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

Compliant morphing structures from twisted bulk metallic glass ribbons

In this work, we investigate the use of pre-twisted metallic ribbons as building blocks for shape-changing structures. We manufacture these elements by twisting initially flat ribbons about their (lengthwise) centroidal axis into a helicoidal geometry, then thermoforming them to make this configuration a stress-free reference state. The helicoidal shape allows the ribbon to have preferred bending directions that vary throughout its length. These bending directions serve as compliant joints and enable several deployed and stowed configurations that are unachievable without pre-twist, provided that compaction does not induce material failure. We fabricate these ribbons using a bulk metallic glass (BMG), for its exceptional elasticity and thermoforming attributes. Combining numerical simulations, an analytical model based on shell theory and torsional experiments, we analyze the finite-twisting mechanics of various ribbon geometries. We find that, in ribbons with undulated edges, the twisting deformations can be better localized onto desired regions prior to thermoforming. Finally, we join together multiple ribbons to create deployable systems. Our work proposes a framework for creating fully metallic, yet compliant structures that may find application as elements for space structures and compliant robots

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 review on optimization in polymer processing

The use of optimization computational tools is of primordial importance for the polymer processing industry, as they provide the means for improving the efficiency of the process without requiring time-consuming and expensive procedures. This review aims to evaluate the application of optimization methodologies to the most important polymer processing technics, including, single and twin-screw extrusion, dies and calibrators, blow-moulding, injection moulding and thermoforming. The most important features of an optimization system will be identified to identify the best practices for each particular situation. These features include the nature of the objective function (single or multi-objective), the type of optimization algorithm, the modelling routine used to evaluate the solutions and the parameters to be optimized. First, the state-of-the-art optimization methodologies generally employed is presented. This will be followed by a detailed review of the literature dealing with this subject. This will be completed by a discussion taking into account the features referred to above. Therefore, it was possible to show that different optimization techniques can be applied to polymer processing with great success

A finite strain thermo-mechanically coupled material model for semi-crystalline polymers

In this work, a thermo-mechanically coupled constitutive model for semicrystalline polymers is derived in a thermodynamically consistent manner. In general, the macroscopic material behaviour of this class of materials is dictated by the underlying microstructure, i.e. by the distribution and structure of crystalline regimes, which form up after cooling from the amorphous melt. In order to account for the latter, the total degree of crystallinity is incorporated as an internal variable and its evolution is prescribed by means of a non-isothermal crystallisation kinetics model. The numerically efficient and robust framework is characterised based on experimental data for Polyamide 6 and shows a promising potential to predict the hyperelastic, visco-plastic material behaviour at various temperature

A finite strain thermo-mechanically coupled material model for semi-crystalline polymers

In this work, a thermo-mechanically coupled constitutive model for semicrystalline polymers is derived in a thermodynamically consistent manner. In general, the macroscopic material behaviour of this class of materials is dictated by the underlying microstructure, i.e. by the distribution and structure of crystalline regimes, which form up after cooling from the amorphous melt. In order to account for the latter, the total degree of crystallinity is incorporated as an internal variable and its evolution is prescribed by means of a non-isothermal crystallisation kinetics model. The numerically efficient and robust framework is characterised based on experimental data for Polyamide 6 and shows a promising potential to predict the hyperelastic, visco-plastic material behaviour at various temperature

Multi-objective optimization of plastics thermoforming

The practical application of a multi-objective optimization strategy based on evolutionary algorithms was proposed to optimize the plastics thermoforming process. For that purpose, in this work, differently from the other works proposed in the literature, the shaping step was considered individually with the aim of optimizing the thickness distribution of the final part originated from sheets characterized by different thickness profiles, such as constant thickness, spline thickness variation in one direction and concentric thickness variation in two directions, while maintaining the temperature constant. As far we know, this is the first work where such a type of approach is proposed. A multi-objective optimization strategy based on Evolutionary Algorithms was applied to the determination of the final part thickness distribution with the aim of demonstrating the validity of the methodology proposed. The results obtained considering three different theoretical initial sheet shapes indicate clearly that the methodology proposed is valid, as it provides solutions with physical meaning and with great potential to be applied in real practice. The different thickness profiles obtained for the optimal Pareto solutions show, in all cases, that that the different profiles along the front are related to the objectives considered. Also, there is a clear improvement in the successive generations of the evolutionary algorithm.This research was funded by NAWA-Narodowa Agencja Wymiany Akademickiej, under grant PPN/ULM/2020/1/00125 and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 734205–H2020-MSCA-RISE2016. The authors also acknowledge the funding by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under the projects UID-B/05256/2020, UID-P/05256/2020, UIDB/00319/2020, MORPHING.TECH— Direct digital Manufacturing of automatic programmable and Continuously adaptable patterned surfaces with a discrete and patronized composition (POCI-01-0247-FEDER-033408)

Thermoforming process effects on structural performance of carbon fiber reinforced thermoplastic composite parts through a manufacturing to response pathway

Thermoforming process of thermoplastic-based continuous CFRP\u27s offer a major advantage in reducing cycle times for large-scale productions, but it can also have a significant impact on the structural performance of the parts by inducing undesirable effects. This necessitates the development of an optimal manufacturing process that minimizes the introduction of undesirable factors in the structure and thereby achieves the targeted mechanical performance. This can be done by first establishing a relationship between the manufacturing process and mechanical performance and successively optimizing it to achieve the desired targets. The current study focuses on the former part, where a manufacturing-to-response (MTR) pathway is established for a continuous fiber-reinforced thermoplastic composite hat structure. The MTR pathway incorporates the thermoforming process-induced effects while determining the mechanical performance and principally comprises of material characterization, finite element simulations, and experimental validation. The composite material system selected for this study is AS4/Nylon-6 (PA6) with a woven layup. At first, the thermoforming simulations are performed above the melt temperature of PA6 using an anisotropic hyperelastic material model, and the process-induced effects such as thickness variation, fiber orientations, and residual stresses are captured from the analysis. Residual stresses developed in the formed structure during quench cooling from the elevated temperature are predicted by the implementation of classical laminate theory (CLT). These results are then mapped onto a duplicate part meshed suitably for mechanical performance analysis. A quasi-static 3-point bend test and a dynamic impact test are carried out and the results are compared with experimental tests. Experimental results from thermoforming, bending and dynamic impact trials show good agreement with the simulation results for the hat structure under consideration. Further, the static and dynamic performance is evaluated for the thermoformed structure and the effects of the thermoforming process are compared numerically, for the cases with and without the inclusion of process effects