Analysis of strength data using two- and three-parameter Weibull models

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Abstract

The strength of ceramic components is adequately described using the Weibull distribution. Values of Weibull modulus and characteristic strength were obtained for two- and three-parameter models for chemically toughened glass and phosphate-bonded investment. The data for glass consisted of strength measurements from fifty specimens loaded in a similar way to operation. The data for phosphate-bonded investment was obtained by measuring four-point bend strength of fifty specimens at room temperature. All values of strength were plotted on modified Weibull probability scales on the x-axis against median ranks on the y-axis. The Weibull modulus for the two-parameter model was determined from the slope of the best fit straight line through the data. For the three-parameter model a correction was made to the “curve” of the two-parameter model by determining the probable value of the lower bound of strength. Ranks were also used to establish tolerance limits for design strengths.

The values of Weibull modulus obtained from the two-parameter and three-parameter models were similar for chemically toughened glass but different for phosphate-bonded investment. The three-parameter Weibull distribution was found to give a more reliable estimate of the Weibull modulus for phosphate-bonded investment.

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