The Definition of Atomic Scale Strain and Its Application in Identifying the Evolution of Microdefects

doi:10.11900/0412.1961.2019.00343

Acta Metall Sin

2020, Vol. 56

Issue (8): 1144-1154 DOI: 10.11900/0412.1961.2019.00343

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The Definition of Atomic Scale Strain and Its Application in Identifying the Evolution of Microdefects

SHENG Ying¹^,², JIA Bin¹^,²(

), WANG Ruheng¹^,², CHEN Guoping¹^,²

1 Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Southwest University of Science and Technology, Mianyang 621010, China
2 School of Civil Engineering and Architecture, Southwest University of Science and Technology, Mianyang 621010, China

Cite this article:

SHENG Ying, JIA Bin, WANG Ruheng, CHEN Guoping. The Definition of Atomic Scale Strain and Its Application in Identifying the Evolution of Microdefects. Acta Metall Sin, 2020, 56(8): 1144-1154.

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Abstract

The strain tensors are commonly defined by the local deformation of continuum. Unlike displacement, strain is not a physical quantity that can be measured directly, and it is calculated from a definition that relies on the gradient of the continuous displacement field. At the microscale, it is difficult to define the local deformation according to the position of each atom which is obtained from the adjacent discrete time interval, so there is no universally accepted definition of strain tensors of atomic scale so far, and none of the molecular dynamics software can be used to calculate the atomic strain until now. In order to define the atomic scale strain, a method for calculating the "deformation" both in the atomic scale and the continuum scale is proposed. In the definition, the discrete deformation gradient is proposed to describe the "deformation" in the atomic scale and the influence weight function of neighborhood atom is introduced. Then the weighted least squares error optimization model is established to seek the optimal coefficients of the weight function and the optimal local deformation gradient of each atom. After that, the advanced multilayer complex genetic algorithm can be used to calculate the atomic strain. Finally, take NiTi alloy as an example, the molecular dynamics evolution model of deformation and failure of NiTi alloy was established. Then the atomic scale strain nephogram at each time was calculated, and the microdefects such as twins were observed by strain nephogram. Compared with the micro-observation experiment of crack tip of NiTi alloy for three-point bending, the rationality of the atomic scale strain definition method established in this study and its application significance in identifying the evolution of microdefects are verified.

Key words: atomic scale strain discrete deformation gradient weight function objective function optimization evolution of microdefect

Received: 15 October 2019

ZTFLH:

O341

Fund: Doctor Foundation in Southwest University of Science and Technology(17zx7149);Open Foundation of Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province(18kfgk12)

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	Ying SHENG
	Bin JIA
	Ruheng WANG
	Guoping CHEN

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https://www.ams.org.cn/EN/10.11900/0412.1961.2019.00343 OR https://www.ams.org.cn/EN/Y2020/V56/I8/1144

Fig.1 General motion in the neighborhood of a discrete atomic particle (Ω₀—reference configuration; Ω₁—current configuration; E₁, E₂, E₃—x, y, z coordinate vectors in Ω₀, respectively; e₁, e₂, e₃—x, y, z coordinate vectors in Ω₁, respectively; X^m, Xⁿ—coordinate vectors of atom m and atom n in Ω₀ at the initial time t₀, respectively; x^m, xⁿ—coordinate vectors of atom m and atom n in Ω₁ at the current time t₁, respectively; ΔX^mn—position of atom n relative to atom m in Ω₀; Δx^mn—position of atom n relative to atom m in Ω₁; χ—mapping from X to x)

Fig.2 Low (a) and high (b) magnified fracture surface SEM images of three point bending NiTi alloy specimens

Fig.3 TEM images of crack surface of NiTi alloy
(a) dislocation pile-up (b) parallel and bended dislocations (c) austenite-martensite phase region
(d) stacking fault bands (e) shear deformation in grains (f) twins

Fig.4 Calculated stress-strain curves of NiTi alloy

Fig.5 Atomic configurations of key points 1~6 in Fig.4, respectively
(a) initial state (b) loading process (c) stress flat during the loading process
(d) loading peak (e) unloading process (f) stress flat during the unloading process

Fig.6 Molecular dynamics simulation results near crack tip of NiTi alloy (The top half is a three-dimensional view, and the bottom half is a top view)
(a) before twins formation (b) twins just formed (c) twins are fully formed

Fig.7 Atomic strain nephograms corresponding to Fig.6
(a) before twins formation (b) twins just formed (c) twins are fully formed

Fig.8 The function image of the weight function ω_n(r) of NiTi alloy (r—dimensionless quantity related to atom distance R_mn and cut-off radius R_cut)

Fig.9 The function images of the weight function ω(r) of NiTi alloy with different R_cut

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