The breakdown of the Weibull behavior in dental zirconias

Abstract

A long-standing regular in the circles of controversy is the debate on the appropriateness of the common practice of treating datasets of strength measurements of brittle materials using Weibull statistics, or if they rather belong to the enclave of other probability distributions. We do not intend to take a slide into that mathematical rabbit hole, here. There have been enough strides on that terrain with valuable insights, 1-5 exposing for one, that small sample sizes, despite in compliance with standard recommendations, cannot offer the means for distinguishing between similar distributions (e.g., Gaussian, Weibull, log-normal). 6 For such experimental practices confined within single specimen sizes, distributions of a set of strength values will almost invariably appear to be of the Weibull type. 7 That alone is no definite testament of a Weibull material, that is, that its strength distribution is determined by an inherent distribution of flaw sizes of monotonically decreasing density, 8 while obeying the original assumption of the weakest link hypothesis. 9,10

Speed-sintering and the mechanical properties of 3–5 mol% Y2O3-stabilized zirconias

“…In the context of sintering, significant changes in m suggest a different dynamic in the densification of the white-body, related not to the heat distribution once both heating rates were very similar, but to the dwell time. Belli and Lohbauer [ 18 ] clearly showed that in dental zirconias, the defect distribution in the fully sintered piece is inherited from the defect distribution in the white-body. Passed down to the sintered analogs, the morphology of critical defects in the white-body constitute junction vertices between spherical spray-dried granulates that failed to reach intimate contact during pressing.…”

“…Here, an alternative sintering program “speed-sintering” was evaluated, and compared to the “conventional sintering” program in terms of physical and mechanical properties as reported in Refs. [ 13 , 18 ]. Sintering was performed in a bottom-lift oven (Vita Zircomat 6000 M Speed, Vita Zahnfabrik) that allows flexible programming of the heating and cooling curves.…”

Statistical analysis of the strength reliability of the MAX phases

“…Moreover, these defects are widely dispersed in size, position, and direction, resulting in a large dispersion of mechanical properties such as the bending strength. To respond this behavior, a probabilistic method based on statistical fracture mechanics is established, where the Weibull statistics is the most commonly used theory in evaluating its strength distribution and reliability 8–10 . In this theory, the statistical parameter m (Weibull modulus) is often used for the dispersion of strength.…”

“…To respond this behavior, a probabilistic method based on statistical fracture mechanics is established, where the Weibull statistics is the most commonly used theory in evaluating its strength distribution and reliability. [8][9][10] In this theory, the statistical parameter m (Weibull modulus) is often used for the dispersion of strength. However, few reports are conducted on the MAX phases with the unique combination of metaland ceramic-like properties.…”

“…However, few reports are conducted on the MAX phases with the unique combination of metaland ceramic-like properties. To date, only Bao et al 11 investigated the strength distribution of Ti 3 SiC 2 by the use of two-parameter (2P) Weibull statistics, where the estimated m at 25 is higher than that of typical ceramics (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), indicating the higher strength stability. This is attributed to the high fracture toughness and damage tolerance of the MAX phases.…”