An Engineer's Approach to Design Ceramic Components:

The load condition of ceramic components is mostly inhomogeneous and multi-axial. An integration procedure throughout the total volume or surface is necessary to calculate the probability of failure of the component. By use of the Weibull statistic it is shown, that the probability of failure of a component is determined by the area with the highest stresses, if the Weibull modulus is equal or greater 20. In those cases the risk of rupture of the remaining volume of the component can be neglected.

The area with the highest stresses is mostly created by notches. An approximate solution is derived, that uses the notch factor and leads to a Weibull statistical estimation. The stress concentration factor is well known in engineering and can be found e.g. in tables. Some calculations by the Finite Element Method and other numerical methods demonstrate sufficient accuracy of the approximate solution. Based on these results a strategy for the design of ceramic components is proposed:
a) Clarifying of the load state (even small deviations in load assumptions can lead to false estimation of the risk of rupture), b) Consideration of a safety factor regarding the tolerable stress, c) Use of convincing material data, d) Identification of the mostly stressed component area, e) Linearization of the stress state in this area, f) Computation of Weibull's Integral respectively the effective volume, f) Summation of the risks of rupture and derivation of the total probability of failure.

For multi-axial stress conditions the Weibull equation is extended and the different mechanisms of fracture according to tension and compression load are taken into account separately when calculating the probability of failure. The idea is based on the statistical extension of Mohr's circle.

 

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