不同温度和扰动应变作用下纳米微裂纹的晶体相场研究

doi:10.19596/j.cnki.1001-246x.8509

摘要/Abstract

摘要：

用晶体相场模型模拟扰动应变下纳米微裂纹的扩展行为，探讨扰动频率及温度对微裂纹扩展行为及稳定性的影响。结果表明: 温度提升在扰动频率较小时能引起脆韧转变，裂纹稳定性因温度升高而下降。扰动频率的提升在温度低于脆韧转变温度时，能在演化初期引起脆韧转变，之后将抑制脆性扩展，但无法引起韧脆转变；当温度高于脆韧转变温度时，扰动频率不再改变裂纹扩展模式。裂纹稳定性随扰动频率的增大先下降后上升。

关键词: 晶体相场, 扰动应变, 温度, 微裂纹

Abstract:

A phase-field-crystal model is used to simulate microcrack growth under disturbance strain. Influences of disturbance frequency and temperature on growth behavior and stability of microcrack are discussed. It shows that: ① Fracture mode is affected by temperature of the system under certain conditions. ② Influence of disturbance frequency on crack propagation behavior is affected by temperature of the system. ③ Stability of crack decreases firstly and then increases with the increase of disturbance frequency. The increase of temperature leads to the decrease of crack stability.

Key words: phase-field-crystal, disturbance strain, temperature, microcrack

李建伟, 项璇, 王景栋, 胡石, 陈铮, 贺元骅. 不同温度和扰动应变作用下纳米微裂纹的晶体相场研究[J]. 计算物理, 2022, 39(6): 717-726.

Jianwei LI, Xuan XIANG, Jingdong WANG, Shi HU, Zheng CHEN, Yuanhua HE. Propagation of Nanoscale Microcrack Under Disturbance Strain at Different Temperatures: Phase-Field-Crystal Model[J]. Chinese Journal of Computational Physics, 2022, 39(6): 717-726.

图/表 7

图1 (a) 单模晶体相场二维相图；(b)初始裂纹与三角晶格点阵之间的取向关系示意图(蓝色六边形框表示三角晶格，绿色方框表示初始裂纹。为便于对比，对两者尺寸进行了相对调整。)；(c) 初始模拟体系(绿色区域表示三角晶格固相区，白色区域表示中心裂纹。)

Fig.1 (a) Two-dimensional phase diagram calculated with one-mode approximation; (b) A schematic of the orientation between the crack and the lattice (The blue hexagon box signifies the triangular lattice. The green square box indicates the crack. The dimensions are relatively adjusted to facilitate analysis.); (c) illustration of the initial simulation system(Green and white regions indicate triangular lattice and central crack, respectively.)

表1 模拟体系及选用参数

Table 1 Parameters of the simulation systems

体系	温度r	频率ω /(10^-5Δt^-1)	体系	温度r	频率ω /(10^-5Δt^-1)	体系	温度r	频率ω /(10^-5Δt^-1)
A₁	-1.0	无扰动	A₂	-0.8	无扰动	A₃	-0.6	无扰动
B₁	-1.0	0.2	B₂	-0.8	0.2	B₃	-0.6	0.2
C₁	-1.0	2	C₂	-0.8	2	C₃	-0.6	2
D₁	-1.0	20	D₂	-0.8	20	D₃	-0.6	20
E₁	-1.0	200	E₂	-0.8	200	E₃	-0.6	200
F₁	-1.0	2 000	F₂	-0.8	2 000	F₃	-0.6	2 000

图2 (a) 体系A1在n = 27 000时的应变分布；(b) 体系A1在n = 27 000时的形貌，白色方框区域为体系在n = 60 000时的形貌；(c) 体系C1在n = 13 000时的形貌，白色方框区域为体系在n = 40 000时的中心裂纹的局部形貌，红色线段指示刃位错的多余原子面；(d) 体系C1在n = 57 000时的形貌；(e) 体系D1在n = 45 000时的裂纹形貌；(f) 体系D1在n = 60 000时的形貌；(g) 体系E1在n = 60 000时的形貌；(h) 体系F1在n = 67 000时的形貌

Fig.2 (a) Strain distribution pattern of system A1 at n = 27 000; (b) Morphology of system A1 at n = 27 000 (The inset is a local morphology around the central crack at n = 60 000.); (c) Morphology of system C1 at n = 13 000 (The inset is a local morphology around the central crack at n = 40 000.); (d) Morphology of system C1 at n = 57 000; (e) Morphology of system D1 at n = 45 000; (f) Morphology of system D1 at n = 60 000; (g) Morphology of system E1 at n = 60 000; (h) Morphology of system F1 at n = 67 000 (The extra half planes of atoms are indicated by the red lines.)

图3 (a) 体系B2在n = 38 000时的形貌，其中红色线段指示刃位错的多余原子面；(b) 体系B2在n = 55 000时的形貌；(c) 体系C2在n = 30 000时的形貌，黑色箭头指示裂纹尖端扩展方向；(d) 体系C2在n = 18 000时的应变分布；(e) 体系C2在n = 57 000时的形貌；(f) 体系D2在n = 60 000时的形貌；(g) 体系E2在n = 60 000时的形貌；(h) 体系F2在n = 60 000时的形貌

Fig.3 (a) Morphology of system B2 at n = 38 000 (The red lines indicate extra half planes of atoms.); (b) Morphology of system B2 at n = 55 000; (c) Morphology of system C2 at n = 30 000 (The black arrows indicate crack propagation direction.); (d) Strain distribution pattern of system C2 at n = 18 000; (e) Morphology of system C2 at n = 57 000; (f) Morphology of system D2 at n = 60 000; (g) Morphology of system E2 at n = 60 000; (h) Morphology of system F2 at n = 60 000

图4 (a) 体系A3在n = 50 000时的形貌；(b) 体系B3在n = 43 000时的形貌；(c) 体系C3在n = 49 000时的形貌；(d) 体系D3在n = 51 000时的形貌；(e) 体系E3在n = 50 000时的形貌；(f) 体系F3在n = 51 000时的形貌

Fig.4 (a) Morphology of system A3 at n = 50 000; (b) Morphology of system B3 at n = 43 000; (c) Morphology of system C3 at n = 49 000; (d) Morphology of system D3 at n = 51 000; (e) Morphology of system E3 at n = 50 000; (f) Morphology of system F3 at n = 51 000

表2 各模拟体系的裂纹扩展模式

Table 2 Crack propagation modes of simulated systems

体系	裂纹扩展模式	体系	裂纹扩展模式	体系	裂纹扩展模式
A₁	脆性扩展	A₂	脆性扩展	A₃	韧性扩展
B₁	脆性扩展	B₂	韧性扩展	B₃	韧性扩展
C₁	韧性扩展	C₂	韧性扩展	C₃	韧性扩展
D₁	韧性扩展	D₂	韧性扩展	D₃	韧性扩展
E₁	韧性扩展	E₂	韧性扩展	E₃	韧性扩展
F₁	韧性扩展	F₂	韧性扩展	F₃	韧性扩展

图5 不同扰动频率及体系温度下中心裂纹失稳开始时间步长

Fig.5 Time step number at which the central crack beginning to lose stability under different disturbance frequencies and system temperatures

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