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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:
In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
Ceramics are usually very brittle, and their flexural strength depends on both their inherent toughness and the size and severity of flaws. Exposing a large volume of material to the maximum stress will reduce the measured flexural strength because it increases the likelihood of having cracks reaching critical length at a given applied load.
Volume, modulus of elasticity, distribution of forces, and yield strength affect the impact strength of a material. In order for a material or object to have a high impact strength, the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and a high material yield strength. [7]
These classifications are polymer matrix composites (PMCs), ceramic matrix composites (CMCs), and metal matrix composites (MMCs). Also, materials within these categories are often called "advanced" if they combine the properties of high (axial, longitudinal ) strength values and high ( axial , longitudinal) stiffness values, with low weight ...
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.
The modulus of elasticity of concrete is relatively constant at low stress levels but starts decreasing at higher stress levels as matrix cracking develops. The elastic modulus of the hardened paste may be in the order of 10-30 GPa and aggregates about 45 to 85 GPa. The concrete composite is then in the range of 30 to 50 GPa.