Foundamental Solution For Coatingmaterials Subjected The Internal Load

With the wide application of surface-treated material in many industries, the problems of coating materials have become unavoidable and therefore drawn considerable attentions. Effective analysis of stress or strain for such a thin-layer structure is very important. Many efforts have been made on obtaining the stress and displacement field quantitatively by different approaches such as theoretical analysis, numerical analysis, and experimental research etc. The theoretical solutions of some typical cases are very meaningful and expected since they can be used not only to solve more sophisticated problems by the Green's function technology, but also can be used as the fundamental solution to improve the numerical accuracy and efficiency.The problems of coating materials with concentrated forces applied in the interior of materials has been analyzed by using the improved image point method. This method has special advantages in dealing with dissimilar material problems. The extensive application of the theoretical solutions are also discussed. With our previous work, the fundamental solution system of thin-filmed materials are completed basically. The detailed research contents and the innotative achievements are summarized as follow.In Chap 1 and 2, considering the wide application of coating materials, recent researches on such material structure are reviewed in perspectives of different analysis approaches. Therefore, the image point method which is very effective in dealing with coating materials problems is introduced in detail.The planar and spatial problems of concentrated forces applied in the interior of semi-infinite coating materials are discussed. Through the reflections of the loading point about the interface and the free surface, two infinite series of image points are introduced, which is different from the previous application of the image point method. The theoretical solutions are given by the analytical functions defined under the corresponding local coordinates with their origins placed at the loading point and image points. Based on the boundary conditions and the interchange law, the analytical functions corresponding to the mirror point of higher order can be determined from that to the lower order ones by the recurrence relationship. The fundamental solution of a concentrated force loading at the interface of two bonded semi-infinite bodies is also obtained and published firstly.The theoretical solutions are discussed. Through the comparisons between the analytical and numerical results, the theoretical solutions are verified. It is found that the theoretical solutions can degrade to some classical fundamental solutions of special problems. For the extensive application of the theoretical solutions, the solutions presented in the polynomial form are deduced and listed in the appendix. From the solution expressions, we can find the convergence of theoretical solution is very rapid, and only the first several image points are sufficient to ensure the accuracy in the most practical cases. The effect of different material properties combinations on the convergence of theoretical solution is also discussed. It is found that the bigger the mismatch between the Young's modulus is, the more image points are needed to get satisfactory accuracy.Based on the previous theoretical solutions, the problems of ring load and Hertz pressure in a coated half-space are studied. The results are discussed in connection with strength evaluation found experimentally.