疲劳寿命在强度稳定综合理论中的运算
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摘要
本文说明了强度稳定综合理论中的切线模量因子、比例极限定律和强度利用率函数等概念是弹性力学有关概念的延伸，既可以用于强度理论，也可以用于稳定理论。
利用应变能定理的概念对切线模量理论进行了新的论证和应用，进一步完善了强度稳定综合理论。
探讨了强度稳定综合理论用于疲劳寿命计算的方法。通过材料力学疲劳性能曲线和断裂力学之间有关参量间的演变关系，得到了疲劳寿命与裂纹半长的关系，即疲劳寿命的折算裂纹长度，建立了两者之间的函数关系并利用这个函数关系说明了疲劳寿命的切线模量因子法，能反映各种材料疲劳寿命的共同变化规律，试验数据可在不同材料之间互相参考使用，具有重大意义。
对已有的材料力学疲劳性能试验曲线进行分析整理，利用试验数据绘制了相对应力应变曲线、切线模量因子曲线和疲劳寿命曲线，利用这三种无量纲参数曲线发现了其中存在的规律性，即在某种程度上实验曲线可以互相取代，并用试验数据对此进行了讨论，并由此推断，如果找出材料彼此的共性或彼此之间的系统误差就可以将一种材料的试验曲线供其它材料参考使用，这是一种估算材料的疲劳寿命的简便方法，对工程而言具有实用性。
本文还与现有的疲劳寿命预测方法进行了横向比较，说明其有独到的优点。
In this dissertation, the fact that the concepts of tangent modulus factor (φ_(1),), proportional limit law (PLL) and strength utilization ratio function (SURF) in the combined theory of strength and stability (CTSS) are the extension of concerned concepts in elastic mechanics is illustrated. These concepts can be applied not only in strength theory but also in stability theory.
By using strain energy theory, tangent modulus theory is farther discussed and applied, and the combined theory of strength and stability is improved.
The approach to apply the combined theory of strength and stability into fatigue analysis is discussed. According to the relationship between material fatigue performance curve and concerned parameters in fracture mechanics, the relationship between fatigue life and crack half length is obtained, that is equivalent crack length of fatigue life. The function relationships between these two aspects are constructed. The experiment data show that this method can express the same character of fatigue life of all kinds of materials and experiment data acquired from different materials can be used each other. That is meaningful.
The existed material fatigue performance test curves are dealt with and analyzed, and the non-dimensional stress-strain curve, tangent modulus factor curve and fatigue life curve are drawn based on the experiment data, and these three non-dimensional parameter curves are used to find the inherent rules that the test curves can be replaced each other to some extent. It can be concluded that if the common character and system error of these materials are found, the test curve of a certain material can be used for reference by another material. This is a simple approach about fatigue life estimate and is engineering practical.
At the same time, the approach proposed in this thesis is compared with
existed approaches to estimate fatigue life, and the result shows its unique advantages.
利用应变能定理的概念对切线模量理论进行了新的论证和应用，进一步完善了强度稳定综合理论。
探讨了强度稳定综合理论用于疲劳寿命计算的方法。通过材料力学疲劳性能曲线和断裂力学之间有关参量间的演变关系，得到了疲劳寿命与裂纹半长的关系，即疲劳寿命的折算裂纹长度，建立了两者之间的函数关系并利用这个函数关系说明了疲劳寿命的切线模量因子法，能反映各种材料疲劳寿命的共同变化规律，试验数据可在不同材料之间互相参考使用，具有重大意义。
对已有的材料力学疲劳性能试验曲线进行分析整理，利用试验数据绘制了相对应力应变曲线、切线模量因子曲线和疲劳寿命曲线，利用这三种无量纲参数曲线发现了其中存在的规律性，即在某种程度上实验曲线可以互相取代，并用试验数据对此进行了讨论，并由此推断，如果找出材料彼此的共性或彼此之间的系统误差就可以将一种材料的试验曲线供其它材料参考使用，这是一种估算材料的疲劳寿命的简便方法，对工程而言具有实用性。
本文还与现有的疲劳寿命预测方法进行了横向比较，说明其有独到的优点。
In this dissertation, the fact that the concepts of tangent modulus factor (φ_(1),), proportional limit law (PLL) and strength utilization ratio function (SURF) in the combined theory of strength and stability (CTSS) are the extension of concerned concepts in elastic mechanics is illustrated. These concepts can be applied not only in strength theory but also in stability theory.
