Diffusion anisotropy and void development under cascade irradiation

Cascade irradiation of metals gives rise to swelling as a result of the creation of voids and the evolution of the void ensemble. Under suitable circumstances, the originally disordered void distribution transforms into to a void lattice. As demonstrated previously, the understanding of the evolution and the unique features of the void ensemble requires a difference in the anisotropy of the diffusion (DAD) of vacancies and self-interstitial atoms (SIAs), which is achieved by one-dimensional diffusion of the SIAs. On the other hand, void swelling has been successfully modeled in terms of three-dimensional diffusion of both vacancies and SIAs. In the present paper it is shown that these seemingly contradicting interpretations and all related observations can be quantitatively reconciled by a small DAD created by only ～1% of SIAs diffusing one-dimensionally. It is also demonstrated that at the initial stage of void-lattice formation, ordering occurs mainly on close-packed crystal planes, which is in contrast to the naïve expectation that one-dimensional diffusion of SIAs should result in a void ordering along close-packed directions. Finally it is found that, in the case of a small DAD, voids annihilate via stochastic shrinkage much faster than by coalescence. This falsifies the argument in the literature that one-dimensional diffusion of SIAs would necessarily lead to the coalescence of voids and destabilization of the void lattice.     

Simulations of the effects of 1-d interstitial diffusion on void lattice formation during irradiation

This paper describes the use of simulation techniques to examine some of the processes involved in the alignment of voids under the influence of one-dimensional self interstitial atom (1-d SIA) transport. The work follows the paper of Heinisch and Singh on this topic but a different and simpler methodology is used. Besides repeating the scenarios studied by Heinisch and Singh, the effects of re-nucleation and the influence of vacancies have been introduced. One of the important processes that emerged from the results was the barrier to precise void alignment caused by the SIA-induced coalescence of aligned voids. This appears to prevent the formation of stable void lattices by any 1-d SIA transport mechanism, a point supported by the initial void alignment in the mechanism requiring swelling values well above those found experimentally. A full consideration of the void lattice phenomenon shows that the one-dimensional diffusion of self-interstitials central to the production bias model of irradiation damage cannot be the only mode of anisotropic diffusion available under irradiation.     

A study of void size growth in nonequilibrium stochastic systems of point defects

We study properties of voids growth dynamics in a stochastic system of point defects insolids under nonequilibrium conditions (sustained irradiation). It is shown thatfluctuations of defect production rate (external noise) increase the critical void radiuscomparing to a deterministic system. An automodel regime of void size growth in astochastic system is studied in detail. Considering a homogeneous system, it is found thatexternal noise does not change the universality of the void size distribution function;the mean void size evolves according to classical nucleation theory. The noise increasesthe mean void size and spreads the void size distribution. Studying dynamics of spatiallyextended systems it was shown that vacancies remaining in a matrix phase are able toorganize into vacancy enriched domains due to an instability caused by an elastic latticedeformation. It is shown that dynamics of voids growth is defined by void sinks strengthwith void size growth exponent varying from 1/3 up to 1/2.     

Stochastic void coarsening

The random nature of diffusing jumps and cascade occurrence produce stochastic fluctuations of the point-defect fluxes. The effect of such fluctuations on the kinetics of void growth is investigated in the present paper. It is found that the non-linear coupling between the stochastic fluctuations and the void sizes may lead to the instability of void evolution within the mean-field theory, when the sizes of voids and their growth rates are both relatively small. The growth rate of voids becomes dominated by the stochastic component, causing the smaller voids to shrink away. This effect is investigated in terms of a non-equilibrium phase transition induced by a purely random stochastic noise. The derived conditions for this non-equilibrium transition are compared favourably with experimental observations. Received: 5 June 2000 / Accepted: 9 October 2000 / Published online: 21 March 2001     

Effects of hydrogen and impurities on void nucleation in copper: simulation point of view

The mechanisms of hydrogen influence on vacancy cluster formation in copper are studied using numerical simulations. Vacancy agglomeration in clusters larger than divacancies is found to be energetically favourable, but in pure copper the cluster creation is prevented by the lack of binding between single vacancies. Hydrogen dissolved in the lattice readily accumulates in vacancy-type defects, changing their properties. A single vacancy can accommodate up to six hydrogen atoms. Hydrogen stabilizes divacancies and promotes vacancy cluster nucleation. In larger vacancy clusters, accumulated hydrogen prevents cluster collapse into stacking fault tetrahedra. In small voids, hydrogen prefers to remain in atomic form at the void surface, but when voids become sufficiently large, hydrogen molecules in the void interior can also be formed. Some common impurities in copper (O, S, P and Ag) contribute to void formation by capturing vacancies in their vicinity. In contrast, substitutional Ni has little effect on vacancy clustering but tends to capture interstitial hydrogen.     

