Multi-scale modeling of the viscoelastic behavior of 3D woven composites

Abstract

A method is presented to predict numerically the homogenized viscoelastic behavior of 3D woven composites using only its constituents' behavior. It is based on elastic homogenizations applied to the Laplace-Carson transform of the time-dependent viscoelastic behavior of the constituents. Two scale chages are necessary: from micro-to meso-scale to obtain the homogenized behavior of the consolidated yarns, and from mesoto macro-scale. The temperature and cure dependent viscoelastic behavior of the matrix is identified from experimental data, using the time-temperature superposition principle with the cure dependent glass transition temperature as reference temperature. The meso-scale representative unit cell of the composite is extracted from X-ray microtomography images. The homogenized viscoelastic behavior is used to calculate the evolution of the apparent moduli of the composite with temperature between −50 • C and 200 • C. The results are in good agreement with experimental data over the temperature range where the matrix behavior was properly identified.While the mechanical behavior of carbon or glass fibers is linear elastic in a good approximation and almost independent of temperature, at least below the glass transition temperature (T g ) of typical thermosetting polymers (usually not exceeding about 200 • C), the mechanical behavior of the polymer matrix depends strongly on temperature and on the degree of cure [14,15,16,17,18,12]. Moreover, it is time dependent, i.e., creep and relaxation phenomena are observed, which may have a significant impact on the residual stresses and the final shape of composite parts [13,19,20,21]. As a consequence, residual stresses can be reduced by adapting the cure cycle such that relaxation phenomena are intensified [13,22].Since in the aeronautical industry highly precise part shapes are required, it is currently common practice to adapt the mold shape several times until the composite part fits the shape tolerances. This procedure of designing a composite part is very expensive, but can be greatly optimized if precise modeling tools are available that predict the generation of residual stresses and the final shape of composites with complex reinforcements, such as three-dimensional (3D) interlock weavings. To improve the accuracy of currently available modeling tools, it is necessary to take into account creep and relaxation and their dependence on temperature and degree of cure during the modeling of the curing and cooling process. The experimental characterization of a composite material required to determine the model parameters is complex and expensive, as 3D strain rate, temperature, and cure dependent mechanical behaviors have to be measured. Furthermore, these properties have to be re-identified, each time the reinforcement architecture is changed. Significant cost reduction is possible if only the constituent materials are fully characterized and the composite properties are predicted using multi-scale models.At small strains, creep, relaxation, and strain rate d...

Study of Critical Material Parameters for Curing Deformation of Aerospace Wing Composites before Numerical Simulation

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