1.Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621999, China 2.School of Applied Technology, Southwest University of Science and Technology, Mianyang 621010, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11572298) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11702280)
Received Date:26 August 2020
Accepted Date:19 November 2020
Available Online:30 March 2021
Published Online:05 April 2021
Abstract:In order to understand further the micro-mechanism of helium bubble punching out of the dislocation loop in α-Fe, it is necessary to study the ultimate pressure characteristics of helium bubble punching out of the dislocation loop. In this paper, a cubic representative volume element (RVE) model of the metal-helium bubble is established. For eight types of spherical helium bubbles with different initial radii, molecular dynamics simulations are carried out with the initial helium-to-vacancy ratio serving as a variable and the ultimate pressure of helium bubble and the critical helium-to-vacancy ratio at the beginning of dislocation loop formation in each model are obtained. The results show that for helium bubbles with dimensionless radius ranging from 2 to 10, both the ultimate pressure and the critical helium-to-vacancy ratio of helium bubble punching out of the dislocation loop decrease nonlinearly with the increase of initial helium bubble radius. The relationships of the ultimate pressure and the critical helium-to-vacancy ratio with the initial radius of helium bubble are fitted respectively according to the simulation results and the fitted two equations are in good agreement with the results of previous theoretical studies. The critical helium-to-vacancy ratio required for helium bubble punching out of the dislocation loop in α-Fe has an obvious size effect. For the helium bubble in the late nucleation stage (e.g. helium bubble with an initial radius of 0.81 nm) and non-ideal gas stage (e.g. helium bubble with an initial radius ranging from 1.00 nm to 2.50 nm), the critical helium-to-vacancy ratios for punching out of the dislocation loop are the same as the initial helium-to-vacancy ratio corresponding to the peak pressure point of helium bubble. But for early or middle nucleation stage, such as helium bubble with an initial radius of 0.50 nm, the critical helium-to-vacancy ratio for punching out of the dislocation loop is about 13.46% greater than the initial helium-to-vacancy ratios corresponding to the peak pressure points. At the initial moment (0 ps), in the cross section passing through the center of cubic RVE, the shear stress is concentrated, and the maximum shear stress of Fe atom array around the helium bubble is located at the intersection points (i.e. at 45°) of diagonal and helium bubble boundary, and it is distributed symmetrically with respect to the double fold lines of the cross section parallel to the sides. Both the range of shear stress concentrating area and the maximum shear stress increase with the initial helium-to-vacancy ratio increasing. The dislocation loop’s punching direction corresponds to the direction of the maximum shear stress. The research in this paper can deepen the understanding of the physical properties of helium bubbles in metals and lay a useful foundation for the subsequent analyzing of the effects of helium bubbles on the macroscopic physical and mechanical properties of materials. Keywords:α-Fe/ helium bubble/ initial helium-to-vacancy ratio/ ultimate pressure
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2.1.分子动力学模型
MD建模和模拟均采用软件LAMMPS实施. 本文对含氦泡的α-Fe采用如下方法建模: 首先建立尺寸为45a0 × 45a0 × 45a0的α-Fe原子阵列模型, Fe原子总数为182250个, 这里a0为其晶格常数, a0 = 2.86 ? (1 ? = 0.1 nm); 然后以模型中心为球心, 删除一定半径范围内的Fe原子, 形成球形孔洞; 最后在孔洞中填入不同数量的He原子, 即可形成氦泡. 该建模方法在文献[19,27]中也有运用. 建立的金属-氦泡的立方体型RVE模型如图1所示. 图1所示模型中, Fe-Fe, He-He和Fe-He之间的相互作用势, 分别采用Ackland等[28]、Aziz等[29]和Gao等[30]开发的势函数. RVE模型的3个晶向[100]、[010]和[001]分别对应于图1中直角坐标系的x, y和z轴, 且3个方向均施加周期性边界条件, 模拟温度保持在300 K, 选用NPT系综, 模拟时间步长为1 fs. 图 1 含氦泡的α-Fe计算模型(图中He → He泡, Fe → Fe基体) Figure1. Model of α-Fe with helium bubble (In Fig. He → helium bubble, Fe → Fe matrix).
根据DXA分析结果得到临界氦空位比, 提取氦泡极限压强, 绘制它们随氦泡初始半径的变化曲线, 如图4所示. 通过拟合数据点, 得到氦泡极限压强${P_{{\rm{ultimate}}}}$和临界氦空位比(nHe/nV)cr与$\bar R$的关系式分别为: 图 4 氦泡极限压强、临界氦空位比随氦泡初始半径的变化 Figure4. Changes of ultimate pressure and critical helium-to-vacancy ratio of helium bubble with initial radius of helium bubble.