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Tensile strength of randomly perforated aluminum plates: Weibull distribution parameters
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10.1063/1.2948942
/content/aip/journal/jap/104/1/10.1063/1.2948942
http://aip.metastore.ingenta.com/content/aip/journal/jap/104/1/10.1063/1.2948942

Figures

Image of FIG. 1.
FIG. 1.

Normalized tensile stresses at fracture (mean value plus standard deviation) as a function of the hole density, near the percolation threshold. The solid line represents a weighted least-squares fit to Eq. (2). The broken line illustrates a weighted least-squares fit performed on assuming and values as postulated in Ref. 4.

Image of FIG. 2.
FIG. 2.

Normalized tensile stresses at fracture as a function of the hole density. This plot includes the totality of data listed in Tables I and II of Ref. 4. The solid line shows a least-squares fit to Eq. (4); the broken lines delineate the 95% prediction band, thus identifying three outliers.

Image of FIG. 3.
FIG. 3.

Weibull statistical analysis of bin-1 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 4.
FIG. 4.

Weibull statistical analysis of bin-2 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 5.
FIG. 5.

Weibull statistical analysis of bin-3 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 6.
FIG. 6.

Weibull statistical analysis of bin-4 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 7.
FIG. 7.

Weibull statistical analysis of bin-5 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 8.
FIG. 8.

Weibull statistical analysis of bin-6 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 9.
FIG. 9.

Weibull statistical analysis of bin-7 data points. The solid lines are least-squares fit; the broken lines delineate the 95% confidence bands. (a) The “Weibull plot” yields and . (b) The failure probability plot yields Weibull parameters as listed in Table I.

Image of FIG. 10.
FIG. 10.

Normalized characteristic strength of perforated aluminum plates pertaining to bins 1–7 (see Table I). Horizontal error bars specify the hole density range of each bin; vertical error bars delimit the 95% confidence band. The solid line illustrates a fit to Eq. (4) with a critical exponent set equal to 0.614, that is, as obtained from fitting the characteristic strength in the vicinity of the percolation threshold (see the inset).

Image of FIG. 11.
FIG. 11.

Weibull shape parameter as derived from tensile strength data pertaining to bins 1–7, plotted against the hole density. Horizontal error bars specify the hole density range of each bin; vertical error bars delimit the 95% confidence band. The solid line illustrates a least-squares fit as specified in Eq. (10).

Image of FIG. 12.
FIG. 12.

Failure probability of perforated aluminum plates as a function of the tensile stress, for hole densities ranging from 0.02 to 0.60. This plot is based on a conventional two-parameter Weibull model with characteristic strength and shape-parameter values as given by Eqs. (9) and (10). Note how the spread of anticipated fracture strengths increases with the hole density .

Tables

Generic image for table
Table I.

Hole density , population , normalized measured strength , normalized characteristic strength , and shape parameter for each of the seven “bins,” or collections of data points pertaining to plates of similar hole density.

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/content/aip/journal/jap/104/1/10.1063/1.2948942
2008-07-01
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Tensile strength of randomly perforated aluminum plates: Weibull distribution parameters
http://aip.metastore.ingenta.com/content/aip/journal/jap/104/1/10.1063/1.2948942
10.1063/1.2948942
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