考虑内禀材料长度变化的广义Aifantis应变梯度塑性模型

赵建锋; 张波; 刘大彪; Avraam A. Konstantinidis; 康国政; 张旭

doi:10.1007/s10409-022-09009-2

Generalized Aifantis strain gradient plasticity model with internal length scale dependence on grain size, sample size and strain

doi: 10.1007/s10409-022-09009-2

1.
Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621999, China
2.
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China
3.
Department of Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
4.
Lab of Engineering Mechanics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

Funds:

the National Natural Science Foundation of China Grant

More Information

Corresponding author: Zhang Xu, E-mail address: xzhang@swjtu.edu.cn (Xu Zhang)

摘要

摘要: 内禀材料长度是应变梯度塑性理论中最重要的参数, 被用于成功地解释了微尺度下金属材料的尺寸效应. 内禀材料长度在应变梯度框架中通常扮演着平衡量纲的角色, 并且其取值依赖于模型. 目前, 内禀材料长度物理意义、与材料微观结构的关联以及随变形的演化尚未完全明确. 本研究对Aifantis应变梯度塑性模型进行了修正, 在其中引入了一个最新提出的幂律形式的内禀材料长度演化关系. 在此基础上进一步考虑晶粒尺寸效应, 基于Hall-Petch关系对Aifantis应变梯度塑性模型进行了扩展. 使用上述修正的模型对细丝扭转的实验结果进行了模拟, 研究结果表明, 内禀材料长度同时取决于试样尺寸和晶粒尺寸, 这些相关性主要由位错间距决定, 并可以通过应变硬化指数很好地描述. 此外, 原始Aifantis模型和修正的Aifantis模型中的内禀材料长度的取值均比Fleck-Hutchinson模型的取值更大.
Abstract: The internal length scale (ILS) is a dominant parameter in strain gradient plasticity (SGP) theories, which helps to successfully explain the size effect of metals at the microscale. However, the ILS is usually introduced into strain gradient frameworks for dimensional consistency and is model-dependent. Even now, its physical meaning, connection with the microstructure of the material, and dependence on the strain level have not been thoroughly elucidated. In the current work, Aifantis’ SGP model is reformulated by incorporating a recently proposed power-law relation for strain-dependent ILS. A further extension of Aifantis’ SGP model by including the grain size effect is conducted according to the Hall-Petch formulation, and then the predictions are compared with torsion experiments of thin wires. It is revealed that the ILS depends on the sample size and grain size simultaneously; these dependencies are dominated by the dislocation spacing and can be well described through the strain hardening exponent. Furthermore, both the original and generalized Aifantis models provide larger estimated values for the ILS than Fleck-Hutchinson’s theory.
- Strain gradient plasticity theory /
- Internal length scale /
- Sample size /
- Grain size

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1. Comparison of the modeling results using Aifantis’ theory with experimental results [42].

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2. The comparison between the modeling results by the grain size-dependent Aifantis’ SGP theory and the experimental measurements of Gan et al. [45].

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3. Comparisons between the modeling results by the generalized Aifantis’ SGP theory and the experimental measurements of Liu et al. [42].

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4. Comparisons between the generalized Aifantis’ SGP modeling results and the experimental results of Gan et al. [45].

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Table 1. Model parameters for the experimental results of Fleck [33] and Liu et al. [42] using the original Aifantis SGP model, i.e., Eq. (11)

Experiment	D (μm)	n	$κ_{0}$ (MPa)	l₀ (μm)
Fleck et al. [33]	12, 15, 30, 170	0.2	226	4.9
Fleck et al. [33]	20	0.2	226	3.9
Liu et al. [42]	18	0.22	359.1	1.23
	30	0.26
	42	0.27
	105	0.30

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Table 2. Model parameters for torsion experiments of Gan et al. [45] using Aifantis’ SGP model with grain size dependence, as expressed by Eq. (14)

D (μm)	d (μm)	n	${\hat{κ}}_{0}$ (MPa)	k_HP(MPa μm^1/2)	c₀ (mN)	l₀ (μm)
20	0.63	0.023	71.4	54.9	1.12	2.82
	1.25	0.061				3.05
	2.4	0.110				3.23
	3.86	0.133				3.36
	8.55	0.144				3.52
	8.93	0.185				3.53
50	0.49	0.046	103.8	73.8	1.63	2.79
	0.84	0.049				2.97
	1.89	0.088				3.22
	4.14	0.153				3.41
	5.34	0.191				3.47
	12.74	0.233				3.62

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Table 3. Parameters for the torsion experiments of Gan et al. [45] using the grain size-dependent Aifantis SGP model, as expressed in Eq. (16)

D (μm)	d (μm)	n	${\hat{κ}}_{0}$ (MPa)	k_HP (MPa μm^1/2)	l₀ (μm)
20	0.63	0.023	91.1	51.3	1.98
	1.25	0.061
	2.4	0.110
	3.86	0.133
	8.55	0.144
	8.93	0.185
50	0.49	0.046	74	44.8	11.0
	0.84	0.049
	1.89	0.088
	4.14	0.153
	5.3412.74	0.1910.233

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Table 4. Model parameters for torsion experiments of Liu et al. [42] using the generalized Aifantis’ SGP model, as expressed in Eq. (25)

D (μm)	n	κ₀ (MPa)	l₀ (μm)
18	0.21	367.9	1.40
30	0.26
42	0.28
105	0.31

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Table 5. Model parameters for the torsion experiments of Gan et al. [45] using the generalized Aifantis’ SGP model with grain size dependence, as expressed by Eq. (27)

D (μm)	d (μm)	n	${\hat{κ}}_{0}$ (MPa)	k_HP (MPa μm^1/2)	l₀ (μm)
20	0.63	0.019	95.7	59.2	2.88
	1.25	0.056
	2.4	0.104
	3.86	0.127
	8.55	0.137
	8.93	0.180
50	0.49	0.030	86.6	78.7	13.9
	0.84	0.027
	1.89	0.059
	4.14	0.122
	5.34	0.162
	12.74	0.204

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Table 6. Obtained ILSs using various models in the torsion of thin copper wires

Experiments	Original Aifantis’ SGP model (μm)	Generalized Aifantis’ SGP model (μm)	Generalized Fleck-Hutchinson’s model (μm)
Liu et al. [42]	1.23	1.4	0.89
Gan et al. [45] (D = 20 μm)	1.98	2.88	0.87
Gan et al. [45] (D = 50 μm)	11.0	13.9	1.52

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