Weibull Analysis

Question 1

What is the assumptions of Weibull treatment?

Answer 1

• volume dependence for the distribution of strength
• failure at any flaw leads to total failure and the material is homogeneous in the
  sense that the flaws are distributed throughout the volume
• a particular statistical distribution function

Question 2

How does the volume and specimen size affect the weibull probability?

Answer 2

larger volume = higher chance of critical flaw = lower strength
Small volume = lower chance = higher strength but it is independent of specimen size

Question 3

What is the effect of the testing method and loading factor on the weibull probability?

Answer 3

For most bend-testing methods, while the stresses increase with increased loading, the shape of the stress field is invariant
There can be failure in two test methods when both are subjected
to the same maximum stress

Question 4

Strength values measured by bending tests is expected to be greater than the tensile
strength. Discuss the effect of increasing Weibull modulus by improving processing of
ceramics.

Answer 4

The bending tests find max stress at the surface testing a smaller volume to measure a higher strength value.
The weibull modulus m is a measure of strength variability so that Low m=high scatter in strength (material is unreliable) and High m → Low scatter, strength values are more predictable and consistent.
Improved processing (e.g., better powder control, fewer voids, cleaner sintering) → Fewer and smaller flaws → More uniform strength distribution. This improvement will increase m so the flaw size distribution becomes narrower, tensile strength increases reducing number of critical flaws = higher safe stress. The strength becomes less sensitive to specimen size or test method.