Availableonlineatwww.sciencedirect.com DIRECTO COMPOSITES SCIENCE AND TECHNOLOGY ELSEVIER Composites Science and Technology 66(2006)435-443 Effect of thermal misfit stress on crack deflection at planar interfaces in layered systems Woong Lee Jae-Min Myoung Yo-Han Yoo, Hyunho Shin Department of Materials Science and Engineering, Yonsei Unirersity, 134 Shinchonl-Dong, Seoul 120-749 First R&D Centre, Agency for Defence Development, P.O. Box 35.1, Yoosung, Taejeon 305-600, Repi Department of Ceramics Engineering, Kangnung National Unirersity, 120 Gangneung Daehangno, Kangnung, Kangwon-do 210-702, Republic of Korea Received 1 April 2005: received in revised form 13 July 2005: accepted 14 July 2005 Available online 26 august 2005 Abstract Deflection of a crack at a planar bi-material interface in a layered system was investigated by considering the effects of the in-plane residual thermal misfit stress. a new parameter based on strains due to mismatch of thermal expansion coefficients was introduced to describe residual stress state independent of length scale. From a numerical analysis, it was predicted that introducing ompressive residual stress in the stiffer intact layers of a composite laminate ahead of a growing primary crack would favour crack deflection by allowing advantageous energetic conditions, which indicates that stronger interfaces can be introduced in layered sys- tems this way to improve overall mechanical properties. It was also predicted that the residual stress effect is negligible if the intact layer is more compliant than the cracked layer supporting a previous analysis and discussion reported elsewher c 2005 Elsevier Ltd. All rights reserved Keywords: Crack deflection; Interface; Residual stress; Layered systems 1. Introduction primary crack terminating at a bi-material interface of layered composites, would also undergo In many materials systems, residual stresses are often the influence of the residual stresses. introduced during fabrication processes due to the mis- Crack deflection at bi-material interfaces in brittle match of coefficient of thermal expansion (CtE)be- matrix composite systems is important as it is a prere- tween constituent materials. The representative quisite to the operation of many toughening mecha examples include layered systems such as ceramic lami- nisms or it is itself practically the only toughening nates [1, 2], thin-film deposited device materials [3, 4] mechanism in some layered systems [7, 8]. It is often as and engineering structures with protective coatings sumed that deflection of a crack terminating at an inter [5, 6]. Presence of residual stress, superposed on the face occurs by a competition between crack penetration stress field due to applied load, will modify the stress dis- across the interface or deflection along the interface(see tributions within the systems thereby causing the Fig. 1). Then the energetic condition for crack deflection changes in the fracture behaviour of these materials. It would be satisfied when strain energy released due to is therefore expected that crack deflection criteria, deter- crack penetration across the interface, p, is lower than mined by the fracture process within the stress field of a the bulk fracture energy, Rm whilst that due to crack deflection along the interface, d, is higher than the Corresponding author. Tel :+82 2 2123 2843/119 813 8192; fax: Interface fracture energy, R i.e. when [9] +8223652680/23652680 E-lmail addresses: woong lee(@yonsei ac kr, cwll0001 Ri ga (x,B) -3538/S- see front matter 2005 Elsevier Ltd. All rights reserved. 016/j. compscitech. 2005.07.015Effect of thermal misfit stress on crack deflection at planar interfaces in layered systems Woong Lee a,*, Jae-Min Myoung a , Yo-Han Yoo b , Hyunho Shin c a Department of Materials Science and Engineering, Yonsei University, 134 Shinchon-Dong, Seoul 120-749, Republic of Korea b First R&D Centre, Agency for Defence Development, P.O. Box 35-1, Yoosung, Taejeon 305-600, Republic of Korea c Department of Ceramics Engineering, Kangnung National University, 120 Gangneung Daehangno, Kangnung, Kangwon-do 210-702, Republic of Korea Received 1 April 2005; received in revised form 13 July 2005; accepted 14 July 2005 Available online 26 August 2005 Abstract Deflection of a crack at a planar bi-material interface in a layered system was investigated by considering the effects of the in-plane residual thermal misfit stress. A new parameter based on strains due to mismatch of thermal expansion coefficients was introduced to describe residual stress state independent of length scale. From a numerical analysis, it was predicted that introducing compressive residual stress in the stiffer intact layers of a composite laminate ahead of a growing primary crack would favour crack deflection by allowing advantageous energetic conditions, which indicates that stronger interfaces can be introduced in layered sys￾tems this way to improve overall mechanical properties. It was also predicted that the residual stress effect is negligible if the intact layer is more compliant than the cracked layer supporting a previous analysis and discussion reported elsewhere.
2005 Elsevier Ltd. All rights reserved. Keywords: Crack deflection; Interface; Residual stress; Layered systems 1. Introduction In many materials systems, residual stresses are often introduced during fabrication processes due to the mis￾match of coefficient of thermal expansion (CTE) be￾tween constituent materials. The representative examples include layered systems such as ceramic lami￾nates [1,2], thin-film deposited device materials [3,4] and engineering structures with protective coatings [5,6]. Presence of residual stress, superposed on the stress field due to applied load, will modify the stress dis￾tributions within the systems thereby causing the changes in the fracture behaviour of these materials. It is therefore expected that crack deflection criteria, deter￾mined by the fracture process within the stress field of a primary crack terminating at a bi-material interface of layered composites, would also undergo changes under the influence of the residual stresses. Crack deflection at bi-material interfaces in brittle matrix composite systems is important as it is a prere￾quisite to the operation of many toughening mecha￾nisms or it is itself practically the only toughening mechanism in some layered systems [7,8]. It is often as￾sumed that deflection of a crack terminating at an inter￾face occurs by a competition between crack penetration across the interface or deflection along the interface (see Fig. 1). Then the energetic condition for crack deflection would be satisfied when strain energy released due to crack penetration across the interface, Gp, is lower than the bulk fracture energy, Rm whilst that due to crack deflection along the interface, Gd, is higher than the interface fracture energy, Ri, i.e. when [9] Ri Rm < Gd Gp ¼ f ða; bÞ; ð1Þ 0266-3538/$ - see front matter
2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.07.015 * Corresponding author. Tel.: +82 2 2123 2843/119 813 8192; fax: +82 2 365 2680/236 526 80. E-mail addresses: woong.lee@yonsei.ac.kr, cwl10001@hanmail.net (W. Lee). Composites Science and Technology 66 (2006) 435–443 COMPOSITES SCIENCE AND TECHNOLOGY www.elsevier.com/locate/compscitech