FCC辐照金属铜材料中氦泡平衡内压的分子模拟及其尺度效应

氦泡内的氦密度及其内压对含氦泡辐照材料的力学性能具有重要影响，本文采用分子模拟方法系统地研究了面心立方金属铜材料内氦泡平衡内压及其尺度效应、温度效应和引起的应力场。基于能量最小原理与应力平衡准则，提出了确定平衡内压的方法，研究发现：1）采用能量最低原理与应力平衡准则所获得的平衡内压是自洽的；2）存在一个临界尺度，当氦泡孔径小于该临界尺度时，平衡内压出现反常尺度效应，即当氦泡孔径小于3nm时，平衡内压并不随孔径减小而明显增大，甚至出现减小的异常现象；3）传统采用基于球形孔洞的理论公式估算严重高估了氦泡平衡内压，引起的误差随氦泡孔径减小而显著增大，如孔径为3nm时，误差超过63%；4）由于纳米孔洞多面体特性和材料的各向异性，即使在平衡内压条件下，基体铜材料内仍存在一定的应力分布，该应力体现出显著的局域特征，即随着距孔洞中心距离的增加而快速下降。此外，本文还提出采用时间平均叠加区域平均来减小热涨落对应力场的影响，取得了较好的效果。

Atomistic study of equilibrium pressure of helium bubble in irradiated FCC copper and its abnormal size effect

Helium density inside helium bubble and its corresponding internal pressure have a significant influence on the mechanical properties of materials with radiation-induced helium bubble. The equilibrium internal pressure, size effect, temperature effect and stress field of FCC copper containing helium bubble are systematically explored by means of molecular simulations in this paper. Based on energy principle and stress criterion, the method to determine the equilibrium internal pressure is proposed. It is found: 1) The Equilibrium pressures of the bubble obtained by means of the criterion of the minimum energy principle and stress criterion are self-consistent. 2) An abnormal size effect of helium bubble on the equilibrium pressure is found, i.e. when the size of the He bubble is less than a critical one, the equilibrium pressure does not increase but drops slightly with the decrease of bubble size, which is different from the prediction of Young-Laplace equation. The critical size for He bubble is about 3 nm. 3) Compared with molecular simulation results, the traditional Young-Laplace equation overestimates the equilibrium internal pressure of helium bubbles, and the error increases significantly with the decrease of the size of helium bubbles. For instance, when the aperture is 3nm, the relative error exceeds 63%.4) Due to the polyhedron characteristics of the nanoscale helium bubble and the anisotropy of the material, there exists an additional stress field in the surrounding copper matrix of the bubble under the action of the equilibrium internal pressure, which implies that helium bubble-induced stress cannot be eliminated by the equilibrium pressure completely. However, this residual stress decreases rapidly as the increase of the distance from the center of the bubble. In addition, a method to reduce the effect of thermal disturbance or fluctuation on the stress field is proposed by means of the superposition of time average and spatial average. The method adopted in this paper can be extended to investigate the effects of helium bubbles on the mechanical properties of irradiated materials and the interaction between irradiated defects.