In this study the plane linear elastic problem of a functionally graded layer which contains periodic cracks is considered. The main objective of this study is to determine the thermal stress intensity factors for edge cracks. In order to find an analytic solution, Young&rsquo / s modulus and thermal conductivity are assumed to be varying exponentially across the thickness, whereas Poisson ratio and thermal diffusivity are taken as constant. First, one dimensional transient and steady state conduction problems are solved (heat flux being across the thickness) to determine the temperature distribution and the thermal stresses in a crack free layer. Then, the thermal stress distributions at the locations of the cracks are applied as crack surface tractions in the elasticity problem to find the stress intensity factors. By defining an appropriate auxiliary variable, elasticity problem is reduced to a singular integral equation, which is solved numerically. The influence of such parameters as the grading, crack length and crack period on the stress intensity factors is investigated.

The steel quality is deteriorated at a continuous casting start. Therefore, material from the first cast slab is cut off and re-melted in the melt shop. If too little is discarded, the inferior quality in the retained length can cause defects like edge cracks during subsequent hot rolling. This means that manufacturing resources are wasted on processing inferior material which has to be re-melted anyways at a later stage. On the other hand, if an excessive length of the first slab is re-melted, good material is wasted. In either case, optimizing the length of the start-scrap material is both economically and environmentally beneficial. Edge cracks are more common in the beginning of the first slab, even though a part is cut off. It is likely that the edge cracks arise due to reduced hot ductility in the first cast material. The purpose of this project is to optimize where the cut should be made in order to achieve the best yield. The hot ductility was investigated by performing hot tensile- and bending tests. The hot tensile tests indicate high hot ductility for the investigated specimens. The area reduction, which is correlated to the hot ductility, is above 70 % for all the investigated specimens. When considering the average area reduction while neglecting possible differences between the heats, the specimens from one meter tend to have a lower hot ductility compared to the other specimens. However, the differences are small. No difference can be seen between edge and middle specimens when only looking at the tensile tests. The bending tests did not crack without notches, even though the maximum load and a test temperature of 750 °C was used. That strongly indicates high hot ductility as well. By using notches, the bending tests cracked and it was shown that edge specimens and specimens from one meter cracked the most. No edge cracks were found, after hot rolling, on the first cast slabs from the investigated heats. / Vid en stränggjutstart är kvalitén på första slaben sämre. På grund av detta så skärs en bit, av det först gjutna slabet av och smälts om i stålverket. Om för lite material kapas av kan det leda till defekter, såsom kantbrakor, under den efterföljande varmvalsningen. Detta innebär att resurser används i onödan för att tillverka material av otillräcklig kvalitet som sedan ändå måste smältas om i ett senare steg. Skärs istället för mycket material bort så smälts prima material om i onödan. Att optimera startskrotlängden är följaktligen positivt både för miljön och rent ekonomiskt. Under varmvalsningen kan defekten kantbrakor, det vill säga sprickor vid kanterna, uppstå. Trots att en bit av det första gjutna slabet skärs av, så är det första slabet fortfarande mest utsatt för kantbrakor. Detta tros bero på nedsatt varmduktilitet i det första gjutna materialet. Syftet med detta projekt är att optimera längden på startskrotet för att spara så mycket användbart material som möjligt. Varmduktiliteten undersöktes genom drag- och bockprovning. Dragproven indikerar hög varmduktilitet för de undersökta proven. Areakontraktionen, som är ett mått på varmduktiliteten, är över 70 % för alla undersökta prov. Medelareakontraktionen, när man bortser från eventuella skillnader mellan chargerna, visar att prov från en meter generellt har något lägre varmduktilitet än de övriga proven. Det är endast små skillnader som uppfattas. Ingen skillnad kan ses mellan kant- och mittenprov när man enbart tittar på dragprovsresultaten. Bockproven sprack inte trots att maximal last användes och att testtemperaturen var 750 °C. Detta tyder också på hög varmduktilitet. Genom att skapa anvisningar kunde man få bockproven att spricka och det visade sig att kantprov och prov från en meter sprack mest. Inga kantbrakor hade uppstått på de första gjutna slabsen under varmvalsningen av försökschargerna.

