Minimum lifetime of ZERODUR® structures based on the breakage stress threshold model: a review

Increasing demand for using the glass ceramic ZERODUR® for optical elements with high mechanical loads called for strength data based on statistical samples larger than 20 specimens. The data now available for a variety of practical surface conditions (ground, lapped, and etched) allow stresses by factors 4 to 10 times higher than before. The larger samples revealed that breakage stresses of ground surfaces follow the three-parameter Weibull distribution. The threshold parameter of this distribution reflects the existence of an upper limit for the microcracks depth within such surfaces. It is equivalent to a minimum strength below which breakage probability is zero. Its use in the well-established crack growth theory allows calculating minimum lifetimes including fatigue using the stress corrosion constant for the prevailing environmental humidity. Long-term loading tests have confirmed the validity of the model. For fully etched surfaces, the Weibull statistics fails because in such cases failure mechanism is not unique anymore. Nevertheless, ZERODUR® with fully etched surfaces that are free from other damages still exhibit minimum breakage stress above 100-MPa tensile stress. The successful satellite mission LISA Pathfinder has confirmed the possibility to apply ZERODUR® for utmost precision experiments together with high mechanical loads.