Three‐dimensional simulation of thermoforming process and its comparison with experiments

Three‐dimensional solid element analysis and the membrane approximated analysis employing the hyperelastic material model have been developed for the simulation of the thermoforming process. For the free inflation test of a rectangular sheet, these two analyses showed the same behavior when the sheet thickness was thin, and they deviated more and more as the sheet thickness increased. In this research, we made a guideline for the accuracy range of sheet thickness for the membrane analysis to be applied. The simulations were performed for both vacuum forming and the plug‐assisted forming process. To compare the simulation results with experiments, laboratory scale thermoforming experiments were performed with acrylonitrile‐butadiene‐styrene (ABS). The material parameters of the hyperelastic model were obtained by uni‐directional hot tensile tests, and the thickness distributions obtained from experiments corresponded well with the numerical results. Non‐isothermal analysis that took into account the sheet, temperature distribution measured directly from the experiments was also performed. It was found that the non‐isothermal analysis greatly improved the predictability of the numerical simulation, and it is important to take into account the sheet temperature distribution for a more reliable simulation of the thermoforming process.     

Influence of initial sheet temperature on ABS thermoforming

Understanding the effects of material and processing parameters on the thermoforming process is critical to the optimization of processing conditions and the development of better materials for high quality products. In this study we investigated the influence of initial temperature distribution over the sheet on the part thickness distribution of a vacuum snap‐back forming process. The linear viscoelastic properties along with the Wagner two parameter nonlinear viscoelastic constitutive model were utilized for numerical simulation of the thermoforming operation. Simulations of pre‐stretched vacuum thermoforming with a relatively complex mold for a commercial refrigerator liner were conducted. THe effects of temperature distribution over the sheet on the part thickness distribution were determined to examine process sensitivity and optimization. Effects of the temperature distribution on the material rheology and polymer/mold friction coefficient are primarily responsible for the changes in the thickness distribution. We found that even small temperature differences over the sheet greatly influenced bubble shape and pole position during the bubble growth stage and played a critical role in determining the part thickness distribution. These results are discussed in terms of rheological properties of polymers such as elongational viscosity and strain hardening.     

Effects of rheological properties and processing parameters on ABS thermoforming

Understanding effects of material and processing parameters on the thermoforming process is critical to the optimization of processing conditions and the development of better materials for high quality products. In this study we investigated the influence of both rheological properties and processing parameters on the part thickness distribution of a vacuum snap‐back forming process. Rheological properties included uniaxial and biaxial elongational viscosity and strain hardening and/or softening while processing parameters included friction coefficient, heat transfer coefficient, and sheet and mold temperatures. The Wagner two parameter nonlinear viscoelastic constitutive model was used to describe rheological behavior and was fit to shear and elongational experimental data. The linear viscoelastic properties along with the Wagner model were utilized for numerical simulation of the thermoforming operation. Simulations of pre‐stretched vacuum thermoforming with a relatively complex mold for a commercial refrigerator liner were conducted. The effects of nonlinear rheological behavior were determined by arbitrarily changing model parameters. This allows determination of which rheological features (i.e., elongational mode, viscosity, and strain hardening and/or softening) are most critical to the vacuum snap‐back thermoforming operation. We found that rheological and friction properties showed a predominant role over other processing parameters for uniform thickness distribution.     

Rheological modeling of plug‐assist thermoforming

Solving problems for thermoforming processes in the production of axisymmetric thin walled plastics is investigated in this research work. A nonlinear viscoelastic rheological model with a new strain energy function is suggested for improvement of physical properties of final product. For model validation, a quantitative relation between stress and technical parameters of plug‐assist thermoforming is determined by comparison of theoretical and experimental results. This process with the proposed rheological model could be suggested for prevention from some technical defects such as wall thickness variations, physical instability during inflation‐shrinkage, and warpage exhibited in the final part of a polymeric sheet thermoforming. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 4148–4152, 2006     

Vacuum forming of thermoplastic foam

The process of thermoforming of foam sheet is analyzed using both finite element modeling and experiments. A simple constitutive model for finite tensile deformations of closed cellular material around its glass transition temperature is proposed, starting from well-known results from Gibson and Ashby (1988). The model is implemented in a finite element code and applied in isothermal vacuum forming simulations. The distributions of thickness and in plane strains are in adequate accordance to the experimental results.     

A viscoelastic–viscoplastic modeling approach for amorphous polymers in vacuum forming simulation

In this study, the simulation of a vacuum forming process employing a micromechanical inspired viscoelastic–viscoplastic model is investigated. In the vacuum forming process, a plastic sheet is heated above the glass transition temperature and subsequently forced into a mold by applying a vacuum. The model consists of a generalized Maxwell model combined with an dissipative element in series. Each Maxwell element incorporates a hyperelastic element in series with a viscous element based on a hyperbolical law. While the generalized Maxwell model considers the relaxation due to molecular alignment, the additional viscous element is a modification based on the approach of Bergström and thus considers molecular chain reptation. The model is designed with the aim to converge to the generalized linear Maxwell model in the limit of small deformation. Furthermore, the viscous modeling is temperature activated and follows the Williams–Landel–Ferry approach in the limit of linear viscoelasticity. To simulate rheological standard experiments, a physical-network-based implementation into Simscape is presented. To validate the performance of the model in thermoforming, it is implemented into Fortran programming language for finite element simulation with Abaqus/Explicit. It can be shown that the simulation is able to predict the thickness in high correlation with experimental results.     

Sensitivity of operating conditions and material properties for thermoforming process

Abstract

The thermoforming process involves three stages: sheet reheat; forming; and solidification. A polymeric sheet is heated in an oven to the desired forming temperature distribution. The sheet is then deformed to take the shape of the mould cavity and subsequently solidified. The deformation of the sheet is assisted by the application of a pressure differential and/or the use of a moving plug.     

The effects of radiation cross‐linking and process parameters on the behavior of polyamide 12 in vacuum thermoforming

Compared to amorphous thermoplastics, semi‐crystalline thermoplastics usually have a smaller processing range for thermoforming, due to their narrow temperature window for the transition from viscoelastic to viscous material behavior. On the other hand, semi‐crystalline thermoplastics offer superior properties for applications like ductility or chemical resistance. Within this article, modification of semi‐crystalline polyamide 12 by radiation cross‐linking with respect to its suitability for vacuum thermoforming as well as the effects of processing parameters and sheet thickness on the resulting strain distributions in thermoformed parts are shown. Experimental thermoforming processing studies in combination with digital image correlation measurements, thermo‐mechanical and elongational rheometry were performed to characterize the behavior of cross‐linked semi‐crystalline thermoplastics in the vacuum thermoforming process. POLYM. ENG. SCI., 2011. ©2011 Society of Plastics Engineers     

Thermodynamic approach of inflation process of K‐BKZ polymer sheet with respect to thermoforming

The problem of modeling and the dynamic finite element simulation of thermoforming process for viscoelastic sheet are considered. The pressure load used in modeling is thus deduced from the thermodynamic law of ideal gases. The viscoelastic behavior of the K‐BKZ model is considered. The Lagrangian formulation together with the assumption of the membrane theory is used in the finite element implementation. The numerical validation is performed by comparing the theoretical solution for the uniaxial and equibiaxial hencky deformation with numerical results. Moreover, the influence of the K‐BKZ constitutive model, for three linear time distribution of airflow rate loading, on the thickness and on the stress distribution in thermoforming of containers made of HDPE are analyzed. POLYM. ENG. SCI., 45:1319–1335, 2005. © 2005 Society of Plastics Engineers     

The role of process parameters in determining wall thickness distribution in plug‐assisted thermoforming

This article describes the results of a comprehensive investigation to determine the link between process parameters and observed wall thickness output for the plug‐assisted thermoforming process. The overall objective of the work was to systematically investigate the process parameters that may be adjusted during production to control the wall thickness distribution of parts manufactured by plug‐assisted thermoforming. The parameters investigated were the sheet temperature, plug temperature, plug speed, plug displacement, plug shape, and air pressure. As well as quantifying the effects of each parameter on the wall thickness distribution, a further aim of the work was to improve the understanding of the physical mechanisms of deformation of the sheet during the different stages of the process. The process parameters shown to have the greatest effect on experimentally determined wall thickness distribution were the plug displacement, sheet temperature, plug temperature, and plug shape. It is proposed that during the plug‐assisted thermoforming of polystyrene the temperature dependent friction between the plug and sheet surface was the most important factor in determining product wall thickness distribution, whereas heat transfer was shown to play a less important role. POLYM. ENG. SCI., 50:1923–1934, 2010. © 2010 Society of Plastics Engineers     

Improved mathematical modeling for the sheet reheat phase during thermoforming

In any thermoforming process, plastic sheet heating is the most important phase as it is responsible for final part quality as well as overall process efficiency and productivity. The goal of the study reported here was to improve existing mathematical models to accurately predict the temperature profile inside a heated sheet, where the model could be used to better control the overall thermoforming process. A mathematical model with temperature dependent, variable sheet material properties including density, thermal diffusivity, specific heat, and thermal conductivity was developed and validated against experimental data. Models with constant and variable plastic sheet properties were created, simulated, and compared in Matlab. The models were validated by experiments which obtained temperature profiles at different depths within a plastic sheet by inserting thermocouples and recording temperatures. Further, the effect of sheet color on heating was investigated by considering two extreme cases: white (transparent) and black (opaque) colored sheets, and the effect of oven air temperature and velocity on sheet heating was also investigated. Results indicated that a variable properties model was needed to control sheet reheating especially with narrow forming windows, and that the heating profiles required for colored and noncolored sheets were very different. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Investigation into thermoformability of hot compacted polypropylene sheet

Abstract

This paper describes an investigation into the thermoformability of a new class of oriented polymeric material recently developed, namely hot compacted polypropylene sheet. Exploitation of any new material requires an intimate understanding of a whole range of factors, amongst which thermoformability is pre-eminent. This is particularly true for oriented polymeric materials, for while the preferred molecular alignment gives enhanced properties such as stiffness, strength, and resistance to impact, the downside is that the stretched molecular chains tend to limit further flow under stress, making thermoforming difficult. The aim of the present study was to establish the critical parameters for successful thermoforming of hot compacted polypropylene sheet.

Elevated temperature tensile tests were used to investigate the stress–strain behaviour of the compacted materials. The crucial parameters were found to be the post-yield modulus, which gives a measure of the resistance of the material to large scale deformation, and the strain to failure, which gives the upper limit on deformation. The post-yield modulus was found to be significantly affected by the test temperature and the high strain hardening behaviour of the material confirmed that significant force is required to thermoform the compacted polypropylene sheets. A hemispherical mould, with built-in gripping plate, was used to carry out a study of the thermoforming behaviour of the compacted sheets, and the results were found broadly to confirm the conclusions of the tensile tests. A linear relationship was found between the tensile force and the postforming force, reinforcing the synergy between the two tests. In addition the forming tests showed that the best temperatures to use were either side of the melting point of the melted and recrystallised phase, depending on the amount of postforming deformation required. Different gripping arrangements were investigated both in which the sheet was fully gripped and in which the sheet was allowed to flow into the mould during forming. The different schemes were found to control whether a successful component could be produced under different conditions and at different ultimate strains. Finally, the tests with the hemispherical mould showed that thermoforming this shape requires significant interlaminar shear deformation, and above 15% strain this resulted in destruction of the interlayer bond. For strains greater than this, successful thermoforming could only be achieved by allowing the material to flow into the mould.     

中空成型和热成型过程的数值分析I.变形过程的数学描述

热成型和中空成型过程实质上是热塑料膜的膨胀过程 ,它们都涉及到材料的大变形。从弹性体有限变形理论出发 ,聚合物膨胀过程被看作是超弹性类似于完全橡胶的变形 ,材料模型采用Ogden和Mooney -Rivlin超弹性模型 ,应变描述采用Green变形张量 ,应力描述采用二阶Piola -Kirchoff应力张量。利用虚功原理得到描述塑料热成型和中空成型过程的数学模型     

Dynamic characteristics of plug‐assist thermoforming process

Plug‐assist thermoforming is a well‐known technique in polymer processing because of its interesting features. The dynamic value of driving‐force for the stretching process is determined based on equilibrium equation. This amount of force is required for applying to a plug to stretch a sheet. It is used for calculation of the required theoretical work and power of a plug‐assist thermoforming process. By using a nonlinear viscoelastic rheological model in the proposed mathematical model, its validity was examined by performing experimental tests on ABS sheets. POLYM. ENG. SCI., 2009. © 2008 Society of Plastics Engineers     

Effects of material properties and contact conditions in modelling of plug assisted thermoforming

Abstract

Thin walled food packaging is commonly manufactured using the plug assisted thermoforming process. In this paper the development of finite element models of the process is described. Work has concentrated on understanding the effects of material properties and contact conditions on the output from these simulations. The results have shown that a viscoelastic model must be used to simulate the deformation behaviour of the plastics. Contact conditions must also be accounted for in the models by including the effects of friction and heat transfer between the sheet and tool surfaces. For improved model accuracy, it is recommended that further experimental work should be carried out to enhance the viscoelastic material models and to provide better understanding of actual contact conditions.     

