Accounting for the recoverable plasticity and size effect in the cyclic torsion of thin metallic wires using strain gradient plasticity

Liu, Dabiao; He, Yuming; Shen, Lei; Lei, Jian; Guo, Song; Peng, Kai

doi:10.1016/j.msea.2015.08.063

Cited by 32 publications

(9 citation statements)

References 54 publications

(105 reference statements)

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“…The effect of strengthening that arises from strain gradients is significant at small material length scales (e.g. Liu et al, 2015). This effect is predicted by Model A, while no such effect is predicted by Model B for the choice of ma-575 terial parameters presented.…”

mentioning

confidence: 88%

“…This work defines strengthening as an apparent delay in plastic flow, while hardening is defined by the combined effect of conventional strain hardening and the additional hardening related to gradients of plastic 10 strain. Recent experiments display evidence of a strengthening behavior in polycrystalline wires under cyclic loading (Liu et al, 2015), and in the average compressive load for thin confined copper films (Mu et al, 2014). However, in the majority of micron-scale experiments (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity

Nellemann

Niordson

Nielsen

2018

European Journal of Mechanics - A/Solids

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Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity Nellemann, C.; Niordson, C. F. ; Nielsen, K.L. AbstractTwo rate-independent strain gradient crystal plasticity models, one new and one previously published, are compared and a numerical framework that encompasses both is developed. The model previously published is briefly outlined, while an in-depth description is given for the new, yet somewhat related, model.The difference between the two models is found in the definitions of the plastic work expended in the material and their relation to spatial gradients of plastic strains. The model predictions are highly relevant to the ongoing discussion in the literature, concerning 1) what governs the increase in the apparent yield stress due to strain gradients (also referred to as strengthening)? And 2), what is the implication of such strengthening in relation to crystalline material behavior at the micron scale? The present work characterizes material behavior, and the corresponding plastic slip evolution, by use of the finite element method.The pure shear problem of an infinite material slab is investigated, with the previously published model displaying strengthening, while the new model does not. In addition to the numerical approach an exact closed form solution, to the pure shear problem, is obtained for the new model, and it is demonstrated that the model predicts proportional straining in the entire plastic regime. Somewhat surprising it is found that the predictions for strain gradient hardening coincide for the two models.

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confidence: 88%

Section: Introductionmentioning

confidence: 99%

Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity

Nellemann

Niordson

Nielsen

2018

European Journal of Mechanics - A/Solids

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“…Under an applied torque, while one dislocation of a dipole moves outward and escape or annihilated, another dislocation moves inward under stress gradients and piles up around the wire center, which results in polarized dislocations (or GNDs) with non-uniform density [10]. The inhomogeneous spatial distribution of GNDs, or the resulted plastic strain gradients, can lead to a strong back stress [5] and may suppress the multiaxial ratcheting of thin wire. Further work on the microstructure observation is needed to clearly explain the multiaxial ratcheting behavior at small-scale.…”

Section: O-wmentioning

confidence: 99%

Ratcheting of 316L stainless steel thin wire under tension-torsion loading

Fu¹,

Yu²,

Chen³

2016

Frattura Ed Integrità Strutturale

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A series of cyclic tension-torsion tests under symmetric shear strain and asymmetric axial stress control in various loading paths are conducted on 100 μm-diameter 316L steel wires applying a micro tensiontorsion fatigue testing apparatus. The ratcheting strain of the thin wire increases with increasing axial mean stress and decreases in a sequence of linear, rhombic and circular paths. The macro-scale based cyclic plastic constitutive models with kinematic hardening rules of the Ohno-Wang (O-W) and the Chen-Jiao-Kim (C-J-K) are evaluated for the thin wire. Comparing with the O-W, the C-J-K predicts more accurately under high axial stress. While the loading path effects on ratcheting for wire specimens are basically simulated, the macro-based models tend to underestimate the effect of phase difference between axial and torsional loadings and the ratcheting evolution in the initial 50 cycles.

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“…Especially, positive plastic dissipation has been ensured by the gradient theory of Gudmundson [33], thanks to the peculiar structure of the constitutive laws for the dissipative stresses, smartly relating the rates of the plastic strain and its gradient to finite stress measures. The role of energetic and dissipative gradient effects has been studied numerically by several authors [40][41][42][43][44]. However, as indicated by Fleck and Willis [45], the degree to which strain gradient effect is mainly energetic or dissipative remains unclear.…”

Section: Introductionmentioning

confidence: 99%

A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory

Borokinni

Liu

2018

Metals

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The mathematical nature of the flow rule for the strain gradient plasticity theory proposed by Nix and Gao (W.D. Nix and H. Gao, J Mech Phys Solids 46(3), 411(1998)) is discussed based on the paradigm developed by Gurtin and Anand (M.E. Gurtin and L. Anand, J Mech Phys Solids 57 (3), 405 (2009)). It is shown that, when investigated on the basis of Gurtin–Anand theory, the Nix–Gao flow rule is a combination of constitutive equations for microstresses, balance law, and a constraint. As an accessory, we demonstrate that the strain gradient term introduced in the model is energetic. The results are obtained by combining a virtual-power principle of Fleck and Hutchinson, and the free-energy imbalance under isothermal conditions.

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Accounting for the recoverable plasticity and size effect in the cyclic torsion of thin metallic wires using strain gradient plasticity

Cited by 32 publications

References 54 publications

Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity

Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity

Ratcheting of 316L stainless steel thin wire under tension-torsion loading

A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory

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