Optimum design of pultrusion process via evolutionary multi-objective optimization

Pultrusion is one of the most cost-effective manufacturing techniques for producing fiber-reinforced composites with constant cross-sectional profiles. This obviously makes it more attractive for both researchers and practitioners to investigate the optimum process parameters, i.e., pulling speed, power, and dimensions of the heating platens, length and width of the heating die, design of the resin injection chamber, etc., to provide better understanding of the process, consequently to improve the efficiency of the process as well as the product quality. Using validated computer simulations is “cheap” and therefore is an attractive and efficient tool for autonomous (numerical) optimization. Optimization problems in engineering in general comprise multiple objectives often having conflict with each other. Evolutionary multi-objective optimization (EMO) algorithms provide an ideal way of solving this type of problems without any biased treatment of objectives such as weighting constants serving as pre-assumed user preferences. In this paper, first, a thermochemical simulation of the pultrusion process has been presented considering the steady-state conditions. Following that, it is integrated with a well-known EMO algorithm, i.e., nondominated sorting genetic algorithm (NSGA-II), to simultaneously maximize the pulling speed and minimize “total energy consumption” (TEC) which is defined as a measure of total heating area(s) and associated temperature(s). Finally, the results of the evolutionary computation step is used as starting guesses for a serial application of a of gradient-based classical algorithm to improve the convergence. As a result, a set of optimal solutions are obtained for different trade-offs between the conflicting objectives. The trade-off solution, thus obtained, would remain as a valuable source for a multi-criterion decision-making task for eventually choosing a single preferred solution for the pultrusion proces

Mechanical Modelling of Pultrusion Process: 2D and 3D Numerical Approaches

The process induced variations such as residual stresses and distortions are a critical issue in pultrusion, since they affect the structural behavior as well as the mechanical properties and geometrical precision of the final product. In order to capture and investigate these variations, a mechanical analysis should be performed. In the present work, the two dimensional (2D) quasi-static plane strain mechanical model for the pultrusion of a thick square profile developed by the authors is further improved using generalized plane strain elements. In addition to that, a more advanced 3D thermo-chemical-mechanical analysis is carried out using 3D quadratic elements which is a novel application for the numerical modelling of the pultrusion process. It is found that the 2D mechanical models give relatively reasonable and accurate stress and displacement evolutions in the transverse direction as compared to the 3D model. Moreover, the generalized plane strain model predicts the longitudinal process induced stresses more similar to the ones calculated in the 3D model as compared with the plane strain model

Pultrusion of a vertical axis wind turbine blade part-I: 3D thermo-chemical process simulation

A novel three dimensional thermo-chemical simulation of the pultrusion process is presented. A simulation is performed for the pultrusion of a NACA0018 blade profile having a curved geometry, as a part of the DeepWind project. The finite element/nodal control volume (FE/NCV) technique is used. First, a pultrusion simulation of a U-shaped composite profile is performed to validate the model and it is found that the obtained cure degree profiles match with those given in the literature. Subsequently, the pultrusion process simulation of the NACA0018 profile is performed. The evolutions of the temperature and cure degree distributions are predicted inside the heating die and in the post-die region where convective cooling prevails. The effects of varying process conditions on the part quality are investigated for two different heater configurations and with three different pulling speeds. Larger through-thickness gradients are obtained for the temperature and degree of cure as the pulling speed increases. This will affect the process induced residual stresses and distortions during manufacturing

Thermo-Chemical Modelling Strategies for the Pultrusion Process

In the present study, three dimensional (3D) numerical modeling strategies of a thermosetting pultrusion process are investigated considering both transient and steady state approaches. For the transient solution, an unconditionally stable alternating direction implicit Douglas-Gunn (ADI-DG) scheme is implemented as a first contribution of its kind in this specific field of application. The corresponding results are compared with the results obtained from the transient fully implicit scheme, the straightforward extension of the 2D ADI and the steady state approach. The implementation of the proposed approach is described in detail. The calculated temperature and cure degree profiles at steady state are found to agree well with results obtained from similar analyses in the literature. Detailed case studies are carried out investigating the computational accuracy and the efficiency of the 3D ADI-DG solver. It is found that the steady state approach is much faster than the transient approach in terms of the computational time and the number of iteration loops to obtain converged results for reaching the steady state. Hence, it is highly suitable for automatic process optimization which often involves many design evaluations. On the other hand sometimes the transient regime may be of interest and here the proposed ADI-DG method shows to be considerably faster than the transient fully implicit method which is generally used by the general purpose commercial finite element solvers. Finally, using the proposed steady-state approach, a design of experiments is carried out for the curing characteristic of the product based on pulling speed and part thicknes

Modelling residual stresses in friction stir welding of Al alloys—a review of possibilities and future trends

Residual stresses are very important in any joining process of materials since they act as pre-stresses in the loading situation of the joint, thereby affecting the final mechanical performance of the component. This is also the case for friction stir welding (FSW) which is a complex solid-state joining process characterized by a pronounced multiphysical behaviour involving phenomena such as change of temperature, material flow, change of microstructures and formation of residual stresses. Thus, models of FSWare typically divided into thermal models, flow models, residual stress models and microstructural models where the classification of the model normally originates from its purpose rather than from the modelling discipline applied. In the present paper, the focus is on presenting and classifying the most important residual stress models for FSW of aluminium alloys in terms of their background, numerical framework and application as well as putting them into proper context with respect to some of the new trends in the field, e.g. coupling with subsequent load analyses of the in-service situation or applying residual stress models of FSWin numerical optimization