强激光辐照下孔洞尺寸对铁相变过程的影响

 利用分子动力学模拟研究了完美单晶铁以及含不同尺寸孔洞的单晶铁相变过程,分析了孔洞尺寸对相变过程的影响。模拟结果表明：孔洞的存在降低了相变的阈值应力,加速了相变区域成核速率和相变传播速率;随着孔洞直径的增大,相变的阈值应力逐渐降低;孔洞也改变了相变的初始成核区域,使相变区域呈现出一个蝴蝶状的形貌;孔洞反射的稀疏波对相变成核区域的影响随孔洞体积增大而增大,导致孔洞周围出现大量的无序结构原子;孔洞体积对相变的影响也体现在了粒子速度空间分布上,压缩过程中孔洞周围出现的大量“热点”导致了更低的粒子速度空间分布。     

高应变率压缩下纳米孔洞对金属铝塑性变形的影响研究

本文利用分子动力学模拟方法研究了含纳米孔洞金属铝在[110]晶向高应变率单轴压缩下弹塑性变形的微观过程. 对比单孔洞和完整单晶的模型, 讨论了多孔金属的应力应变关系及其位错发展规律. 研究结果表明, 对于多孔模型的位错积累过程, 位错密度随应变的增加可大致分为两个线性阶段. 由同一个孔洞生成的位错在相互靠近过程中, 其滑移速度越来越小; 随着位错继续滑移, 源自不同孔洞的位错之间开始交叉相互作用导致应变硬化. 达到流变峰应力之后又由于位错密度增殖速率升高发生软化. 当应变增加到11.8%时, 所有孔洞几乎完全坍缩, 并观察到在此过程中有棱位错生成.     

Phase-field modeling of void evolution and swelling in materials under irradiation

Void swelling is an important phenomenon observed in both nuclear fuels and cladding materials in operating nuclear reactors. In this work we develop a phase-field model to simulate void evolution and void volume change in irradiated materials. Important material processes, including the generation of defects such as vacancies and self-interstitials, their diffusion and annihilation, and void nucleation and evolution, have been taken into account in this model. The thermodynamic and kinetic properties, such...     

Unlimited damage accumulation in metallic materials under cascade-damage conditions

Most experiments on neutron or heavy-ion cascade-produced irradiation of pure metals and metallic alloys demonstrate unlimited void growth as well as development of the dislocation structure. In contrast, the theory of radiation damage predicts saturation of void size at sufficiently high irradiation doses and, accordingly, termination of accumulation of interstitial-type defects. It is shown in the present paper that, under conditions of steady production of one-dimensionally (1-D) mobile clusters of self-interstitial atoms (SIAs) in displacement cascades, any one of the following three conditions can result in indefinite damage accumulation. First, if the fraction of SIAs generated in the clustered form is smaller than some finite value of the order of the dislocation bias factor. Second, if solute, impurity or transmuted atoms form atmospheres around voids and repel the SIA clusters. Third, if spatial correlations between voids and other defects, such as second-phase precipitates or dislocations, exist that provide shadowing of voids from the SIA clusters. The driving force for the development of such correlations is the same as for void lattice formation and is argued to be always present under cascade-damage conditions. It is emphasised that the mean-free path of 1-D migrating SIA clusters is typically at least an order of magnitude longer than the average distance between microstructural defects; hence, spatial correlations on the same scale should be taken into consideration. A way of developing a predictive theory is discussed. An interpretation of the steady-state swelling rate of ～1%/displacement per atom (dpa) observed in austenitic steels is proposed.     

Void formation in Nickel during high temperature proton irradiation

Pure Ni foils, doped with He from 0 to 28 appm, were irradiated with protons at temperatures in the range 0.3–0.6 T_m (T_m = melting point in °K) and void formation was studied. The influence of He doping, irradiation temperature and alloying were investigated. For constant He content and proton fluence, void number density and swelling are maximum at about 400°C, while the void size increases with temperature. Most voids are octahedral in shape with no sign of truncation. Helium is required to nucleate voids, and lowering the stacking fault energy by alloying suppresses void formation completely. Present results suggest that void nucleation is inhomogeneous. Some implications of these findings are discussed.     

