A study of mechanical properties of pure and nitrogen-doped ultrananocrystalline diamond films under various loading conditions

To better understand the mechanical responses of ultrananocrystalline diamond (UNCD) under various loading conditions, a numerical study is performed to investigate the size, loading rate and temperature effects on the material properties of pure and nitrogen-doped UNCD films. Since the UNCD growth mechanism is not completely understood yet, a simple procedure by combining kinetic Monte Carlo and molecular dynamics (MD) methods is developed to form a polycrystalline UNCD block with an artificial grain boundary (GB). By randomly inserting different numbers of nitrogen (N) atoms into the GB of the resulting polycrystalline UNCD films, N-doped UNCD films can be formed. The responses of the simulated pure and N-doped UNCD films with various grain sizes are then investigated by applying displacement-controlled tensile loading under different rates and temperatures in the MD simulations. The simulation results presented in this paper provide a better understanding of the combined size, rate and thermal effects on the material responses of pure and N-doped UNCD films.     

多晶石墨烯拉伸力学性能及其影响因素的灵敏度分析

晶粒尺寸、温度和应变率等对纳米材料的力学性能有重要影响。本文通过分子动力学（MD）数值模拟,分析了不同晶粒尺寸多晶石墨烯在不同温度、拉伸应变率下的杨氏弹性模量、极限应力、极限应变等拉伸力学性能。结果表明,晶粒尺寸、温度和拉伸应变率对拉伸力学性能有较大影响。利用正交实验法,分别分析了杨氏弹性模量、极限应力和极限应变对晶粒尺寸、温度和拉伸应变率的敏感程度。结果表明,杨氏弹性模量和极限应力对影响因素的敏感程度由大到小依次为晶粒尺寸、温度和拉伸应变率;极限应变对影响因素的敏感程度由大到小依次为晶粒尺寸、拉伸应变率和温度。研究结果可为多晶石墨烯的理论研究和工程应用提供参考。     

Mechanical properties of ultrananocrystalline diamond thin films relevant to MEMS/NEMS devices

The mechanical properties of ultrananocrystalline diamond (UNCD) thin films were measured using microcantilever deflection and membrane deflection techniques. Bending tests on several free-standing UNCD cantilevers, 0.5 μm thick, 20 μm wide and 80 μm long, yielded elastic modulus values of 916–959 GPa. The tests showed good reproducibility by repeated testing on the same cantilever and by testing several cantilevers of different lengths. The largest source of error in the method was accurate measurement of film thickness. Elastic modulus measurements performed with the novel membrane deflection experiment (MDE), developed by Espinosa and co-workers, gave results similar to those from the microcantilever-based tests. Tests were performed on UNCD specimens grown by both micro and nano wafer-seeding techniques. The elastic modulus was measured to be between 930–970 GPa for the microseeding and between 945–963 GPa for the nanoseeding technique. The MDE test also provided the fracture strength, which for UNCD was found to vary from 0.89 to 2.42 GPa for the microseeded samples and from 3.95 to 5.03 for the nanoseeded samples. The narrowing of the elastic modulus variation and major increase in fracture strength is believed to result from a reduction in surface roughness, less stress concentration, when employing the nanoseeding technique. Although both methods yielded reliable values of elastic modulus, the MDE was found to be more versatile since it yielded additional information about the structure and material properties, such as strength and initial stress state.     

Three-dimensional local stress analysis on grain boundaries in polycrystalline material

In order to understand the initiation behavior of microstructurally small cracks in a stress corrosion cracking condition, it is important to know the tensile normal stress acting on the grain boundary (normal GB stress). The local stress in a polycrystalline body is enhanced by the inhomogeneity which stems from the shape and orientation of each grain. The stress in a three-dimensional polycrystalline body consisting of 100 grains with random orientation, under a remote uniform tensile stress condition, is evaluated by the finite element method. It was revealed that the local stress on the polycrystalline body is inhomogeneous under uniform applied stress and becomes large at those grain boundaries that are perpendicular to the load axis, though there is large fluctuation. It was also shown that the normal GB stress tends to be large near the triple points due to the deformation constraint caused by adjacent grains. Finally, the maximum stress on the surface of a large component caused by the inhomogeneity was evaluated by using Gumbel statistics.     

