A Lagrangian inverse analysis technique for studying dynamic mechanical properites of brittle materials based on digital image correlation
-
摘要: 利用分离式Hopkinson压杆作为加载系统，借助超高速数字图像相关性分析方法，发展了长杆试件拉氏反分析实验技术，并用于研究脆性材料在小变形条件下的动态本构特性。通过超高速相机实时拍摄冲击加载下长杆试件变形的散斑图像，再对散斑图像进行数字图像相关性（digital image correlation，DIC）分析，获得长杆试件表面速度场和应变场。随后，以脆性材料PMMA（polymethyl methacrylate）为例，从DIC分析得到的速度场中提取出不同拉格朗日位置上质点速度时程曲线，构建路径线连接整个速度场，再结合零初始条件，数值求解得到了试件中的应力时程曲线，消去时间参数后，获得了脆性材料PMMA的动态应力-应变曲线，并与Hopkinson压杆实验和准静态压缩实验的结果进行了对比，揭示了PMMA材料在小应变条件下的黏弹性本构响应特征。Abstract: Based on the Hopkinson pressure bar and digital image correlation (DIC) techniques, a new Lagrangian inverse analysis experimental method was proposed to study the dynamic constitutive relation of brittle materials. A series of speckle images of long specimen deformation were recorded by an ultra-high-speed camera. The speckle images were processed by DIC to derive the velocity fields and strain fields on the surface of a long specimen. Based on the multi-particles velocity history curves measured by DIC, the whole velocity fields were constructed by many path lines. Then, a Lagrangian inverse analysis method was established for the dynamic constitutive relation of brittle rate-dependent PMMA materials by numerical solution. The results were compared with those of Hopkinson pressure bar test and quasi-static compression test, which display the characteristics of viscoelastic constitutive response of PMMA under the condition of small strain.
-
图 2 不同时刻的DIC分析得到的位移场云图
Figure 2. Displacement field measured from DIC at different times
-
[1] 王礼立, 王永刚.应力波在用SHPB研究材料动态本构特性中的重要作用[J].爆炸与冲击, 2005, 25(1):17-25. doi: 10.3321/j.issn:1001-1455.2005.01.004WANG Lili, WANG Yonggang. The important role of stress wave in the study on dynamic constitutive behavior of materials by SHPB[J]. Explosion and Shock Waves, 2005, 25(1):17-25. doi: 10.3321/j.issn:1001-1455.2005.01.004 [2] 王礼立, 朱珏, 赖华伟.冲击动力学研究中实测波信息的解读分析[J].高压物理学报, 2010, 24(4):279-285. http://d.old.wanfangdata.com.cn/Conference/6414825WANG Lili, ZHU Jue, LAI Huawei. Understanding and interpreting of the measured wave signals in impact dynamics studies[J]. Chinese Journal of High Pressure Physics, 2010, 24(4):279-285. http://d.old.wanfangdata.com.cn/Conference/6414825 [3] FOWLES R. Conservation relations for spherical and cylindrical stress waves[J]. Journal of Applied Physics, 1970, 41:2740-2741. doi: 10.1063/1.1659298 [4] GRADY D E. Experimental analysis of spherical wave propagation[J]. Journal of Geophysical Research, 1973, 78:1299-1307. doi: 10.1029/JB078i008p01299 [5] SEAMAN L. Lagrangian analysis for multiple stress or velocity gages in attenuating waves[J]. Journal of Applied Physics, 1974, 45:4303-4314. doi: 10.1063/1.1663050 [6] 唐志平.Lagrange分析方法及其新进展[J].力学进展, 1993, 23(3):348-359. doi: 10.3321/j.issn:1000-0992.1993.03.007TANG Zhiping. Lagrangian analysis and its recent developments[J]. Advances in Mechanics, 1993, 23(3):348-359. doi: 10.3321/j.issn:1000-0992.1993.03.007 [7] 陈叶青, 冯叔瑜.