Summary
Results of investigations made of the strengths of powders have been found to fit a general eq. for a yield locus at constant bulk density of the form: (τ/C) n=σ/T+1, whereσ is the applied compressive stress andτ is the applied shear stress. The parametern for any particular powder is independent of bulk density and can be used to classify powders according to their flow properties. Experimentally determined values of tensile strengthT and cohesionC are both shown to have a similar type of power law relationship with bulk density. The relationships between shear stress, normal stress and bulk density for powders are represented by surfaces in a 3-dimensional space analogous to a similar concept recently developed in soil mechanics. The relationships greatly simplify the laboratory measurements required for hopper design.
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Abbreviations
- a :
-
unit cell size
- A :
-
parameter in eq. [11]
- B :
-
constant in eq. [1]
- C :
-
cohesion
- C′ :
-
coefficient defined by eq. [20]
- e :
-
voidage
- E :
-
Young's modulus
- f c, fy :
-
functions ofσ andτ defining the consolidation and yield loci
- F c, Fy :
-
functions ofI 1,I 2,I 3 defining the consolidation and yield loci
- G :
-
rigidity modulus
- I 1,I 2,I 3 :
-
invariants of the stress tensor
- m :
-
parameter in eq. [11]
- n :
-
parameter in eq. [12]
- p :
-
stress parameter used in the triaxial tester
- q:
-
stress parameter used in the triaxial tester
- r c :
-
critical separation of neighbouring particles
- T :
-
tensile strength measured under simple tensile stress
- T′ :
-
tensile strength measured under constrained tensile stress
- w :
-
water content
- γ :
-
shear strain
- λ :
-
constant in eq. [1]
- μ :
-
constant in eq. [1] and [13], coefficient of friction
- ν :
-
Poisson's ratio
- ϱ :
-
bulk density
- σ :
-
applied compressive stress
- σ′1,σ′2,σ′3 :
-
applied compressive stresses in the triaxial tester
- τ :
-
applied shear stress
References
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Dr. Jenike's helpful comments are appreciated.
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Ashton, M.D., Cheng, D.C.H., Farley, R. et al. Some investigations into the strength and flow properties of powders. Rheol Acta 4, 206–218 (1965). https://doi.org/10.1007/BF01969257
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DOI: https://doi.org/10.1007/BF01969257