Computational modelling of some problems of elasticity and viscoelasticity with applications to thermoforming process

Copyright @ 2012 Northwestern Polytechnical University and ISCIThe reliability of computational models of physical processes has received much attention and involves issues such as the validity of the mathematical models being used, the error in any data that the models need, and the accuracy of the numerical schemes being used. These issues are considered in the context of elastic, viscoelastic and hyperelastic deformation, when finite element approximations are applied. Goal oriented techniques using specific quantities of interest (QoI) are described for estimating discretisation and modelling errors in the hyperelastic case. The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is then treated, with the aim of estimating engineering QoI and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered. The techniques are applied to thermoforming processes where sheets are inflated into moulds to form thin-walled structures

Press forming a 0/90 cross-ply advanced thermoplastic composite using the double-dome benchmark geometry

A pre-consolidated thermoplastic advanced composite cross-ply sheet comprised of two uniaxial plies orientated at 0/90° has been thermoformed using tooling based on the double-dome bench-mark geometry. Mitigation of wrinkling was achieved using springs to apply tension to the forming sheet rather than using a friction-based blank-holder. The shear angle across the surface of the formed geometry has been measured and compared with data collected previously from experiments on woven engineering fabrics. The shear behaviour of the material has been characterised as a function of rate and temperature using the picture frame shear test technique. Multi-scale modelling predictions of the material’s shear behaviour have been incorporated in finite element forming predictions; the latter are compared against the experimental results

An ElectroThermal Digital Twin for Design and Management of Radiation Heating in Industrial Processes

The design and management of thermoforming systems based on radiation heat transfer require the development of a mathematical model that can be used at all stages of the system's life cycle. For this reason, in this paper, we present a digital twin based on a hybrid ElectroThermal model that can integrate mathematical equations and data acquired in the field. The model's validity is verified with experiments performed on a test bench. The presented model is modular and can be easily used to represent new configurations of the heating elements for simulation and design. Thanks to the low computational complexity of the proposed Digital Twin, it enables the development of advanced control strategies and the analysis and optimization of the main geometric parameters of the system. In addition, it can support the identification of the best configuration and choice of measurement points

Finite element and automatic remeshing methods for the simulation of complex blow molded polymer components

International audienceThis paper presents a three dimensional finite element model of the extrusion blow molding process. The code Tform3 has the following characteristics: membrane formulation, linear triangle elements, updated Lagrangian implicit formulation, viscoelastic differential constitutive equations. The paper presents a brief recall of the formulation and then addresses three key issues of the simulation: automatic identification of constitutive equation parameters, automatic remeshing, coupling between gas pressure and inflation. An example of application to the extrusion blow molding of a bottle is presented

Experimental investigation and computational modelling of the thermoforming process of thermoplastic starch

