13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- On Mixed-Mode Fracture Christopher Harvey1, Liangliang Guan1, Huimin Xie2, Simon Wang1,* 1 Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK 2 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China * Corresponding author: s.wang@lboro.ac.uk Abstract This paper reports the authors’ recent work on mixed-mode fracture in fiber-reinforced laminated composite beams and plates. The work considers the so-called one-dimensional fracture which propagates in one-dimension and consists of only mode I and mode II fracture modes. Fracture interfaces are assumed to be either rigidly or cohesively bonded. Analytical theories are developed within the contexts of both classical and first-order shear deformable laminated composite theories. When a rigid interface is assumed for brittle fracture, there are two sets of orthogonal pure modes in classical theory, and there is only one set of orthogonal pure modes in shear-deformable theory. A mixed-mode fracture is partitioned by using these orthogonal pure modes. The classical and shear deformable partitions can be regarded as either lower or upper bound partitions for 2D elasticity, and hence approximate 2D elasticity partition theories are developed by ‘averaging’ the classical and shear deformable partitions. When cohesively bonded interfaces are assumed for adhesively joined interfaces, the classical and shear deformable theories give the same pure modes. Approximate partition theories are also developed for 2D elasticity. Numerical investigations demonstrate excellent agreement with the corresponding analytical theories. Experimental data considered shows that the failure locus is strongly linear. Keywords Composite, Energy release rate, Failure locus, Mixed-mode fracture, Orthogonal pure modes 1. Introduction Delamination is a major concern in the application of laminated composite materials. Although it occurs often together with other fracture modes such as fiber breakage, matrix cracking and intra-laminar cracking, pure delamination is always an important research topic which provides insight and understanding of lamina interfacial mechanics, and it often occurs in one-dimensional delamination. A delamination is called one-dimensional when its crack front propagates only in one direction. Familiar examples are through-width delamination in laminated composite beams, circular ring shape delamination in laminated composite plates and shells, etc., as shown in Fig. 1. A distinct feature of one-dimensional delamination is that it usually consists of only the mode I and mode II fracture modes without any mode III. The study of one-dimensional delamination is of great importance for several reasons. It is the most fundamental problem in the fracture mechanics of materials. It is often used in experimental tests, such as the double cantilever beam (DCB), end-loaded split (ELS) and end-notched flexure (ENF) tests, to obtain the critical energy release rate (ERR) or toughness of a lamina interface in either pure mode I or mode II delamination. In the case of a mixed mode, it is often used to investigate delamination propagation criteria. Moreover, many practical cases of delamination in structures made of fiber-reinforced laminated composites can be approximated as one-dimensional. For example, the separation of stiffeners and skins in stiffened plate or shell panels made of laminated composite materials can be approximated as one-dimensional through-width delamination, and the separation of two material layers in laminated composite plates and shells in a drilling process can be approximated as one-dimensional circular ring-type delamination, etc. Because of its importance, one-dimensional delamination has attracted the attention of many researchers including many of the world leaders in the areas of fracture mechanics and composite materials. The primary goal is to develop analytical theories to determine pure delamination modes
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