Viscoelastic modeling of regular cross-ply laminantes
Marian Klasztorny, Tadeusz Niezgoda
Quarterly No. 3, 2009 pages 223-227
DOI:
keywords: regular cross-ply laminate, homogenization, constitutive equations of viscoelasticity, computer-aided algorithm
abstract The paper concerns regular cross-ply fibre-reinforced-plastic (CP xFRP) laminates, i.e., a stack of plies of configuration. Each ply is a UD xFRP composite, i.e. an isotropic hardening plastic reinforced with long monotropic fibres packed unidirectionally in a hexagonal scheme. The plies are identical with respect to their thickness and microstructure. A polymer matrix of the laminate is an advanced viscoelastic isotropic material described by normal and fractional exponential functions, reflecting short-, moderate- and long-term viscoelastic processes. Fibres are made of a monotropic elastic material. The considerations are limited to stress levels protecting geometrically and physically linear viscoelastic behaviour of the material. The study presents a method for viscoelastic modelling of regular CP xFRP laminates, based on the exact stiffness theory of CP xFRP and on the elastic - viscoelastic analogy principle. Five independent elasticity compliances of a UD xFRP composite have been expressed in terms of the elasticity shear compliance of a viscoelastic isotropic polymer matrix. The elastic-viscoelastic analogy principle gives complex compliances of a UD xFRP composite dependent on complex shear compliance of the matrix. These compliances are used to determine complex compliances of a CP xFRP laminate. Standard constitutive equations of linear viscoelasticity of CP xFRP laminates are developed. The homogenized laminate is modelled as linearly viscoelastic orthotropic continuum described by 6 effective elasticity constants and 6 effective viscoelasticity coefficients. There are introduced the RLTC (relative long-term creep) coefficients dependent of micro- and meso-structure of the laminate as well as of the viscoelastic properties of the matrix, fully describing the standard viscoelasticity equations. A set of RLTC coef-ficients is calculated analytically. The method adopts the exact and approximate complex compliances of the laminate. A com-puter-aided algorithm presented in the study for calculation RLTC coefficients has been programmed in PASCAL. A regular CP CFRP laminate of configuration, denoted with the symbol CP U/E53, has been examined as an example. Each ply is the UD U/E53 composite. The matrix (E53 hardening plastic) is made of Epidian 53 epoxide resin, reinforced with UTS 5631 carbon fibres produced by Tenax Fibers. Diagrams presenting the selected storage and loss compliances of the laminate are presented as well. 4,0/90Snn 40/90,Snn.