表面裂纹与任意杂质相互作用的半解析研究：裂纹角度、杂质材质与位置效应的系统分析

杨博政; 宋恒旭; 李璞; 金晓清

doi:10.21656/1000-0887.460204

表面裂纹与任意杂质相互作用的半解析研究：裂纹角度、杂质材质与位置效应的系统分析

doi: 10.21656/1000-0887.460204

杨博政^{1, 2,},
宋恒旭^{1, 3, ,},
李璞⁴,
金晓清²

1.
中国科学院力学研究所超常环境非线性力学全国重点实验室, 北京 100190
2.
重庆大学航空航天学院, 重庆 400030
3.
中国科学院大学工程科学学院, 北京 100049
4.
四川大学空天科学与工程学院空间先进机构与智能飞行器教育部重点实验室, 机器人卫星四川省国防科技重点实验室, 成都 610065

(本刊青年编委宋恒旭来稿)

基金项目:

中国科学院战略先导B类项目 XDB0620101

国家自然科学基金 52205192

国家自然科学基金 52575201

国家自然科学基金 12502114

详细信息

作者简介:
杨博政(2002—)，男，博士生(E-mail: ybz468947778@163.com)

通讯作者:
宋恒旭(1988—)，男，研究员，博士(通信作者. E-mail: songhengxu@imech.ac.cn)

中图分类号: O34
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- 文章访问数: 166
- HTML全文浏览量: 56
- PDF下载量: 41
- 被引次数: 0
出版历程
- 收稿日期: 2025-11-17
- 修回日期: 2025-12-08
- 刊出日期: 2026-08-01

A Semi-Analytical Study of the Interaction Between Surface Cracks and Arbitrary Inhomogeneities: Systematic Analysis of Crack Angles, Material Contrasts, and Positional Effects

Yang Bozheng^{1, 2
,},
Song Hengxu^{1, 3
, ,},
Li Pu⁴,
Jin Xiaoqing²

1.
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing 100190, P.R. China
2.
College of Aerospace Engineering, Chongqing University, Chongqing 400030, P.R. China
3.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, P.R. China
4.
Key Laboratory of Advanced Spatial Mechanism and Intelligent Spacecraft(Ministry of Education), Robotic Satellite Key Laboratory of Sichuan Province, School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, P.R. China

(Contributed by Song Hengxu, Member of the Youth Editorial Board of AMM)

摘要

摘要: 本文围绕半平面中表面裂纹与任意形状杂质的相互作用行为，基于数值等效夹杂法与分布位错技术构建了统一的半解析求解框架，并通过一系列算例系统评估了裂纹角度、杂质材质以及杂质位置对应力强度因子与局部应力场的影响规律. 算例结果表明：裂纹角度的变化会显著改变裂尖附近的应力分布特征，倾斜裂纹产生更强的模式耦合；杂质材质对相互作用效应高度敏感，硬质杂质使Ⅰ型应力强度因子减小、Ⅱ型应力强度因子增大，而软质杂质则表现出相反趋势；随着杂质逐渐远离自由边界，其对裂尖的扰动作用明显减弱. 所有算例的半解析计算结果均与有限元解保持良好一致，应力强度因子误差小于4.5%，验证了所建半解析框架的可靠性. 上述算例研究揭示了多因素耦合作用下裂纹-杂质相互作用的主要规律，可为复杂材料与结构中损伤演化机理的分析提供有价值的参考.
- 表面裂纹 /
- 杂质 /
- 半解析方法 /
- 应力强度因子
Abstract: A unified semi-analytical framework combining the numerical equivalent inclusion method (NEIM) and the distributed dislocation technique (DDT) was employed to investigate the interaction between surface cracks and arbitrarily shaped inhomogeneities in a half-plane. Several representative examples were simulated to systematically examine the effects of crack angles, inhomogeneity stiffnesses, and the inhomogeneity distances from the free surface on the stress intensity factors and local stress fields. The results show that, the crack angle leads to notable changes in the crack-tip field and induces pronounced mode coupling. Stiff inhomogeneities decrease Mode Ⅰ stress intensity factor but increase Mode Ⅱ, whereas soft inhomogeneities exhibit the opposite trend. As the inhomogeneity moves farther from the free surface, its perturbation to the crack-tip field becomes significantly weaker. The semi-analytical results agree well with the finite element solutions, with discrepancies below 4.5%, demonstrating the accuracy and efficiency of the present framework. The numerical examples provide clear insight into the dominant mechanisms governing crack-inhomogeneity interaction under multiple influencing parameters.
- surface crack /
- inhomogeneity /
- semi-analytical method /
- stress intensity factor
edited-by

edited-by
注释:

