Measurements and calculations of stresses in metal-ceramic systems |
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Authors: | P Dorsch |
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Institution: | (1) Fürstentum Liechtenstein, Vaduz |
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Abstract: | Deflection changes dependent on temperature and thickness of ceramics have been measured on ceramic-coated metal strips, using a modified commercial dilatometer.The deflections are not only dependent on the difference in the thermal expansion coefficients of the two materials, but are also influenced by the thickness ratio of the ceramic to the metal. The stresses existing in the ceramic have been calculated for the surface layer and for the layer in the transition zone ceramic/metal. The results have shown that there is no proportional relation between the value of deflection and the stresses in the ceramic; however, the maxima in the deflection curves coincide with the peaks shown in the stress curves. From a certain thickness ratio of ceramic to metal — determined by the Young's moduli of the materials — tensile stresses in the surface of the ceramic occur even at the higher expansion coefficient of the metal.
Zusammenfassung An mit Keramik beschichteten Metallstreifen wurden in einem modifizierten, handelsüblichen Dilatometer Ausbiegungsänderungen in Abhängigkeit von der Temperatur und der Keramikdicke gemessen. Die Verformungen hängen nicht allein von der Differenz der thermischen Ausdehnungskoeffizienten der beiden Werkstoffe ab, sondern werden auch durch das Dickenverhältnis von Keramik zu Metall beeinflusst. Die in der Keramik vorhandenen Spannungen wurden für die Oberflächenschicht und für die Schicht in der Grenzzone Keramik/Metall berechnet. Die Ergebnisse haben gezeigt, daß kein proportionaler Zusammenhang zwischen der Grösse der Ausbiegung und den Spannungen in der Keramik vorhanden ist. Maxima in den Ausbiegungskurven fallen jedoch mit ausgezeichneten Punkten in den Spannungskurven zusammen. Ab einem durch die Elastizitäts-Moduln der Werkstoffe bestimmten Dickenverhältnis von Keramik zu Metall treten auch bei einem grösseren Ausdehnungskoeffizienten des Metalls Zugspannungen in der Oberfläche der Keramik auf.
Résumé On a mesuré, sur des bandes de métal recouvertes de céramique et en se servant d'un dilatomètre commercial modifié, les changements de déflection qui dépendent de la température et de l'épaisseur des céramiques.Les déflections dépendent non seulement de la différence des coefficients de dilatation thermique des deux matériaux, mais aussi du rapport des épaisseurs respectives de la céramique et du métal. Les contraintes existant dans la céramique ont été calculées pour la couche superficielle et pour la couche de la zone de transition céramique/métal. Les résultats ont montré qu'il n'y a pas de relation de proportionnalité entre la valeur de la déflection et les contraintes dans la céramique; cependant, les maximums des courbes de déflection coïncident avec les pics des courbes de contrainte. A partir d'un certain rapport d'épaisseur de la céramique au métal — déterminé par les modules d'Young des matériaux — les contraintes d'allongement à la surface de la céramique se produisent même si le métal possède un coefficient de dilatation plus élevé.
