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strain gradient plasticity: energetic or dissipative?

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Acta Mechanica Sinica 2015年第4期31卷 465-472页

作者： N.A.Fleck J.R.Willis Department of Engineering University of Cambridge Department of Applied Mathematics and Theoretical Physics University of Cambridge

Abstract For an infinite slab of strain gradient sensitive material subjected to plane-strain tensile loading, compu- tation established and analysis confirmed that passivation of the lateral boundaries at some stage of loading inhibits plastic deformation upon further loading. This result is not surprising in itself except that, remarkably, if the gradient terms contribute to the dissipation, the plastic deformation is switched off completely and only resumes at a clearly defined higher load, corresponding to a total strain ec, say. The analysis presented in this paper confirms the delay of plastic deformation following passivation and determines the exact manner in which the plastic flow resumes. The plastic strain rate is continuous at the exact point ec of resumption of plastic flow and, for the first small increment Ae = e - ec in the imposed total strain, the corresponding increment in plastic strain, AeP, is proportional to （Ae）2. The constant A in the relation AeP（0） = A（Ae）2, where AeP（0） denotes the plastic strain increment at the centre of the slab, has been determined explicitly; it depends on the hardening modulus of the material. The presence of energetic gradient terms has no effect on the value of ec unless the dissipative terms are absent, in which case passivation reduces the rate of plastic deformation but introduces no delay. This qualitative effect of dissipative gradient terms opens the possibility of experimen- tal discrimination of their presence or absence. The analysisemploys an incremental variational formulation that is likely to find use in other problems.

关键词： strain gradient plasticity Boundary passivation Incremental variational principle

Damage and fracture with strain gradient plasticity for high-capacity electrodes of Li-ion batteries

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Science China(Technological Sciences) 2021年第7期64卷 1575-1582页

作者： SANG MengSha CHEN YaoXing JIANG WenJuan WANG Yan ZOU YouLan MA ZengSheng National-Provincial Laboratory of Special Function Thin Film Materials and School of Materials Science and EngineeringXiangtan UniversityXiangtan 411105China School of Information and Electronic Engineering Hunan University of Science and TechnologyYueyang 411201China

In consideration of the high-density dislocations from the lithiation process of high-capacity electrodes in Li-ion batteries, in this paper, a new elastoplastic model is established to describe the diffusion-induced deformation and damage fracture. With the help of the relative physical quantities and state of charge, the surface damage and fracture behaviors of electrode materials are discussed based on the elastic-perfectly plastic(PP) and the strain gradient plasticity(SGP) theories, respectively. The results show that the lithiation deformation could be alleviated by reducing the electrode scale, and the plastic flow can play an essential role in the extrusion ratcheting effect relating to the upper surface fracture. Furthermore, the interface damage is more likely to appear by increasing the initial bond stiffness at the upper surface, which has little effect on the later fracture. A strong size effect is also found in the damage and fracture critical curves for the PP and SGP models.

关键词： Li-ion battery failure criterion damage strain gradient plasticity

On dissipative gradient effect in higher-order strain gradient plasticity: the modelling of surface passivation

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Acta Mechanica Sinica 2020年第4期36卷 840-854页

作者： Fenfei Hua Dabiao Liu Department of Mechanics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment Wuhan 430074China

The phenomenological flow theory of higher-order strain gradient plasticity proposed by Fleck and Hutchinson(J.Mech.Phys.Solids,2001)and then improved by Fleck and Willis(J.Mech.Phys.Solids,2009)is used to investigate the surface-passivation problem and micro-scale plasticity.An extremum principle is stated for the theory involving one material length scale.To solve the initial boundary value problem,a numerical scheme based on the framework of variational constitutive updates is developed for the strain gradient plasticity theory.The main idea is that,in each incremental time step,the value of the effective plastic strain is obtained through the variation of a functional in regard to effective plastic strain,provided the displacement or deformation gradient.Numerical results for elasto-plastic foils under tension and bending,thin wires under torsion,are given by using the minimum principle and the numerical scheme.Implications for the role of dissipative gradient effect are explored for three non-proportional loading conditions:(1)stretch-passivation problem,(2)bending-passivation problem,and(3)torsion-passivation problem.The results indicate that,within the Fleck-Hutchinson-Willis theory,the dissipative length scale controls the strengthening size effect,i.***.the increase of initial yielding strength,while the surface passivation gives rise to an increase of strain hardening rate.

关键词： strain gradient plasticity Dissipative length scale Passivation Size effect Non-proportional loading

A SEPARATED LAW OF HARDENING IN strain gradient plasticity

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Acta Mechanica Sinica 1997年第2期13卷 161-164页

作者：张林 Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China

This paper presents a separated law of hardening in plasticity with strain gradient effects. The value of the length parameter l contained in this model was estimated from the experimental data for copper.

