# Theoretical approach to determine dynamic fatigue strength characteristics of ceramics under variable loading rates on the basis of SCG concept

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## Abstract

This paper presents a theoretical approach to determine the dynamic fatigue strength characteristics of ceramics under variable loading rates on the basis of the slow crack growth (SCG) concept. First, a probabilistic effective inert strength model was derived on the basis of the SCG concept in conjunction with the Weibull distribution for ceramics subjected to multi-stage loading. Second, a four-point bending test was conducted on \(\hbox {Al}_{{2}}\hbox {O}_{{3}}\) under constant and two-stage variable loading rates, and the fracture surface was then observed. The experimental data that depend on loading rates can be unifiedly evaluated after converting the data to the effective inert strength, obeying the three-parameter Weibull distribution. In addition, the Weibull plots of the inert strength, which were calculated from the inclusion size on the fracture surface using the grain fracture model, showed good agreement with the three-parameter Weibull distribution for the converted effective inert strength. These analytical results theoretically indicate that dynamic fatigue under variable loading rates occurs by obeying SCG at the inclusion. Further, the inert strength and its scatter depend on the size and distribution of inclusions.

## Keywords

Ceramics Variable loading rate Dynamic fatigue strength SCG Inclusion size Inert strength## Notes

### Acknowledgements

I would like to show my greatest appreciation to Prof. K. Ogi (Ehime University, Japan) whose comments and advice were highly valuable throughout the course of my study.

### Funding

This work was supported by JSPS KAKENHI [Grant Number 17K14563].

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