粘弹性力学在高温铸造合金单向拉伸试验中的应用
Application of Viscoelasticity Mechanics into Uniaxial Tensile Test of High Temperature Cast Alloy

作者: 田红亮 , 朱大林 , 秦红玲 :三峡大学机械与材料学院,宜昌;

关键词: 麦克斯韦模型开尔文模型蠕变曲线应力–应变微分型本构关系 Maxwell Model Kelvin Model Creep Curve Stress-Strain Differential Constitutive Relation

摘要:

给出了Kelvin链的应力–应变微分型本构关系。全面考虑初始条件,推导了Burgers四参量流体、Kelvin- Maxwell六参量模型在阶跃函数单向应力作用下的总应变通解。Burgers四参量流体、Kelvin-Maxwell六参量模型都可以近似地描述金属材料蠕变曲线的前两个阶段,但都不能反映第三个阶段。铸造Mar-M200合金蠕变曲线的计算表明,两种理论预测与实验测量的结果的一致性较好,特别是Kelvin-Maxwell六参量模型的最大相对误差仅为5.4765779%。

The stress-strain differential constitutive relation was given for Kelvin chain. On basis of all the initial conditions taken into account, the general solutions of total strain were derived for Burgers fluid with 4 parameters and Kelvin-Maxwell model with 6 ones under the step function uniaxial stress. Both Burgers fluid with 4 parameters and Kelvin-Maxwell model with 6 ones could approximately describe the former two stages of creep curve but not reflect the third stage. Numerical calculation for cast Mar-M200 alloy creep curve shows that two theories predictions are in good agreement with test measurement results, especially the maximum relative error of Kelvin-Maxwell model with 6 parameters is only 5.4765779%.

文章引用: 田红亮 , 朱大林 , 秦红玲 (2013) 粘弹性力学在高温铸造合金单向拉伸试验中的应用。 力学研究, 2, 7-12. doi: 10.12677/IJM.2013.21002

参考文献

[1] M. R. Falvo, R. M. Taylor II, A. Helser, et al. Nanometre-scale rolling and sliding of carbon nanotubes. Nature, 1999, 397(6716): 236-238.

[2] Q. Wang, V. K. Varadan and S. T. Quek. Small scale effect on elastic buckling of carbon nanotubes with nonlocal contin-uum models. Physics Letters A, 2006, 357(2): 130-135.

[3] Y. Q. Zhang, G. R. Liu and X. Y. Xie. Free transverse vibrations of dou-ble-walled carbon nanotubes using a theory of nonlocal elasticity. Physical Review B, 2005, 71(19): 195404-1-195404-7.

[4] 徐斌, 欧进萍, 姜节胜等. 经典阻尼系统响应求解的分离变换辛解法[J]. 机械强度, 2008, 30(1): 001-005.

[5] 冯振宇. 四种粘弹性模型薄板的自由振动[J]. 西安公路交通大学学报, 1998, 18(3): 59-63.

[6] 祝彦知, 程楠, 薛保亮. 四种粘弹性地基上弹性地基板的自由振动解[J]. 强度与环境, 2001, 3: 31-41.

[7] 祝彦知, 薛保亮, 王广国. 粘弹性地基上粘弹性地基板的自由振动解析[J]. 岩土力学与工程学报, 2002, 21(1): 112-118.

[8] C. M. Wang. Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions. Journal of Engineering Mechanics, 1995, 121(6): 763-765.

[9] 李元媛, 蔡睿贤. 矩形薄板弯曲的严格简明解析解[J]. 机械工程学报, 2008, 44(10): 72-76.

[10] A. A. Pisano, P. Fuschi. Closed form solution for a nonlo-cal elastic bar in tension. International Journal of Solids and Structures, 2003, 40(1): 13-23.

[11] X. C. Zhao, Y. J. Lei and J. P. Zhou. Strain analysis of nonlocal viscoelastic Kelvin bar in tension. Applied Mathematics and Mechanics (English Edition), 2008, 29(1): 67-74.

[12] 赵雪川, 雷勇军, 周建平. 非局部Kelvin粘弹性直杆受轴向拉力作用的应变分析[J]. 应用数学和力学, 2008, 29(1): 62- 68.

[13] Y. Q. Zhang, G. R. Liu and X. Han. Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure. Physics Letters A, 2006, 349(5): 370-376.

[14] C. Q. Sun, K. X. Liu and G. X. Lu. Dynamic torsional buckling of multi-walled car-bon nanotubes embedded in an elastic medium. Acta Mechanica Sinica, 2008, 24(5): 541-547.

[15] 诸德超, 邢誉峰. 工程振动基础[M]. 北京: 北京航空航天大学出版社, 2004: 89-96.

[16] 赵雪川, 雷勇军, 唐国金. 传递函数法在非局部弹性梁动力学分析中的应用[J]. 振动与冲击, 2007, 26(5): 4-7.

[17] 杨挺青. 粘弹性力学[M]. 武汉: 华中理工大学出版社, 1990: 24-28.

[18] 申鸿恩. 粘弹性理论应用一例[J]. 力学与实践, 1984, 6(5): 18-21.

[19] 冶军. 美国镍基高温合金[M]. 北京: 科学出版社, 1978: 340- 350.

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