Matrix cracking in polymer matrix composites under bi-axial loading

A model to predict the matrix crack evolution in a continuous fiber polymer composite laminate under in-plane bi-axial static loading has been presented in the current work. Oblique co-ordinate based shear lag analysis was used to estimate the stress distribution inside the cracked [0/90] s cross-ply T300/934 carbon fiber reinforced plastic (CFRP) laminate. Weibull probability distribution has been used to account for the variation in ply transverse strength. Size-dependent strength due to variation in ply thickness has been accounted for by appropriate volume scaling based Weibull scale factor. The Weibull parameters have been estimated using a ‘master laminate’ crack evolution data. By applying incremental stress to the laminate, using the probabilistic variation of transverse strength and the stress at a material point, the new crack location has been identified using the Hashin matrix cracking criterion. The reciprocal of the normal distance between two cracks has been termed as crack density. The crack density evolution for cross-ply laminates with an increase in applied loading has been estimated for various bi-axial ratios and compared with the data available from the literature. A good correlation is found to exist between the literature evolution data and current simulation predictions. Keywords: Matrix cracking; Bi-axial loading; Weibull strength * Corresponding author. Tel.: +91-80-25086316; fax: +91-80-25086301 E-mail address: jaganmail@gmail.com 2 Jagannathan et al./ Structural Integrity Procedia 00 (2018) 000–000 1. Introduction The use of polymer matrix composites (PMCs) in structural airframes as compared to conventional aluminum alloys has been increasing steadily; today 50% by weight of the new Boeing 787 airframe is made from PMCs. The first indigenous Indian light combat aircraft (LCA) uses PMCs for more than 40% of its weight. Aircraft structures undergo time-varying structural loads during their operation and are subject to environmental degradation and external damage threats like impact, runway debris, hailstorm, etc. These events can cause initiation as early as the first cycle and evolution of multi-scale structural degradation steadily with loading due to their inherent inhomogeneous and distinctly anisotropic nature. The commonly observed damages are matrix cracking, interfacial fiber-matrix de-bonding, fiber breaks, delamination, fiber micro-buckling, etc., under static and fatigue loading, Berthelot (2003), Harris (2003). Matrix cracking happens to be the most dominant mode of damage to first appear in a laminate. Matrix cracking generally leads to loss of stiffness, local stress redistribution and most importantly, a path for moisture or other fluid ingression leading to further reduction in composite strength or loss of its integrity, Talreja and Singh (2012). Experimental investigation of matrix cracking and its effects on composite materials have been extensively reported and reviews on such findings are available in the literature, Berthelot (2003), Talreja and Singh (2012). Following matrix crack saturation, also referred to as ‘characteristic damage state’, delamination is observed to initiate at the matrix crack tips, growing slowly and steadily. Fiber breaking is also observed at all the above stages. At the final stages of life, linking up delamination, the complex interaction of matrix cracks and fiber breaking is observed leading to the final failure of the laminate. The damages are randomly distributed across various length scales and locations; oriented in different directions, Highsmith and Reifsnider (1982), Reifsnider and Jamison (1982). Energy based models have been successfully used to predict the matrix crack initiation and evolution, Singh (2008). Energy-based models utilize the critical energy released during new matrix crack formation as a parameter to predict the matrix cracking, Nairn (2000). Various stress analysis methods have been developed to estimate the stresses or energy in the cracked laminate, Talreja and Singh (2012). In strength-based models, as the local stresses reach the strength at a point, a new matrix crack is assumed to initiate. Strength-based models fail to predict the crack initiation when deterministic single strength obtained from the uni-directional (UD) laminate experiments are used. However, successful prediction of matrix cracking behavior has been reported if statistical strength distribution is considered Jagannathan et al. (2016); studies have shown that the matrix cracks initiate at locations of largest voids created during the manufacturing process and the matrix crack evolution rate can be correlated to the statistical variation of flaws, Nairn (2000), Berthelot (2003), Talreja and Singh (2012). Cross-ply laminates matrix cracking has been extensively studied and reported in the literature, Berthelot (2003). Various models have been used to predict the stiffness of the cracked laminate as a function of crack density estimated using the above approaches. In the simplest model termed ply-discount method, the stiffness of cracked ply is assumed zero and discounted while estimating the stiffness of the laminate. An extensive review of different models can be found in the literature by Talreja and Singh (2012). In most practical applications, a multi-axial loading scenario exists. Most of the models developed in the literature are limited to uni-axial loading condition and have not addressed matrix cracking under bi-axial loading. It has been reported that when a cross-ply laminate is subjected to in-plane bi-axial loading, splitting in 0o ply occurs in addition to matrix cracking in the 90o ply by Montesano and Singh (2015). In particular, such bi-axial loading conditions are expected to occur under thermal loading of composite cylindrical shells. There have been limited studies to account for cross-ply laminates under bi-axial loading conditions by Spain (1971), Adams et al. (1986), Maddocks (1995), Montesano and Singh (2015). All the models developed have used some form of energy parameter to predict the matrix cracking in the cross-ply laminate. In this work, an attempt has been made to predict the matrix cracking in cross-ply laminates using statistical strength-based approach under bi-axial loading condition