Thickness effects in polycrystalline thin films: Surface constraint versus interior constraint

The uniaxial tension behavior of polycrystalline thin films, in which all grain boundaries (GBs) are penetrable by dislocations, is investigated by two-dimensional discrete dislocation dynamics (DDD) method with a penetrable dislocation-GB interaction model. In order to study thickness effect on the tensile strength of thin films with and without surface treatment, three types of thin films are comparatively considered, including the thin films without surface treatment, with surface passivation layers (SPLs) of nanometer thickness and with surface grain refinement zones (SGRZs) consisting of nano-sized grains. Our results show that thickness effects and their underlying dislocation mechanisms are quite distinct among different types of thin films. The thicker thin films without surface treatment are stronger than the thinner ones; however, opposite thickness effects are captured in the thin films with SPLs or SGRZs. Moreover, the underlying dislocation mechanisms of the same thickness effects of thin films with SPLs and SGRZs are different. In the thin films with SPLs, the thickness effect is caused by the sharp increase of dislocation density near the film-passivation interface, while it is mainly due to the sharp decrease of dislocation density within the refined surface grains of the thin films with SGRZs. No matter in what type of thin films, thickness effect gradually disappears when the number of grains in the thickness direction is large enough. Our analysis reveals that general mechanism of those thickness effects lies in the competition between the exterior surface-constraint and interior GB-constraint on gliding dislocations.     

含氢原子缺陷晶界的剪切行为

针对4个α-Fe对称倾斜晶界,采用分子静力学考察了4个晶界中H原子偏析能的分布特征,并采用分子动力学方法研究了晶界内植入不同数量H原子对其在室温条件下剪切行为的影响.H原子通过随机方式植入界面内,利用植入H原子数量与晶界面积的比值来定义H原子面密度ρ.在含H原子晶界剪切行为分析过程中,重点考察了在不同H原子密度ρ下,4个晶界的初始塑性临界应力和晶界迁移位移的变化趋势以及4个晶界在加载过程中的微观变形机理.研究表明:晶界内的H原子偏析能明显偏低,4个晶界附近的H原子会自发向晶界内偏析;随着植入H原子数量的逐渐增多,晶界的初始塑性临界应力和后续变形阶段应力均会降低.晶界内植入H原子会从本质上改变晶界的微观变形机理,进而影响晶界在外载荷条件下的迁移属性.与不含H原子晶界的变形机理对比发现,加载过程中晶界的微结构会发生剧烈的演化,H原子的扩散和团簇化效应会导致晶界内出现纳米孔缺陷.     

Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II

In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of the theory. We demonstrate size effects and the development of strong inhomogeneity in simple shearing of plastically constrained grains. Non-locality in elastic straining leading to a strong Bauschinger effect is analyzed. Low shear strain boundary layers in constrained simple shearing of infinite layers of polycrystalline materials are not predicted by the model, and we justify the result based on an examination of the no-dislocation-flow boundary condition. The time-dependent, spatially homogeneous, simple shearing solution of PMFDM is studied numerically. The computational results and an analysis of continuous dependence with respect to initial data of solutions for a model linear problem point to the need for a nonlinear study of a stability transition of the homogeneous solution with decreasing grain size and increasing applied deformation. The continuous-dependence analysis also points to a possible mechanism for the development of spatial inhomogeneity in the initial stages of deformation in lower-order gradient plasticity theory. Results from thermal cycling of small scale beams/films with different degrees of constraint to plastic flow are presented showing size effects and reciprocal-film-thickness scaling of dislocation density boundary layer width. Qualitative similarities with results from discrete dislocation analyses are noted where possible.We discuss the convergence of approximate solutions with mesh refinement and its implications for the prediction of dislocation microstructure development, motivated by the notion of measure-valued solutions to conservation laws.     

Ab initio LDA+U prediction of the tensile properties of chromia across multiple length scales

Periodic density functional theory (DFT) and DFT+U calculations are used to evaluate various mechanical properties associated with the fracture of chromia (Cr₂O₃) along the [0 0 0 1] and directions. The properties investigated include the tensile strength, elastic constants, and surface energies. The tensile strengths are evaluated using an ideal tensile test, which provides the theoretical tensile strength, and by fitting the calculated data to universal binding energy relationships (UBER), which permit the extrapolation of the calculated results to arbitrary length scales. The results demonstrate the ability of the UBER to yield a realistic estimate of the tensile strength of a 10-μm-thick sample of Cr₂O₃ using data obtained through calculations on nanoscopic systems. We predict that Cr₂O₃ will fracture most easily in the direction, with a best estimate for the tensile strength of 386 MPa for a 10 μm grain, consistent with flexural strength measurements for chromia. The grain becomes considerably stronger at the nanoscale, where we predict a tensile strength along the same direction of 32.1 GPa for 1.45 nm crystallite. The results also provide insight into the origin of the direction dependence of the mechanical properties of Cr₂O₃, with the differences in the behavior along different directions being related to the number of Cr-O bonds supporting the applied tensile load. Additionally, the results shed light on various practical aspects of modeling the mechanical properties of materials with DFT+U calculations and in using UBERs to estimate the mechanical properties of materials across disparate length scales.     

