本文對含硬膜之可撓式高分子薄板在受到力偶或彎曲曲率下進行黏彈性力學分析，且加入製程中殘留應變的考量，並應用於可撓式有機發光二極體(Flexible及Rollable OLED)硬膜層表面破裂條件之討論。
　　由彈性力學分析下，得知若欲將Stoney formula運用於硬膜軟基板結構上，需增加一修正值；且整體結構之曲率可由各層材料之曲率累加而得，其中修正值也具有可疊加之關係。黏彈性分析下也具有相同關係，但其中修正值與時間相關。
　　對FOLED的分析中發現，隨著ITO硬膜沈積厚度減少，整體結構所能承受之應變降低，並可加以推算ITO硬膜勁度在6～24 間的臨界彎曲曲率半徑。且FOLED在定力矩作用下，因PET基板具有應力鬆弛特性，表面應變會隨時間逐漸上升，故最大表面應變將出現在長時間使用下，並可能產生破裂，此推論在彈性力學分析無法發現；若為循環力矩，在產品負載頻率高時，每次循環應變之振幅相對較小;頻率低時，同樣負載反而會造成較大的應變振幅，而使得產品有提早產生裂紋之危機。
　　在FOLED中，利用阻隔層可增強對水氧氣之阻隔性，本文分析結果得知過高勁度之阻隔層反而會造成表面應變的增加，並在長時間使用下造成裂紋的產生。因此本文提供可依結構及用途選擇合適阻隔層之方法，並預估其產生裂紋之時間。

　　The purpose of this paper is to execute the viscoelastic analysis of flexible polymer layer with hard film under externally bending couple or curvature and the influence of the residual strain induced during the process. The analytical results are then discussed against the conditions of causing crack onset strain of FOLED (Flexible and Rollable Organic Light-Emitting Diode).
　　From the elastic analysis, it knows that curvature of flexible substrate with hard film must be modified from the Stoney formula by a correction factor. Furthermore, the curvature of multilayered thin-film structure can be modified by adding up correction factor of each layer. From viscoelastic analysis, the results are the same, but the correction factor must depend on time.
　　In the analysis of FOLED, the top surface strain is smaller with the reduction of ITO film thickness. Also the analytical results can provide critical radii of curvature for ITO stiffness from 6 to 24 KN/m. Under constant bending moment condition, because of the relaxation in the PET substrate, the surface strain is increased with time, and may have maximum value over a long time and may cause fracture. This conclusion can not be drawn from the elastic analysis. Under cyclic bending moment condition, the lower frequency strain amplitude is larger than that of higher frequency, and may lead to crack.
　　Adding a barrier layer can improve the resistance of water vapor and oxygen transmission into FOLED. In the analysis, it is concluded that higher stiffness of barrier layer induces higher surface strain, and may result in cracking. Therefore, this paper provides a methodology of choosing barrier layer based on the structure and its purpose and then estimate the time of crack forming.

[1]　Stoney G.G., “The Tension of Metallic Films Deposited by Electrolysis,” Proceedings of the Royal Society of London, Vol.A82, pp.172-177, 1909.
[2]　Townsend P.H., Barnett D.M., and Brunner T.A., “Elastic Relationships in Layered Composite Media with Approximation for the Case of Thin Films on a Thick Substrate,” J. Appl. Phys., Vol.62, Issue 11, pp.4438-4444, 1987.
[3]　Yanaka M., Tsukahara Y., Nakaso N., and Takeda N., “Cracking Phenomena of Brittle Films in Nanostructure Composites Analysed by A Modified Shear Lag Model with Residual Strain,” J. Mater. Sci., Vol.33, pp.2111-2119, 1998.
[4]　Yanaka M., Kato Y., Tsukahara Y., Takeda N., “Effects of Temperature on the Multiple Cracking Progress of Sub-micron Thick Glass Films Deposited on a Polymer Substrate,” Thin Solid Films 356, pp.337-342, 1999.
[5]　Suo Z., Ma E.Y., Gleskova H., and Wagner S., “Mechanics of Rollable and Foldable Film=on=Foil Electronics,” Appl. Phys. Lett., Vol. 74, pp.117-1179, 1999.
[6]　Yu J., Kim J.G., Chung J.O., and Cho D.H., “An Elastic /Plastic Analysis of the Intrinsic Stresses in Chemical Vapor Deposited Diamond Films on Silicon Substrates,” J. Appl. Phys., Vol. 88, No. 3, pp.1688-1694, 2000.
[7]　Park S.K., Han J.I., Moon D.G., and Kim W.K., “Mechanical Stability of Externally Deformed Indium-Tin-Oxide Films on Polymer Substrates,” Jpn. J. Appl. Phys., Vol.42, pp.624-629, 2003.
[8]　Letterier Y., Fisher C., Mdico L., Demarco F., Mnson J.–A.E., Bouten P., DeGoede J., and Nairn J.A., “Mechanical Properties of Transparent Functional Thin Films for Flexible Display,” 46th Annual Technical Conference Proceedings, 2003.
[9]　李佩璇, “含硬膜之可撓性基板的力學分析及應用,” 國立成功大學工程科學系碩士論文,中華民國九十四年六月.
[10]　Pope M., Kallmann H., and Magnante P., “Electroluminescence in Organic Crystals,” J. Chem. Phys., Vol. 38, 2042, 1963.
[11]　Tang C.W., and Van Slyke S.A., “Organic Electroluminescent Diodes,” Appl. Phys. Lett. Vol. 51, pp.913-915, 1987.
[12]　Burroughes J.H., Bradley D.D.C., Brown A.R., Marks R.N., MacKay K., Friend R.H., Burn P.L., and Holmes A.B., “Light Emitting Diodes based on Conjugated Polymers,” Nature (London) 347, pp.539-541, 1990.
[13]　Williams M.L., Landel R.F., and Ferry J.D.,Amer. Chem. Soc., 77, 3701, 1955
[14]　Schapery R.A., “Correspondence Principle and a Generalized J Integral for Large Deformation and Fracture Analysis of Viscoelastic Media,” International J. of Fracture, Vol.25, pp. 195-223.
[15]　O’Brien D.J., Mather P.T., and White S.R., “Viscoelatic Properties of an Epoxy Resin during Cure,” J. Comp. Mater., Vol.35, No.10, pp.883-904, 2001.
[16]　Letterier Y., “Durability of Nanosized Oxygen-barrier Coatings on Polymers,” Pro. Mater. Sci. 48, pp.1-55, 2003.
[17]　Letterier Y., Mdico L., Demarco F., Mnson J.–A.E., Betz U., Escol M.F., Kharrazi Olsson M., and Atamny F., “Mechanical Integrity of Transparent Conductive Oxide Films for Flexible Polymer-based Displays,” Thin Solid Films, 460, pp.156-166, 2004.