The effects of chirality and boundary conditions on the mechanical properties of single-walled carbon nanotubes

The effects of chirality and boundary conditions on the elastic properties and buckling behavior of single-walled carbon nanotubes are investigated using atomistic simulations. The influences of the tube length and diameter are also included. It is found that the elastic properties of carbon nanotubes at small deformations are insensitive to the tube chirality and boundary conditions during compression. However, for large deformations occurred upon both compression and bending, the tube buckling behavior is shown to be very sensitive to both tube chirality and boundary conditions. Therefore, while the popular continuum thin shell model can be successfully applied to describe nanotube elastic properties at small deformation such as the Young’s modulus, it cannot correctly account for the buckling behavior. These results may allow better evaluation of nanotube mechanical properties via appropriate atomistic simulations.     

The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials

A nanoscale continuum theory is established to directly incorporate interatomic potentials into a continuum analysis without any parameter fitting. The theory links interatomic potentials and atomic structure of a material to a constitutive model on the continuum level. The theory is applied to study the linear elastic modulus of a single-wall carbon nanotube. The Young's modulus predicted by this nanoscale continuum theory agrees well with prior experimental results and atomistic studies.     

Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction,elastic Poisson's ratio,Young's modulus and yield strength

In this work the relationship between the structural disorder and the macroscopic mechanical behavior of nanoporous gold under uniaxial compression was investigated, using the finite element method. A recently proposed model based on a microstructure consisting of four-coordinated spherical nodes interconnected by cylindrical struts, whose node positions are randomly displaced from the lattice points of a diamond cubic lattice, was extended. This was done by including the increased density as result of the introduced structural disorder. Scaling equations for the elastic Poisson's ratio, the Young's modulus and the yield strength were determined as functions of the structural disorder and the solid fraction. The extended model was applied to identify the elastic–plastic behavior of the solid phase of nanoporous gold. It was found, that the elastic Poisson's ratio provides a robust basis for the calibration of the structural disorder. Based on this approach, a systematic study of the size effect on the yield strength was performed and the results were compared to experimental data provided in literature. An excellent agreement with recently published results for polymer infiltrated samples of nanoporous gold with varying ligament size was found.     

薄壁金属空心球结构压缩力学性能研究

金属空心球结构是一种新型的超轻多孔金属材料。本文对直接堆积和胶合堆积的两球、三球金属空心球列组元进行了单轴准静态压缩实验,分析压缩过程的变形情况,得出其应力/屈曲极限、有效弹性模量、有效应力-应变曲线,并讨论了发生屈服/屈曲的原因。基于实验现象作者提出了三种边界条件,通过分析的方法导出列组元的有效弹性模量公式,其预测值与实验结果较为符合。通过对两种不同堆积模式面组元的压缩实验,研究了金属空心球结构的力学性能和垮塌规律,分析其比刚度和比体积能量吸收值,讨论了两种不同堆积模式的面组元的特点和优越性,发现HC堆积模式具有更好的力学性能。同时对比三球列组元的有效弹性模量发现,SC堆积模式的有效弹性模量只与堆积层数有关。     

Elastic modulus measurements of vertically aligned multi walled carbon nanotubes carpets by using the nanoindentation technique

Electrical, thermal and mechanical properties of Vertically Aligned Multi Walled Carbon NanoTubes (VA-MWCNT) make them an ideal candidate to replace some of conventional materials in micro and nano-electronic components. Integrating this material in micro components requires a good knowledge of their properties. As the electrical and thermal properties, the MWCNT mechanical properties are difficult to assess. Several techniques have been developed to estimate the CNT Young's modulus and the obtained results cover a large range of scale. In this study, we propose an indirect technique for MWCNT carpet Young's modulus measurements by using the nanoindentation technique. Nanoindentation tests are performed on a metallic film deposited on MWCNT. The measured equivalent reduced modulus takes into account the elastic properties of the metallic thin film and those of the MWCNT substrate. Bec et al. model, introduced in 2006, is used to separate elastic properties, and thus determine the MWCNT reduced Young’s modulus which is estimated between 329 and 352 GPa. Knowing the indenter mechanical properties, we estimate the Young’s modulus in the 461 to507 GPa range.     

Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity

The main objective of this paper is to develop a generalized finite element formulation of stress integration method for non-quadratic yield functions and potentials with mixed nonlinear hardening under non-associated flow rule. Different approaches to analyze the anisotropic behavior of sheet materials were compared in this paper. The first model was based on a non-associated formulation with both quadratic yield and potential functions in the form of Hill’s (1948). The anisotropy coefficients in the yield and potential functions were determined from the yield stresses and r-values in different orientations, respectively. The second model was an associated non-quadratic model (Yld2000-2d) proposed by Barlat et al. (2003). The anisotropy in this model was introduced by using two linear transformations on the stress tensor. The third model was a non-quadratic non-associated model in which the yield function was defined based on Yld91 proposed by Barlat et al. (1991) and the potential function was defined based on Yld89 proposed by Barlat and Lian (1989). Anisotropy coefficients of Yld91 and Yld89 functions were determined by yield stresses and r-values, respectively. The formulations for the three models were derived for the mixed isotropic-nonlinear kinematic hardening framework that is more suitable for cyclic loadings (though it can easily be derived for pure isotropic hardening). After developing a general non-associated mixed hardening numerical stress integration algorithm based on backward-Euler method, all models were implemented in the commercial finite element code ABAQUS as user-defined material subroutines. Different sheet metal forming simulations were performed with these anisotropic models: cup drawing processes and springback of channel draw processes with different drawbead penetrations. The earing profiles and the springback results obtained from simulations with the three different models were compared with experimental results, while the computational costs were compared. Also, in-plane cyclic tension–compression tests for the extraction of the mixed hardening parameters used in the springback simulations were performed for two sheet materials.     

复杂应力状态下木材力学性能的数值模拟

针对木材复杂的各向异性材料特点,建立了能反映木材正交各向异性弹性、抗拉和抗压强度不等、抗拉或抗剪时发生脆性破坏而受压时发生塑性变形等特性的本构模型。将木材弹性应力—应变关系简化为正交各向异性;选用Yamada-Sun强度准则来判断木材抗压时是否屈服,抗拉或抗剪时是否发生应变软化;通过引入损伤因子和弹性应变能,建立了木材...     

基于努氏硬度表征大块金属玻璃的力学性能

采用多种载荷对14种大块金属玻璃进行努氏硬度测试,结果表明努氏硬度随载荷的增加而降低,最后趋于稳定,即材料受到正压痕尺寸效应的影响,并利用Meyer定律、弹塑性变形模型、Hays-Kendall模型和比例试样阻力模型对这种现象进行了解释,因此在压痕表面未产生裂纹时应采用较大载荷下趋于稳定的硬度值对杨氏弹性模量E和屈服强...     

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young''s moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young''s moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.     

Stress-Dependent Elastic Behaviour of a Titanium Alloy at Elevated Temperatures

In this study the influence of stress and temperature on the elastic modulus during fully-reversed low cycle fatigue of the titanium alloy Ti6242 is examined. The change of the elastic properties with stress manifests itself in a crescent-like shaped hysteresis loop of stress vs. plastic strain at very low amplitudes, i.e. below the technical yield stress. A quadratic extension of Hooke??s law with a second constant ??k?? is applied. The parameters are determined all along the unloading curve in tension and compression. The approach results in the alignment of the hysteresis loop so that they become vertical, i.e. the elastic strain is accurately described. The value and sign of ??k?? depend on whether the deformation occurs in tension or compression. Like the Young??s modulus E ₀, ??k?? also depends on temperature. At temperatures up to 550°C the values of ??k?? in tension and compression do not change during fatigue life. However, at 650°C thermally activated slip processes lead to changes of both, E ₀ and ??k??.     

Transmission of a screw dislocation across a coherent, non-slipping interface

Current research on nanocrystalline metals and nanoscale multilayer thin films suggests extraordinary plastic strength is due to confinement of slip to individual grains or layers. To assess the magnitude of confinement, a Peierls model of slip transmission of a screw dislocation across a coherent, non-slipping interface is presented. The results reflect that large interfacial barriers to transmission are generated by rapid fluctuations in dislocation line energy near the interface due to elastic modulus mismatch, stacking fault energy mismatch, and antiphase boundary energy for transmission into an ordered phase. Coherency stress is predicted to dramatically alter the dislocation core configuration and impart additional strength regardless of the sign. Contributions to strength are not additive due to nonlinear coupling via the dislocation core configuration. The predicted barrier strength for a coherent (0 0 1) Cu/Ni interface is comparable to atomistic (EAM) results but larger than estimates from hardness data.     

利用材料拉压异必无损检测残余应力的新方法

用实验手段研究了若干种材料在弹性范围内的拉压异性,发现某些材料的拉伸弹性模量与压缩弹必模量相差高达60%,从分析拉压异性产生的机理,描述了拉压导师性材料的应力应变关系,在此基础上提出了一种基于材料拉压异性的残余应力无损检测新方法,并进行了弯曲和扭转残余应力的典型实验,结果证明在某些条件下它是十分有效的,具有简便、精度高的特点。     

Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations

This work is a review of experimental methods for observing and modeling the anisotropic plastic behavior of metal sheets and tubes under a variety of loading paths, such as biaxial compression tests; biaxial tension tests on metal sheets and tubes using closed-loop electrohydraulic testing machines; the abrupt strain path change method for detecting a yield vertex and subsequent yield loci without unloading; in-plane stress reversal tests on metal sheets; and multistage tension tests. Observed material responses are compared with the predictions of phenomenological plasticity models. Special attention is paid to the plastic deformation behavior of materials commonly used in industry, and to verifying the validity of conventional anisotropic yield criteria for those materials and associated flow rules at large plastic strains. The effects of using appropriate anisotropic yield criteria on the accuracy of simulations of forming defects, such as large springback and fracture, are also presented to highlight the importance of accurate material testing and modeling.     