拉格朗日分析方法研究现状及应用中应注意的问题[J].爆炸与冲击, 1998, 18(1):91-96. http://www.bzycj.cn/CN/abstract/abstract10386.shtmlCHEN Yeqing, FENG Shuyu. Present conditions of Lagrangian analysis and problems should be consided in the use[J]. Explosion and Shock Waves, 1998, 18(1):91-96. http://www.bzycj.cn/CN/abstract/abstract10386.shtml [8] 陶为俊, 浣石, 蒋国平.基于最小二乘法的Lagrange分析方法研究[J].振动与冲击, 2012, 31(12):98-101. http://d.old.wanfangdata.com.cn/Periodical/zdycj201221020TAO Weijun, HUAN Shi, JIANG Guoping. Lagrangian analysis method based on least square[J]. Journal of Vibration and Shock, 2012, 31(12):98-101. http://d.old.wanfangdata.com.cn/Periodical/zdycj201221020 [9] 陶为俊, 浣石.沿时间逐步求解应力的拉格朗日分析方法研究[J].物理学报, 2012, 20:200703. doi: 10.7498/aps.61.200703TAO Weijun, HUAN Shi. Study on Lagrangian analysis for solving the stress gradually along the time[J]. Acta Physica Sinica, 2012, 20:200703. doi: 10.7498/aps.61.200703 [10] 林英睿, 王占江, 李运良, 等.依球面波粒子速度研究材料的本构关系[J].解放军理工大学学报(自然科学版), 2007, 8(6):606-610. http://d.old.wanfangdata.com.cn/Periodical/jfjlgdxxb200706009LIN Yingrui, WANG Zhanjiang, LI Yunliang, et al. Constitutive relation using particle velocity data of spherical waves[J]. Journal of PLA University of Science and Technology (Natural Science Edition), 2007, 8(6):606-610. http://d.old.wanfangdata.com.cn/Periodical/jfjlgdxxb200706009 [11] WANG L, ZHU J, LAI H. A new method combining Lagrangian analysis with Hopkinson pressure bar technique[J]. Strain, 2011, 47:173-182. doi: 10.1111/str.2011.47.issue-2 [12] WANG Lili, DING Yuanyuan, YANG Liming. Experimental investigation on dynamic constitutive behavior of aluminum foams by new inverse methods from wave propagation measurements[J]. International Journal of Impact Engineering, 2013, 62:48-59. doi: 10.1016/j.ijimpeng.2013.06.002 [13] 丁圆圆, 杨黎明, 王礼立.对基于质点速度测量的拉格朗日分析法的进一步探讨[J].宁波大学学报(理工版), 2012, 25(4):83-87. http://d.old.wanfangdata.com.cn/Periodical/nbdxxb-lg201204019DING Yuanyuan, YANG Liming, WANG Lili. A further discussion on the lagrangian analysis method based on particle velocity wave profiles measurements[J]. Journal of Ningbo University (Natural Science and Engineering), 2012, 25(4):83-87. http://d.old.wanfangdata.com.cn/Periodical/nbdxxb-lg201204019 [14] DING Yuanyuan, WANG Shilong, ZHENG Zhijun, et al. Dynamic crushing of cellular materials:A unique dynamic stress-strain state curve[J]. Mechanics of Materials, 2016, 100:219-231. doi: 10.1016/j.mechmat.2016.07.001 [15] 蒋国平, 浣石, 郝洪, 等.钢纤维高强混凝土材料的气炮试验研究[J].物理学报, 2013, 62(1):016201. http://d.old.wanfangdata.com.cn/Periodical/wlxb201301052JIANG Guoping, HUAN Shi, HAO Hong, et al. Performance of steel reinforced high strength concrete investigated in the gas gun experiment[J]. Acta Physica Sinica, 2013, 62(1):016201. http://d.old.wanfangdata.com.cn/Periodical/wlxb201301052 [16] 张磊, 胡时胜, 梁宗宪.利用拉氏分析研究冲击载荷下混凝土应力-应变曲线[J].工程力学, 2005, 22(4):163-166. doi: 10.3969/j.issn.1000-4750.2005.04.030ZHANG Lei, HU Shisheng, LIANG Zongxian. Lagrange analysis of the stress-strain relation of concrete material under impact[J]. Engineering Mechanics, 2005, 22(4):163-166. doi: 10.3969/j.issn.1000-4750.2005.04.030 [17] 赖华伟, 王礼立.