EI、Scopus 收录

 引用本文: 王志强, 蔡力勋, 黄茂波. 平面幂律塑性I型裂纹尖端应力场全解. 力学学报, 2023, 55(1): 95-112.
Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of mode-I crack under plane and power-law plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 95-112.
 Citation: Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of mode-I crack under plane and power-law plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 95-112.

## FULL SOLUTION FOR CHARACTERIZING STRESS FIELDS NEAR THE TIP OF MODE-I CRACK UNDER PLANE AND POWER-LAW PLASTIC CONDITIONS

• 摘要: 在航空航天、船舶、石油管道和核电等领域, 服役结构或部件在长期极端条件下运行, 不可避免地会产生裂纹, 因此, 为研究含裂纹结构的准静态断裂行为, 必须了解裂纹尖端附近区域的应力应变场特点. 对于幂律材料裂纹构元, 研究平面应变和平面应力条件下I型裂纹尖端应力场的解析分布. 基于能量密度等效和量纲分析, 推导了能量密度中值点代表性体积单元 (representative volume element, RVE)的等效应力解析方程, 并定义其为应力因子, 进而针对有限平面应变和平面应力紧凑拉伸(compact tension, CT)试样和单边裂纹弯曲(single edge bend, SEB)试样, 以应力因子作为应力特征量, 并构造用于表征裂尖等效应力等值线的蝶翅轮廓式和扇贝轮廓式三角特殊函数, 提出描述幂律塑性条件下平面I型裂纹尖端应力场的半解析模型. 该半解析模型形式简单, 对CT和SEB试样的裂尖应力场的预测结果与有限元分析的结果比较表明, 两者之间均密切吻合, 模型公式可直接用于预测I型裂纹尖端应力分布, 方便于断裂安全评价和理论发展.

Abstract: In the fields of aerospace, ships, oil pipelines and nuclear power, there will be cracks inevitably in structure or component part when running for a long time under extreme conditions. Therefore, it is necessary to explore the features of the stress-strain fields near the crack tip, to study the quasi-static fracture behavior of cracked structures. In this paper, the stress distributions near the tip of mode-I cracked specimens under plane strain and plane stress conditions are studied for power-law hardening material. Based on the energy density equivalence and dimensional analysis, the analytical equation of equivalent stress of representative volume element (RVE) with the median energy density of a finite-dimensions specimen is proposed, and it is defined as the stress factor. Furthermore, for compact tension (CT) and single edge bend (SEB) finite size specimens under plane strain and plane stress conditions, the stress factor is used as a characteristic variable, and a special trigonometric function is assumed to characterize butterfly-wings type or scallop type contour lines of the equivalent stress near the mode-I crack tip, and then a semi-analytical model for compact tension specimens and single edge bend specimens under plane strain and plane stress and fully plastic conditions is proposed to describe the stress fields near the crack tip. As shown in comparing results given by finite element analysis to those predicted by the model for stress fields near the crack tip of the two cracked specimens, all agree well with each other. The semi-analytical model of stress field near the crack tip proposed in this paper is simple in form and accurate in result. It can be directly used to predict the stress distribution near the tip of mode-I crack, which is convenient for fracture safety evaluation and theoretical development.

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