A new hardening law for strain gradient plasticity

A new hardening law of the strain gradient theory is proposed in this paper, which retains the essential structure of the incremental version of conventional J(2) deformation theory and obeys thermodynamic restrictions. The key feature of the new proposal is that the term of strain gradient plasticity is represented as an internal variable to increase the tangent modulus. This feature which is in contrast to several proposed theories, allows the problem of incremental equilibrium equations to be stated without higher-order stress, higher-order strain rates or extra boundary conditions. The general idea is presented and compared with the theory given by Fleck and Hutchinson (Adv. in Appl. Mech. (1997) 295). The new hardening law is demonstrated by two experimental tests i.e. thin wire torsion and ultra-thin beam bending tests. The present theoretical results agree well with the experiment results.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Size Effect and Geometrical Effect of Solids in Micro-Indentation Test

Micro-indentation tests at scales of the order of sub-micron show that the measured hardness increases strongly with decreasing indent depth or indent size, which is frequently referred to as the size effect. At the same time, at micron or sub-micron scale, another effect, which is referred to as the geometrical size effects such as crystal grain size effect, thin film thickness effect, etc., also influences the measured material hardness. However, the trends are at odds with the size-independence implied by the conventional elastic-plastic theory. In the present research, the strain gradient plasticity theory (Fleck and Hutchinson) is used to model the composition effects (size effect and geometrical effect) for polycrystal material and metal thin film/ceramic substrate systems when materials undergo micro-indenting. The phenomena of the "pile-up" and "sink-in" appeared in the indentation test for the polycrystal materials are also discussed. Meanwhile, the micro-indentation experiments for the polycrystal Al and for the Ti/Si_3N_4 thin film/substrate system are carried out. By comparing the theoretical predictions with experimental measurements, the values and the variation trends of the micro-scale parameter included in the strain gradient plasticity theory are predicted.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

Toughness Of Ni/Al2O3 Interfaces As Dependent On Micron-Scale Plasticity And Atomistic-Scale Separation

Ceramic/metal interfaces were studied that fail by atomistic separation accompanied by plastic dissipation in the metal. The macroscopic toughness of the specific Ni alloy/Al2O3 interface considered is typically on the order of ten times the atomistic work of separation in mode I and even higher if combinations of mode I and mode II act on the interface. Inputs to the computational model of interface toughness are: (i) strain gradient plasticity applied to the Ni alloy with a length parameter determined by an indentation test, and (ii) a potential characterizing mixed mode separation of the interface fit to atomistic results. The roles of the several length parameters in the strain gradient plasticity are determined for indentation and crack growth. One of the parameters is shown to be of dominant importance, thus establishing that indentation can be used to measure the relevant length parameter. Recent results for separation of Ni/Al2O3 interfaces computed by atomistic methods are reviewed, including a set of results computed for mixed mode separation. An approximate potential fit to these results is characterized by the work of separation, the peak separation stress for normal separation and the traction-displacement relation in pure shearing of the interface. With these inputs, the model for steady-state crack growth is used to compute the toughness of the interface under mode I and under the full range of mode mix. The effect of interface strength and the work of separation on macroscopic toughness is computed. Fundamental implications for plasticity-enhanced toughness emerge.

理想塑性材料裂纹顶端附近的渐近解

<正> Hutchinson和Shih在讨论幂硬化材料裂纹顶端附近的渐近解时同时提出了理想塑性材料的应力分布(位移和应变是无法确定的)。本文指出,对于理想塑性材料来说,裂纹顶端附近的应力分布并非唯一的。下面讨论平面应变的情况,结果不难推广到其他情况。

在混合硬化材料中I型裂纹定常扩展时的尖端场

本文采用和的混合线性硬化材料塑性本构关系,求得了平面应变与平面应力状态下Ⅰ型定常扩展裂纹尖端附近场的渐近解。Amazigo和Hutchinson的结果相当于本文解当混合硬化参数β=1且略去二次塑性区的情况。本文的数值计算结果表明,混合硬化参数β对尖端场的应力应变分布有着显著的影响。

Crack deflection at an interface between dissimilar elastic-materials

A crack intersecting an interface between two dissimilar materials may advance by either penetrating through the interface or deflecting into the interface. The competition between deflection and penetration can be assessed by comparison of two ratios: (i) the ratio of the energy release rates for interface cracking and crack penetration; and (ii) the ratio of interface to material fracture energies. Residual stresses caused by thermal expansion misfit can influence the energy release rates of both the deflected and penetrating crack. This paper analyses the role of residual stresses. The results reveal that expansion misfit can be profoundly important in systems with planar interfaces (such as layered materials, thin film structures, etc.), but generally can be expected to be of little significance in fiber composites. This paper corrects an earlier result for the ratio of the energy release rate for the doubly deflected crack to that for the penetrating crack in the absence of residual stress.

微薄梁三点弯曲的尺度效应研究

应用高灵敏度的力传感器以及时间序列电子散斑干涉法,同时测出了不同厚度纯镍薄片三点弯曲试件的抗力与变形,得到薄梁中心点处的载荷与挠度曲线.应用Fleck和Hutchinson的偶应力理论,结合平面应变弯曲模型,建立了薄梁处于弹性状态和弹塑性状态的控制方程,应用Runge-Kutta法进行数值求解,并将计算得到的载荷-挠度曲线以及无量纲化弯矩-表面应变曲线和实验结果进行了比较.在理论计算过程中,没有拟合任何材料参数,所有的材料参数均来自实验测量的结果,材料特征尺度也是根据Stolken和Evans的工作给出的.结果表明:应用偶应力理论预测的结果和实验结果符合良好,而经典理论的预测结果与实验不相符合.

