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首页> 外文期刊>Journal of Materials Research >Modeling of exact viscoelastic stresses in bilayer systems due to thermal and/or lattice mismatch: Maxwell model
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Modeling of exact viscoelastic stresses in bilayer systems due to thermal and/or lattice mismatch: Maxwell model

机译：由于热和/或晶格失配而导致双层系统中精确粘弹性应力的建模：Maxwell模型

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摘要

The exact solution of viscoelastic stresses in the bilayer system due to thermal and/or lattice mismatch is derived if both layers are Maxwell materials. When the thickness of one layer is much smaller than that of the other layer, the viscoelastic stresses in the bilayer system can be reduced to that of the thin film/substrate system. The relative film thickness and the position in the thin film/ substrate systems are included in this solution. The average film stress decreases with increasing the normalized time and finally approaches zero in a long time. As the relative film thickness is equal to or less than 0.001, the average film stresses of the zeroth-order approximation, first-order approximation, and Hsueh and Lee model [J. Appl. Phys. 91, 2760 (2002)] are close to that of exact solution. Nevertheless, as the relative film thickness is larger than 0.001, the accuracies of the zeroth-order approximation, first-order approximation, and Hsueh and Lee model are dependent on the normalized time and relative film thickness.
机译：如果两层都是麦克斯韦材料，则可以得出由于热和/或晶格失配而导致的双层系统中粘弹性应力的精确解。当一层的厚度比另一层的厚度小得多时，双层系统中的粘弹性应力可以减小到薄膜/基板系统中的粘弹性应力。该解决方案中包括相对膜厚度和薄膜/基板系统中的位置。平均膜应力随归一化时间的增加而减小，并在很长时间内最终接近零。当相对膜厚度等于或小于0.001时，零阶近似，一阶近似和Hsueh和Lee模型的平均膜应力[J.应用物理91，2760（2002）]接近于精确解。但是，当相对膜厚大于0.001时，零阶近似，一阶近似以及Hsueh和Lee模型的精度取决于归一化时间和相对膜厚度。

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  • 来源
    《Journal of Materials Research》 |2011年第11期|p.1392-1398|共7页
  • 作者

    Hsiang-Chun Hsueh; Donyau Chiang; Sanboh Lee;

  • 作者单位

    Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300, Taiwan;

    Instrument Technology Research Center, National Applied Research Laboratories, Hsinchu 30076, Taiwan;

    Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300, Taiwan;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);
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