一种由圆柱体试件的侧向压缩力-位移关系同时测量材料弹性模量和泊松比的新方法
|
摘要
材料的弹性模量和泊松比是材料表征的重要力学参数,传统的压缩试验需要同时测量荷载、压缩和横向变形,才能实现对弹性模量和泊松比的同时测量。本文从Hertz接触理论出发,推导出弹性圆柱体在侧向压缩下的位移-力关系公式,在该关系式中位移与力的关系除与试件的几何尺寸相关外,还取决于材料的弹性模量和泊松比。因此,可以通过对侧向压缩试验测得的力-位移关系进行非线性拟合,得到材料的弹性模量和泊松比。本文通过对硅胶材料开展轴向与侧向压缩试验,对比两种试验测量得到的弹性模量和泊松比,结果较为一致,验证了本文提出方法的可行性。对于模量较小的软物质,因加载过程的荷载常常较小,系统测量的位移可代表试件的变形位移,故本文提出的新测量方法特别适合应用于该类型材料的相关性能测量。
Young′s modulus and Poisson′s ratio are significant mechanical parameters to characterize the properties of the materials. However, the simultaneous measurement of them is not easy in the traditional compression experiments as the pressure, the displacements and the lateral deformation are all needed to be gauged at the same time. In this work, the formula of the displacement-force relationship under the lateral compression is deduced based on the Hertz contact theory. The relationship is determined by the geometric parameters of the materials as well as the Young′s modulus and the Poisson′s ratio. Therefore, the Young′s modulus and the Poisson′s ratio can be obtained by nonlinear fitting of the force-displacement relationship measured under lateral compression. The feasibility of the method is verified by comparing the measurements in the axial and the lateral compression tests of silica gel materials, which are in good agreement. As for the soft materials with lower elastic modulus, the load is often smaller in the loading process, so it is rational to substitute the displacement obtained from the testing machine for the actual displacement of the specimen, which makes the new method especially suitable for related mechanical properties measurement of this type of materials.
Young′s modulus and Poisson′s ratio are significant mechanical parameters to characterize the properties of the materials. However, the simultaneous measurement of them is not easy in the traditional compression experiments as the pressure, the displacements and the lateral deformation are all needed to be gauged at the same time. In this work, the formula of the displacement-force relationship under the lateral compression is deduced based on the Hertz contact theory. The relationship is determined by the geometric parameters of the materials as well as the Young′s modulus and the Poisson′s ratio. Therefore, the Young′s modulus and the Poisson′s ratio can be obtained by nonlinear fitting of the force-displacement relationship measured under lateral compression. The feasibility of the method is verified by comparing the measurements in the axial and the lateral compression tests of silica gel materials, which are in good agreement. As for the soft materials with lower elastic modulus, the load is often smaller in the loading process, so it is rational to substitute the displacement obtained from the testing machine for the actual displacement of the specimen, which makes the new method especially suitable for related mechanical properties measurement of this type of materials.
引文
[1] Scheibert J,Prevost A,Debrgeas G,et al.Stress field at a sliding frictional contact:Experiments and calculations[J].Journal of the Mechanics and Physics of Solids,2009,57(12):1921-1933.
[2] 蒋锐,胡小方,许晓慧,等.纳米压痕法研究PZT压电薄膜的力学性能[J].实验力学,2007,22(6):575-580 (JIANG Rui,HU Xiaofang,XU Xiaohui,et al.Study of mechanical properties of PZT piezoelectric film by nano-indentation technique[J].Journal of Experimental Mechanics,2007,22(6):575-580 (in Chinese))
[3] 苏飞,张铮,熊吉,等.电镀铜薄膜力学性能的实验研究[J].实验力学,2012,27(5):565-569 (SU Fei,ZHANG Zheng,XIONG Ji,et al.Experimental study of mechanical properties for electroplated copper film[J].Journal of Experimental Mechanics,2012,27(5):565-569 (in Chinese))
[4] 彭先洪,郝松林.影像云纹法测量材料泊松比的实验研究[J].实验力学,1992,7(2):202-207 (PENG Xianhong,HAO Songlin.Measurement of Poisson′s ratio of nonmetal materials by shadow moire method[J].Journal of Experimental Mechanics,1992,7(2):202-207 (in Chinese))
