A Lagrangian inverse analysis technique for studying dynamic mechanical properites of brittle materials based on digital image correlation
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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.
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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
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