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A modified Weibull treatment for the analysis of strength-test data from non-identical brittle specimens

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Abstract

Powder compacts (e.g., pharmaceutical tablets) manufactured on commerically available machines are not strictly identical but show inevitable variability in their weights, thicknesses and compaction pressures. Consequently, the variability in fracture-stress data obtained from such brittle specimens is greater than that due to the inherent strength variability of the material itself. A modified Weibull analysis has been developed so that a more accurate estimate of the inherent variability of the mechanical strength of the material can be derived from test data obtained from commercially produced compacts; its application is illustrated.

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Abbreviations

D :

diameter

f(ρυ) :

relative frequency of occurrence of specimens with densityρ and volumeυ

F :

minimization function

i :

ascending rank number of a fracture stress

m :

Weibull modulus

N tot :

number of specimens in a batch

N(ρυ) :

number of specimens with densities in the rangeρ toρ + dρ and volumes in the rangeυ toυ + dυ

P f :

failure probability

p u :

upper punch compaction pressure

t :

thickness

υ :

volume

w :

weight

W f :

fracture load

ρ :

density

σ f :

fracture stress

¯σ f :

mean fracture stress of a batch

¯σ f(ρυ):

mean fracture stress of specimens with densityρ and volumeυ

σ 0 :

scale parameter or normalizing factor

σ u :

location parameter or threshold stress

References

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Authors and Affiliations

  1. Department of Pharmacy, University of Nottingham, Nottingham, UK

    J. W. Kennerley

  2. Department of Pharmacy, Chelsea College, London, UK

    J. M. Newton

  3. Simon Engineering Laboratories, University of Manchester, Manchester, UK

    P. Stanley

Authors
  1. J. W. Kennerley
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  2. J. M. Newton
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  3. P. Stanley
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Kennerley, J.W., Newton, J.M. & Stanley, P. A modified Weibull treatment for the analysis of strength-test data from non-identical brittle specimens. J Mater Sci 17, 2947–2954 (1982). https://doi.org/10.1007/BF00644674

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  • DOI: https://doi.org/10.1007/BF00644674

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