By using strain energy theory, tangent modulus theory is farther discussed and applied, and the combined theory of strength and stability is improved.
The approach to apply the combined theory of strength and stability into fatigue analysis is discussed. According to the relationship between material fatigue performance curve and concerned parameters in fracture mechanics, the relationship between fatigue life and crack half length is obtained, that is equivalent crack length of fatigue life. The function relationships between these two aspects are constructed. The experiment data show that this method can express the same character of fatigue life of all kinds of materials and experiment data acquired from different materials can be used each other. That is meaningful.
The existed material fatigue performance test curves are dealt with and analyzed, and the non-dimensional stress-strain curve, tangent modulus factor curve and fatigue life curve are drawn based on the experiment data, and these three non-dimensional parameter curves are used to find the inherent rules that the test curves can be replaced each other to some extent. It can be concluded that if the common character and system error of these materials are found, the test curve of a certain material can be used for reference by another material. This is a simple approach about fatigue life estimate and is engineering practical.
At the same time, the approach proposed in this thesis is compared with
existed approaches to estimate fatigue life, and the result shows its unique advantages.
引文
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[73] 航空工业部科学技术委员会编．应变疲劳分析手册．科学出版社，1987年8月139-148P
[2] 郑修麟，金属疲劳的定量理论．西北工业大学出版社．1994年1月，65P
[3] 徐灏．疲劳强度．高等教育出版社出版，1988年8月
[4] 王中光等译，李家宝校．材料的疲劳．国防教育出版社，1993年10月
[5] 中国力学学会，力学——迎接21世纪新的挑战．力学与实践，1985，2
[6] 陈铁云，沈惠申．结构的屈曲．上海科学技术文献出版社，1993，12
[7] Shanley, FR (1946). The Column Paradox, J.Aero.Sci.,13
[8] Shanley, FR (1947). Inelastic Column Theory, J.Aero.Sci.,14,5: 261-168P
[9] 王仁，黄克智，朱兆祥．塑性力学进展．中国铁道出版社，1988，12：268-305P
[10] Lorenze, R(1908). Achsensymmetrische Verzerrungen in dünnwandigen Hohlzylinder, Z.V.D.I. 52,1706-1713P
[11] Lorenze, R(1911). Achsensymmetrische Verzerrungen in dünnwandigen Hohlzylinder, Physik, Zeits Leipzig, Jahrg 12,241-260P
[12] Timoshenko, SP(1910). Einige Stabilitats Problem der Elastizitatstheorie, Z. Math.Physik 58,337-352P
[13] Timoshenko, SP(1914). Buckling of Cylinders, Bull, Electrotechnical Institute, St. Petersbury, Ⅺ
[14] Southwell, RV(1914).On the General Theory of Elastic stability. Phil.Trans.Roy.(London)213,A, 197-244P
[15] Lundquist, EE(1933). Strength Tests of Thin-Walled Duralumin Cylinders in Compression, NACA TR-473
[16] Roberston, A(1929).The Strength of Tubular Struts, ARC Rep.and Mem., Nol185
[17] Flupple, W(1932). Die Stabilitat der Kreiszylinderschale, In genienieur-Archiv. Band Ⅲ5, 463-506P
[18] Wilson, WM, and Newmark, NM(1993).The Strength of Thin Cylindrical Shells as Columns,Bull.255,Fng.Fxp.Station,Univ.of Illinois
[19] Karman, Th.Von, and Tsien, HS(1939). The Buckling of Spherical Shells by External Pressure, J.Aero.Scie.,7,43-50P
