point of flow)

Typical qualitative classification:

• ffc < 1: not fluent
• 1 < ffc < 2: very cohesive
• 2 < ffc < 4: cohesive
• 4 < ff_c < 10: good flow
• ffc ≥ 10: free-flowing.

This index is used, for example, to classify the siloability of a powder.

Effective friction angle φ_e

The effective internal friction angle φ_e can be determined from the yield points, which characterises the slope of the shear line in the σ–τ diagram. A simple relationship is:

tan(φ_e) = τ / σ

• τ: shear stress at the yield point
• σ: Normal stress at the yield point

The effective internal friction angle φ_e is an important parameter for the design of silo hoppers and discharge devices.