关键词： strain gradient plasticity separated law of hardening

Generalizing J_2 flow theory: Fundamental issues in strain gradient plasticity

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Acta Mechanica Sinica 2012年第4期28卷 1078-1086页

作者： John W. Hutchinson School of Engineering and Applied Sciences Harvard University

It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.

关键词： strain gradient plasticity Deformation plasticity J2 flow theory of plasticity

Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg-4Al using in situ tensile testing in scanning electron microscope and HR-EBSD

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Journal of Magnesium and Alloys 2024年第5期12卷 1815-1829页

作者： Eunji Song Mohsen Taheri Andani Amit Misra Department of Materials Science and Engineering University of Michigan Department of Mechanical Engineering University of Michigan

In situ tensile testing in a scanning electron microscope(SEM) in conjunction with high-resolution electron backscatter diffraction(HR-EBSD) under load was used to characterize the evolution of geometrically necessary dislocation(GND) densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg-4Al alloy. The increase in GND density was investigated at plastic strains of 0 %,0.6 %, 2.2 %, 3.3 % from the area including 76 grains and correlated with(i) geometric compatibility between slip systems across grain boundaries, and(ii) plastic incompatibility. We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility, from which uniaxial tensile stress-strain response of polycrystalline Mg-4Al are computed and compared with experimental measurement. The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.

关键词： Mg Al alloys Grain boundaries Geometrically necessary dislocations strain gradient plasticity HR-EBSD

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金属细丝扭转中的尺寸效应与钝化效应

Acta Mechanica Sinica 2023年第2期39卷 183-190页

作者：谢宇阳雷剑华奋飞胡建辉刘大彪何玉明 School of Aerospace Engineering Huazhong University of Science and Technology Wuhan 430074China Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment Wuhan 430074China

本文对直径在25-50微米、有无钝化层的微尺度铜丝进行了扭转测试,开展了尺度效应与钝化效应的实验研究.通过磁控溅射制备了镀钛铜丝试样,在扭转测试中观察到直径减小和钝化层存在引起的屈服强度和流动应力的增加.与未钝化铜丝相比,钝化... 详细信息

本文对直径在25-50微米、有无钝化层的微尺度铜丝进行了扭转测试,开展了尺度效应与钝化效应的实验研究.通过磁控溅射制备了镀钛铜丝试样,在扭转测试中观察到直径减小和钝化层存在引起的屈服强度和流动应力的增加.与未钝化铜丝相比,钝化铜丝中存在更加明显的尺度效应,钝化铜丝的规范化扭矩随着直径减小而增加更为显著.基于Fleck-Hutchinson应变梯度塑性理论对铜丝的扭转响应进行了预测,数值结算结果与实验数据吻合较好,并阐明了钝化层对铜丝扭转变形影响的物理机制。

关键词： Torsion Copper wire Passivation effect Size effect strain gradient plasticity

PARTICULATE SIZE EFFECTS IN THE PARTICLE-REINFORCED METAL-MATRIX COMPOSITES

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Acta Mechanica Sinica 2001年第1期17卷 45-58页

作者：魏悦广 LNM Institute of Mechanics Chinese Academy of Sciences Beijing China 100080

The influences of I,article size on the mechanical properties of the particulate metal matrix composite;are obviously displayed in the experimental observations. However, the phenomenon can not be predicted directly using the conventional elastic-plastic theory. It is because that no length scale parameters are involved in the conventional theory. In the present research, using the strain gradient plasticity theory, a systematic research of the particle size effect in the particulate metal matrix composite is carried out. The roles of many composite factors, such as: the particle size, the Young's modulus of the particle, the particle aspect ratio and volume fraction, as well as the plastic strain hardening exponent of the matrix material, are studied in detail. In order to obtain a general understanding for the composite behavior, two kinds of particle shapes, ellipsoid and cylinder, are considered to check the strength dependence of the smooth or non-smooth particle surface. Finally, the prediction results will be applied to the several experiments about the ceramic particle-reinforced metal-matrix composites. The material length scale parameter is predicted.

关键词： size effect strain gradient plasticity the particle-reinforced metal-matrix composite

The indenter tip radius effect in micro- and nanoindentation hardness experiments

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Acta Mechanica Sinica 2006年第1期22卷 1-8页

作者： Fan Zhang Yonggang Huang Keh-Chih Hwang FML Department of Engineering MechanicsTsinghua University Beijing 100084 China Dept. of Mechanical and Industrial Engineering University of Illinois Urbana IL 61801 USA

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments （indentation depths in the micrometer range）, but it does not always hold in nanoindentation experiments （indentation depths approaching the nanometer range）. Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao＇s relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix＇s experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor.

关键词： Taylor dislocation model strain gradient plasticity Indentation Nix-Gao relation