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| NUMERICAL SOLUTION OF ELASTIC ENERGY OF ELLIPTIC INCLUSIONS ORIENTED IN <100>,<110>AND <111> DIRECTIONS IN CUBIC CRYSTALS |
| by Yah Benda; Wu Jiansheng and Lin Dongliang (T. L. Lin) (Shanghai Jiaotong University) and Y. T. Chou (Department of Metallurgy and Materials Science; Leihigh University; U. S. A.; Adjunct Professor in Shanghai Jiaotong University; China) |
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Cite this article:
by Yah Benda; Wu Jiansheng and Lin Dongliang (T. L. Lin) (Shanghai Jiaotong University) and Y. T. Chou (Department of Metallurgy and Materials Science; Leihigh University; U. S. A.; Adjunct Professor in Shanghai Jiaotong University; China). NUMERICAL SOLUTION OF ELASTIC ENERGY OF ELLIPTIC INCLUSIONS ORIENTED IN <100>,<110>AND <111> DIRECTIONS IN CUBIC CRYSTALS. Acta Metall Sin, 1981, 17(5): 489-505.
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Abstract The elastic inclusion problem, that is the calculation of the stress-strain field and the elastic energy of an anisotropic elastic medium with an elastic inclusion contained in it, is one of the important problems in materials science.Especially, the variation of the elastic energy of the system with the orientations of the inclusion in the medium (i. e. the orientational dependence of the elastic energy), and the orientation of the inclusion corresponding to the minimum of the elastic energy of the system are of great theoretical land practical significance in the investigations of the habit orientations of the phase transformations and precipitate particles, the prediction of the microcracking direction as well as the optimum distribution of the reinforcement fibers in the composites.Based on the "Point Force-Line Force Method" given by H. Y. Yang and Y.T. Chou in 1976, a general computer program is compiled, which is applicable to the numerical calculation of the elastic energy of the elliptical inclusion oriented in any direction of the anisotropic medium for the generalized plane problem. The values of the elastic energy of the elliptic inclusions with their cylinder axes along the <100>, <110> and <111> directions in cubic metals Fe, Nb and Al were computed, and the dependence of elastic energies on the orientation of cross elliptic sections, which was rotating around their cylindcr axes, has been illustrated explicitly in graphic charts.The following conclusions arc deduced from the calculation results:1. The system has its elastic energy when the inclusion is lying on the crystal planes and oriented along the crystal directions of low indexes.2. The elastic energy of the system with the inclusion subjected to pure shear strain is 1/3-1/2 of that with the inclusion subjected to principal strain.3. The elastic energy of the anisotropic system with thin plate inclusions is very small. As the elliptic index e=b/a→0 the elastic energy of the system approaches nil.4. If the boundary energy could be neglected, the new phase and the precipitate with the lowest elastic energy would take the thin plate shape and shear mode in phase transformations and precipitation.
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Received: 18 May 1981
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