Viscoelastic homogenization of 3D woven composites with damping validation in temperature and verification of scale separation

Abstract

Estimation of damping can be of great importance for turbomachines, where vibration based instabilities like flutter occur. The paper discusses a numerical method to predict the homogenized viscoelastic behavior of 3D woven composites, used in fan blades, from elementary constituent behavior. Yarn and weave microstructures are considered in a two scale homogenization. The matrix and fibers are considered homogeneous with linear viscoelastic and elastic behavior respectively. Temperature and frequency dependence of matrix properties are characterized by complex moduli. Confrontation of numerical predictions with modal damping of a modified Oberst experiment, for a temperature range of -40 to 120 °C, gives good results in terms of absolute value and trends. The homogenization is formulated using matrix operations, which enables the simple use of model reduction techniques for parametric studies on temperature and leads to energy fraction analyses useful to gain understanding of how different components of the constitutive laws contribute to damping and change with temperature. Finally, since weaving patterns have a scale of a few centimeters, that is not small compared to gradients found in the experiment, exact solutions for responses to regular volume loads are used to characterize the validity of the scale separation hypothesis as a function of wavelength.