[20] Karman, Th. von,Dunn, LG, and Tsien, HS(1940). The Influence of Curvature on the Buckling Characteristic of Structures, J. Aero.Scie.,7,276P
[21] Karman, Th.Von, and Tsien, HS(1941). The Buckling of Thin Cylindrical Shells Under Axial Compression, J.Aero.Scie.,8,303P
[22] 李云龙．壳体的稳定性理论及其应用．上海力学，2，1998：71-78P
[23] 陈铁云，沈惠申．结构的屈曲．上海科学技术文献出版社，1993，12
[24] 周承倜．薄壳弹塑性稳定理论．国防工业出版社，1979，12
[25] 梁炳文，胡世光．弹塑性稳定理论．国防工业出版社，1983，11
[26] Stein, M(1962). The Effect on the Buckling of Cylinders of Prebuckling Deformations and Stresses Induced by Edge Support, NASA TN D-1510 217-224P
[27] Stein, M(1964). The Influence of Prebuckling Deformations and Stresses on the Buckling of Perfect Cylinders, NASA TRR-190
[28] Stein, M(1968). Some Recent Advances in the Investigation of Shell Buckling. AIAA J. 6,12,2339-2345P
[29] Tielemann, WF, and Esslinger, ME(1967). On the Postbuckling Behavior of Thin-Walled Axially Compressed Circular Cylinders of Finite Length, Proc. Symp.on the Theory of Shells, ed by D.Muster,433-479P, Univ.of Houston
[30] Yamaki, N, Otomo, K, and Matsuda, K(1975). Experiments on the
Postbuckling Behavior of Circular Cylindrical Shells Under Compression, Exp.Mech. 15,23-28P
[31] Friedrichs, Ko, and Stoker, JJ(1939). The Non-linear Boundary Value Problem of the Buckled Plate, Nat.Acad.Sci.U.S.A.,25,532-540P
[32] Friedrichs, KO(1941). On the Minimum Buckling Load for Spherical Shells, Theodore von Karman Anniversary Volume, California Institute of Technology, 258-272P
[33] Fung, YC, and Wittrick, WH(1995). A Boundary Layer Phenomenon in the Large Deflection of Thin Plates, Quart.J.Mech.Appl.Math.,8,part 2, 191-210P
[34] 黄克智，蒋智翔，郑思梁．薄壳简单边界效应理论的二次渐近方程．力学学报．13，6(1981)550-561P
[35] 林鸿荪．圆板屈曲问题中的边界现象．弹性圆薄板大挠度问题．中国科学院出版社，99-116，1954P
[36] Masur, EF, and Chang, CH(1964). Development of Boundary Layers in Buckled Plates, J.Eng.Mech.,ASCE.90,2,33-50P
[37] Shen, HS, and Chen, TY(1990). A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells Under Axial Compression, Adv. Appl. Math. &Mech. in China,Vol.2,155-172P
[38] Neale, KW(1975). Effect of Imperfections on the Plastic Buckling of Rectangular Plates, J.Appl.Mech.,42,115-120P
[39] Needleman, A(1976). An Analysis of the Imperfection Sensitivity of Square Elastic-plastic Plates under Axial Compression, Int. J. Solids Structures, 12,185-201P
[40] Rectliffe, AY(1968).Yhe Strength of Plates of Plates in Compression. Cantab Ph.D. Thesis
[41] Jerzy Maciejewaski and Jerzy Zlelneca(1984).Nonlinear Stability Problem
of an Elastic-plastic Open Conical Shell, Rozprawy Inzynierskic, Vol 32,3,361-330P
[42] Weichert, D(1984).Stability of Geometrically Non-linear Elasticplastic Shells, PT163-T165,ZAMM.Zeitschrift fur Angewandte Mathemalik and Mechabik,64,4
[43] Hill, R(1978). Aspects of Invariance in Solid Mech. Aspects in Appl. Mech.,Vol 18,1-75P
[44] Hutchinson, JW(1974). Plastic Buckling, Advances in Appl. Mech. Vol 14,67-143P
[45] Hutchinson, JW(9173). Post-bifurcation Behavior in the Plastic Range. J. Mech. Phy. Solids,Vol 21,163-190P
[46] Bushnell,D(1985).Computerized Buckling Analysis of Shells, Martinus Nij hoff Publishers, Dordrecht
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