Wall thickness distribution in plug-assist vacuum formed strawberry containers

An experimental study on the influence of processing parameters namely film temperature, plug velocity, and temperature on wall thickness distribution in plug-assist vacuum thermoformed fresh strawberry container using high-impact polystyrene is presented. Film temperatures of 118, 125, 136, 150, and 165°C, plug velocities of 0.15, 0.20, and 0.27 m/s, and plug temperatures of 25, 60, 100, 123, and 135°C were used in the thermoforming. Increasing the plug velocity resulted in improved wall thickness distribution due to elastic deformation of the plastic sheet during thermoforming. Decreasing the stretching time and the temperature difference between the plastic film and plug was important for good wall thickness distribution. Better wall thickness was obtained at the plug velocity of 0.27 m/s and the plug temperature of 123°C.     

Thermoforming process of amorphous polymeric sheets: Modeling and finite element simulations

A temperature and strain rate dependent model for the thermoforming process of amorphous polymer materials is proposed. The polymeric sheet is heated at a temperature above the glass transition temperature then deformed to take the mold shape by the means of an applied pressure. The applied process temperature is taken uniform throughout the sheet and its variation is due only to the adiabatic heating. The behavior of the polymeric material is described by a micromechanically‐based elastic‐viscoplastic model. The simulations are conducted for the poly(methyl methacrylate) using the finite element method. The polymer sheet thickness and the orientation of the polymer molecular chains show an important dependence on the process temperature, the applied pressure profile, and the contact forces with the mold surface. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

ABS树脂真空吸塑成型

介绍了ＡＢＳ树脂的真空吸塑成型技术,详细阐述了真空吸塑工艺,并探讨了原料、设备、模具对工艺的影响及成成型工艺条件的控制。     

Experimental study on the dynamics of thermoforming of polystyrene

An experimental study of the dynamics of thermoforming a high-impact polystyrene sheet was undertaken to evaluate the effect of evacuation rate and temperature on the rate of sheet deformation and the wall thickness distribution of the molded part. The studies were conducted using an instrumented cylindrical mold having an adjustable bottom insert to vary the depth of draw. The evaculation rate was varied by introducing a flow restriction in the form of an orifice plate in the base of the mold. The deformation rate of the sheet was determined by means of fiber-optic infrared detectors located at various depths within the mold. Mold contact sensors also provided information with regard to the deformation process after contact with the mold surface had been achieved. The evaluation characteristics were monitored by a pressure transducer. A three-level, two-variable factorial design was conducted to provide information of the influence of the principal operating conditions and their interactions on the measured response variables. Reliable predictive expressions were derived for the minimum pressure, time to reach minimum pressure, overall forming time, and wall thickness near the lip of the mold. The wall thickness at other locations around the periphery of the mold contour was found to be relatively insensitive to the rate of evacuation and material temperature.     

A new hybrid approach using the explicit dynamic finite element method and thermodynamic law for the analysis of the thermoforming and blow molding processes for polymer materials

In this work, the problem of the modeling of thermoforming and blow molding processes for viscoelastic sheet are considered. To take account of the enclosed gas volume, responsible for inflation of the thermoplastic membrane (which contributes significantly to the strength and stiffness of a thermoplastic structure), we considered thermodynamic approach to express external work in terms of a closed volume. The pressure load is thus deduced from the thermodynamic law of ideal gases. The viscoelastic behavior of the K‐BKZ model is considered. The Lagrangian formulation together with the assumption of the membrane theory is used in the explicit dynamic finite element implementation. The numerical validation is performed by comparing the theoretical bubble free inflation with numerical results. Moreover, the influence of the K‐BKZ constitutive model on the thickness and stress distribution in the thermoforming of containers is presented. POLYM. ENG. SCI., 46:1554–1564, 2006. © 2006 Society of Plastics Engineers