损伤力学方法预估板状构件的疲劳裂纹形成寿命
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摘要
金属构件疲劳失效是许多工程领域中关系到机械设备与工程结构使用安全性以及成本经济性的一个重要因素,由于工程需要的迫切性与疲劳问题的复杂性,将损伤力学应用于疲劳分析是一个重要的研究方向。疲劳失效主要由两部分组成:裂纹形成和裂纹扩展。对于裂纹形成阶段,传统的分析方法还存在一定的难度;而裂纹扩展阶段,目前大多是采用断裂力学方法进行分析。相对而言,对于裂纹扩展阶段的分析,要比裂纹形成阶段的分析成熟合理,所以,对疲劳裂纹形成寿命问题的研究有一定的意义。
本文主要是研究建立大范围损伤条件下板状构件疲劳裂纹形成问题的耦联系统及能量原理,并应用其推导板状构件疲劳裂纹形成寿命预估的封闭解答,得到分析板状构件疲劳裂纹形成寿命的新体系。
应用虚功原理推导了平面应力板状构件疲劳裂纹形成寿命的封闭解。对大范围损伤条件下平面应力板状构件的疲劳裂纹形成寿命预估问题,采用变分原理进行了分析。定义了该问题的耦联系统,建立了该耦联系统的零差功原理、耦联势能原理和耦联余能原理。应用耦联势能原理导出了平面应力板状构件在大范围损伤条件下的疲劳裂纹形成寿命预估的封闭解。
作为本文方法的应用,对平面应力板状构件疲劳裂纹形成寿命进行了计算,给出了预估其疲劳裂纹形成寿命的方法,并计算了算例。与试验数据进行比较,预测结果较为理想,在大范围损伤的情况下,采用此方法预估板状构件的疲劳裂纹形成寿命是可行的,并预估了不同几何形状的板状构件疲劳裂纹形成寿命。
Fatigue failure of metal component is an important factor relating to mechanical equipment and engineering structural use safety and cost economy in many engineerings. And the application of damage mechanics in fatigue analysis is becoming an important research direction owing to the urgency of engineering requirements and the complexity of fatigue problems.The fatigue failure process consists of two stages:fatigue crack initiation and crack propagation. It has certain difficulty in the use of traditional analysis method in analyzing crack initiation. Second, crack propagation, in which stage fracture mechanics method is mostly adopted at present. Comparatively speaking, the analysis of crack propagation stage is more mature and reasonable than that of crack initiation stage, therefore, the study on problem of crack initiation lives has certain significance.
This paper mainly studies the establishment of energy principle and coupled system of fatigue crack initiation problem of plate-like component with large range damage conditions, then the closed form solution of prediction to crack initiation lives of plate-like components is derived based on the above achievements, and finally, a new system on the analysis to crack initiation lives of plate-like components is obtained.
Applying virtual work principle, the closed form solution is obtained for evaluating crack initiation lives of a plate-like component under plane stress. Applying variational principles, fatigue crack initiation lives is evaluated for a plate-like component with large range damage. Coupled system is defined firstly, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of a plate-like component under plane stress.
As an application, fatigue crack initiation lives of the plate-like components is evaluated, the method is given for evaluating its fatigue crack initiation lives. Compared with the experimental data to predict the results more desirable, the use of this method predicts fatigue crack initiation lives of plate-like component with large range damage is feasible,and predicts fatigue crack initiation lives of different geometric shapes of plate-like components.
本文主要是研究建立大范围损伤条件下板状构件疲劳裂纹形成问题的耦联系统及能量原理,并应用其推导板状构件疲劳裂纹形成寿命预估的封闭解答,得到分析板状构件疲劳裂纹形成寿命的新体系。
应用虚功原理推导了平面应力板状构件疲劳裂纹形成寿命的封闭解。对大范围损伤条件下平面应力板状构件的疲劳裂纹形成寿命预估问题,采用变分原理进行了分析。定义了该问题的耦联系统,建立了该耦联系统的零差功原理、耦联势能原理和耦联余能原理。应用耦联势能原理导出了平面应力板状构件在大范围损伤条件下的疲劳裂纹形成寿命预估的封闭解。
作为本文方法的应用,对平面应力板状构件疲劳裂纹形成寿命进行了计算,给出了预估其疲劳裂纹形成寿命的方法,并计算了算例。与试验数据进行比较,预测结果较为理想,在大范围损伤的情况下,采用此方法预估板状构件的疲劳裂纹形成寿命是可行的,并预估了不同几何形状的板状构件疲劳裂纹形成寿命。
Fatigue failure of metal component is an important factor relating to mechanical equipment and engineering structural use safety and cost economy in many engineerings. And the application of damage mechanics in fatigue analysis is becoming an important research direction owing to the urgency of engineering requirements and the complexity of fatigue problems.The fatigue failure process consists of two stages:fatigue crack initiation and crack propagation. It has certain difficulty in the use of traditional analysis method in analyzing crack initiation. Second, crack propagation, in which stage fracture mechanics method is mostly adopted at present. Comparatively speaking, the analysis of crack propagation stage is more mature and reasonable than that of crack initiation stage, therefore, the study on problem of crack initiation lives has certain significance.