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Plastic packaging waste currently forms a significant part of municipal solid waste and as such is causing increasing environmental concerns. Such packaging is largely non-biodegradable and is particularly difficult to recycle or to reuse due largely to its complex compositions. Apart from limited recycling of some easily identifiable packaging wastes that can be separated economically, such as bottles, most packaging waste ends up in landfill sites. In recent years, in an attempt to address this problem in plastic packaging, the development of packaging materials from renewable plant resources has received increasing attention and a wide range of bioplastic materials based on starch are now available. Environmentally these bioplastic materials also reduce reliance on oil resources and have the advantage that they are biodegradable and can be composted upon disposal to reduce the environmental impact. Many food packaging containers are produced by thermoforming processes in which thin sheets are inflated under pressure into moulds to produce the required thin -wall structures. Hitherto these thin sheets have almost exclusively been made of oilbased polymers and it is for these that computational models of thermoforming processes have been developed. Recently, in the context of bioplastics, commercial thermoplastic starch sheet materials have been developed. The behaviour of such materials is influenced both by temperature and, because of the inherent hydrophilic characteristics of the materials, by moisture content. Both of these aspects affect the behaviour of bioplastic sheets during the thermoforming process. This thesis describes experimental work and work on the computational modelling of thermoforming processes for thermoplastic starch sheets using a commercially available material. The experimental work has been carried in order to characterise the deformation behaviour of the material with regard to different temperature, moisture contents and strain rates. Thermoforming of the material was performed and samples produced were used for comparison and verification of the computational modelling of the thermoforming process. In the first attempt to model the thermoforming process, a hyperelastic constitutive equation was established to approximate the material behaviour taking account of the combined effects of temperature and moisture content and a simple ii membrane model with constrained deformation was used to model an axisymmetric case of thermoforming. Simulations with this model showed that moisture content mostly affects the pressure required to push the sheet into the mould while moisture variation during thermoforming has little effect on the final thickness distribution of the product. Considerable discrepancies were found in the thickness distribution between the predictions from the model and the experimental measurements. Further attempts were made to take account of the elasto-plastic behaviour of the material and a more complex three-dimensional FE model was developed using ANSYS/LS-DYNA. Based on the findings in the simpler modelling work, no attempt was made to incorporate the moisture content effect on material behaviour but the material parameters for the elasto-plastic constitutive equation were obtained from high speed tensile tests so that moisture variation during thermoforming could be minimised and neglected. The predictions from this model have led to significant improvements in prediction of the thickness distribution which has become much closer to the experimental measurements in comparison with the hyperelastic model. This work provides some important insights into thermoforming of thermoplastic starch materials: a) Deformation behaviour of such materials depends strongly on the moisture content and the temperature, both of which affect behaviour during thermoforming processes, including the preheating stage; b) moisture variation during the thermoforming process has a significant effect on the pressure required for the deformation. This also leads to variation of moisture content distribution in the final product, which in turn affects the material properties such as ductility or impact strength at different positions in the thermoformed structure; c) thermoforming of thermoplastic starch materials can be simulated more accurately by an elasto-plastic model and the LS-DYNA algorithm in comparison with a hyperelastic membrane model. This work has provided useful information on thermoforming of thermoplastic starch materials with particular reference to the design of thermoforming tools and to the careful control of processing conditions including preheating. It has also laid a solid foundation for future work on how the moisture variation impacts on the formation of defects such as incomplete forming due to material hardening and fracture due to loss of ductility

A Manufacturing-To-Response Pathway for Formed Carbon Fiber Reinforced Polymer Composite Structures

Over the past decade, there has been an increased adoption of thermoplastic and thermoset based continuous carbon fiber reinforced polymer (CFRP) composites for structural applications in several industries. Among the different manufacturing methods, thermoforming process for thermoplastic based continuous CFRP’s offer a major advantage in reducing cycle times for large scale productions. Similarly, out-of-autoclave curing process for thermoset based continuous CFRP’s using heated tooling enables production of large composite structures. However, these manufacturing processes can have a significant impact on the structural performance of parts by inducing undesirable effects. These effects include inhomogeneous fiber orientations, thickness variations, and residual stresses in the formed CFRP structures. This necessitates the development of an optimal manufacturing process that minimizes the introduction of the undesirable factors in the structure and thereby achieves the targeted mechanical performance. This can be done by first establishing a relationship between manufacturing process and mechanical performance and successively optimizing it to achieve the desired targets. To this end, a few attempts have been made to connect the design, manufacturing, and structural simulation steps in series, by developing virtual process chains (CAE chains) and mapping methods. However, the recent publications implementing these methods are missing some of the relevant effects or steps of the manufacturing process. The present work establishes two Manufacturing-to-Response (MTR) pathways for end-to-end analysis of CFRP composite structures. The current study focuses on establishing a relationship between manufacturing process and mechanical performance. As case studies, the MTR pathway was implemented for 1. thermoplastic based Composite Hat structure manufactured by thermoforming process and 2. thermoset based Composite Boom structure manufactured by Out-of-Autoclave (OOA) molding process using self-heated tool. The pathway primarily comprised of material characterization, finite element simulations and experimental validation. The first case study details the MTR pathway for thermoforming process of Composite Hat structure. Thermoforming process effects were studied and incorporated in structural analysis. The second case study details a framework of the MTR pathway for OOA molding of Composite Boom structure. The first two steps of the pathway namely Composite boom tool design and curing analysis were accomplished as a part of the present study. The MTR pathway(s) were validated experimentally for the Composite Hat structure and validation for the Composite Boom structure is planned for future work. Both studies indicated the significance of incorporating the manufacturing process effects into the structural performance of a composite structure