Mechanics Research Communications 35(2008)576-582 Contents lists available at Science Direct MECHANICS Mechanics research communications ELSEVIER journalhomepagewww.elsevier.com/locate/mechrescom Energy-based and local approaches to the strength analysis of ceramic laminates with thermal residual stresses through the finite element method P VenaE Bertarelli D Gastaldi, R Contro Dipartimento di ingegneria Strutturale, Laboratory of Biological Structure Mechanics, Politecnico di Milano, Piazza Leonardo da vinci, 32, 20133 Milano, Italy ARTICLE IN FO A BSTRACT Article hist This paper deals with the strength analysis of ceramic laminates subjected to residual d 18 February 2008 stress fields. In particular, alumina/mullite/zirconia ceramic materials have been taken into Available online 12 April 2008 consideration. To this purpose, an energy-based approach and a micromechanical local pproach have been used within the framework of the finite element method. The results obtained through the numerical analyses are consistent with the ex ding a correct estimation of the limit strength lower bound on the external applied loads, below which no crack propagation occurs, can be identified. The local approach has led to a strength distribution that deviates from the typical Weibull Linear elastic fracture mechanics distribution: this is owed to the residual stress field. Indeed, a stress-dependent Weibull Finite element method modulus has been found. e 2008 Elsevier Ltd. All rights reserved. 1 Introduction Ceramic materials show many interesting properties like high thermal shock resistance, chemical inertness and excellent tribological behavior. These properties confer passive biocompatibility, high wear resistance and low friction coefficient that make the based materials suitable for critical applications in many field energy conversion, precision mechanics and engines, cutting tools and biomechanical devices. The main limitation to the use of ceramic materials in structural applications is owed to their low reliability, i.e. their high catter in failure strength and low fracture toughness. This behavior is directly related to the presence of flaws originated during the production processes and the service. The standard deviation of measured strength is often too large to allow a safe desig Many efforts have been made with the purpose to increase the reliability of ceramic materials: a promising approach is the design and manufacturing of laminates with pre-determined residual stress fields. Layers of ceramic composites with different composition are stacked, obtaining a graded ceramic, in order to develop a specific residual stress profile as a result of the sintering process. The thermal stresses are due to the mismatch of the mean coefficient of thermal expansion between the layers and between the different grains in the same layer (Green et al, 1999: Sergo et al, 1997). The particular case of alumina/zirconia laminates is discussed in Vena(2005)from the modeling standpoint. It is well known that a compressive residual stress at the surface of the laminates has beneficial effects on strength. Sim la ly, a compressive layer placed at a certain depth can significantly increase the toughness of the material (vena et al Corresponding author Tel: 23994236;fax:+390223994220 dress: vena(stru polimi it(P. 13/s-see front matter e 2008 Elsevier Ltd. All rights reserved doi: 10.1016/j. mechrescom. 2008.04.003Energy-based and local approaches to the strength analysis of ceramic laminates with thermal residual stresses through the finite element method P. Vena *, E. Bertarelli, D. Gastaldi, R. Contro Dipartimento di Ingegneria Strutturale, Laboratory of Biological Structure Mechanics, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy article info Article history: Received 18 February 2008 Received in revised form 2 April 2008 Available online 12 April 2008 Keywords: Ceramic laminates Weibull statistic Linear elastic fracture mechanics Finite element method abstract This paper deals with the strength analysis of ceramic laminates subjected to residual stress fields. In particular, alumina/mullite/zirconia ceramic materials have been taken into consideration. To this purpose, an energy-based approach and a micromechanical local approach have been used within the framework of the finite element method. The results obtained through the numerical analyses are consistent with the experimental ones, providing a correct estimation of the limit strength; furthermore, a lower bound on the external applied loads, below which no crack propagation occurs, can be identified. The local approach has led to a strength distribution that deviates from the typical Weibull distribution; this is owed to the residual stress field. Indeed, a stress-dependent Weibull modulus has been found. 2008 Elsevier Ltd. All rights reserved. 1. Introduction Ceramic materials show many interesting properties like high thermal shock resistance, chemical inertness and excellent tribological behavior. These properties confer passive biocompatibility, high wear resistance and low friction coefficient that make the ceramic-based materials suitable for critical applications in many fields among which energy conversion, precision mechanics and engines, cutting tools and biomechanical devices. The main limitation to the use of ceramic materials in structural applications is owed to their low reliability, i.e. their high scatter in failure strength and low fracture toughness. This behavior is directly related to the presence of flaws originated during the production processes and the service. The standard deviation of measured strength is often too large to allow for a safe design. Many efforts have been made with the purpose to increase the reliability of ceramic materials: a promising approach is the design and manufacturing of laminates with pre-determined residual stress fields. Layers of ceramic composites with different composition are stacked, obtaining a graded ceramic, in order to develop a specific residual stress profile as a result of the sintering process. The thermal stresses are due to the mismatch of the mean coefficient of thermal expansion between the layers and between the different grains in the same layer (Green et al., 1999; Sergo et al., 1997). The particular case of alumina/zirconia laminates is discussed in Vena (2005) from the modeling standpoint. It is well known that a compressive residual stress at the surface of the laminates has beneficial effects on strength. Sim￾ilarly, a compressive layer placed at a certain depth can significantly increase the toughness of the material (Vena et al., 0093-6413/$ - see front matter 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechrescom.2008.04.003 * Corresponding author. Tel.: +39 02 2399 4236; fax: +39 02 2399 4220. E-mail address: vena@stru.polimi.it (P. Vena). Mechanics Research Communications 35 (2008) 576–582 Contents lists available at ScienceDirect Mechanics Research Communications journal homepage: www.elsevier.com/locate/mechrescom