Les aciers inoxydables austéno-ferritiques présentent une microstructure biphasée dans laquelle se mêlent austénite et ferrite. Leurs caractéristiques mécaniques élevées ainsi que leur bonne tenue en corrosion en font un candidat sérieux pour remplacer les aciers inoxydables austénitiques. Malheureusement, la faible forgeabilité de ces alliages rend la fabrication de tôles particulièrement critique. En effet, le phénomène de « crique de rive » est fréquemment rencontré au cours des étapes du laminage à chaud. Par conséquent, cela nécessite des opérations supplémentaires comme le découpage des rives, ce qui aboutit à une augmentation des coûts de production. Les différents facteurs influençant la ductilité à chaud de ces aciers sont passés en revue afin d'identifier quels sont les zones d'ombres. La synthèse bibliographique révèle deux zones d'ombres : d'une part, le manque d'un essai de ductilité à chaud permettant de discriminer différentes microstructures en terme de résistance à la propagation de fissure à haute température ; et d'autre part l'absence de données quantitative concernant la partition de la déformation entre la ferrite et l'austénite lors des étapes de mise en forme à chaud. Le concept de travail essentiel de rupture a été appliqué à hautes températures. Il a été démontré que cette méthode est fiable et discriminante pour quantifier la résistance à la propagation de fissure à haute température. Elle permet également de générer un paramètre physique pertinent pour optimiser les microstructures par rapport à un mode de mise en forme donné. La technique conventionnelle de micro-grilles a été adaptée de manière à cartographier à haute température les déformations à l'échelle de la microstructure. Cette technique fournit en plus des résultats qualitatifs concernant les mécanismes de déformations, des données quantitatives à propos de la partition de la déformation entre la ferrite et l'austénite. Ces données peuvent être utilisées afin de valider les modèles qui prédisent le comportement à chaud des aciers duplex pendant les premières étapes du laminage à chaud. Les deux outils developpés au cours de cette étude permettent de donner des solutions pour éviter le phénomène de « crique de rives ». / The Duplex Stainless Steels (DSS) are defined as a family of stainless steels consisting of a two-phase microstructure involving δ-ferrite and γ-austenite. Exceptional combinations of strength and toughness together with good corrosion resistance under critical working conditions designate DSS a suitable alternative to conventional austenitic stainless steels. Unfortunately, the relatively poor hot workability of these alloys makes the industrial processing of flat products particularly critical. Cracking of the coils during hot rolling along the edges is frequently reported. As a consequence, additional operations like grinding, discontinuous processing or scraping are often required, leading to increased manufacturing costs. The different parameters affecting the hot working of duplex stainless steels have been reviewed in order to identify which are the missing pieces of the puzzle. The bibliographical review reveals that two pieces are missing in the hot workability puzzle. On the one hand, it is necessary to develop a new hot ductility test which allows discriminating microstructures in terms of high temperature tearing resistance, and on the other hand, quantitative data about the strain partitioning between ferrite and austenite during the hot working operations are needed. The Essential Work of Fracture concept has been applied at high temperature. It has been demonstrated that this method is a reliable and discriminating tool for quantifying the high temperature tearing resistance and to generate a physically relevant index to guide the optimization of microstructures towards successful forming operations. A modified micro-grid technique has been developed to experimentally simulate the local state of deformation of different duplex microstructures at high temperature. This technique provides qualitative results about the deformation features as well as quantitative data about the strain partitioning between ferrite and austenite. The micro-strain distributions measured can be used to validate the models predicting the hot deformation of duplex stainless steels during the roughing-mill operations. The two tools developed in this investigation allow suggesting possible remedies for the edge cracking phenomenon.