[5] 谭晓华,仇巍,李晓雷,等.软材料接触力学问题的实验研究[J].实验力学,2010,25(5):509-515 (TAN Xiaohua,QIU Wei,LI Xiaolei,et al.Experimental analysis of mechanics problem within soft material contact field in large deformation[J].Journal of Experimental Mechanics,2010,25(5):509-515 (in Chinese))
[6] 单桂芳,杨伟,冯建民,等.材料泊松比测试方法的研究进展[J].材料导报,2006(3):15-20 (SHAN Guifang,YANG Wei,FENG Jianmin,et al.Advances in test methods for Poisson′s ratio of materials[J].Material Review,2006(3):15-20 (in Chinese))
[7] 陈新忠,曹远威,刘世伟,等.基于数字图像的非接触式泊松比测试方法[J].煤炭学报,2014,39(S2):366-371 (CHEN Xinzhong,CAO Yuanwei,LIU Shiwei,et al.Non-contact testing method for Poisson ratio based on digital image[J].Journal of China Coal Society,2014,39(S2):366-371 (in Chinese))
[8] 瞿启云,曹爱民,焦平,等.基于三维数字图像相关法测量复合材料泊松比[J].材料科学与工程学报,2018,36(2):258-262 (QU Qiyun,CAO Aimin,JIAO Ping,et al.Measurement of Poisson ratio of composite materials based on tridimensional digital-image relativity method[J].Journal of Materials Science & Engineering,2018,36(2):258-262 (in Chinese))
[9] 申志彬,邓斌,潘兵.推进剂粘弹性泊松比测试的数字图像相关方法[J].固体火箭技术,2016,39(4):513-518 (SHEN Zhibin,DENG Bin,PAN Bing.Digital image correlation method for measuring viscoelastic Poisson′s ratio of propellant[J].Journal of Solid Rocket Technology,2016,39(4):513-518 (in Chinese))
[10] 潘兵.数字图像相关方法及其在实验力学中的应用[D].清华大学,2007:4-7 (PAN Bing.Research on digital image correlation with its application in experimental mechanics[D].Tsinghua University,2007:4-7 (in Chinese))
[11] Timoshenko S P,Goodier J N.弹性理论(第3版)[M].北京:清华大学出版社,2004:398-418 (Timoshenko S P,Goodier J N.Theory of elasticity(3rd ed)[M].Beijing:Tsinghua University Press,2004:398-418 (in Chinese))
[2] 蒋锐,胡小方,许晓慧,等.纳米压痕法研究PZT压电薄膜的力学性能[J].实验力学,2007,22(6):575-580 (JIANG Rui,HU Xiaofang,XU Xiaohui,et al.Study of mechanical properties of PZT piezoelectric film by nano-indentation technique[J].Journal of Experimental Mechanics,2007,22(6):575-580 (in Chinese))
[3] 苏飞,张铮,熊吉,等.电镀铜薄膜力学性能的实验研究[J].实验力学,2012,27(5):565-569 (SU Fei,ZHANG Zheng,XIONG Ji,et al.Experimental study of mechanical properties for electroplated copper film[J].Journal of Experimental Mechanics,2012,27(5):565-569 (in Chinese))
[4] 彭先洪,郝松林.影像云纹法测量材料泊松比的实验研究[J].实验力学,1992,7(2):202-207 (PENG Xianhong,HAO Songlin.Measurement of Poisson′s ratio of nonmetal materials by shadow moire method[J].Journal of Experimental Mechanics,1992,7(2):202-207 (in Chinese))
[5] 谭晓华,仇巍,李晓雷,等.软材料接触力学问题的实验研究[J].实验力学,2010,25(5):509-515 (TAN Xiaohua,QIU Wei,LI Xiaolei,et al.Experimental analysis of mechanics problem within soft material contact field in large deformation[J].Journal of Experimental Mechanics,2010,25(5):509-515 (in Chinese))
[6] 单桂芳,杨伟,冯建民,等.材料泊松比测试方法的研究进展[J].材料导报,2006(3):15-20 (SHAN Guifang,YANG Wei,FENG Jianmin,et al.Advances in test methods for Poisson′s ratio of materials[J].Material Review,2006(3):15-20 (in Chinese))
[7] 陈新忠,曹远威,刘世伟,等.基于数字图像的非接触式泊松比测试方法[J].煤炭学报,2014,39(S2):366-371 (CHEN Xinzhong,CAO Yuanwei,LIU Shiwei,et al.Non-contact testing method for Poisson ratio based on digital image[J].Journal of China Coal Society,2014,39(S2):366-371 (in Chinese))
[8] 瞿启云,曹爱民,焦平,等.基于三维数字图像相关法测量复合材料泊松比[J].材料科学与工程学报,2018,36(2):258-262 (QU Qiyun,CAO Aimin,JIAO Ping,et al.Measurement of Poisson ratio of composite materials based on tridimensional digital-image relativity method[J].Journal of Materials Science & Engineering,2018,36(2):258-262 (in Chinese))
[9] 申志彬,邓斌,潘兵.推进剂粘弹性泊松比测试的数字图像相关方法[J].固体火箭技术,2016,39(4):513-518 (SHEN Zhibin,DENG Bin,PAN Bing.Digital image correlation method for measuring viscoelastic Poisson′s ratio of propellant[J].Journal of Solid Rocket Technology,2016,39(4):513-518 (in Chinese))
[10] 潘兵.数字图像相关方法及其在实验力学中的应用[D].清华大学,2007:4-7 (PAN Bing.Research on digital image correlation with its application in experimental mechanics[D].Tsinghua University,2007:4-7 (in Chinese))
[11] Timoshenko S P,Goodier J N.弹性理论(第3版)[M].北京:清华大学出版社,2004:398-418 (Timoshenko S P,Goodier J N.Theory of elasticity(3rd ed)[M].Beijing:Tsinghua University Press,2004:398-418 (in Chinese))
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |