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Studies examining organic brittle materials highlight the consistency and variability of the Weibull modulus within naturally occurring ceramics such as human dentin and abalone nacre. Research on human dentin [ 14 ] samples indicates that the Weibull modulus remains stable across different depths or locations within the tooth, with an average ...
For most normal-scale applications to metals and fine-grained ceramics, except for micrometer scale devices, the size is large enough for the Weibull theory to apply (but not for coarse-grained materials such as concrete). From Eq. 2 one can show that the mean strength and the coefficient of variation of strength are obtained as follows:
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress.They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength.
The first source of variability is statistical, due to the limitations of having a finite sample size to estimate parameters such as yield stress, Young's modulus, and true strain. [7] Measurement uncertainty is the most easily minimized out of these three sources, as variance is proportional to the inverse of the sample size.
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Thus, there is a probabilistic nature to be accounted for in the design of ceramics. The Weibull distribution predicts the survival probability of a fraction of samples with a certain volume that survive a tensile stress sigma, and is often used to better assess the success of a ceramic in avoiding fracture.
The theoretical strength of a solid is the maximum possible stress a perfect solid can withstand. It is often much higher than what current real materials can achieve. The lowered fracture stress is due to defects, such as interior or surface cracks.
Each type of ceramic – including heavy clays (used for building), refractories, glass, pottery and porcelain – had its own subculture and empirical methods. Kingery built a theoretical foundation for ceramics on solid state physics and crystallography , creating a new field called physical ceramics . [ 2 ]