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The Weibull modulus is a dimensionless parameter of the Weibull distribution. It represents the width of a probability density function (PDF) in which a higher modulus is a characteristic of a narrower distribution of values.
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 Weibull distribution (usually sufficient in reliability engineering) is a special case of the three parameter exponentiated Weibull distribution where the additional exponent equals 1. The exponentiated Weibull distribution accommodates unimodal, bathtub shaped [33] and monotone failure rates.
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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The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following probability density function: [3] = + ()valid for , where | | < is the entropic index associated with the Kaniadakis entropy, > is the scale parameter, and > is the shape parameter or Weibull modulus.
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.