Athermal strength is the fundamental ability of a material to permanently withstand stresses caused by external forces, which can be defined as ‘permanent strength’ and should be considered as a fundamental mechanical property for assessing structural material strength. For the Al–Mg alloy JIS A5052, our experimental results showed that submicrometer-order grain refinement by severe plastic deformation (SPD) processing at room temperature does not significantly increase strain-rate sensitivity observed in uniaxial tensile tests, but significantly decreases its permanent strength. The strain-rate sensitivity exponent m evaluated via uniaxial tensile tests at a standard strain rate ( \(\dot{\varepsilon }=1\times {10}^{-2}/\text{s}\) ) and at an ultralow strain rate ( \(\dot{\varepsilon }=1\times {10}^{-6}/\text{s}\) ) of specimens having an average grain size of 0.92 µm was rather small, i.e., \(m=0.014\) . However, the permanent strength of the specimen was only 40 pct of the flow stress observed in a standard uniaxial tensile test at a strain rate of \(1\times {10}^{-2}/\text{s}\) and it was increased to 80 pct after low-temperature annealing. Grain refinement associated with repeated SPD processing contributed to a reduction in permanent strength and the Hall–Petch relationship was not applicable to as-SPDed specimens. On the other hand, it was shown that the permanent strength in annealed samples followed the Hall–Petch relationship. In other words, the Hall–Petch relationship explains softening that occurs as the grain size coarsens, but does not directly support the assertion that grain refinement leads to strengthening. This observation suggests that evaluating material strength-based solely on uniaxial tensile tests entails the risk of overlooking unexpected reductions in permanent strength due to differences in processing history or improvements in permanent strength resulting from annealing. Structural design on the premise of existence of a linear elasticity region cannot guarantee the safety, unless it is ensured that the permanent strength is higher than an assumed allowable stress. We emphasize the importance of evaluating permanent strength.