智能微尺度力学的研究

对于宏观材料的力学性能的研究通常基于传统的连续介质力学;然而,当研究对象小到微/纳米尺度时,材料缺陷等因素对微观材料力学性能影响程度将不同于宏观材料。此时,材料将表现出明显的尺度效应等力学性能。用传统连续介质理论将不能解释此现象。因此,许多学者基于正问题思想对微观材料的力学性能进行研究:Fleck-Hutchinson提出了机遇传统弹塑性理论的塑性应变梯度理论;Nix-Gao提出了基于位错理论的塑性应变梯度理论;Gerberich等提出了基于比表面能的微尺度材料尺度效应理论[3]。Kelchner等提出用分子动力学模拟方法获得微/纳米材料的力学性能[4]。这些理论都在一定程度上解释了微观材料力学性能的尺度效应。然而,这些理论仅限于理论研究阶段,且存在一定局限性。

铃兰族的系统学研究

铃兰族隶属广义的百合科，辖白穗花、吉祥草、铃兰、夏须草、万年青、开口箭和蜘蛛抱蛋七属．除开口箭属和蜘蛛抱蛋属外．其余5属皆为单型属。属间界限明确，但系统关系模糊．本文针对上述特点及存在问题，开展了下述工作： 一、形态： 根据大量的栽培植株观察和标本研究，对族内各属形态特征进行了详细研究，并报道了开口箭属的一个新种，对一些性状在系统发育研究中的重要性作了评估。 二、解剖： 本文对族内各属花维管束、根部和茎部的管状分子、叶片维管束和叶表皮特征等资料进行了综合，为系统发育研究积累资料。 三、花粉： 本文对铃兰族，特别是蜘蛛抱蛋亚族25种植物的花粉形态进行了电镜扫描，将蜘蛛抱蛋亚族的花粉划分为椭圆形具单槽、球形具单槽、球形无萌发孔沟三个类型，花粉形态的演化趋势为单槽，无萌发孔沟，椭圆形，球形。花粉形态与花结构和核型特征密切相关。 四、染色体： 本文对蜘蛛抱蛋属13种植物进行了核型报道，对各属染色体资料进行了详尽的总结分析．除夏须草属染色体数目为2n＝40外，铃兰族其余各属染色体数目为2n ＝38 (36)，核型分为单型性和二型性两大类，染色体数目、核型类型和花部式样密切相关．x＝19为族内染色体原始基数，x＝18为派生基数．核型演化趋势由对称→不对称演化，单型→二型性演化，此外，对核型进化的机制也进行了讨论。 根据上述研究结果，运用系统学原理，本文对铃兰族内系统发育关系进行了探讨，结论如下： 1、夏须草属为族内异质类群，建议将其从族内移出。其余各属构成一单系类群。 2、开口箭属和蜘蛛抱蛋属下皆可分为两大类群，且各具相关性状。 3、开口箭属内两大类群表现为复系关系。具单型性核型并具远极单槽花粉的开口箭种类与万年青属单系发生，而具二型性核型、无萌发沟孔花粉的开口箭种类则与蜘蛛抱蛋属成单系关系。 4、铃兰族与沿阶草族系统位置接近，与黄精族则稍远。 5、无可靠证据支持Hutchinson (1934)认为天南星科起源于铃兰族内蜘蛛抱蛋亚族的观点。 此外，本文选用21种限制性内切酶，对族内各属叶绿体DNA中rbcL基因片段的PCR产物进行酶切处理，计确定76个酶切位点，包括19个突变位点，并对RFLP结果进行聚类分析。结果与形态、染色体和孢粉学证据基本吻合。

The stripe-backed weasel Mustela strigidorsa: taxonomy, ecology, distribution and status

1. The stripe-backed weasel Mustela strigidorsa is one of the rarest and least-known mustelids in the world. Its phylogenetic relationships with other Mustela species remain controversial, though several unique morphological features distinguish it from congeners. 2. It probably lives mainly in evergreen forests in hills and mountains, but has also been recorded from plains forest, dense scrub, secondary forest, grassland and farmland. Known sites range in altitude from 90 m to 2500 m. Data are insufficient to distinguish between habitat and altitudes which support populations, and those where only dispersing animals may occur. 3. It has been confirmed from many localities in north-east India, north and central Myanmar, south China, north Thailand, north and central Laos, and north and central Vietnam. Given the limited survey effort, the number of recent records shows that the species is not as rare as hitherto believed. Neither specific nor urgent conservation needs are apparent.

Polyphasic characterization of water bloom forming Raphidiopsis species (cyanobacteria) from central China

Two strains of Raphidiopsis Fritsch et Rich were isolated from a fishpond in Wuhan city, China and rendered axenic, and characterized by a combination of morphological, physiological, biochemical and genetic methods. Morphologically the strains were identified as Raphidiopsis mediterranea Skuja (straight trichomes) and R. curvata Fritsch et Rich (coiled trichomes). These two strains demonstrated slight differences in optimal temperature range and GC content, while sharing some common characteristics including inability to grow hetertrophically, similar salinity tolerance (up to 0.78%) and an identical fatty acid composition. Cyanotoxins were not found in the strain of R. mediterranea, however, the strain of R. curvata contained both deoxycylindrospermopsin and cylindrospermopsin. Phylogenetic affiliations inferred from 16S rRNA gene sequences demonstrated that both Raphidiopsis strains clustered with Cylindrospermopsis, demonstrating their phylogenetic ties to Nostocaceae. (c) 2007 Elsevier B.V. All rights reserved.