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![softcy](/content/km4517063k7x4161/xxlarge1100.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![zcy](/content/km4517063k7x4161/xxlarge1079.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) , ![chcy](/content/km4517063k7x4161/xxlarge1095.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![yacy](/content/km4517063k7x4161/xxlarge1103.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![zcy](/content/km4517063k7x4161/xxlarge1079.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![vcy](/content/km4517063k7x4161/xxlarge1074.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![zhcy](/content/km4517063k7x4161/xxlarge1078.gif) ![dcy](/content/km4517063k7x4161/xxlarge1076.gif) ![zcy](/content/km4517063k7x4161/xxlarge1079.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![chcy](/content/km4517063k7x4161/xxlarge1095.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![bcy](/content/km4517063k7x4161/xxlarge1073.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![yacy](/content/km4517063k7x4161/xxlarge1103.gif) ![zhcy](/content/km4517063k7x4161/xxlarge1078.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![yacy](/content/km4517063k7x4161/xxlarge1103.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) . ![Vcy](/content/km4517063k7x4161/xxlarge1042.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![zcy](/content/km4517063k7x4161/xxlarge1079.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) , ![chcy](/content/km4517063k7x4161/xxlarge1095.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![ucy](/content/km4517063k7x4161/xxlarge1091.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![vcy](/content/km4517063k7x4161/xxlarge1074.gif) ![ycy](/content/km4517063k7x4161/xxlarge1099.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![gcy](/content/km4517063k7x4161/xxlarge1075.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![bcy](/content/km4517063k7x4161/xxlarge1073.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![dcy](/content/km4517063k7x4161/xxlarge1076.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![vcy](/content/km4517063k7x4161/xxlarge1074.gif) ![ycy](/content/km4517063k7x4161/xxlarge1099.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![yacy](/content/km4517063k7x4161/xxlarge1103.gif) ![zhcy](/content/km4517063k7x4161/xxlarge1078.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) . ![Icy](/content/km4517063k7x4161/xxlarge1048.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![shcy](/content/km4517063k7x4161/xxlarge1096.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![shchcy](/content/km4517063k7x4161/xxlarge1097.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![dcy](/content/km4517063k7x4161/xxlarge1076.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) , ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![shchcy](/content/km4517063k7x4161/xxlarge1097.gif) ![softcy](/content/km4517063k7x4161/xxlarge1100.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![dcy](/content/km4517063k7x4161/xxlarge1076.gif) ![ucy](/content/km4517063k7x4161/xxlarge1091.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![YUcy](/content/km4517063k7x4161/xxlarge1070.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![gcy](/content/km4517063k7x4161/xxlarge1075.gif) ![ecy](/content/km4517063k7x4161/xxlarge1101.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) , ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![yacy](/content/km4517063k7x4161/xxlarge1103.gif) ![gcy](/content/km4517063k7x4161/xxlarge1075.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![vcy](/content/km4517063k7x4161/xxlarge1074.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![yucy](/content/km4517063k7x4161/xxlarge1102.gif) ![shchcy](/content/km4517063k7x4161/xxlarge1097.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ucy](/content/km4517063k7x4161/xxlarge1091.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![vcy](/content/km4517063k7x4161/xxlarge1074.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![khcy](/content/km4517063k7x4161/xxlarge1093.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) , ![chcy](/content/km4517063k7x4161/xxlarge1095.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![khcy](/content/km4517063k7x4161/xxlarge1093.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![dcy](/content/km4517063k7x4161/xxlarge1076.gif) ![shchcy](/content/km4517063k7x4161/xxlarge1097.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![dcy](/content/km4517063k7x4161/xxlarge1076.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![zhcy](/content/km4517063k7x4161/xxlarge1078.gif) ![pcy](/content/km4517063k7x4161/xxlarge1087.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![bcy](/content/km4517063k7x4161/xxlarge1073.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![vcy](/content/km4517063k7x4161/xxlarge1074.gif) ![ycy](/content/km4517063k7x4161/xxlarge1099.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![kcy](/content/km4517063k7x4161/xxlarge1082.gif) ![ocy](/content/km4517063k7x4161/xxlarge1086.gif) ![ecy](/content/km4517063k7x4161/xxlarge1101.gif) ![fcy](/content/km4517063k7x4161/xxlarge1092.gif) ![fcy](/content/km4517063k7x4161/xxlarge1092.gif) ![tscy](/content/km4517063k7x4161/xxlarge1094.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![scy](/content/km4517063k7x4161/xxlarge1089.gif) ![shcy](/content/km4517063k7x4161/xxlarge1096.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![rcy](/content/km4517063k7x4161/xxlarge1088.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![ncy](/content/km4517063k7x4161/xxlarge1085.gif) ![icy](/content/km4517063k7x4161/xxlarge1080.gif) ![mcy](/content/km4517063k7x4161/xxlarge1084.gif) ![iecy](/content/km4517063k7x4161/xxlarge1077.gif) ![tcy](/content/km4517063k7x4161/xxlarge1090.gif) ![acy](/content/km4517063k7x4161/xxlarge1072.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) ![lcy](/content/km4517063k7x4161/xxlarge1083.gif) .
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本文献已被 SpringerLink 等数据库收录! |
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