Rippling and a phase-transforming mesoscopic model for multiwalled carbon nanotubes

We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated by experimental observations and large-scale atomistic-based simulations. The model is analyzed, validated against large-scale simulations, and exercised in examples of interest. It is shown that modelling MWCNTs as linear elastic beams can result in poor approximations that overestimate the elastic restoring force considerably, particularly for thick tubes. In contrast, the proposed model produces very accurate predictions both of the restoring force and of the phase pattern. The size effect in the bending response of MWCNTs is also discussed.     

A relaxation method for the energy and morphology of grain boundaries and interfaces

The energy density of crystal interfaces exhibits a characteristic “cusp” structure that renders it non-convex. Furthermore, crystal interfaces are often observed to be faceted, i.e., to be composed of flat facets in alternating directions. In this work, we forge a connection between these two observations by positing that the faceted morphology of crystal interfaces results from energy minimization. Specifically, we posit that the lack of convexity of the interfacial energy density drives the development of finely faceted microstructures and accounts for their geometry and morphology. We formulate the problem as a generalized minimal surface problem couched in a geometric measure-theoretical framework. We then show that the effective, or relaxed, interfacial energy density, with all possible interfacial morphologies accounted for, corresponds to the convexification of the bare or unrelaxed interfacial energy density, and that the requisite convexification can be attained by means of a faceting construction. We validate the approach by means of comparisons with experiment and atomistic simulations including symmetric and asymmetric tilt boundaries in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. By comparison with simulated and experimental data, we show that this simple model of interfacial energy combined with a general microstructure construction based on convexification is able to replicate complex interfacial morphologies, including thermally induced morphological transitions.     

Deformation of plastically compressible hardening-softening-hardening solids

Motivated by a model of the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the deformation of a class of compressible elastic-viscoplastic solids with a hardening-softening-hardening variation of flow strength with plastic strain. In previous work (Hutchens et al. 2011) a constitutive relation was presented and used to model the response of VACNT pillars in axisymmetric compression. Subsequently, it was found that due to a programming error the constitutive relation presented in the paper (Hutchens et al. 2011) was not the one actually implemented. In particular, the plastic flow rule actually used did not satisfy plastic normality. Here, we present the constitutive formulation actually implemented in the previous work (Hutchens et al. 2011). Dynamic, finite deformation, finite element calculations are carried out for uniaxial compression, uniaxial tension and for indentation of a "half-space" by a conical indenter tip. A sequential buckling-like deformation mode is found in com- pression when there is plastic non-normality and hardening-softening-hardening. The same material characterization gives rise to a Lüders band-like deformation mode in ten- sion. When there is a deformation mode with a sharp front along mesh boundaries, the overall stress-strain response contains high frequency oscillations that are a mesh artifact. The responses of non-softening solids are also analyzed and their overall stress-strain behavior and deformationmodes are compared with those of hardening-softening- hardening solids. We find that indentation with a sharp in- denter tip gives a qualitatively equivalent response for hardening and hardening-softening-hardening solids.     

纯钼烧结体压缩变形本构模型建立

基于可压缩连续材料的屈服准则和塑性本构关系,推导了粉末烧结材料的压缩变形屈服条件,采用真空烧结技术制备了不同密度的钼,通过在MTS810实验机上进行单向压缩试验,研究了在不同的初始密度,变形温度和应变速率的条件下,纯钼烧结休压缩变形流变应力的变化规律.建立了其流变应力的经验回归模型,进而确定了纯钼烧结材料压缩变形的屈服...     

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress-strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading-reloading cycles are presented.     

铝蜂窝结构单向压缩、失稳和破坏机制研究

采用结构代表胞元模型数值模拟了在没相对密度范围的单型铝蜂窝结构在单向压缩过程中的变形、失稳和破坏现象。我们推广了转角刚度方法,并结合数值模拟结果分析了结构失稳和破坏的三种不同特征及相应 拗观力学机制,计算了结构代表胞元开始失稳分岔时的宏观应力σT,其值与有限元数值计算和实验得到的结构宏观极限应力σu一致吻合。     

纳米晶钽在单向拉伸载荷下的分子动力学模拟

利用分子动力学方法模拟了纳米晶钽在单轴拉伸载荷作用下的微观结构演化情况. 结果表明纳米晶钽在塑性变形过程中可以发生从BCC到FCC, HCP结构的应力诱导相变. FCC 结构原子百分比的最大值和试样的抗拉强度成线性关系,据此可推出一个相变发生的临界应 力值. 应变率越大,相变滞后于应力越严重. 当应变达到一定值时,试样会发生晶间断裂现 象,定量分析发现纳米晶钽晶间裂纹初始形成应变不受平均晶粒尺寸的影响,而与应变率和 模拟温度有着密切的关系.     

Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals

The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out for uniaxial plane strain compression of a single crystal block and for uniform pure bending of a single crystal foil. The compressed block has loading surfaces that are penetrable or impenetrable to dislocations. This allows for a study of the two types of higher-order boundaries available, and a significant effect of higher-order boundary conditions on the overall deformation mode of the block is observed. The bent foil has free surfaces through which dislocations can go out of the material, and we observe a strong size-dependent mechanical response resulting from the surface condition assumed.     

A cellular automaton model for a bridge traffic bottleneck

A cellular automaton (CA) model is proposed in this paper to analyze a bridge traffic bottleneck. The simulation results with this model show that there are several phase transitions in the traffic average density, velocity and flow for each lane under a periodic boundary condition. An unstable phase in the traffic average density and velocity for the upstream and downstream lanes of the bridge is shown in a range of initial traffic densities. The critical points of the phase transitions and the phenomenon of the unstable phase found in the simulation are also explained with the mean-field theory.The project supported by the National Natural Science Foundation of China(70371067 and 10347001), the Key Project of Chinese Ministry of Education(02115) and the New Century Talent Plan of Guangxi Province in China(2001204).The English text was polished by Ron Marshall.     

