A strength-ductility trade-off usually occurs when grains are refined to increase strength. A question arises on if there exists a grain size for the best strength-ductility combination, i.e., with the highest possible strain energy density limit and strength simultaneously. This issue is crucial for guiding the design of strong and tough structural materials. Here we reveal an optimum grain size ($d_{optimum}$) on the order of a few micrometers, at which the strain energy density limit, estimated as the product of strength and uniform elongation, reaches a maximum while maintaining reasonably high yield strength. The $d_{optimum}$ is found to exist in a series of single-phase FCC, BCC and HCP materials, indicating it as a universal phenomenon. Theoretical models on the grain size-dependence of uniform elongation and ultimate strength are developed by considering dislocation accumulation in grain boundary affected region (Gbar) and grain interior based on the classical Kocks-Mecking-Estrin model. Combined with the Hall-Petch relationship, the models accurately predict the $d_{optimum}$. Importantly, the models disclose this $d_{optimum}$ to be close to twice of the characteristic width of Gbar ($l_{Gbar}$), suggesting that it is exactly at or near the critical grain size with the strongest intragranular strain gradient effects.

当细化晶粒以增加强度时，通常会发生强度-延展性权衡。问题是是否存在最佳强度-延展性组合的晶粒尺寸，即同时具有最高可能的应变能密度极限和强度。这个问题对于指导强韧结构材料的设计至关重要。在这里，我们揭示了最佳晶粒尺寸（$d_{op吨我米你米}$) 在几微米的量级上，此时应变能密度极限（估计为强度和均匀伸长率的乘积）达到最大值，同时保持相当高的屈服强度。这$d_{op吨我米你米}$被发现存在于一系列单相 FCC、BCC 和 HCP 材料中，表明它是一种普遍现象。基于经典的 Kocks-Mecking-Estrin 模型，通过考虑晶界影响区域 (Gbar) 和晶粒内部的位错积累，开发了关于均匀伸长率和极限强度的晶粒尺寸依赖性的理论模型。结合 Hall-Petch 关系，模型准确地预测了$d_{op吨我米你米}$. 重要的是，模型揭示了这一点$d_{op吨我米你米}$接近 Gbar 特征宽度的两倍（${升}_{GbAr}$), 表明它恰好处于或接近具有最强晶内应变梯度效应的临界晶粒尺寸。