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Surface cracks lead to the decrease of the glass lifetime. A better understanding of cracks self-healing can give a method to increase the glass durability. In a previous study [1], the self-healing behavior of radial cracks generated indentation in float silicate glass has been analyzed when heat treated above glass transition temperature. Two main types of radial crack evolution are observed: (1) either very large crack morphological changes, or (2) a simple direct crack closure. We associate these two phenomena respectively to the effects of capillarity forces induced by surface energy minimization or to the effects of residual stress release. The type of crack evolution is proposed to be mainly depending on glass viscosity: it favors or impedes morphological changes driven by capillarity forces. Similar studies are also performed in others glass types, such as borosilicates or tin surface of float glass. We observe that the glass composition is also important as it probably determines potential hydration. But to go deeper in the analysis, we also focus on the measurement of surface tension in the typical temperature range of cracks thermal healing. These measurements are performed on a "home-made" apparatus, with a small mobile furnace moving along a glass fiber. These measurements of surface tension combined with low temperature viscosity measurements should allow us to confirm our hypothesis of cracks morphological changes driven by capillarity forces. [1] R. Girard, A. Faivre, F. Despetis, " Influence of water on crack self-healing in soda-lime silicate glass" (accepted by J. Am. Ceram. Soc.).