This paper mainly studies the establishment of energy principle and coupled system of fatigue crack initiation problem of plate-like component with large range damage conditions, then the closed form solution of prediction to crack initiation lives of plate-like components is derived based on the above achievements, and finally, a new system on the analysis to crack initiation lives of plate-like components is obtained.
Applying virtual work principle, the closed form solution is obtained for evaluating crack initiation lives of a plate-like component under plane stress. Applying variational principles, fatigue crack initiation lives is evaluated for a plate-like component with large range damage. Coupled system is defined firstly, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of a plate-like component under plane stress.
As an application, fatigue crack initiation lives of the plate-like components is evaluated, the method is given for evaluating its fatigue crack initiation lives. Compared with the experimental data to predict the results more desirable, the use of this method predicts fatigue crack initiation lives of plate-like component with large range damage is feasible,and predicts fatigue crack initiation lives of different geometric shapes of plate-like components.
引文
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13俞树荣,曹睿,严志刚,陈剑虹.钝化的预裂纹尖端产生的短裂纹对解理断裂的影响.机械工程学报, 2005, 41(3): 47-52
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2程育仁,缪龙秀,侯炳麟.疲劳强度.北京:中国铁道出版社,1990:1-4
3徐灏.疲劳强度.北京:高等教育出版社, 1988:2-9
4Л.М.什科利尼克.疲劳试验方法手册.陈玉坤译.上海:上海科技出版社, 1983:1-12
5金丹,陈旭.多轴随机载荷下的疲劳寿命估算方法.力学进展, 2006, 36(1):65-74
6付德龙,张莉,程靳.基于塑性应变能的多轴低周疲劳寿命预测模型.工程力学, 2007, 24(3):54-57
7石多奇,杨晓光,王延荣.一种考虑拉伸保持效应的多轴疲劳寿命模型.力学学报, 2006, 38(2):255-261
8蒋荟,杨晓华.预腐蚀后拉伸超载对LC4CS铝合金疲劳性能的影响.中国工程科学, 2006, 8(2):44-46
9范志超,陈学东,蒋家羚. 16MnR钢循环蠕变-疲劳交互作用损伤力学模型.固体力学学报, 2006, 27(1):65-70
10陈学东,范志超,陈凌,蒋家羚,杨铁成.三种疲劳蠕变交互作用寿命预测模型的比较及其应用.机械工程学报, 2007,43(1):62-68
11蒋家羚,陈凌.疲劳-蠕变交互作用的寿命预测探讨.材料研究学报, 2007, 21(5): 537-541
12莫涛,赵杰. OCr18Ni9裂纹试样的室温蠕变现象及对裂纹扩展的延滞效应.机械强度, 2007, 29(6):997-1000
13俞树荣,曹睿,严志刚,陈剑虹.钝化的预裂纹尖端产生的短裂纹对解理断裂的影响.机械工程学报, 2005, 41(3): 47-52
14李晶晶,田常海,汪越胜. U71Mn和U75V钢轨钢疲劳短裂纹的扩展行为.钢铁研究学报, 2006, 18(4):37-40
15陈立杰,谢里阳.某低压涡轮工作叶片高温低循环疲劳寿命预测.东北大学学报, 2005, 26(7):673-676
16陈立杰,江铁强.低循环疲劳寿命预测的幂指函数模型.机械强度, 2006, 28(5): 761-765
17高镇同.疲劳应用统计学.北京:国防工业出版社, 1986:1-187
18 T.V.Duggan, J. Byrne. Fatigue as a Design Criterion. London: Macmillan Press, 1977:128-211
19 H.T.Carten, T.J.Dolan. Cumulative Fatigue Damage. Proceedings of an International Conferrence on Fatigue of Metals, London, 1956,1:235-246
20吴富民.结构疲劳强度.西安:西北工业大学出版社, 1985:150-179
21 N.E.Dowling, W.R.Brose,W.K.Wilson. Notched Member Fatigue Life Prediction by the Local Stress Strain Approach. Fatigue Under Complex Loading, 1977:SAE6:55-84
22王中,高镇同.疲劳缺口系数和复杂载荷下寿命估算.力学学报, 1986,18(4):335-340
23 Yao W X. Stress Field Intensity Approach for Prediction Fatigue Life. International Journal of Fatigue, 1993,15(3):243-245
24 L.M.Kachanov. On Rupture Time under Condition of Crack. Izv. Akad. Nauk SSSR,Otd. Techn. Nauk, 1958,8:26-31(in Russian)
25 Y.N.Rabotvov. On the Equation of State for Creep. Progress in Applied Mechanics, 1963:307-315
26 J.Jason, J.Hult. Fracture Mechanics and Damage Mechanics, a Combined Approach. J.de Mech.Appl.,1977,1(1):59-64
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