The Thickness Thinning Criterion of Vacuum Forming Refrigerator Inner Liner for HIPS

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1 Advanced Materials Research Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland The Thickness Thinning Criterion of Vacuum Forming Refrigerator Inner Liner for HIPS Wenbin Su 1, a, Tao Li 1, b, Xiangbing Sun 1 and Baojian Liu 2 1 School of mechanical engineering, Xi an Jiaotong University, Xi an , P.R. China 2 College of Chemistry & Chemical Engineering, Shaanxi University of Science & Technology, Xi an , P.R. China a wbsu@mail.xjtu.edu.cn, b imlee24@gmail.com Keywords: Vacuum forming; Numerical simulation; Thickness thinning Abstract. In this paper, the regularity of thickness thinning was analyzed from the perspective of controlling the plastic deformation energy during the forming process, then a thickness thinning criterion based on vacuum forming was proposed, and then the forming mechanism of thickness thinning was revealed. Experiment results have shown that the proposed thickness thinning criterion can predict the quality of refrigerator inner liner under new forming condition effectively. Introduction Vacuum forming is a popular and diversified process for sheet-based consumer products widely used in cars, toys and drainage channels for their various advantages. However, some problems still exist in vacuum forming products, the principal is the lower strength due to local thickness reduction. Much research remains to be conducted to perfect the understanding of this design and manufacturing process. During vacuum forming, the principal concern during production is whether the product thickness can meet the technical requirements, in other words, the forming limit criterion. Pierpaolo Carlone et al. [1] simulated the vacuum forming of box-shaped pieces, showed the minimum value of thickness located at the upper part of the sheet, and also pointed out the simulated process leads to a non optimal part forming. N.Billon [2] researched the thermoforming of the thin plastic sheet and pointed out the thickness thinning might result in non-conformance products; C.P.J. O'Connor et al. [3] simulated samples of cups and selected the optimal material models through measured minimum thickness; B. Bekisli et al. [4] regarded the controlling of the non-uniform thickness distribution on the final part as the optimized goal for improving thermoforming process. Based on the author s knowledge, most of the research work predicted the quality of vacuum forming product based on the minimum thickness of product at present. In this paper, the forming mechanism of thickness thinning was revealed based on the principle of the total plastic work, and then the vacuuming forming limit criterion was established to predict the quality of products from designing mold to setting forming conditions. The proposed thickness thinning criterion helps to shorten the production development cycle, and decrease the develop cost in practice. Vacuum Forming Vacuum forming is a simplified version of thermoforming. During the vacuum forming progress, a plastic sheet is clamped onto a single-surface mold and heated to the forming temperature, and then it was stretched with the mold rose, and held against the mold by applying vacuum between the mold surface and the sheet, cooled by compressed air, trimmed the web away. Two different points can be draw from vacuum forming and sheet metal forming: the one is the forming temperature, the other is forming process. The difference of forming temperature is especially significant, as the sheet metal forming limit criterion based on plastic work is established All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-12/05/16,08:42:21)

2 620 Emerging Focus on Advanced Materials under room temperature, while plastic sheet vacuum forming under high temperature, usually And the creative place of this paper is to explain the forming mechanism of thickness thinning, and then the establishment of the vacuuming forming limit criterion. To establish the vacuuming forming limit criterion, the value of total plastic work is essential. In this study, the value of plastic work was obtained by simulation. An example of vacuum formed refrigerator liner simulation method has been introduced used the software T-SIM, then the thickness distribution, equivalent stress and equivalent strain can be obtained. Finite Element Simulation Geometry. At the beginning of the process, an initial flat sheet of material was defined with a 3.6mm constant initial thickness and 760 by 660 millimeters square in the plane direction; the mold was 553 by 475 millimeters square in the plane direction, with the height 447mm. Constitutive Model. T-SIM uses the K-BKZ type single integral nonlinear viscoelastic constitutive model in which stress is a function of strain and rate of strain. A better material data fitting is achieved by three different damping functions, proposed by Bernstein et al. and Kaye. The time-integral constitutive equation of the K-BKZ model was given by: t = 1 ' ' s( t) h( I1, I 2) C ( t, t ) µ ( t t ). (1) Where s( t) is a stress tensor, t is the previous time, t is the current time, C 1 ( t, t ) is the Finger strain tensor and µ ( t t ) h( I and 1, I2) are a material memory function and a damping function of two strain invariants, respectively. Furthermore, the damping function µ G( t t ) t N i ( t t )/ τi ( t t ) = = e G( t t ) i= 1 a τ i. (2) ai τ and i Where is relaxation modulus, i is mode number and are relaxation modulus and relaxation time. And the key work of establish constitutive model is to obtain the data of relaxation time spectrum. Material. The material used in this study was HIPS D6007 sheet, which was provided by XinFei electric Co., Ltd, the thickness of this sheet was 3.6mm. In order to establish a material model which could describe the polymers deformation behavior precisely, the authors obtained the relaxation time spectrum by the DMA-Q800, produced by TA Corporation, according to ISO [5].The data was shown in Table 1. Table 1 Relaxation time spectrum of HIPS Mode number i Relaxation time τ [s] Relaxation modulus α [Pa] Forming Conditions. The suitable forming temperature for HIPS sheet is always set as 130 ~180, in this study 140 was adopted according to the production practice. Mold temperature and ambient temperature were taken as 80 and 50 respectively, heat transfer

