A simple, easy-to-use and physically meaningful analytical (mathematical) model has been developed for the prediction of thermal stresses in an elastic bonded elongated cylindrical tri-material body of finite length. The model has been developed in application to an optical silica fiber embedded (soldered) into Silicon. The body is fabricated at an elevated (soldering, curing) temperature and is subsequently cooled down to a low (room, operation or testing) temperature. Thermal stresses arise because of the thermal contraction mismatch of the dissimilar materials in the body. The addressed stresses include radial, tangential and axial normal stresses acting in the body’s mid-portion, as well as the interfacial shearing stresses that concentrate at the body’s ends. The numerical example is carried out for the case of a “soft” (silver-tin) solder in application to structures, in which an optical silica fiber is soldered into a silicon chip (silicon photonics technology). It is concluded that the appropriate solder material and its thickness should be selected based on the predictions obtained on the basis of the developed model, so that the radial and the longitudinal interfacial stresses in the solder ring are sufficiently low.
"Thermal stress in an optical silica fiber embedded (soldered) into silicon", Proc. SPIE 10108, Silicon Photonics XII, 101080L (20 February 2017); doi: 10.1117/12.2247035; https://doi.org/10.1117/12.2247035