Predicting the flow stress and dominant yielding mechanisms: analytical models based on discrete dislocation plasticity

Hu, Jianqiao; Song, Hengxu; Liu, Zhanli; Zhuang, Zhuo; Liu, Xiaoming; Sandfeld, Stefan

doi:10.1038/s41598-019-56252-x

Cited by 19 publications

(6 citation statements)

References 61 publications

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“…Second, for metals, the electric force may be so noticeable that it may dominate dislocation dynamics. Third, conclusions upon plastic deformations, as are built on classical dislocation dynamics where the electric force has been neglected [48], e.g., DDD [31][32][33][34][35][36][37][38][39][40][41][42], may need to be re-examined carefully by adding the electric force. A comparison between this theory and associated experimental observations needs to be performed in the future.…”

Section: Correction For Image Forcementioning

confidence: 99%

“…Three-dimensional DDD was utilized to delve into the nano-indentation behaviors affected by grain boundaries for an aluminum bicrystal [37]. Based on DDD, dominant yielding mechanisms in single-crystalline copper nano-pillars was investigated [38], and for dislocation nucleation mechanism a transition from dislocation multiplication to surface nucleation was observed [38]. Two-dimensional DDD simulations were performed to minimally capture the phenomenology of nanocrystalline deformation [39].…”

Section: Introductionmentioning

confidence: 99%

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Electric features of dislocations and electric force between dislocations

Huang

2020

Mathematics and Mechanics of Solids

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Dislocations and dislocation dynamics are the cores of material plasticity. In this work, the electric features of dislocations were investigated theoretically. An intrinsic electric field around a single dislocation was revealed. In addition to the well-known Peach–Koehler force, it was established that an important intrinsic electric force exists between dislocations, which is uncovered here for the first time and has been neglected since the discovery of dislocations. The electric forces may be large and sometimes could exceed the Peach–Koehler force for metals and some dielectric materials with large dielectric constant. Therefore, the electric force is anticipated to play a vital role in dislocation dynamics and material plasticity. Moreover, an external electric field could exert an electric force on dislocations and a threshold electric field was subsequently discovered above which this force enables dislocations to glide. Interestingly, it was found that some dislocations move in one direction, but others move in reverse in an identical electric field, which is in agreement with experimental observations. Despite dislocation motion under an electric field, to one’s surprise, both edge and screw dislocations do not carry net charges by themselves, which may tackle the long-standing puzzle on the charges of dislocations. These findings may supply people with new fundamental knowledge on dislocations as well as dislocation dynamics, and may assist people in understanding related phenomena.

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Section: Correction For Image Forcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electric features of dislocations and electric force between dislocations

Huang

2020

Mathematics and Mechanics of Solids

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“…[5]). This modeling approach has been successful at reproducing qualitatively the scale-free statistical properties of plastic slip avalanches [6][7][8] and the size dependence of plastic yield [9,10]. The model is nonetheless empirical in the way reaction rates and dislocation mobilities are introduced as ad hoc tuning parameters.…”

Section: Introductionmentioning

confidence: 99%

Stress in ordered systems: Ginzburg-Landau-type density field theory

2021

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We present a theoretical method for deriving the stress tensor and elastic response of ordered systems within a Ginzburg-Landau-type density field theory in the linear regime. This is based on spatially coarse graining the microscopic stress which is determined by the variation of a free energy with respect to mass displacements. We find simple expressions for the stress tensor for phase field crystal models for different crystal symmetries in two and three dimensions. Using tetradic product sums of reciprocal lattice vectors, we calculate elastic constants and show that they are directly related to the symmetries of the reciprocal lattices. We also show that except for bcc lattices there are regions of model parameters for which the elastic response is isotropic. The predicted elastic stress-strain curves are verified by numerical strain-controlled bulk and shear deformations. Since the method is independent of a reference state, it extends also to defected crystals. We exemplify this by considering an edge and screw dislocation in the simple cubic lattice.

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“…From modeling and simulation perspective, Groma et al 11 studied dislocation patterns in a two‐dimensional continuum dislocation theory. Hu et al 12 used discrete dislocation dynamics (DDD) simulations to investigate dislocation pattern formation in single crystalline copper pillar and study the related yielding mechanisms. Moreover, Ispanovity et al 13 developed a stochastic continuum model for statistically stored and geometrically necessary dislocation densities.…”

Section: Introductionmentioning

confidence: 99%

Finite temperature atomistic‐informed crystal plasticity finite element modeling of single crystal tantalum (α‐Ta) at micron scale

Xie

2021

Numerical Meth Engineering

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In this work, we have developed a temperature‐dependent higher‐order Cauchy–Born (THCB) rule for multiscale crystal defect dynamics (MCDD) of crystalline solids based on the harmonic approximation. As a template, we employed the THCB rule to develop an atomistic‐informed constitutive model for the body‐centered cubic (BCC) single crystal tantalum (α‐Ta). Considering the effect of strain gradients in different process zone elements, the corresponding higher order stress are used to model crystal plasticity of single crystal α‐Ta. Different from face‐centered cubic crystals, BCC crystals are strongly influenced by temperature. It is shown in this article that the developed finite temperature atomistic‐informed crystal plasticity finite element method is able to capture the temperature‐dependent dislocation substructure and hence crystal plastic deformation. The main contributions and novelties of the present work are highlighted by following findings: (1) A THCB rule and an atomistic‐informed strain gradient theory have been developed, and the corresponding temperature‐related higher‐order stress and elastic tensor formulations are derived; (2) The finite temperature MCDD provides an atomistic‐informed crystal plasticity finite element method that can simulate anisotropic crystal plasticity in any orientation within stereographic triangle at micron scale and above; (3) The developed MCDD is able to capture the non‐Schmid effects of BCC single crystal tantalum (α‐Ta); (4) The developed MCDD is able to capture the size effect of single crystal plasticity; and (5) The finite temperature MCDD can simulate the temperature dependent dislocation substructure, and it captures cross‐slip in single crystal tantalum at low temperature (∼20 K) and captures dislocation cell structure at high temperature (∼500 K).

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Predicting the flow stress and dominant yielding mechanisms: analytical models based on discrete dislocation plasticity

Cited by 19 publications

References 61 publications

Electric features of dislocations and electric force between dislocations

Electric features of dislocations and electric force between dislocations

Stress in ordered systems: Ginzburg-Landau-type density field theory

Finite temperature atomistic‐informed crystal plasticity finite element modeling of single crystal tantalum (α‐Ta) at micron scale

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