A modified Weibull treatment for the analysis of strength-test data from non-identical brittle specimens |
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Authors: | J W Kennerley J M Newton P Stanley |
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Affiliation: | (1) Department of Pharmacy, University of Nottingham, Nottingham, UK;(2) Department of Pharmacy, Chelsea College, London, UK;(3) Simon Engineering Laboratories, University of Manchester, Manchester, UK |
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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.Nomenclature
D
diameter
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f()
relative frequency of occurrence of specimens with density and volume
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F
minimization function
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i
ascending rank number of a fracture stress
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m
Weibull modulus
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N
tot
number of specimens in a batch
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N()
number of specimens with densities in the range to + d and volumes in the range to + d
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P
f
failure probability
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p
u
upper punch compaction pressure
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t
thickness
-
volume
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w
weight
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W
f
fracture load
-
density
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f
fracture stress
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¯
f
mean fracture stress of a batch
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¯
f()
mean fracture stress of specimens with density and volume
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0
scale parameter or normalizing factor
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u
location parameter or threshold stress |
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Keywords: | |
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