INDIAN INSTITUTE OF TECHNOLOGY KANPUR Department of Materials and Metallurgical Engineering Virtual Laboratories for Thermal Processing and Characterization of Materials

Fitting Data to a Weibull Distribution Function

The maximum bending stress, ie, bending strength is given by the following equation:

                   

where, P_max is the maximum load (fracture load), L is the span of bottom supports (in the threee point bend test), b is the width and h is the thickness of the glass slide.

The modulus of elasticity can be calculated by the following equation:

                   

where, s is the slope of the load versus displacement curve taken at two points in the initial linear region.

The probabilities of failure and success are defined as:

The Weibull distribution is given below:

where m is the Weibull modulus. The significance of the Weibull modulus can be thought of the consistency. Sets with very high Weibull modulus have a much more distinct threshold of failure which is often preferred. Sets with low Weibull modulus have a more broad range of failures. In order to determine the Weibull modulus fit a straight line to the following equation.      

The slope of the fitted line gives the Weibull modulus.