The inert failure strains (εf) of glass fibers from the compositional series 25Na2O · xAl2O3 · (75 − x)SiO2, where 0 less-than-or-equals, slant x less-than-or-equals, slant 32.5, were measured at 77 K using a two-point bending technique. Failure strain decreases when Al2O3 replaces SiO2, from 20.9% for x = 0 to 13.7% for x = 32.5. The failure strain depends on the testing speed, or faceplate velocity (Vfp) of the two-point bender. For glasses with relatively low alumina contents (x < 10), εf decreases with increasing Vfp, a behavior noted in an earlier study of sodium silicate glasses [J. Non-Cryst. Solids, in press]. For glasses with greater alumina contents (x greater-or-equal, slanted 15), εf shows little dependence on Vfp, as is found for silica fibers. The replacement of SiO2 with Al2O3 strengthens the glass network through the replacement of non-bridging oxygens with oxygens that bridge neighboring alumina and silica tetrahedra. This stronger (more cross-linked) network is less distorted at high stresses and so does not allow such large strains before failure. The dependence of εf on testing rate (Vfp) appears to be related to the presence of non-bridging oxygens in the glass network and the relaxation of these sites, as indicated by internal friction studies of similar glasses. This may explain the greater values of εf at the slower Vfp for the less cross-linked networks.