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation

Nanoindentation experiments have shown that microstructural inhomogeneities across the surface of gold thin films lead to position-dependent nanoindentation behavior [Phys. Rev. B (2002), to be submitted]. The rationale for such behavior was based on the availability of dislocation sources at the grain boundary for initiating plasticity. In order to verify or refute this theory, a computational approach has been pursued. Here, a simulation study of the initial stages of indentation using the embedded atom method (EAM) is presented. First, the principles of the EAM are given, and a comparison is made between atomistic simulations and continuum models for elastic deformation. Then, the mechanism of dislocation nucleation in single crystalline gold is analyzed, and the effects of elastic anisotropy are considered. Finally, a systematic study of the indentation response in the proximity of a high angle, high sigma (low symmetry) grain boundary is presented; indentation behavior is simulated for varying indenter positions relative to the boundary. The results indicate that high angle grain boundaries are a ready source of dislocations in indentation-induced deformation.     

Tunable band structures of polycrystalline graphene by external and mismatch strains

Lacking a band gap largely limits the application of graphene in electronic devices. Previous study shows that grain boundaries (GBs) in polycrystalline graphene can dramatically alter the electrical properties of graphene. Here, we investigate the band structure of polycrystalline graphene tuned by externally imposed strains and intrinsic mismatch strains at the GB by density functional theory (DFT) calculations. We found that graphene with symmetrical GBs typically has zero band gap even with large uniaxial and biaxial strain. However, some particular asymmetrical GBs can open a band gap in graphene and their band structures can be substantially tuned by external strains. A maximum band gap about 0.19 eV was observed in matched-armchair GB (5, 5) | (3, 7) with a misorientation of θ = 13° when the applied uniaxial strain increases to 9%. Although mismatch strain is inevitable in asymmetrical GBs, it has a small influence on the band gap of polycrystalline graphene.     

晶粒数量对多晶集合体初始各向异性的影响

Taylor类多晶晶体粘塑性模型被用于研究晶粒数量对随机分布多晶体拉伸塑性各向异性的影响。分别沿包含不同晶粒数量的多晶集合体的各方向进行单向拉伸数值模拟实验，得到多晶集合体各方向在一定等效应变下的等效应力，并用云图和等高线表示在多晶体的参考球面上。定义了描述多晶集合体各向异性程度的参考指标。讨论了三种确定晶体随机取向的方法。计算结果表明：晶粒数量有限的多晶集合体的应力应变响应仍有一定的各向异性，且随着晶粒数量增多，多晶集合体的各向异性程度降低；就所包含晶粒数相同的多晶集合体来说，在确定晶粒随机取向时，选取不同的方法对它的各向异性程度也有一定的影响。     

A Sequential Tensile Method for Rapid Characterization of Extreme-value Behavior in Microfabricated Materials

A high-throughput sequential tensile test method has been developed to characterize the fracture strength distribution of microfabricated polycrystalline silicon, the primary structural material used in microelectromechanical systems (MEMS). The resulting dataset of over 1,000 microtensile tests reveals subtle extreme-value behavior in the tails of the distribution, demonstrating that the common two-parameter Weibull distribution is inferior to a three-parameter Weibull model. The results suggest the existence of a cut-off or threshold stress (1.446 GPa for this particular material) below which tensile failure will not occur. The existence of a cut-off stress suggests that the material’s flaw size distribution and toughness distribution are both also bounded. From an application perspective, the cut-off stress provides a statistically-sound basis for reliable design. While the sequential method is demonstrated here for tensile strength distributions in polycrystalline silicon MEMS, the technique could be extended to a wide range of mechanical tests (bending strength, elastic modulus, fracture toughness, creep, etc.) for both microsystem and conventional materials.     

Micromechanics of substrate-supported thin films

The mechanical properties of metallic thin films deposited on a substrate play a crucial role in the performance of micro/nano-electromechanical systems (MEMS/NEMS) and flexible electronics. This article reviews ongoing study on the mechanics of substrate-supported thin films, with emphasis on the experimental characterization techniques, such as the rule of mixture and X-ray tensile testing. In particular, the determination of interfacial adhesion energy, film deformation, elastic properties and Bauschinger effect are discussed.     

