Effect of interstitial ${\left\langle {100} \right\rangle }$ dislocation loop on expansion of micro-crack in body centered cubic iron investigated by molecular dynamics method
1.School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China 2.Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China 3.Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China
Abstract:The interactions between the energetic particles and atoms in materials would result in the atomic displacements and the associated radiation defects. The interstitial dislocation loop, as one of the primary radiation defects, is formed by the clustering of the supersaturated self-interstitial atoms from the displacement damages in body centered cubic (bcc) iron based materials. The radiation hardening, embrittlement, swelling, creep, etc. are generally related to these loops and their interactions with other defects. In addition, the irradiation would also result in the formation of the micro-cracks from the surface of the materials and also from the interface of grains, precipitates, and gas-bubbles inside the materials, which would result in the irradiation assisted stress corrosion crack (IASCC). Therefore, to understand the interaction between interstitial dislocation loop and micro-crack under the irradiation, is one of key steps to understand the underlying mechanism of IASCC. In this work, the interaction between interstitial dislocation loop and micro-crack is simulated by molecular dynamics method on an atomic scale. The distance, relative position between them and radius of dislocation loop, as the main factors affecting their interactions, are studied to explore the underlying reason for inducing the micro-crack to expand on the slip plane. The simulation results indicate that when the interaction between them dominates the whole process with the distance between them within the critical value, the dislocation network containing the $ \langle 100 \rangle $ and 1/2$ \langle 111 \rangle $ segments, would interact with the crack tip to inhibit the crack from expanding through the pinning effect. When the size of loop is different, the pining effect would be available only when the interaction between loop core and crack tip dominates with the distance between them within the critical value. All these results provide new understanding for further exploring the IASCC under irradiation. Keywords:radiation damage/ micro-crack/ dislocation loop/ molecular dynamics simulation
将材料在非辐照条件下服役时微裂纹的扩展定义为自由微裂纹的扩展, 通过对比此种微裂纹的扩展, 研究辐照形成的间隙型位错环对相同微裂纹扩展的影响. 计算模型如图1(a)所示, 根据第2节的方法, 得到了自由微裂纹的扩展过程及结果. 研究发现, 当自由微裂纹在外应力下开始扩展, 初始状态如图2(a)所示, 裂纹的尖端在外力作用下逐渐变得凹凸不平, 随着裂纹进一步扩展, 裂纹尖端开始沿着系统的滑移面开始向上或向下扩展, 从而使得微裂纹的对称面从XOZ面变为滑移面(如图2(b)); 随着扩展在滑移面上进行, 裂纹尖端沿其伯格斯矢量方向在裂纹扩展的滑移面上运动, 使得裂纹很容易扩展到材料表面, 造成材料的断裂, 最终结果如图2(c)所示. 对上述过程采用变换随机数种子的多次模拟统计得到相同的结果, 证明自由微裂纹的扩展与相应的滑移面紧密相关, 从而造成了裂纹从原来的对称面改变方向变为沿滑移面扩展. 当裂纹尖端有缺陷时, 如本项工作中的间隙型位错环与微裂纹的相互作用, 可能会影响微裂纹的扩展是否会沿着滑移面, 这些结果在3.2—3.4节中阐述. 图 2 外应力作用下自由微裂纹扩展的过程 (a)?(c) 1.0, 40.0 和122.4 ps时的形貌 Figure2. Expansion of free micro-crack under the effect of external stress: (a)?(c) Results at time of 1.0, 40.0, and 122.4 ps, respectively.
23.2.位错环与裂纹尖端距离的影响 -->
3.2.位错环与裂纹尖端距离的影响
