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Strength of glass using Weibull Statistics

الكلية كلية هندسة المواد     القسم قسم البوليمرات والصناعات البتروكيمياوية     المرحلة 3
أستاذ المادة قتيبة حسين محمد المرزوكي       6/10/2011 5:06:04 PM
Strength of glass using Weibull Statistics
Introduction
The mechanism that determines the strength of glass materials is quite different from that of common
metals. While the strength of metals can be calculated in a straight forward manner by the Young s
Modulus, the determination of glass strength is not nearly as deterministic Therefore a statistical method is
needed to estimate the probability that a glass breakage will occur for a given amount of stress. This
method is known as the Weibull Distribution.
Glass Failure Mechanisms
The amount of force a glass material can take before failure depends more on its surface quality than on the
properties of the material itself. Every glass surface has tiny microcracks which occur during the grinding
and polishing of the optical surfaces. The depth of these microcracks on the surface will determine the
strength of the glass, and the deepest cracks will be the weakest points where breakage will occur.
Subsequently, each polishing operation with finer grains will reduce the depth of the surface microflaws
and accordingly make the material stronger. The flaw depth versus the grind is illustrated in figure 1
below:
Glass Strength Determination via Weibull Distribution
In determining the strength of a glass material, the model that is most frequently used for predicting the
probability of glass fracture due to a given stress follows a distribution known as Weibull Distribution.
This distribution was popularized in a paper published in 1951 entitled “A Statistical Distribution Function
of Wide Applicability” by Waloddi Weibull.
There are two types of Weibull distributions; a two parameter, and a three parameter distribution. In the
more common two parameter Weibull Distribution, the probability of failure is given by the equation:

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