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基于辛几何方法测定Ⅰ型应力强度因子

Determination of mode Ⅰ stress intensity factor based on symplectic geometry

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为得到高精度的Ⅰ型应力强度因子,提出了 一种基于辛几何方法测定裂纹尖端Ⅰ型应力强度因子的方法.通过在裂纹尖端构建扇形区域,分离辛几何方法下裂纹尖端的全状态向量,结合裂纹尖端的位移场,计算出裂纹的应力强度因子.利用Ⅰ型裂纹尖端位移场的理论解,研究了扇形区域的特征点个数、圆心角大小以及半径长度对应力强度因子精确度的影响.研究结果表明:特征点个数对该方法求解Ⅰ型应力强度因子的精度的影响较大,特征点个数大于37时,相对误差稳定趋向于0;扇形圆心角对应力强度因子的精度影响较小,但是相同精度要求下,不同的扇形圆心角需要的特征点个数不同;扇形半径过小时,由于断裂过程中裂纹尖端塑性区域的影响,应力强度因子的解不稳定且相对误差较大.对比相对误差可以发现该方法计算得到的Ⅰ型应力强度因子的精度较高,且该方法只需得到裂纹尖端的位移场就可以精确得到应力强度因子,解决了以往求解体系在复杂应力等情况下求解步骤复杂,导致无法精确得到Ⅰ型应力强度因子的难题.
In order to obtain the mode Ⅰ stress intensity factor with high accuracy,a method for determi-ning mode Ⅰ stress intensity factor based on symplectic geometry method is proposed.By constructing a fan-shaped region at the crack tip,separating the full state vector of the crack tip under the symplectic ge-ometry method,combined with the displacement field at the crack tip,the stress intensity factor is calculat-ed.Based on the theoretical solution of the displacement field around the mode Ⅰ crack tip,the effects of the number of characteristic points,the size of center angle and radius length on the accuracy of stress in-tensity factor are studied.The results show that the number of characteristic points has a great influence on the accuracy of solving mode Ⅰ stress intensity factor by this method.As the number of characteristic points is greater than 37,the relative error tends to 0 stably;the sector center angle has little effect on the accura-cy of stress intensity factor,but under the same accuracy requirements,different sector center angles need different number of feature points;as the sector radius is too small,the solution of stress intensity factor is unstable and the relative error is large due to the influence of the plastic region at the crack tip in the frac-ture process.By comparing the relative errors,it can be found that the accuracy of the mode Ⅰ stress inten-sity factor calculated by the proposed method is high,and the stress intensity factor can be accurately ob-tained only by obtaining the displacement field around the crack tip.It solves the problem that the previous solution system has complex steps in the case of complex stress,resulting in the inability to accurately ob-tain the mode Ⅰ stress intensity factor.

fracture mechanicssymplectic geometry methodstress intensity factormode Ⅰ crack

代树红、吴尧、肖雨轩

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辽宁工程技术大学,123000阜新

断裂力学 辛几何方法 应力强度因子 Ⅰ型裂纹

国家自然科学基金重点项目辽宁省高等学校创新人才辽宁省教育厅基础项目

U183920051LR2019031LJ2019JL006

2024

应用力学学报
西安交通大学

应用力学学报

CSTPCD北大核心
影响因子:0.398
ISSN:1000-4939
年,卷(期):2024.41(4)
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