The failure initiation of a brazed structure made of Silicon Carbide components is analysed by means of a two-scale analysis and a twofold failure criterion using both a maximum released energy and a maximum tensile stress conditions. In a first step, two asymptotic expansions are settled to describe the perturbation caused by the emergence of the thin solder layer on the free edge surface of the structure, at the macro and micro levels. The resulting far field evidences a logarithmic term. This is mainly due to different elastic properties of the two materials leading to a conflicting necking effect. In a second step, the failure criterion is established; the two conditions lead to two branches depending on the thickness of the solder layer, one is governed by the energy condition and the other by the stress condition. Predictions agree almost well with experiments carried out at room temperature on brazed specimens of SiC with different Silicon based solders.