三维准静载弹塑性弯曲裂纹张开位移
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摘要
主要研究准静载荷作用下的三维弹塑性弯曲裂纹尖端的张开位移问题。综合考虑了准静作用应力,三维塑性区域边界上正应力与剪应力,利用二阶摄动方法计算了三维弹塑性弯曲裂纹尖端的张开位移。用数值解法计算出三维弹塑性弯曲裂纹尖端张开位移,作图分析了三维弹塑性弯曲裂纹尖端张开位移与三维裂纹体几何尺寸之间的变化关系。三维弹塑性弯曲裂纹尖端张开位移随着三维裂纹体厚度的增大而减小,随着三维裂纹体厚度的均匀增大,三维弹塑性弯曲裂纹尖端张开位移尺寸不断减小,减小的幅度越来越小,最终趋于平面应变状态下的弹塑性弯曲裂纹尖端张开位移尺寸。当三维裂纹体几何尺寸相同时,三维弯曲裂纹尖端张开位移尺寸随外载荷的不断增大而逐渐增大。建立了一个计算三维弹塑性弯曲裂纹尖端张开位移尺寸的崭新理论模型。
In this article, three dimensional elastic-plastic curved crack tip opening displacement under quasi-static loads has been mainly studied, and three dimensional curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method, where the effects of quasi-static applied stresses and quasi-static normal and shear stresses on the boundaries of plasticity area are synthetically taken into considerations. Three dimensional curved elastic-plastic crack tip opening displacement has been calculated by numerical solutions, diagrams have been constructed to analyse the transformation relationships between curved crack tip opening displacement and three dimensional crack body geometrical measurement. Curved crack tip opening displacement will decrease when three dimensional crack body thickness increases. When crack body thickness increases evenly, three dimensional curved crack tip opening displacement will continuously decrease, furthermore, the decrease extent will be more and more slightly, and tend to plane strain state ultimately. Curved crack tip opening displacement will increase when external loads increase with the same crack body thickness. A new theoretical model where curved crack tip opening displacement was calculated has been established in three dimensional crack body.
In this article, three dimensional elastic-plastic curved crack tip opening displacement under quasi-static loads has been mainly studied, and three dimensional curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method, where the effects of quasi-static applied stresses and quasi-static normal and shear stresses on the boundaries of plasticity area are synthetically taken into considerations. Three dimensional curved elastic-plastic crack tip opening displacement has been calculated by numerical solutions, diagrams have been constructed to analyse the transformation relationships between curved crack tip opening displacement and three dimensional crack body geometrical measurement. Curved crack tip opening displacement will decrease when three dimensional crack body thickness increases. When crack body thickness increases evenly, three dimensional curved crack tip opening displacement will continuously decrease, furthermore, the decrease extent will be more and more slightly, and tend to plane strain state ultimately. Curved crack tip opening displacement will increase when external loads increase with the same crack body thickness. A new theoretical model where curved crack tip opening displacement was calculated has been established in three dimensional crack body.
引文
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[11] 郭万林,于培师.构件三维断裂与疲劳力学及其在航空工程中的应用[J].固体力学学报,2010,31(5): 553-571 GUO WanLin,YU PeiShi.Three dimensional fracture and fatigue mechanics of structures and its application in aeronautical engineering[J].Chinese Journal of Solid Mechanics,2010,31(5): 553-571
[12] 杨大鹏. 微弯延伸裂纹断裂特性的研究[D]. 武汉:华中科技大学,2006: 20-28YANG DaPeng.Research on fracture behaviors of slightly curved extension crack[D]. Wuhan:Huazhong University of Science and Technology,2006: 20-28(In Chinese).
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[2] Wei-Qiu Chen.Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling[J].Acta Mechanica Sinica,2015,31(5):601-626
[3] 王璐,王正,于森. 高温低周疲劳表面短裂纹合体与干涉行为的实验研究及数值模拟[J].机械强度,2008,30(4):642-646.WANG Lu,WANG Zheng,YU Sen.Experimental study and numerical simulation on coalescence and interference of short cracks for low cycle fatigue at high temperature[J].Journal of Mechanical Strength,2008,30(4):642-646 (In Chinese).
[4] Sheng-Qi Yang, Yan-Hua Huang, P. G. Ranjith, Yu-Yong Jiao, Jian Ji.Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression[J].Acta Mechanica Sinica,2015,31(6):871-889
[5] 丁振宇,王效贵,高增梁. 加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟[J].工程力学,2013,30(8):244-250.DING ZhenYu, WANG XiaoGui, GAO ZengLiang. Numerical simulation of the effect of loading history and crack closure on crack propagation behaviour[J]. Engineering Mechanics, 2013,30(8):244-250 (In Chinese).
[6] 赵振华,陈伟,吴铁鹰. 高低周复合载荷对钛合金疲劳裂纹扩展性能的影响[J]. 机械科学与技术, 2012,31(4):643-647.ZHAO ZhenHua, CHEN Wei, WU TieYing. The effect of combined cycle fatigue load on the fatigue crack propagation of Titanium alloy[J]. Mechanical Science and Technology for Aerospace Engineering, 2012,31(4):643-647 (In Chinese).
[7] Chengqi Sun Xiaolong Liu Youshi Hong.A two-parameter model to predict fatigue life of high-strength steels in a very high cycle fatigue regime[J].Acta Mechanica Sinica,2015,31(6):383-391
[8] 丁遂栋, 孙利民. 断裂力学 [M]. 北京:机械工业出版社, 1997:148-169DING SuiDong, SUN LiMin. Fracture Mechanics[M]. Beijing:Machine Industry Press, 1997:148-169 (In Chinese)
[9] 杨卫. 宏微观断裂力学 [M]. 北京:国防工业出版社, 1995:65-70YANG Wei. Macro micro fracture mechanics[M]. Beijing:National Defence Industry Press, 1995: 65-70 (In Chinese)
[10] 杨大鹏,赵耀,白玲. 准静载荷作用下的弹塑性微弯延伸裂纹塑性区[J]. 应用力学学报, 2010,27(2): 401-405YANG DaPeng, ZHAO Yao,BAI Ling. Research on plasticity area of slightly curved extension elasticity-plasticity crack under quasi static loads[J]. Chinese Journal of Applied Mechanics, 2010, 27(2): 401-405 (In Chinese).
[11] 郭万林,于培师.构件三维断裂与疲劳力学及其在航空工程中的应用[J].固体力学学报,2010,31(5): 553-571 GUO WanLin,YU PeiShi.Three dimensional fracture and fatigue mechanics of structures and its application in aeronautical engineering[J].Chinese Journal of Solid Mechanics,2010,31(5): 553-571
[12] 杨大鹏. 微弯延伸裂纹断裂特性的研究[D]. 武汉:华中科技大学,2006: 20-28YANG DaPeng.Research on fracture behaviors of slightly curved extension crack[D]. Wuhan:Huazhong University of Science and Technology,2006: 20-28(In Chinese).
[13] 张斌.材料结构宏观三维断裂和微观破坏行为研究[D]. 南京:南京航空航天大学,2005: 20-25ZHANG Bin.Three dimensional fracture of macro-structure and failure of micro-materials[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2005: 20-25(In Chinese).