Dynamic tensile (spall) fracture of pure Pb and Sn in solid and molten states is investigated by MD simulations. The influence of unwettable inclusions on the spall strength is revealed. Mechanical model of fracture is fitted to MD data at the strain rate $$10^{\mathrm {9}}$$ 10 9 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 and used for calculation of the rate dependencies of spall strength in the range from $$10^{\mathrm {4}}$$ 10 4 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 to $$10^{\mathrm {9}}$$ 10 9 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 in comparison with the experimental data. The model takes into account homogeneous nucleation of pores, activation of pores on unwettable inclusions or other heterogeneities and change in pore size, which is viscous for melt and elastic-plastic for solid. In the case of pure uniform material, the homogeneous nucleation gives a slow decrease in spall strength with decreasing strain rate; the calculated values significantly exceed experimental results for moderate strain rates of $$10^{\mathrm {4}}$$ 10 4 – $$10^{\mathrm {5}}$$ 10 5 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 . Accounting of unwettable inclusions removes this contradiction and provides correspondence to experimental data. A power-law size distribution of inclusions gives in the case of melt the power-law dependence of spall strength on strain rate that coincides with the experimental data for molten Sn. In the case of solid metal, the spall strength at moderate strain rates is determined by the yield strength. Therefore, the initial power law decrease in the spall strength is replaced by almost constant level at moderate strain rates. This behavior corresponds to the existing experimental data for solid Pb. Transfer to the homogeneous nucleation mode takes place for solid and molten metals at ultra-high strain rates, when the concentration of pores activated on the existing heterogeneities is not enough for the stress relaxation.

中文翻译：

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固体和熔融铅和锡的剥落强度的应变率依赖性

通过 MD 模拟研究了纯 Pb 和 Sn 在固态和熔融状态下的动态拉伸（剥落）断裂。揭示了不可润湿夹杂物对剥落强度的影响。断裂力学模型在应变率 $$10^{\mathrm {9}}$$ 10 9 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 下拟合到 MD 数据并使用用于计算 $$10^{\mathrm {4}}$$ 10 4 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 到 $ 范围内的剥落强度的速率相关性$10^{\mathrm {9}}$$ 10 9 $$\hbox {s}^{\mathrm {-1}}$$ s - 1 与实验数据相比。该模型考虑了孔隙的均匀成核、不可润湿夹杂物上的孔隙活化或其他非均质性以及孔隙尺寸的变化，对于熔体来说是粘性的，对于固体来说是弹塑性的。在纯均质材料的情况下，随着应变率的降低，均匀成核使剥落强度缓慢降低；计算值显着超过 $$10^{\mathrm {4}}$$ 10 4 – $$10^{\mathrm {5}}$$ 10 5 $$\hbox {s}^{ 中等应变率的实验结果\mathrm {-1}}$$ s - 1 。不可润湿夹杂物的计算消除了这一矛盾，并提供了与实验数据的对应关系。在熔体的情况下，夹杂物的幂律尺寸分布给出了剥落强度对应变速率的幂律依赖性，这与熔融锡的实验数据一致。在固体金属的情况下，中等应变率下的剥落强度由屈服强度决定。因此，在中等应变率下，剥落强度的初始幂律下降被几乎恒定的水平所取代。这种行为对应于固体铅的现有实验数据。当固体和熔融金属在超高应变率下转移到均匀成核模式时，当现有异质性上激活的孔隙浓度不足以实现应力松弛时。