Out-of-plane modulus of semi-auxetic laminates

Materials that possess negative Poisson's ratio are termed “auxetic solids”. The out-of-plane modulus of a laminate consisting of alternating positive and negative isotropic laminas (semi-auxetic laminate) is investigated in this paper. It is herein shown that the use of the inverse rule-of-mixture for obtaining the out-of-plane Young's modulus of a laminate is valid only for conventional laminates and fully auxetic laminates. The Young's modulus by inverse rule-of mixture significantly underestimates the out-of-plane Young's modulus of a semi-auxetic laminate. It is also shown that under certain conditions, the out-of-plane Young's modulus of a semi-auxetic laminate exceeds even the direct rule-of-mixture. A correction term is developed herein for incorporation into the inverse rule-of-mixture.     

Modification of the elastic properties of nanostructures with surface charges in applied electric fields

The influences of applied electric fields and surface charges on elastic modulus of nanostructures such as nanowires and nanofilms are investigated within the framework of classic continuum mechanics. Under an applied electric field, the surfaces of structures are subjected to the electrostatic forces (negative pressure) along the direction of the electric field, and the resulting surface charges also change the surface mechanical properties due to the Hellman–Feynman (H–F) forces. Through incorporating the surface energy from the negative pressure and the H–F forces into surface free energy, the exact and analytical expressions of the effective elastic modulus of nanowires and nanofilms are addressed by considering the surface energy effects on the elastic modulus of nanostructures, which involves the contribution of the applied electric field and surface charges. The numerical results indicate that applied electric fields parallel to the axis of the nanowire and nanofilms enhance the transverse Young's modulus while reducing axial modulus of nanostructures. The effective modulus of nanowires and nanofilms with lateral surface charges depends on the surface charges density and the sign of the charges. In addition, the effect of electric field and surface charges on Young's moduli of nanowires and nanofilms has been found to be sensitive to structural geometric dimensions such as the thickness of the film and the diameter of the wire.     

纳米金属丝拉伸破坏及其应变率效应

建立了适于研究纳米金属快速变形破坏过程的分子动力学模型,并对不同应变率工况下不同截面尺寸单晶镍纳米丝的零温单向拉伸破坏过程进行了分子动力学模拟.模拟得到各种纳米镍丝的应力-应变曲线、屈服应变、屈服强度、断裂强度和初始弹性模量,提出了纳米金属丝快速变形力学性能的应变率效应预测公式并加以验证.计算表明金属纳米丝的屈服应变与尺寸和应变率无关,屈服强度、断裂强度和弹性模量与应变率呈对数关系.     

SHPB试验中岩石试件的端面不平行修正

为研究短圆柱体岩石试件端面不平行对岩石动力学特性测试结果的影响,采用有限元分析软件LS-DYNA对9种端面不平行度和5种杨氏模量的岩石试件开展SHPB(split Hopkinson pressure bar)试验数值模拟,对岩石选用HJC(Holmquist-Johnson-Cook)本构模型。数值模拟结果表明,当端面不平行度在0.40%以内时,端面不平行对动态应力测试结果的影响可忽略不计;但对动态应变测试结果的影响较大。当杨氏模量一定时,平均应变率测试误差和峰值应变测试误差随端面不平行度增大呈线性增大;当端面不平行度一定时,平均应变率测试误差和峰值应变测试误差随杨氏模量增大也呈线性增大。对数值模拟得到的平均应变率测试误差和峰值应变测试误差实施二元线性回归分析,提出了SHPB试验中端面不平行岩石试件平均应变率和峰值应变的修正公式。     

A special mechanical behavior of gels and its micro mechanism

It is found in experiment of gel specimen that the elastic modulus under tension can be 1.6 times of that under compression. In order to explain this phenomenon, a micro model that consists of network and water is proposed. It is assumed that the macromolecular chains can only sustain tensile force but not compression along chains. Based on this constitutive model, the elastic moduli of gels under tension, compression and shear are derived for small strain case. The irregular behavior of gels predicated by this model are consistent with the results of experiment.     

Unstable crack motion is predictable

Yoffe's linear theory of dynamic brittle fracture suggests that crack motion will be unstable beyond ∼70% of the Rayleigh speed, a prediction that is not supported by experiment. We show by atomistic simulations that hyperelasticity, the elasticity of large strains, plays a governing role in the instability dynamics of brittle fracture. A simple, yet remarkable, scaling model based on an effective elastic modulus (the secant modulus at the stability limit) gives successful predictions for the onset speed of the crack instability.