Zhu, Hui
(2023)
Analytical and experimental investigation of incremental sheet forming of thermoplastics.
PhD thesis, University of Nottingham.
Abstract
Incremental sheet forming (ISF) is a promising flexible manufacturing process and has drawn increasing attention in the past decades. The final shape of ISF formed part is accumulated by localised deformation under the forming tool. Extensive research has shown that it is especially advantageous in manufacturing small-batch and customised sheet parts because of its distinctive features of flexibility, adaptability, applicability, improved material formability and associated benefits in energy efficiency and reduced costs. Apart from metals, thermoplastics are also widely used engineering materials in different fields as they have great advantages in resistance to impact, temperature and load carrying capability. As a result, ISF of thermoplastics has been noticed in recent years.
This thesis reports the findings of analytical and experimental investigations on ISF and its application in thermoplastics. By revealing the mechanical behaviour of thermoplastics and the deformation mechanism of ISF, a new constitutive model for thermoplastics, and new analytical models for ISF force and contact pressure prediction are developed. Focus is also given to the experimental study of thermoplastic-based ISF process and the application in manufacture of customised cranial plates.
A new phenomenological constitutive model is proposed to predict the mechanical behaviour of thermoplastics. The new constitutive model and the method to determine the parameters of the model are introduced. In the new model, a transition function is proposed to enable a smooth transition of the flow stress behaviours under both small-strain and large-strain conditions. In validating the model with testing data of Polyether ether ketone (PEEK) and Polycarbonate (PC), it is found that this new model is able to predict different phases of the flow stress behaviour of thermoplastics in consideration of the effect of strain, strain rate and temperature. Although the basic trends of tensile and compressive behaviours of PEEK and PC materials are different, the new constitutive model can be used to represent these behaviours effectively. In addition, the results show that the new model gives a favourable prediction of the PC material at high strain rate conditions. Compared with Johnson-Cook, Nasraoui et al., Duan-Saigal-Greif-Zimmerman (DSGZ) and Mulliken-Boyce models, the new model presents an improved level of accuracy on the mechanical behaviour of thermoplastics in a wide range of deformation conditions.
A new analytical model for forming force prediction in the ISF process is presented. The modelling of contact region, thickness distribution and strain components are carried out as the basis for the prediction of vertical and horizontal forces. The effect of local contact behaviour, material deformation and stretching, as well as the less investigated behaviours of global elastic bending, change of deformation mode and contact condition change are considered in the derivation. The force prediction model at both plane strain and biaxial tension condition area is developed based on the differences in contact region and thickness distribution between these two different deformation states. Validated by ISF tests for a truncated cone and pyramid part with varying drawing angles, the prediction of force history captures well the fluctuation of different force components due to the change of deformation conditions and provides an insight into the material deformation mechanisms and the correlation to forming force characteristics of the whole ISF process. In a practical case, the developed model is successfully applied to the force prediction in ISF-based cranial plate manufacture. The developed model is also validated by a series of ISF tests with different process parameters. Compared with other models, the developed analytical model has the capability to predict both peak and stabilised forces and is more accurate in most cases of the whole ISF process.
An analytical model is developed to predict the contact pressure distribution in ISF for the first time. Referring to the contact mechanics of sheet indentation, the size of contact area, maximum contact pressure and pressure distribution are predicted by the analytical method based on the revealing of the local tool-sheet contact behaviour in ISF. Point based method is used to implement and visualise the analytical model. The validity of the developed analytical model is confirmed by comparison with FE simulation for ISF of titanium grade 1 (TA1) sheet and heat-assisted ISF of PEEK sheet in different aspects. The effect of mesh size in FE simulation is analysed to have an influence on the discrepancy between analytical and simulation results.
Experimental study is carried out to test the feasibility of ISF of PEEK and polymethyl methacrylate (PMMA) sheets at elevated temperature. Heat-assisted ISF setup, force and temperature measurement systems are developed and tested to investigate the effect of spindle speed, feed rate and geometry on temperature distribution, forming force variation, thickness distribution, formed geometry and formability. Results show that spindle speed has the most significant influence on temperature distribution and forming accuracy in ISF of PEEK and PMMA. For ISF of PEEK, preheating temperature of 130 °C and spindle speed of 100 rpm is recommended compared to 1000 rpm, while for ISF of PMMA, 100 °C and 100 rpm can be useful. Based on the experimental tests, ISF-based manufacture of PEEK and PMMA cranial plates is presented and regarded as an effective alternative to cranial reconstruction. Apart from experimental observations, the fracture mechanism, geometric inaccuracy, and twist behaviour are discussed and considered as challenging issues in ISF of thermoplastics.
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