Determination of Transverse Shear Stresses and Delamination in Composite Laminates Using Finite Elements
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Determination of Transverse Shear Stresses and Delamination in Composite Laminates Using Finite Elements
8.1 Introduction In this chapter, we present a simple and efficient method of analysis for the shear flexible shells and composite laminates using the finite element framework discussed in the previous chapters (See also Woelke et al. 2008). Transverse shear strains and stresses are especially important in the analysis of composite laminates. This is because advanced filamentary composite materials are susceptible to thickness effects, as their effective transverse shear modulus is substantially smaller than the effective elastic modulus in the fiber direction. Moreover, increasing use of composite laminates in various branches of industry requires analysis of these structures beyond the elastic behavior and up to failure. Composite laminates have various modes of failure: delamination, debonding, fiber cracking, and matrix yielding and cracking. Thus, determination of the accurate distribution of transverse shear stresses across the thickness of the laminate demands special attention. One of the most common failure modes is delamination caused by the transverse shear stresses. To accurately model composite plates and shells and address the issues related to failure, it is necessary to include transverse shear stresses in analyses. We use a description of shear effects based on the Mindlin-Reissner theory of plates, modified to improve the model’s accuracy. The Mindlin-Reissner theory leads to a constant distribution of the transverse shear stresses across the laminate thickness. This representation is inexact, as the transverse shear stress function is actually parabolic through the thickness of the lamina and not continuous through the laminate. To improve the accuracy of shear stress prediction, a shear correction function is applied, obtaining a parabolic distribution of shear stresses across the thickness of the laminate without changing the definitions of the shell kinematics. The correction function satisfies the boundary conditions, enforcing zero shear stresses on the outer surfaces of the laminas. Although using a second-order strain function through the thickness of the composite laminate is a significant improvement over a constant one, it still results in an undesired strain continuity through the thickness. Substantial stiffness variations of the individual laminas lead to “jumps” of the shear stress gradients at lamina interfaces. As failure analysis focuses on stresses, we adopt a transformed section method that assumes a continuous shear strain distribution. The transverse shear stresses are calculated using the effective G.Z. Voyiadjis, P. Woelke, Elasto-Plastic and Damage Analysis of Plates and Shells, C Springer-Verlag Berlin Heidelberg 2008
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8 Determination of Transverse Shear Stresses and Delamination
section properties, i.e., first and second moments of area, allowing for accurate determination of the stress distribution through the thickness. The formulation is a generaliza
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