当材料中存在辐照形成的间隙型位错环后, 模型如图1(b)所示. 首先研究间隙型位错环位于计算胞的中心时微裂纹的扩展情况. 由于微裂纹的对称平面均是位于XOZ平面上, 因此, 微裂纹与位错环均是以XOZ为对称面. 当R = 1.5 nm, d = 1.5 nm时, 随着模拟的进行, 裂纹在应力作用下裂口逐渐变大, 导致裂纹尖端处变得凹凸不平(如图3(a)所示). 对此过程研究表明, 在微裂纹的初始扩展过程中, 尖端没有形成新的位错线片段, 主要原因可能在于本项工作中, 主要研究微裂纹形核结束后的扩展阶段, 而没有包含形核阶段, 因此, 在裂纹扩展的初始阶段, 没有新的位错线片段的形成. 由于位错环为$\left\langle {100} \right\rangle $间隙型位错环, 在给定的温度和模拟时间内, 其状态基本保持不变没有发生位错环的位移. 在应力作用下, 随着时间的延长, 微裂纹尖端逐渐沿着–X方向扩展, 当时间达到17.7 ps时, 位错环与裂纹尖端发生接触反应, 生成$\left\langle {100} \right\rangle $和1/2$\left\langle {111} \right\rangle $共存的位错网络. 如果没有间隙型位错环, 如3.1节的自由微裂纹扩展, 不会形成$\left\langle {100} \right\rangle $和1/2$\left\langle {111} \right\rangle $共存的位错网络. 这些位错网络的形成, 位错密度的升高, 使得$\left\langle {100} \right\rangle $位错环与形成的位错网络反应加速, 最后导致$\left\langle {100} \right\rangle $位错环完全被吸收, 与裂纹尖端形成包含$\left\langle {100} \right\rangle $和1/2$\left\langle {111} \right\rangle $片段的位错网络, 如图3(b)所示, 图中红色线段为$\left\langle {100} \right\rangle $片段, 长度为5.79 nm, 绿色线段为1/2$\left\langle {111} \right\rangle $片段, 长度为8.34 nm. 同时, 正是位错环与裂纹尖端形成位错网络导致裂纹尖端的扩展速度变慢, 主要原因是形成的位错网络对裂纹尖端扩展的钉扎作用, 抑制了微裂纹的快速扩展, 使得材料表现出更好的抗裂纹扩展的性能, 意味着需要更大的外应力才能使裂纹进一步扩展. 随着反应在外应力下的进行, 裂纹尖端在越过位错网络施加的势垒后, 再次不断向内扩展, 同时, 尖端形貌发生严重形变, 但是$\left\langle {100} \right\rangle $位错片段和1/2$\left\langle {111} \right\rangle $共存的位错片段仍然存在, 如图3(c)所示, $\left\langle {100} \right\rangle $片段为5.99 nm, 1/2$\left\langle {111} \right\rangle $片段为3.18 nm, 裂纹尖端依然处于较中心位置, 而没有像自由微裂纹扩展一样, 发生沿着滑移面的裂纹开裂. 图 3d = 1.5 nm, R = 1.5 nm, 位错环与微裂纹扩展的相互作用过程, (a)?(c)分别为15, 20和120 ps时的形貌 (a) 反应初始阶段在微裂纹尖端形成凹凸不平; (b)二者反应形成位错网络阶段; (c) 裂纹尖端被位错网络钉扎并保持在XOZ平面 Figure3. Interaction between interstitial dislocation loop with radius R = 1.5 nm and micro-crack with distance to loop d = 1.5 nm. (a) to (c) are results at time of 15, 20, and 120 ps: (a) The initial stage with the formation of rugged crack tip; (b) the state with the formation of dislocation network after the interaction between loop and crack; (c) the final state with crack tip pinned by dislocation network located on XOZ plane.
以上分析发现, 位错环与微裂纹尖端发生反应形成位错网络, 会在一定程度上抑制微裂纹的扩展. 因此, 可以通过增加微裂纹和位错环之间的距离, 来研究二者的反应及对微裂纹扩展的影响. 当d由1.5增加到2.0及2.5 nm时, 模拟同样揭示出类似的反应的过程, 当d = 3.0 nm时, 模拟发现随着裂纹的开裂, 在位错环与裂纹尖端发生接触反应之前, 裂纹尖端已经开始沿滑移面开裂 (如图4(a)); 发生接触之后尖端形成了$\left\langle {100} \right\rangle $和1/2$\left\langle {111} \right\rangle $片段, 随着反应的进行, $\left\langle {100} \right\rangle $片段逐渐减少, 整个位错网络转化为以1/2$\left\langle {111} \right\rangle $位错线段为主, 如图4(b), 其中$\left\langle {100} \right\rangle $线段长度为0.59 nm, 1/2$\left\langle {111} \right\rangle $线段长度为11.08 nm. 以1/2$\left\langle {111} \right\rangle $片段为主的位错网络会导致在滑移面上容易发生滑移, 当密度比较低时难以形成钉扎结构, 裂纹尖端在应力场下不断向侧上方沿滑移面方向开裂, 随着位错网络不断反应, 形成一段两端终结于裂纹尖端侧表面、长度为14.42 nm的1/2$\left\langle {111} \right\rangle $位错线段(如图4(c)), 未能抑制裂纹尖端进一步沿滑移面开裂, 造成材料断裂. 可以得出当位错环与裂纹尖端反应形成的位错网络中$\left\langle {100} \right\rangle $片段减少时, 位错网络对裂纹尖端开裂的抑制作用减弱, 因此, 可以推断出$\left\langle {100} \right\rangle $位错片段及密度高的1/2$\left\langle {111} \right\rangle $位错片段在抑制裂纹尖端扩展中可能起到主要作用. 图 4d = 3.0 nm, R = 1.5 nm, 位错环与微裂纹扩展的相互作用过程, (a)?(c)分别为46, 75和122.6 ps时的形貌 (a)微裂纹在滑移面上开始扩展的初始阶段; (b)形成以1/2$\left\langle {111} \right\rangle $为主的位错网络阶段; (c)微裂纹沿滑移面扩展导致材料断裂的阶段 Figure4. Interaction between interstitial dislocation loop with radius R = 1.5 nm and micro-crack with distance d = 3.0 nm to loop. (a) to (c) are results at time of 46, 75, and 122.6 ps: (a) The stage at the beginning of crack on slip plane by changing the expansion direction; (b) the state with the formation of dislocation network and 1/2$\left\langle {111} \right\rangle $ segments dominate the network; (c) the final state with crack expansion on slip plane, resulting in the fracture of material.