Chapter 8 Thermal Strain Measurement Using Digital Image Correlation with Systematic Error Elimination Manabu Murata, Shuichi Arikawa, Satoru Yoneyama, Yasuhisa Fujimoto, and Yohei Omoto Abstract This research aims to develop a method for measuring small strains at minute area on an electronic packaging using digital image correlation. To this end, the systematic error in the measured displacement is corrected by using the relation between measured displacement and actual displacement. This relation is obtained by measuring rigid rotation and in-plane translation. The strain distribution with high spatial resolution can be obtained from the displacement distribution because the systematic error that affects the resolution of the strain is eliminated. This error elimination method is applied to the thermal strain measurement of a bimaterial which is composed of copper and steel. Results show that high spatial resolution strain distributions at minute area can be obtained by using this method. Keywords DIC • Electronic packing • Thermal strain • High magnification • Systematic error elimination 8.1 Introduction Electronic packaging is the component of electronic devices. The packaging consists of heterogeneous materials such as solder and silicon, so its coefficient of thermal expansion on the packaging is not uniform. Therefore, thermal stress and strain occur when it is used. Because of this thermal stress, cracks in solder and delamination of silicon tip occur on a packaging, and these cause breakdowns of an electrical product. In the past, this thermal strain is evaluated by direct measurement such as strain gage and simulated by numerical analysis [1]. However, with offering technical advantages of mechanical products in recent year, electronic packaging is more downsizing, so evaluation of strain by strain gage is difficult. In addition, the selection of boundary condition for finite element analysis is difficult because some heterogeneous materials on electronic packaging complicate the condition. Meanwhile, in the condition like this, optical measurement is better because it can measure deformation in full visual field indirectly. There are some researches which measure thermal strain on electronic packaging by an optical method [2]. Digital image correlation (DIC) is one of the optical measurement methodologies [3]. The displacement distribution can be obtained from two pictures which are before and after the deformation. In addition, the experiment environment and the procedure of DIC are simpler than any other optical methods. However, displacement distribution obtained by DIC contains characteristic a systematic error. This is because of interpolation of gray level, speckle pattern of specimen and lack of gray level caused by gap between sensors in a CCD camera and so on. This systematic error is very small like few hundreds of a pixel, but this error affects strain obtained by DIC. The strain is calculated as the displacement gradient, so correct strain cannot be obtained if the displacement contains the systematic error. In the past, some researchers investigate the method for reduction of systematic error in displacement obtained by DIC. Schireier et al. [4] picked up gray level distribution shapes in images and investigated the effects of this for the results of measurements. As a result, it was shown that systematic error increase when images contain high frequency contents, and the error could be reduced by reduction of high frequency content using a low pass filter. Bornet et al. [5] investigated the effect of speckle pattern size and the order of interpolation function for the measurement error. As a result, it was shown that M.Murata (*) • S. Yoneyama Department of Mechanical Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa 252-5258, Japan e-mail: c5615123@aoyama.jp S. Arikawa Department of Mechanical Engineering Informatics, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki-shi, Kanagawa 214-0031, Japan Y. Fujimoto • Y. Omoto Mitsubishi Electric Corporation Advanced Technology Research and Development Center, 8-1-1 Tsukaguchi-honmachi, Amagasaki-shi, Hyogo 661-8661, Japan #The Society for Experimental Mechanics, Inc. 2017 S. Yoshida et al. (eds.), Advancement of Optical Methods in Experimental Mechanics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-41600-7_8 71
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