On the influence of frictional contact law formulations on the calculation of failure probabilities in ceramics

• We analyse the impact of the contact model on the failure probabilities of ceramics.
• The derivative of stress intensity factor with respect to the crack length is used.
• The calculation of stress intensity factors for varying crack orientation is improved.
• The use of a micromechanically motivated contact law is advocated.

Ceramic materials require specific design rules because of their brittle nature, relying on failure probabilities computed from stress fields obtained by a numerical method, most commonly the finite element method. As one of the major advantages of ceramic materials is their high hardness and wear resistance, they are often found in applications involving contact and wear. In computational contact mechanics, the most popular contact algorithm is the penalty method. In the present article, the influence of the penalty coefficient on the computed failure probabilities is investigated. Similarly, this contact algorithm, with a purely numerical control parameter, is compared to a micromechanically motivated contact law, which explicitly takes into consideration both surface roughness and material hardness. Finally, because of the high stress gradients found in many situations involving contacting bodies, failure probabilities computed under the hypothesis of a constant or inhomogeneous stress field along the crack length are compared.