Fe-Cr合金辐照空洞微结构演化的相场法模拟

Fe-Cr合金作为包壳材料在高温高辐照强度等极端环境下服役,产生空位和间隙原子等辐照缺陷,辐照缺陷簇聚诱发空洞、位错环等缺陷团簇,引起辐照肿胀、晶格畸变,导致辐照硬化或软化致使材料失效.理解辐照缺陷簇聚和长大过程的组织演化,能更有效调控组织获得稳定服役性能.本文采用相场法研究Fe-Cr合金中空洞的演化,模型考虑了温度效应对点缺陷的影响以及空位和间隙的产生和复合.选择400—800 K温度区间、0—16 dpa辐照剂量范围的Fe-Cr体系为对象,研究在不同服役温度和辐照剂量下的空位扩散、复合和簇聚形成空洞的过程.在400—800 K温度区间,随着温度的升高,Fe-Cr合金空洞团簇形核率呈现出先升高后下降的趋势.考虑空位与间隙的重新组合受温度的影响可以很好地解释空洞率随温度变化时出现先升高后降低的现象.由于温度的变化将影响Fe-Cr合金中原子离位阀能,从而影响产生空位和间隙原子.同一温度下,空洞半径和空洞的体积分数随辐照剂量的增大而增大.辐照剂量的增大,级联碰撞反应加强,空位与间隙原子大量产生,高温下空位迅速的扩散聚集在Fe-Cr合金中将形成更多数量以及更大尺寸的空洞.     

Void formation in irradiated Nickel 270

Nickel 270 (99.98 per cent nominal purity) was irradiated in EBR-II to fluences ranging from 1 × 10¹⁸ to 1.5 × 10²² neutrons/cm² at temperatures between 375 and 525°C. Voids were observed in all specimens in concentrations of 1 to 3 × 10¹⁴/cm³, independent of temperature and fluence. At low fluences the voids were non-homogeneously distributed. These observations are interpreted in terms of void nucleation on sites existing in the material prior to irradiation. The results are compared with other observations on nickel of comparable and higher purity. Large differences exist not only in the magnitude of void concentrations but also in temperature and fluence dependencies. These differences indicate that a single, void nucleation mechanism is not operative and that impurities play an important role in determining the nature and amount of damage produced by neutron irradiation at elevated temperatures.     

Atomic collision cascades on void evolution in vanadium

Molecular dynamics simulations were performed to study void evolution subject to unidirectional self-bombardment and radiation-induced variation of mechanical properties in single crystalline vanadium. 3D simulation cells of perfect body-centered cubic (BCC) vanadium, as well as those with one, two, four, and six voids, were investigated. For the no void case, the maximum number of defects, maximum volumetric swelling, and the number of defects left in bulk after a sufficiently long recovery period increased with higher primary recoil energy. For the cases containing voids, a primary recoil energy was carefully assigned to an atom so as to initiate a dense collision spike in the voids center, where some self-interstitial atoms gained kinetic energy by secondary replacement collision sequence traveling along the ? 111? direction. It is found that the larger or the greater the number of voids contained initially in the box, the larger the normalized void volume, and the smaller the volumetric swelling after sufficient recovery of systems. In the single void case, the void became elongated along the bombarding direction; in the multiple void cases, the voids coalesced only when the intervoid ligament distance was short. After sufficient relaxation of the irradiated specimen, a hydrostatic tension was exerted on the box, where the voids were treated as dislocation sources. It is shown that with higher primary recoil energy, the yield stress dropped in cases with smaller or fewer voids but rose in those with larger or greater number of voids. This radiation-induced softening to hardening transition with increasing dislocation density can be attributed to the combined effects of the defect-induced dislocation nucleation and the resistance of defects to dislocation motion. Moreover, as the primary recoil energy increased, the ductility of vanadium in the no void case decreased, but was only slightly changed in the cases containing void.     

