Initiation and Evolution of Matrix Cracking in Non-Symmetric Laminates under in-Plane and Flexural Loading

Abstract

A constitutive model of progressive matrix cracking in fibers reinforced laminated composite is developed for the case of both membrane and flexural deformation. The progressive damage model makes use of the following key ingredients i) an appropriate material model for calculating the reduced thermo--elastic properties of the laminate containing individual plies affected by matrix cracking, ii) an energy based damage evolution criterion inspired by Fracture Mechanics, iii) an homogenization technique inspired by Continuum Damage Mechanics, iv) an iterative procedure in order to detect the conditions for damage growth in individual plies of the laminate, and to increase the damage level when the conditions are met, and v) the Classical Laminate Theory in order to describe the overall membrane and flexural deformation of the laminated composite. These elements are integrated into a new progressive damage model, where both the degraded mechanical properties of the laminate for given levels of matrix cracking in individual plies, and the matrix cracking process (both onset and progression) under applied loading are regarded.;Crack densities in individual plies of the laminates are the damage state variables of the model. This formulation is unlike the progressive damage models for laminated composites implemented in most of the FEA commercial packages, where softening laws are implemented in order to describe the stiffness reduction and the damage evolution. By using the ply crack densities as state variables the model is able to predict and to keep track of the crack density in individual plies during the loading history, which can be of interest in application where the permeability of the laminate is a limiting design factor. One example of this kind of application can be pressure vessels containing fluids or gases. Thermal residual stresses are taken into account in the present analytical model, which can extend the predictive capabilities of the model to applications in the range of cryogenic temperatures.;The process of matrix cracking under I, II, or mixed I--II modes conditions are included in the present model. The loading case can be in--plane, flexural or combination of the two. There is no limitation on the configuration of the laminate or on the number of the cracking plies, as it is the case of the most models available in the literature, where only symmetric stacking sequences are addressed.;The analytical model is validated against available experimental data for the case of both membrane and flexural loading

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