20 INSTITUTE OF SMART STRUCTURES AND SYSTEMS Turning Lamb Mode based Crack Growth Prediction for G IC Determination in Laminated Composites C. Ramadas a,1 , Avinash Hood a , Anoop Anand a , Krishnan Balasubramaniam b and Makarand Joshi a a Composites Research Centre, R&DE(E), DRDO, Alandi Road, Pune, India-411 015 b Centre for Non-destructive Evaluation, Indian Institute of Technology Madras, Chennai, India-600 036 Corresponding author: rd_mech@yahoo.co.in 1 Abstract A turning Lamb mode propagates from one sub-laminate to the other at a delaminated region. In the present work, an attempt has been made to explore the use of the fundamental symmetric and anti- symmetric Turning Lamb modes for the prediction of crack growth for the determination of the strain energy release rate (G IC ) in a laminated composite specimen. Expressions based on Time-of-Flight were derived to estimate the crack growth. The proposed methodology has been validated through numerical simulations. INSTITUTE OF SMART STRUCTURES AND SYSTEMS (ISSS) JOURNAL OF ISSS J. ISSS Vol. 2 No. 1, pp. 20-26, March 2013. REGULAR PAPER Available online at www.isssonline.in/journal/02paper03.pdf Paper presented at ISSS International Conference on Smart Materials Structures & Systems, January 4-7, 2012, (ISSS 2012) Bangalore, India 20 Keywords: Turning Lamb Modes, Crack Growth, Strain Energy Release Rate (G IC ) 1. Introduction The extensive use of fibre-reinforced polymer composites as structural engineering materials in automotive, aerospace and military applications is due to their excellent mechanical properties, impact resistance, light weight and their amenability to be tailored as per external loads [Autar Kaw, 1997]. Since laminated composites have weak out-of-plane strength properties, they are prone to delamination type damages [Sridharan, 2010]. Delamination, being debilitating damage, reduces the life of the component and its structural integrity. Typically, delamination acts as a crack-like defect between the laminae interface which grows when the structure is subjected to tensile loads. The fracture toughness of the polymer matrix and the interfacial shear strength between the matrix and the fibre are of prime importance in monitoring the through- thickness properties of the composites. Lamb waves, also known as guided waves, propagate in the sagittal plane in a traction-free plate. For isotropic media, Helmholtz decomposition is used to obtain individual equations for longitudinal and shear waves [Rose, 1999] from three coupled partial differential equations, which are stress equilibrium equations expressed in terms of displacements. Lamb waves can propagate long distances in plate-like and cylindrical structures. They also have through-thickness displacements/ stresses, and provide information along the line-of- sight. Lamb waves are dispersive; viz. velocity depends on the product of frequency and thickness. Depending on the relationship between the displacement profiles and thickness, the modes are classified into symmetric (S n ) and anti-symmetric (A n ) modes. The specific order (represented by the subscript ‘n’) of these two modes depends on the excitation frequency and thickness of an isotropic plate. However, in an anisotropic plate, it also depends on the direction of propagation. When a Lamb wave mode encounters a defect in its path of propagation, the wave reflects, scatters and the mode converts into other mode types. Hence, these waves can be used for Non-destructive Evaluation (NDE) [Islam et al, 1994] as well as Structural