Comparison of viscoelasticity models for the prediction of residual stresses in wind turbine rotor blades

Abstract

In the composite materials of wind turbine rotor blades, residual stresses develop due to the manufacturing processes [1]. During the curing of the polymeric matrix, chemical shrinkage is present. Moreover, different coefficients of thermal expansion of the composite constituents combined with the application of external heat, the exothermal nature of the chemical reaction, and the cool-down after curing result in non-uniform and remanent deformations and thus in residual stresses.

In thin and curved composite parts, the residual stresses relax due to spring-in or spring-back deformations, see Figure 1. In thick parts, however, the structural stiffness avoids these deformations. The residual stresses can thus reach significant magnitudes and can trigger damage initiation already during the manufacturing process [2]. As they superimpose to the mechanical loading, residual stresses can also reduce the load levels for crack initiation on quasi-static ultimate loads, or can accelerate fatigue damage formation [3]. For reliable ultimate and fatigue strength predictions of wind turbine rotor blades, it is thus important to have a reliable and accurate model at hand for the calculation of the residual stresses.

The aim of this work is to find a suitable viscoelasticity model for the calculation of residual stresses. We compare three different three-dimensional viscoelasticity models that consider the manufacturing processes in glass fiber/epoxy composites used in wind turbine rotor blades: (i) the CHILE model [4], (ii) the improved CHILE model [5], and (iii) the Maxwell model [5]. The CHILE model subdivides the curing process into three stages, the initial stage, the accumulating stage and the final stage. In the initial and final stages, the mechanical properties are approximately constant. In the accumulating stage, the mechanical properties, i. e. stiffnesses, are considered to increase linearly with the degree of cure. Since the chemo-mechanical coupling due to the network formation in the polymeric matrix is complex, the improved CHILE model was developed. Therein, the change of mechanical properties on curing is a function of the temperature profile. The chemo-mechanical coupling is thus transferred to thermo-mechanical coupling. The Maxwell model is a classical rheological model consisting of a number of springs and dampers in a parallel and serial order, which can express the change of the mechanical properties in an exponential form.

The models are implemented as user subroutines in the finite element solver Abaqus. With each of the aforementioned models, representative numerical simulations are carried out. The simulations focus on thick laminates, because they do not relax by spring-in or spring-back deformations. Hence, it is expected that the residual stresses are critical here. Such thick laminates are used in spar caps of wind turbine rotor blades for instance. The results are compared by means of physical soundness and criticality on crack initiation for ultimate and fatigue loads. This means that the residual stresses are compared both qualitatively and quantitatively. Moreover, we compare the numerical efficiency of the different models by looking at the respective computational costs.