Flaws contained in ceramics have a strong correlation to the fracture strength. They are characterized by several factors, such as a size, an angle, a position, and shape. When the combination of them takes the most dangerous state under a certain loading, the flaw is called as the weakest one which determines the strength of ceramic body.
y. Particularly, flaw-size is the most influential factor to fracture strength. In spite of the importance, researches on the flaw-sizes distribution are not enough. First, we adopted a gamma distribution as a probability model for flaw size distribution. Taking the flaw-size as a random variable, the logarithms of the probability density function for gamma distribution is expressed by Eq.(1).
…(1),
.
We found the first term in the right hand side
is two orders of magnitude larger than the
second and third ones. So the equation can be
approximated as follows.
…(2)
Several experimental data set [1,2]are used for the
estimation of the parameter of gamma
distribution [1,2]. Figure.1 shows vs
relation of the observed flaw-size data. Open and closed circles and open triangle in the figure are the experimental data for 3 kinds of alumina ceramics[1], and the closed square shows that of silicon nitride[2]. The solid lines in Fig.1 are the regression curves calculated from Eq.(2). It is seen that all the flaw-size data are linearized in sufficient accuracy. This result should greatly contribute to estimate fracture strength distribution of ceramics.
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