Erik Damhof, Principal Researcher at Corus Staal BV, succesfully defended his PhD thesis 'Numerical-experimental analysis of thermal shock damage in refractory materials' on3 June 2010 at Eindhoven University of Technology. It was the first M2i thesis defence on non-metallic material modelling. Erik pursued his research project at Corus and because of the kenniswerkersregeling he had the opportunity to work together with the TU/e and M2i on this research project.
At my department, the Ceramics Research Centre, we compare refractory materials by testing and modelling to see which one will work better. My doctoral work consisted of modelling thermal shock damage in coarse grained refractory materials. This happens due to distributed thermal expansion obtained by temperature differences in the material. Together with TNO, Gouda Vuurvast and the TU/e a project on this subject has been started, funded bij Agentschap NL. Within this project already another PhD sub-project was ongoing on micro-modelling of refractory material. My PhD project followed a complementary macroscopic approach and thus fitted well within the scope of the multi-partner project. Within Corus the doctoral investigation was part of the Seedcorn programme which focusses on knowledge development aimed at a longer term application. At the TU/e I was guided by my supervisors Marc Geers and Marcel Brekelmans of the Mechanics of Materials group from the Faculty of Mechanical Engineering. I went to Eindhoven about once a month to discuss the progress with them. Particularly the beginning the project required a lot of free time during the weekends to catch up on the computational mechanics part. Besides that there has been a lot of discussion with the colleagues of Corus especially on the application of the developed modelling tools. Then, after a certain time you realize that you have become an expert yourself. 
Fig. 1. SEM image (SEI) of a typical micro-structure of a heterogeneous, coarse grain refractory material
A typical characteristic of refractory materials used at Corus is the coarse grained, heterogeneous microstructure which involves mismatches of thermal expansion of the grains, matrix and binding phase at the micro scale. This causes the refractory ceramics to be sensitive to damage development induced by even a uniform temperature distribution after heating up the material very slowly. Besides, that non-uniform thermal expansion and accompanying stresses and damage result from temperature differences in the material caused by heating-up or cooling-down rapidly. This can occur for example when the temperature of a steel ladle is too low when liquid steel is poured in or when the hot refractory lining becomes exposed to cold air after emptying the ladle respectively.
Fig. 2 Damaged slag ring with rounded-off brick ends due to (sudden) thermal expansion after filling of the ladle; the horizontal surface cracks at the brick ends are induced by sudden contraction due to the contact with ambient air after emptying of the ladle [1]
The material behaviour of the refractory ceramics has been modelled by adopting a damage approach to which end a failure parameter has been introduced which lies between 0 (no damage, nothing wrong) and 1 (damaged complety, loss of material integrity) [2]. To deal with the distinctive microscopic behaviour and resulting small-scale damage special terms have been added to the theoretical modelling framework. Although the modelling of steel sheet is considerably different than refractory ceramics, damage approaches have also been used to describe the failure behaviour of for example drinking cans during the forming process which is investigated at the other research departments. The developed modeling tools can be used to predict the lifetime of iron and steelmaking installations. This is faciliated by the coupling of the material model programmed in Matlab with the commerical Finite Element package Ansys which is better suitable to model complex steelmaking installations. The nice thing of Matlab is that you can bring in all kind of temperature-dependent relations for the thermo-mechanical material properties measured at my department. With Ansys we calculate the thermo-elastic stresses, subsequently you calculate the material degradation with Matlab followed by another thermo-elastic calculation with degraded material properties in Ansys. If the damage values 0.15 the lifetime of a ladle may be improved by lowering the downtime between the process stages preventing high temperature differences during filling with liquid steel. Also the application of refractory lining materials with more favourable properties against thermal shock may be readily investigated with the computational model. Geometrical aspects such as refractory brick shapes also contribute to the lifetime and availability of the steelmaking installation.
A main challenge of the PhD research was the validation of the thermal shock damage model with suitable experiments [3]. It is hardly possible to investigate the occurrence of thermal shock in practice. Because of the high process temperatures it is very difficult to come close. In order to validate the numerical model it is neccesary to design experiments involving the controlled and reproducible application of thermal shock in refractory material. Another complication factor is that you want to quantify the damage evolution occuring in the thermal shock tests. Because of the good cooperation with colleagues of the casting department, we found a solution for this problem. This department has access to an open induction furnace to melt metals for creating various grades for research purposes. In this case the furnace has been used to make an aluminium smelt. Refractory test samples were brougth into contact with the aluminium bath surface to induce a one-sided thermal shock in the refractory material. The thermal shock damage was assessed by measuring the transit time of sound waves at various sample locations. Micro-cracks and damage caused by thermal shock lead to a longer transit time of the waves. By comparing the transit time measured before and after the experiment you get a measure for the damage. A nice feature of the numerical model is that its results can be reworked into the sound velocity and transit time of sound waves travelling through damaged material enabling the comparison with the experimental results. There are also other ways to test thermal shock with for example a gas flame. The heat is then however not equally distributed over the sample surface. The molten aluminium test as well as the damage characterization method are reproducible and fits our process conditions.
The main conclusions of my PhD research is that a damage approach is a viable way to quantify the degradation of coarse grain refractory material allowing a straightforward experimental validation of the developed theoretical framework of which the application is facilitated by the coupling of Ansys and Matlab.
For this project I worked together with other companies: TNO, Gouda Vuurvast and quite some internees helping out on the experimental part of the project. At TNO some initial thermal shock experiments have been performed whilst Gouda Vuurvast contributed to the project by providing test sample material.
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[1] K. Andreev, H. Harmuth, “Numerische Simulation des mechanischen und thermo- mechanischen Verhaltens der Feuerfestzustellungen von Stahlpfannen”, In: Proc. of Gesteinshüttenkolloquium 2001, Leoben, Österreich, pp. 91-99, 2001
[2] F. Damhof, W.A.M. Brekelmans, M.G.D. Geers, Non-local modeling of thermal shock damage in refractory materials, Engng. Fracture Mech., 75, 4706-4720, (2008)
[3] F. Damhof, W.A.M. Brekelmans, M.G.D. Geers, Experimental analysis of the evolution of thermal shock damage using transit time measurement of ultrasonic waves, Journal of the European Ceramic Society, 29, 1309-1322, (2009)
