Abstract: Existing dynamic strength criteria fail to reflect the closed-loop physical mechanism of "increasing strain rate → growing high-stress regions → decreasing fragment size → rising compressive strength." In this work, experimental observations and theoretical models concerning the strain-rate dependence of average fragment size are comprehensively reviewed and analyzed, based on which a strain rate-average fragment size (SR-AFS) model is proposed and validated. On this basis, an energy balance criterion for dynamic compressive strength of quasi-brittle materials considering the average fragment size (DCSEB-AFS criterion) is established. Finally, the DCSEB-AFS criterion is verified against experimental datasets covering two classic evolution patterns of dynamic uniaxial compressive strength, and further comparative analyses are performed against several widely accepted existing criteria. The results demonstrate that: (1) the average fragment size remains nearly constant at low strain rates, declines nonlinearly and rapidly with increasing strain rate, and finally converges to a constant threshold; the proposed SR-AFS model is capable of precisely reproducing the inherent nonlinear relationship between average fragment size and strain rate; (2) the DCSEB-AFS criterion elucidates the intrinsic mechanism of the strain-rate effect on the dynamic uniaxial compressive strength of quasi-brittle materials: at the peak of the dynamic stress-strain curve, an increase in strain rate leads to the formation of undamaged local damage zones (LDZ), namely high-stress regions, around more internal defects inside specimens, which consequently improves the dynamic uniaxial compressive strength; when the stress-strain curve enters the post-peak stage, numerous LDZs induced by high strain rates fail and trigger extensive crack generation, resulting in a decline in the average fragment size of specimens; (3) the DCSEB-AFS criterion accurately captures both characteristic trends of dynamic strength evolution, and its overall predictive accuracy is comparable to that of the Gebbeken-Greulich criterion and the NDUS criterion. This paper establishes a dynamic strength criterion capable of reflecting the closed-loop mechanism of quasi-brittle material failure, thereby providing a theoretical basis for simultaneously predicting the fragmentation and failure of engineering structures under impact loading.