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Predicting the Dependability of Ceramics Using Fast-fracture Reliability Analysis Theory

Examples of Ceramics for FEA
September 5, 2014 By: Michael Bak

When faced with designing an engineering structure with the strongest material, material scientists may recommend ceramics.  Ceramics are considered as one of the strongest materials?  Didn't that dinner plate break into a dozen pieces when I dropped it the other night?

Ceramics are used in many engineering applications, including the tiles on the Space Shuttle, the coatings of jet engine turbine blades, biomedical implants, disk brakes, missile nose cones, and ball bearings.  Advanced structural ceramic materials have many desirable properties for use in engineering applications, such as low density, the ability to retain strength at high temperatures, and favorable wear properties. However, ceramics are brittle materials.  The lack of ductility and yielding capability leads to low strain tolerance, low fracture toughness and large variations in observed fracture.

Predicting the reliability of engineering ceramics requires a different approach than what is typically used with other engineering materials.  Observations show that failure of advanced monolithic ceramics closely follows the weakest link theory, which assumes that the structure will fail when the weakest link fails.  The presence of microscopic flaws, which are present as a result of material processing or environmental factors, become sites of large stress concentrations when loads are applied.  Due to the brittle nature of the ceramic material, failure will typically occur immediately at the onset of fracture initiating from one of these flaws.  The observed scatter in component strength is caused by the severity of the flaw distribution.

The most common approach in performing ceramic life prediction is using fast-fracture reliability analysis theory, which is a statistical approach based on the weakest link theory in which the final result is the probability of survival for a given loading.   The weakest link theory has several important features:

1) Compressive stresses do not play a major role in failure of ceramic structures.

2) The number and severity of flaws is a function of the material volume and surface area, i.e. the size effect is a major factor in the reliability of ceramics.

3) Component failure may not be initiated at the point of highest stress, and therefore the entire stress solution is required.

The reliability analysis is based on determining the probability of survival of each "link" in the structure using the crack density function, and then summing over all "links" to find the probability of survival of the entire structure.  The crack density function was introduced by Weibull and is defined as the number of flaws per unit volume with strength less than or equal to the uniform tensile strength of the material.  The function has two parameters, a shape parameter (m) and a scale parameter , which are found from uniaxial or flexure specimen testing.  Parameters can be determined for both surface and volume flaws.

Ceramic fast-fracture calculations are usually not included in standard finite element codes, and thus special-purpose codes or user-defined solutions are required.  For those readers who work with ceramic components, how do you evaluate the reliability of your parts?