A two-dimensional dislocation dynamics model of the plastic deformation of polycrystalline metals

Two-dimensional dislocation dynamics (2D-DD) simulations under fully periodic boundary conditions are employed to study the relation between microstructure and strength of a material. The material is modeled as an elastic continuum that contains a defect microstructure consisting of a preexisting dislocation population, dislocation sources, and grain boundaries. The mechanical response of such a material is tested by uniaxially loading it up to a certain stress and allowing it to relax until the strain rate falls below a threshold. The total plastic strain obtained for a certain stress level yields the quasi-static stress-strain curve of the material. Besides assuming Frank-Read-like dislocation sources, we also investigate the influence of a pre-existing dislocation density on the flow stress of the model material. Our results show that - despite its inherent simplifications - the 2D-DD model yields material behavior that is consistent with the classical theories of Taylor and Hall-Petch. Consequently, if set up in a proper way, these models are suited to study plastic deformation of polycrystalline materials.     

On the Generation of Discrete Isotropic Orientation Distributions for Linear Elastic Cubic Crystals

We consider a model for the elastic behavior of a polycrystalline material based on volume averages. In this case the effective elastic properties depend only on the distribution of the grain orientations. The aggregate is assumed to consist of a finite number of grains each of which behaves elastically like a cubic single crystal. The material parameters are fixed over the grains. An important problem is to find discrete orientation distributions (DODs) which are isotropic, i.e., whose Voigt and Reuss averages of the grain stiffness tensors are isotropic. We succeed in finding isotropic DODs for any even number of grains N≥4 and uniform volume fractions of the grains. Also, N=4 is shown to be the minimum number of grains for an isotropic DOD. This revised version was published online in August 2006 with corrections to the Cover Date.     

Q345钢和H62黄铜声发射信号及力学行为的关系研究

本文利用声发射装置采集了Q345钢和H62黄铜两种材料拉伸过程中的动态声信号。结果发现两种材料在线弹性阶段末端都会产生大量声发射信号,但有明显屈服流动的Q345钢在硬化阶段的开始时段也会产生信号峰值。为了研究两种材料在拉伸变形过程中声发射的微观机制,本文采用扫描电镜下原位拉伸实验方式观察了两种材料在不同拉应力下晶粒内部滑移线的产生和演变过程。在此基础上总结出了两种材料声发射信号与力学行为的关系,指出应以第一次声发射信号的峰值对应的工作应力作为材料屈服应力及其合理性,并按此标准给出H62黄铜的屈服应力为193MPa。     

随机晶界分布对铝多晶材料晶间破坏行为的影响

采用二维随机有限元方法研究了准静态拉伸载荷下细观随机不均匀的粗晶粒铝多晶试件晶间破坏的力学行为．探讨了随机晶界的数量和分布对材料断裂性能的影响。     

Defect redistribution within a continuum grain boundary plasticity model

The mechanical response of polycrystalline metals is significantly affected by the behaviour of grain boundaries, in particular when these interfaces constitute a relatively large fraction of the material volume. One of the current challenges in the modelling of grain boundaries at a continuum (polycrystalline) scale is the incorporation of the many different interaction mechanisms between dislocations and grain boundaries, as identified from fine-scale experiments and simulations. In this paper, the objective is to develop a model that accounts for the redistribution of the defects along the grain boundary in the context of gradient crystal plasticity. The proposed model incorporates the nonlocal relaxation of the grain boundary net defect density. A numerical study on a bicrystal specimen in simple shear is carried out, showing that the spreading of the defect content has a clear influence on the macroscopic response, as well as on the microscopic fields. This work provides a basis that enables a more thorough analysis of the plasticity of polycrystalline metals at the continuum level, where the plasticity at grain boundaries matters.     

Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis

The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.     

Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

A mechanism-based constitutive model is presented for the inelastic deformation and fracture of ceramics. The model comprises four essential features: (i) micro-crack extension rates based on stress-intensity calculations and a crack growth law, (ii) the effect of the crack density on the stiffness, inclusive of crack closure, (iii) plasticity at high confining pressures, and (iv) initial flaws that scale with the grain size. Predictions of stress/strain responses for a range of stress states demonstrate that the model captures the transition from deformation by micro-cracking at low triaxiality to plastic slip at high triaxialities. Moreover, natural outcomes of the model include dilation (or bulking) upon micro-cracking, as well as the increase in the shear strength of the damaged ceramic with increasing triaxiality. Cavity expansion calculations are used to extract some key physics relevant to penetration. Three domains have been identified: (i) quasi-static, where the ceramic fails due to the outward propagation of a compression damage front, (ii) intermediate velocity, where an outward propagating compression damage front is accompanied by an inward propagating tensile (or spallation) front caused by the reflection of the elastic wave from the outer surface and (iii) high velocity, wherein plastic deformation initiates at the inner surface of the shell followed by spalling within a tensile damage front when the elastic wave reflects from the outer surface. Consistent with experimental observations, the cavity pressure is sensitive to the grain size under quasi-static conditions but relatively insensitive under dynamic loadings.