用改进的基于质点速度测量的拉格朗日分析方法研究尼龙动态力学特性[J].实验力学, 2011, 26(2):221-227. http://d.old.wanfangdata.com.cn/Periodical/sylx201102017LAI Huawei, WANG Lili. Nylon dynamic mechanical behavior study through a modified Lagrangian analysis based on particle velocity profile measurement[J]. Journal of Experimental Mechanics, 2011, 26(2):221-227. http://d.old.wanfangdata.com.cn/Periodical/sylx201102017 [18] BARKER L M, HOLLENBACK R E. Laser interferometer for measuring high velocities of any reflecting surface[J]. Journal of Applied Physics, 1972, 43(11):4469-4675. https://www.researchgate.net/publication/224521486_Laser_Interferometer_for_Measuring_High_Velocities_of_Any_Reflecting_Surface [19] WENG Jidong, TAN Hua, HU Shaolou, et al. New all-fiber velocimeter[J]. Review of Scientific Instruments, 2005, 76(9):093301. doi: 10.1063/1.2008989 [20] WU Xianqian, WANG Xi, WEI Yanpeng, et al. An experimental method to measure dynamic stress-strain relationship of materials at high strain rates[J]. International Journal of Impact Engineering, 2014, 69(4):149-156. https://www.sciencedirect.com/science/article/pii/S0734743X14000554 [21] LEA L J, JARDINE A P. Application of photon Doppler velocimetry to direct impact Hopkinson pressure bars[J]. Review of Scientific Instruments, 2016, 87(2):023101. doi: 10.1063/1.4940935 [22] SUTTON M A, ORTEU J J, SCHREIER H. Image correlation for shape, motion and deformation measurements:Basic concepts, theory and applicants[M]. New York:Springer, 2009:81-116. [23] SATO K, YU Q, HIRAMOTO J, et al. A method to investigate strain rate effects on necking and fracture behaviors of advanced high-strength steels using digital imaging strain analysis[J]. International Journal of Impact Engineering, 2014, 75:11-26. https://www.sciencedirect.com/science/article/pii/S0734743X1400147X [24] LIU J, SALETTI D, PATTOFATTO S, et al. Impact testing of polymeric foam using Hopkinson bars and digital image analysis[J]. Polymer Testing, 2014, 36:101-109. doi: 10.1016/j.polymertesting.2014.03.014 [25] 申海艇, 蒋招绣, 王贝壳, 等.基于超高速相机的数字图像相关性全场应变分析在SHTB实验中的应用[J].爆炸与冲击, 2017, 37(1):15-20. http://www.bzycj.cn/CN/abstract/abstract9680.shtmlSHEN Haiting, JIANG Zhaoxiu, WANG Beike, et al. Full field strain measurement in split Hopkinson tension bar experiments by using ultra-high-speed camera with digital image correlation[J]. Explosion and Shock Waves, 2017, 37(1):15-20. http://www.bzycj.cn/CN/abstract/abstract9680.shtml [26] 刘剑飞, 胡时胜, 王道荣.用于脆性材料的Hopkinson压杆动态实验新方法[J].实验力学, 2001, 16(3):283-290. http://d.old.wanfangdata.com.cn/Periodical/sylx200103007LIU Jianfei, HU Shisheng, WANG Daorong. A novel experimental method of Hopkinson pressure bar system for brittle materials[J]. Journal of Experimental Mechanics, 2001, 16(1):283-290. http://d.old.wanfangdata.com.cn/Periodical/sylx200103007 -
下载:
图(8)
计量
- 文章访问数: 4967
- HTML全文浏览量: 1415
- PDF下载量: 41
- 被引次数: 0