Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct Time-dependent damage analysis for viscoelastic-viscoplastic structural laminates under biaxial loading Thomas Berton a , Sandip Haldar a , John Montesano b , Chandra Veer Singh a,c, ⁎ a Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto M5S 3E4, Canada b Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Ave. West, Waterloo N2L 3G1, Canada c Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto M5S 3G8, Canada ARTICLE INFO Keywords: Glass fibres Creep Damage mechanics Computational modelling Finite element analysis (FEA) ABSTRACT Many composite structures are required to sustain severe thermo-mechanical loads over extended periods of time, during which viscoelastic and viscoplastic behavior can cause the progression of micro-damage. In this paper, a new computational multi-scale model that couples micro-damage mechanics with Schapery’s theory of viscoelasticity and viscoplasticity has been developed to predict time-dependent damage evolution in laminates under constant biaxial loading. After validation with experimental data, the new model capabilities are show- cased by predicting damage evolution in two distinct laminates under different axial and transverse loads over time. It is found that damage evolution in both laminates is highly sensitive to the biaxial loading levels, and that crack multiplication in each ply is dependent on stacking sequence and ply orientation. The developed multi- scale model may be a suitable design tool for composite structures required to endure long-term loads in de- manding environments. 1. Introduction Composite laminates are increasingly used as structural components in aerospace, marine, energy, and construction applications due to their high stiffness-to-weight ratios and equivalent mechanical performance to their metallic alloy counterparts [1]. While the stiffness of these materials in the pristine state can be predicted accurately using classical laminate theory, the prediction of progressive failure processes under various loading conditions remains challenging due to the hierarchical structure of fiber-reinforced laminates and the complexity of observed damage modes [2,3]. Moreover, favourable environmental conditions may cause laminates to exhibit significant rate-dependent deformations due to the susceptibility of the polymer matrix [4]. Such behaviour is becoming more important since polymer composites are increasingly used for primary structural applications. For example, aerospace ap- plications of novel composite materials can involve high service tem- peratures [5], under which these properties of the matrix will be more important. Previous studies have shown that unidirectional glass-fibre and carbon-fibre epoxy plies can exhibit creep behaviour in the trans- verse and shear directions in which matrix behaviour is dominant [6,7]. Several experimental studies have also found that matrix micro-crack density is affected by the time-dependent properties of the laminates [6,8–10]. Nguyen and Gamby [7], for example, found that for lower rates of loading, crack density evolution for a given amount of applied stress in a non-linear viscoelastic cross-ply laminate was larger than that for higher loading rates. The authors developed a non-linear time- dependent shear-lag model to interpret this trend, and concluded that the experimental results of crack density evolution for different strain rates were due to the inherently different fracture properties of the matrix. Raghavan and Meshii [9] observed similar results for a cross-ply CFRP. They also studied the evolution of damage during a creep test, and observed that damage could progress under a constant load over time, which had a significant effect on creep strain evolution. Fitoussi et al. studied the effects of matrix viscosity on damage evolution in random glass fiber composites [11] by subjecting a short glass fiber composite to impact loading and monitoring experimentally the evo- lution of micro-damage mechanisms. They found that increasing the strain rate delayed the onset of damage. For laminates under tensile loads, ply micro-cracking is usually the first mode of damage and occurs through the nucleation of matrix cracks which rapidly propagate along the width of the laminate parallel to the fibers, and extend through the ply thickness [12,13]. In order to understand the effect of ply micro-cracking, several models have been developed (see [12] for detailed review). These include analytical models such as the shear-lag model [14–16], variational-based methods [17,18], Crack Surface Displacement-based methods [19] and self- https://doi.org/10.1016/j.compstruct.2018.06.117 Received 12 March 2018; Received in revised form 15 May 2018; Accepted 28 June 2018 ⁎ Corresponding author at: Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto M5S 3E4, Canada. E-mail address: chandraveer.singh@utoronto.ca (C.V. Singh). Composite Structures 203 (2018) 60–70 Available online 30 June 2018 0263-8223/ © 2018 Elsevier Ltd. 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