1) (本刊青年编委宋恒旭来稿)

HTML全文

图 1 DDT求解表面裂纹示意图

Figure 1. Schematic diagram of solving a surface crack using DDT

下载: 全尺寸图片幻灯片

图 2 NEIM求解杂质问题示意图

Figure 2. Schematic of solving inhomogeneity using NEIM

下载: 全尺寸图片幻灯片

图 3 不同角度的表面裂纹示意图

Figure 3. Schematic of surface cracks with different angles

下载: 全尺寸图片幻灯片

图 4 不同裂纹角度下得到的沿目标线的应力场σ_ij/σ₀

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. Stress field components σ_ij/σ₀ along the target line corresponding to various crack angles

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图 5 角度为-45°的表面裂纹与矩形杂质相互作用示意图

Figure 5. Schematic of the interaction between a -45° surface crack and a rectangular inhomogeneity

下载: 全尺寸图片幻灯片

图 6 不同弹性模量比E₂/E₁下得到的沿目标线的应力场σ_ij/σ₀

Figure 6. Stress field components σ_ij/σ₀ along the target line corresponding to different elastic modulus ratios E₂/E₁

下载: 全尺寸图片幻灯片

图 7 角度为-45°的表面裂纹与不同位置的圆形杂质相互作用示意图

Figure 7. Schematic of the interaction between a -45° surface crack and circular inhomogeneities in different positions

下载: 全尺寸图片幻灯片

图 8 不同位置h₀/r₀的杂质与表面裂纹相互作用下得到的沿目标线的应力场σ_ij/σ₀

Figure 8. Stress field components σ_ij/σ₀ along the target line for the interaction between a surface crack and an inhomogeneity at various position ratios h₀/r₀

下载: 全尺寸图片幻灯片

表 1 不同裂纹角度θ得到的无量纲应力强度因子

Table 1. Dimensionless stress intensity factors under different crack angles θ

	θ=－45°			θ=90°			θ=45°
	this paper	FEM	error/%	this paper	FEM	error/%	this paper	FEM	error/%
β_Ⅰ	1.250	1.251	0.094	1.988	2.002	0.720	1.250	1.253	0.254
β_Ⅱ	0.646	0.652	0.848	0	0	0	-0.646	-0.647	0.143

下载: 导出CSV

表 2 不同弹性模量比E₂/E₁下得到的无量纲应力强度因子

Table 2. Dimensionless stress intensity factors corresponding to different elastic modulus ratios E₂/E₁

	E₂/E₁=2			E₂/E₁=1			E₂/E₁=0.5
	this paper	FEM	error/%	this paper	FEM	error/%	this paper	FEM	error/%
β_Ⅰ	1.061	1.081	1.831	1.250	1.251	0.094	1.464	1.513	3.231
β_Ⅱ	0.658	0.675	2.634	0.646	0.652	0.848	0.591	0.618	4.334

下载: 导出CSV

表 3 不同杂质与自由边界的距离h₀/r₀下得到的无量纲应力强度因子

Table 3. Dimensionless stress intensity factors corresponding to different distances h₀/r₀ from the inhomogeneity to the free surface

	h₀/r₀=1.0			h₀/r₀=1.5			h₀/r₀=2.0
	this paper	FEM	error/%	this paper	FEM	error/%	this paper	FEM	error/%
β_Ⅰ	1.123	1.149	2.133	1.067	1.099	2.884	1.107	1.135	2.459
β_Ⅱ	0.694	0.704	1.458	0.626	0.642	2.479	0.598	0.610	1.968

下载: 导出CSV

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