Effect of voids and pressure on melting of nano-particulate and bulk aluminum

Molecular dynamics simulations are performed using isobaric–isoenthalpic (NPH) ensembles to study the effect of internal defects in the form of voids on the melting of bulk and nano-particulate aluminum in the size range of 2–9 nm. The main objectives are to determine the critical interfacial area required to overcome the free energy barrier for the thermodynamic phase transition, and to explore the underlying mechanisms for defect-nucleated melting. The inter-atomic interactions are captured using the Glue potential, which has been validated against the melting temperature and elastic constants for bulk aluminum. A combination of structural and thermodynamic parameters, such as the potential energy, Lindemann index, translational-order parameter, and radial-distribution functions, are employed to characterize the melting process. The study considers a variety of void shapes and sizes, and results are compared with perfect crystals. For nano aluminum particles smaller than 9 nm, the melting temperature is size dependent. The presence of voids does not impact the melting properties due to the dominancy of nucleation at the surface, unless the void size exceeds a critical value beyond which lattice collapse occurs. The critical void size depends on the particle dimension. The effect of pressure on the particulate melting is found to be insignificant in the range of 1–300 atm. The melting behavior of bulk aluminum is also examined as a benchmark. The critical interfacial area required for the solid–liquid phase transition is obtained as a function of the number of atoms considered in the simulation. Imperfections such as voids reduce the melting point. The ratio between the structural and thermodynamic melting points is 1.32. This value is comparable to the ratio of 1.23 for metals like copper.     

基于孔洞体胞模型铸造镁合金ML308的本构方程

铸造镁合金不可避免地包含许多微孔洞,这些微孔洞在材料的后续加工及服役过程中将发生演化,并对材料的力学行为产生重要影响.基于球形孔洞体胞模型,提出微孔洞长大及形核方程,它们构成微孔洞的演化方程.根据孔洞演化将造成材料性质弱化的物理机制,将微孔洞演化以弱化函数的形式引入到非经典弹塑性本构方程,得到考虑孔洞演化的铸造镁合金弹塑性本构方程.发展与本构方程相应的有限元数值分析程序,用其模拟了铸造镁合金ML308的微孔洞演化及力学行为,计算结果与实验结果符合较好. 关键词： 铸造镁合金 孔洞体胞模型 孔洞演化方程 本构方程     

Multiscale simulations of damage of perfect crystal Cu at high strain rates

We use the molecular dynamics code, large-scale atomic/molecular massively parallel simulator (LAMMPS), to simulate high strain rate triaxial deformation of crystal copper to understand void nucleation and growth (NAG) within the framework of an experimentally fitted macroscopic NAG model for polycrystals (also known as DFRACT model). It is seen that void NAG at the atomistic scales for crystal copper (Cu) has the same qualitative behaviour as the DFRACT model, albeit with a different set of parameters. The effect of material temperature on the nucleation and growth of voids is studied. As the temperature increases, there is a steady decrease in the void NAG thresholds and close to the melting point of Cu, a double-dip in the pressure–time profile is observed. Analysis of this double-dip shows disappearance of the long-range order due to the creation of stacking faults and the system no longer has a face centred cubic (fcc) structure. Molecular dynamics simulation of shock in crystal Cu at strain rates high enough to cause spallation of crystal Cu are then carried out to validate the void NAG parameters. We show that the pre-history of the material affects the void nucleation threshold of the material. We also simulate high-strain-rate triaxial deformation of crystal Cu with defects and obtain void NAG parameters. The parameters are then used in a macroscale hydrodynamic simulation to obtain spallation threshold of realistic crystal Cu. It is seen that our results match experimental results within the limit of 20% error.     

强冲击载荷下含杂质的纯铝中微孔洞长大的动力学行为

采用LS-DYNA瞬态动力学有限元程序,对平板撞击加载下含初始杂质的纯铝样品中微孔洞的成核与长大进行了数值模拟。结果表明:微孔洞首先在杂质与基体的边界处成核,随后在局部严重塑性变形驱动下快速线性增长;微孔洞半径的增长速率与冲击加载强度两者之间近似成线性关系;材料屈服强度和初始杂质的大小对微孔洞相对的增长速率有明显的影响;当微孔洞长大阈值取屈服强度的3.5倍时,数值仿真结果与理论分析结果基本一致,这有助于进一步认识孔洞长大的动力学行为。     

Improbability of void growth in aluminum via dislocation nucleation under typical laboratory conditions

The rate at which dislocations nucleate from spherical voids subjected to shear loading is predicted from atomistic simulation. By employing the latest version of the finite temperature string method, a variational transition state theory approach can be utilized, enabling atomistic predictions at ordinary laboratory time scales, loads, and temperatures. The simulation results, in conjunction with a continuum model, show that the deformation and growth of voids in Al are not likely to occur via dislocation nucleation under typical loadings regardless of void size.