The multi-axial deformation behavior of bulk metallic glasses at high homologous temperatures

In this work, we study the behavior of a recently-developed Lanthanum-based bulk metallic glass under uniaxial and multi-axial stress-states using the constitutive model developed by Thamburaja and Ekambaram (2007). The material parameters in the constitutive model are fitted to match the stress–strain responses obtained from a set of simple compression experiments conducted at temperatures within the supercooled liquid region under a variety of strain rates spanning approximately three decades. With the material parameters calibrated, we show that the aforementioned constitutive model is able to accurately predict the force vs. displacement responses of representative experiments conducted under multi-axial stress-states at temperatures within the supercooled liquid region, namely three-point bending and the superplastic forming of a miniature gear component. In particular, the evolution of the specimen geometry during the deformation under multi-axial loading conditions are also well-predicted by the constitutive model.     

Effect of inner gas pressure on the elastoplastic behavior of porous materials: A second-order moment micromechanics model

A new micromechanics model based on the second-order moment of stress is established to investigate the effect of gas pressure on the nonlinear macroscopic constitutive relationship of the porous materials. The analytical method agrees well with numerical simulation based on the finite element method. Through a systematic study, we find that the gas pressure has a prominent effect on the nonlinear deformation behavior of the porous materials. The gas pressure can cause tension–compression asymmetry on the uniaxial stress–strain curve and the nominal Poisson’s ratio. The pore pressure significantly reduces the initial yield strength and failure strength of the porous metals, especially when the relative density of the material is small. The gas phase also strongly compromises the composite strength when the temperature is increased. The model may be useful for the evaluation of mechanical integrity of porous materials under various working conditions and working temperatures.     

泡沫铝的单向力学行为

本文对不同孔径的开孔泡沫铝材料的单向拉伸性能和单向压缩性能进行了研究,揭示了泡沫铝材料的变形机理,并且发现相对密度不是确定材料力学属性的唯一参数,孔径大小对材料的力学性能也有一定的影响。基于实验数据,我们讨论了材料的宏观力学性能和微观结构的联系,并利用Ramberg-Osgood模型描述了材料的单轴拉伸一维应力应变关系。     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

闭孔泡沫金属变形模式的有限元分析

运用有限元软件ABAQUS/Explicit模拟了三维Voronoi闭孔泡沫金属在不同的冲击速度下的变形行为。随着冲击速度的提高,得到了3种变形模式:准静态均匀模式、过渡模式和冲击模式,并以相对密度和冲击速度为坐标建立了变形模式图。引入应力均匀性指标和变形局部化指标,确定了模式转化的临界速度,并与已有的冲击速度预测公式进行了比较。根据临界速度的数值和理论结果,提出了一种确定锁定应变的方案,结果介于压实应变和完全密实应变之间。     

Four-Point Bending Test of Determining Stress-Strain Curves Asymmetric between Tension and Compression

A method of determining both uniaxial tension and compression stress-strain curves from the result of a single four-point bending test was demonstrated. Stress-strain curves of magnesium showing tension-compression asymmetry due to twinning deformation and those of an S45C steel due to the Bauschinger effect were calculated. The Mayville-Finnie equation was modified slightly for this calculation. The calculation is sensitive to small change in the slope of bending curve, revealing an aspect of inverse problem.     

Large Deformation of Nitinol Under Shear Dominant Loading

Full-field quantitative strain maps of phase transformation and plasticity in Nitinol under large shear-dominated deformation are presented. To achieve a shear-dominated deformation mode with relatively uniform stresses and strains, a shear compression specimen (SCS) geometry was utilized. Shear deformation appears to impede the development of the strain localization during phase transformation that is seen in uniaxial testing. The shear-dominant deformation of Nitinol in the plastic regime exhibits low hardening and results in the development of significant strain inhomogeneity.     

A non-linear viscoelastic model for ceramics at high temperatures

High-temperature mechanical behavior of ceramics is characterized by non-linear rate dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to rupture. Moreover, rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the non-linear, asymmetric time-dependent behavior, a new non-linear viscoelastic model is proposed. Non-linearity and asymmetry are introduced in the volumetric component. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Non-linear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of rupture lives. Numerical simulation results compare well with results of four-point bending experiments.     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

A continuum model for intermittent deformation of single crystal micropillars

Strain bursts are often observed during compression tests of single crystal micropillars. In this work, we formulate a new continuum model that accounts for the strain bursts within the framework of crystal plasticity. The strain bursts are separated from the loading stage (nearly elastic loading) by introducing a dimensionless constant in the continuum model, and are detected by load serrations. The boundary conditions in the context of micropillar compression are studied and they are shown to be changing and unpredictable as plastic deformation proceeds. To evaluate the validity of our model, finite element simulations of the uniaxial compression tests on nickel micropillars are performed. Our simulations produce clearly visible strain bursts during the plastic flow and the produced intermittent flows are comparable with the experimental observations. For the bulk crystal, a series of strain bursts is identified in the course of plastic flow, despite an apparently smooth stress–strain response. We also show that the intermittent flow is intensified in the micrometer-scale due to both increasing numbers of the successive strain bursts and increasing amplitude of the strain burst, when the specimen size decreases. Finally, we show that the occurrences of the strain bursts are always associated with negative values of the second-order work.