Coupling between homogenization techniques and brittle mechanics for modelling the behaviour of micro-cracked refractory linings
Résumé
During service, refractory linings are often subjected to severe thermo-mechanical loadings. Accordingly, these masonries may behave linearly or nonlinearly in a viscoelastic and/or viscoplastic manner. It is then interesting to investigate the creep behaviour and cracking of refractory linings. In the last decades, multi-level techniques have demonstrated their efficiency for predicting the global and local behaviour of masonry structures with low numerical cost. In this context and as a first step, we propose in this work to model masonry with safe bricks and a mortar following the Burgers or modified Maxwell rheological models at its safe and microcracked states. The proposed model is based on the coupling between linear homogenization technique and the Griffith theory. This allows the determination of the effective creep function of the microcracked mortar. The time-dependent macroscopic behaviour of the masonry is determined thanks to analytical periodic homogenization technique. The relevance of the proposed model is evaluated by reference to a numerical solution computed by finite elements method based on an incremental scheme. A similar methodology can be then adapted to viscoplastic masonries at safe and micro-cracked states using one of the available linearization schemes. 1. Introduction In the iron and steel industry, the refractory lining of furnaces is often made of masonry in which joints between bricks may be either mortared or dry (i.e. without mortar [1]). In most cases, refractory brick linings are installed with mortar because its use to bond the brickwork provides more resistance to thermal shock and a cushion at the brick joint [7]. The temperature inside these structures can reach 1650 degrees which induces nonlinear mechanical behaviour for the masonry and even leads to the initiation and propagation of cracks in the joints. Note that a thick mortar tends to decrease the stiffness of structure and increases the likelihood of the possible penetration of process materials into the joints, resulting in the deterioration of the lining. So, the use of thin mortar joint is appropriate and necessary in designing the refractory brick lining system. Concerning the creep behaviour of the mortar which can be induced by severe service conditions, various rheological models namely the Maxwell, Kelvin-Voigt, Ross, Burgers and Modified-Maxwell models may be investigated [5]. A number of rheological models are examined to assess their ability to predict the creep of masonry. It was proved that the Modified Maxwell model is the most accurate. According to this result, the Burgers model, namely a Maxwell system connected in series with a Kelvin-Voigt one, and the Modified Maxwell scheme (a parallel combination of the Maxwell model and a spring) models are adopted in this paper to describe the mortar joint's creep. Moreover, in the literature, there are few works investigating the global and local behaviour of viscoelastic masonry. For instance, Cecchi and Tralli [3] used the asymptotic homogenization technique to deduce the behaviour of a safe (without cracks) viscoelastic periodic masonry cell. The effective behaviour of a masonry prism is provided due to periodic homogenization. In the present study, the coupling between the Griffith's theory and the dilute scheme [4] will be applied to provide the effective behaviour of a micro-cracked mortar [6]. In a second step, the expressions proposed in [3] are extended to determine the effective behaviour of a periodic microcracked viscoelastic masonry cell. As a first application, the case of a compressed wall was treated in order to assess the
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