3 Advanced Materials Research Vols h coefficient between sheet and the mold m was 800 W / (m K), coefficient of friction between HIPS and aluminum was And the pressure of around 60kPa and -100kPa was applied on the sheet for blowing phase and the final vacuuming phase respectively. Thickness Thinning Criterion establishment Total Plastic Work. In plastic sheet forming operation, large plastic deformation is commonly observed, from the beginning of deformation process to the sheet thickness thinned to the minimum allowed, and this process can be understood as the result of accumulation of plastic deformation energy. In the field of bulk forming, criterion based on the total plastic work is widely used in the prediction of ductile fracture, and then the method has been introduced to the field of sheet forming. The total plastic work equation is given by: W ε σ ε = d 0 (3) Where σ and ε are the equivalent (Mises) stress and strain, respectively. Since the total plastic work is used in the form of integral function, so the non-linear paths of equivalent stress and equivalent strain can be considered. Criterion based on the total plastic work can be used to predict plastic sheet forming limit, when the integration of equivalent stress strain reaches a critical constant C, the plastic sheet namely achieved the forming limit. Then the Eq. 4 can be expressed as: ε f σdε = C 0 (4) f Where ε is the equivalent (Mises) strain of product thickness thinning, C is a constant. Calculation of Total Plastic Work Constants. In practice, that C is a constant, and the veracity of its value has a direct impact on the accuracy of prediction. The following research was focus on the value of total plastic work about the top corner where was prone to thinning. According to the requirement of process, the allowed minimum thickness 0.40mm was thought as the lower limit. Fig.1 and Fig.2 showed the curve of the equivalent stress and equivalent strain paths during the thickness of the top corner reduced from 3.6mm to 0.4mm, respectively. Then, the integration of equivalent stress- equivalent strain is the desired total plastic work (x-axis is the equivalent stress, y-axis is the equivalent strain), shown in Fig.3. The value of total plastic work is: W = MJ/m 3. In the same way, the values of the total plastic work at different thickness can be got, displayed in Fig.4. Fig.4 showed that with the thickness of the refrigerator liner product decreasing the total plastic work increased. According to the definition of the total plastic work, the easier to forming, the less energy is needed, and vice versa. When the thickness reduced from 3.6mm to 0.4mm, the total plastic work W will be up to MJ/ m 3.Therefore, the critical total plastic work C was equal to MJ/m 3. Fig. 1 Equivalent stress paths curve Fig. 2 Equivalent strain paths curve

4 622 Emerging Focus on Advanced Materials Fig. 3 The total plastic work Fig. 4 The total plastic work of different thickness The Total Plastic Work under Different Forming Conditions. In front part of this paper, the total plastic work was got with the sheet thickness of 3.6mm and the forming temperature of 140. To study the critical total plastic work under different sheet thickness and forming temperature, a series of experiments were designed, shown in Table 2. Table 2 The total plastic work for different sheet thickness and forming temperature[mj/m 3 ] Sheet foming Sheet thickness [mm] temperature [ ] In order to intuitively analyze the experimental results, firstly the data in Table 2 was converted to matrix by using the Origin 7.5, and then the 3D surface and lines with labels contour for total plastic work ware got through the graphics function of the software, shown in Fig.5, Fig.6 respectively. Fig. 5 3D surface for total plastic work Fig. 6 Lines with labels contour for total plastic work

5 Advanced Materials Research Vols From Fig.6 can obtained that under the same forming temperature, with the thickness of sheet increased from 3.2mm to 4.0mm, the forming was becoming more difficult, and the total plastic work was increasing; what s more, under the same thickness of sheet, with the forming temperature increased from 130 to 150, the forming was becoming easier, and the total plastic work is decreasing. Therefore, the thickness thinning criterion based on total plastic work can be got easily under a new forming condition. Experimental Verifications In order to verify the accuracy of total plastic work criterion proposed, experiments were carried out in Xinfei electric Co., Ltd. In order to convenience for analysis, firstly four groups of sheet thickness and forming temperature, denoted by points (3.4,135), (3.4,145),(3.8,145),(3.8,135), were chosen as the object of validation. After the numerical simulation, the total plastic work criterion of selected forming conditions was 0.84, 1.96, 1.08 and 3.25 MJ/m 3, respectively, seen in Fig. 6. In these experiments, when the total plastic work reached the given values corresponding to the forming conditions, the minimum thickness of the refrigerator liner were 0.398mm, 0.406mm, 0.401mm and 0.403mm respectively. The results were around 0.4mm, just as the allowed minimum thickness. Therefore, the accuracy of the proposed thickness thinning criterion can satisfy the needs of production practice. Conclusions (1).The author proposed the thickness thinning criterion based on vacuum forming to predict the quality of refrigerator liner, and revealed the forming mechanism of thickness thinning. (2).Through analyzing the obtained lines with labels contour for total plastic work, the thickness thinning criterion was obtained under different sheet thickness and different forming temperature. (3). Experiment results have shown that the proposed thickness thinning criterion can predict the quality of vacuum formed refrigerator liner effectively. Acknowledgements The authors would like to express their sincere thanks to XinFei electric Co., Ltd. for providing the experimental conditions. References [1] Pierpaolo Carlone, Gaetano Salvatore Palazzo, in: Finite Element Analysis of The Theroforming Manufacturing Process Using The Hyperelastic Mooney-Rivlin Model: volume 3980 of Computational Science and its applications (2006), p [2] N.Billon, in: Constitutive model for HIPS in the Theroforming Range: volume 1 of Computational Science and its Applications (2008), p [3] C.P.J. O'Connor, G. Menary and P.J.Martin, in: Finite element analysis of the thermoforming of poplypropylene: volume 1 of International Journal of Material Forming (2008), p [4] B. Bekisli and HF. Nied, in: Thermoforming of Knitted Composite Structures: FEM Simulation and Experiments: volume 3 of International Journal of Material Forming (2010), p [5] ISO6721-6, in: Methods of Testing Plastics-Part 3: Mechanical properties-method 323C: Shear vibration-non-resonance method: British Standard (1996).

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