- Email: [email protected]
Stress monitoring of PET beverage bottles by Digital Photoelasticity
Manufacturing Letters 15 (2018) 9–13
Contents lists available at ScienceDirect
Manufacturing Letters journal homepage: www.elsevier.com/locate/mfglet
Letters
Stress monitoring of PET beverage bottles by Digital Photoelasticity R.G.R. Prasath a,⇑, Thomas Newton b, Steven Danyluk a,b a b
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA Polaritek Systems Inc, 1640 Powers Ferry Road, Building 27, Suite 301, Marietta, GA 30067, USA
a r t i c l e
i n f o
Article history: Received 11 December 2017 Accepted 16 December 2017 Available online 18 December 2017 Keywords: Inspection Monitoring Residual stresses Biaxial and uniaxial stretching
a b s t r a c t Polyethylene Terephthalate (PET) is used in many packaging applications. PET is especially important in the carbonated soft drink industry, where the pressure of carbonation and the imposed and residual stresses in the bottle bases can sometimes lead to cracking, and failures. In the process of bottle blowing, residual stresses are created and remain in the bottle base as a result of the uniaxial and biaxial stretching in these regions. It is advantageous to measure these residual stresses and the mode of stretching, which may be related to the failure characteristics of the bottle bases. Photoelasticity can be used to examine these residual stresses in the sidewalls and bases of bottles. This work reports on a residual stress measurement tool for the bottle blowing industry. Ó 2017 Society of Manufacturing Engineers (SME). Published by Elsevier Ltd. All rights reserved.
1. Introduction For the past several years, Polyethylene Terephthalate (PET) has been widely used for packaging of carbonated beverages, drinking water and other liquids. PET’s demand for packaging in the beverage and bottled water industries is increasing due to its strength, light weight and recyclability. PET bottles are made by traditionally known injection blow molding processes [1]. In this process, a preform is heated then inserted into the blow mold chamber as it is simultaneously blown using high pressure air. The bottle is blown until stretched to the walls of the cold mold [2,3]. Once the material freezes it retains its shape and the finished bottle is removed from the mold. In the blowing operation PET undergoes molecular reorientation which causes the formation of residual stress in the material [4]. In addition to this, residual stresses are also modified by creep, shrinking and aging. Stresses retained due to the blow molding process influences the stress crack resistance once the bottle is filled with carbonated beverages at 60 psi. This residual stress plays a major role in affecting the performance of the filled beverage bottles along with other factors like the presence of micro voids, cracks and crystallinity. It would be very helpful to predict the stress crack resistance based on measurement of the residual stress at blown bottle bases and preform bases. So far attempts have been made to develop Finite element models to predict the bottle stresses. Translucent PET has birefringence property that allows for a measure of the residual stress by photoelasticity. This
⇑ Corresponding author. E-mail address: [email protected] (R.G.R. Prasath).
paper reports on how birefringence can be used when light transmits through the thickness of PET. Photoelasticity refers to the transmission of polarized white light and its influence by birefringence. Polarized light passing through a birefringent material will display retardation between the ordinary and extra-ordinary light rays. Fast and slow rays will be aligned to the stress. This technique is non-contact and provides the information of principal stress difference (isochromatics) and principal stress direction (isoclinics) in the form of fringe contours [5]. With the availability of high resolution digital cameras, recording of images is straight-forward and is called digital transmission photoelasticity where the information of isochromatics (N) and isoclinics (h) at every pixel over the model domain is obtained [6]. Phase shifting and polarization stepping techniques [7] have also been developed to measure the isochromatic and isoclinic parameters from the experimentally recorded digital images. Further, the developments in the intensity-based phase shifting/ polarization stepping techniques allows for low retardation measurements applicable for residual stress measurements when external loading of the specimen is not present. In this paper the ten-step method has been used for recording the images. Ramji and Prasath [8] have done an error analysis to find the effectiveness of the ten-step methodology over photoelastic parameter estimation and they recommended the ten-step method for accurate photoelastic parameter estimation. This paper outlines one example of the 10-step photoelastic retardation to measure residual stresses in unpressurized bottle bases. The systematic statistical analysis of stress data gives us the confidence in understanding the stress crack resistance and bottle failures.
https://doi.org/10.1016/j.mfglet.2017.12.010 2213-8463/Ó 2017 Society of Manufacturing Engineers (SME). Published by Elsevier Ltd. All rights reserved.
10
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
2. Methodology Fig. 1 shows the schematic representation of a circular polariscope arrangement used for retardation measurement. A bottle is shown horizontal with the light being transmitted through the neck. A white light source has been used and the polarizer, ana-
lyzer and quarter-wave plates are matched with the wavelength. A JAI colour 3CCD camera is used for recording images. Maxwell’s stress optic law can then be used to find the absolute magnitude of the differences in normal principal stresses by measuring the Fringe number. The stress optic law for the plane stress is given by the equation
Fig. 1. Schematic of experimental setup.
Fig. 2. Half liter Bottle Base (a) Dark-field image (b) Distribution of Biaxial Center distance (mm) and stress (MPa) (c) Maximum Shear Stress (MPa) Plot (d) Three-dimensional maximum shear stress plot.
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
NF r k ; Fr ¼ C t
ð1Þ
d C ¼ h ðr1 r2 Þ 2p k
ð2Þ
r1 r2 ¼ and
N¼
The Maximum Shear Stress, smax ¼ NF2tr is written with the Tresca criterion equivalentwhere d – Relative retardation k – Wavelength of light Fr – Material Stress Fringe value N/mm/fringe C – Relative stress-optic coefficient t – Thickness of the sample The ten-step phase shifting technique [8] has been used for the photoelastic parameter estimation [9] and maximum shear stress calculation. A software program controls the motions and positions of the optical elements and the CCD camera, and the stress calculations are plotted as stress maps. 3. Residual stress measurements in bottle bases There are three types of bottle bases analyzed to show the variation in stresses captured experimentally. These bottles were randomly picked from a commercial supermarket. These stresses vary with shape of the blowing mold, temperature, pre-blow pressure, blow pressure and cooling. Even though the process conditions are not known for the bottles use in this study, the differences in
11
the fringe and stress maps verify that the bottles can be sorted by the measurement. Fig. 2 shows the results of 500 ml PET bottle base. The dark field is shown in Fig. 2a is correlated to the stress maps in Fig. 2c and d. An inspection of Fig. 2a around the Gate center shows that the PET is radially stretched and the circular fringes reveal hoop stress. Beyond this region, the material is stretched biaxially and indicated by ‘X’- shaped fringe feature. White dots marked in Fig. 2a show the location of the biaxial points near to the Gate. In addition, yellow dots show the secondary biaxial locations. Fig. 2b shows a bar chart of the secondary biaxial point distances (radial distance measured from the center of the Gate) and the stress at these locations is helpful in the understanding how the material is stretched during the blow molding. From the stress plots 2c and 2d it is seen that the stresses are a maximum around the gate and also at the locations of the feet. Fig. 2d shows the three dimensional plot of stress gradients of the bottle base. The biaxial center distance at the locations marked with yellow dots varies in this case from location 1 to 5 as 12.09, 11.36, 11.54, 11.39 and 12.20 mm. The measured maximum shear stress at locations 1–5 are 29.9, 28.3, 29.0, 28.7 and 30 MPa. During the blowing operation, it was assumed as these biaxial centers are at equal distance from the Gate and its stress values are same. But due to variations in the process conditions and influence of other factors these values are different. This is the important parameter to measure in terms of symmetry to predict the bottle failure when it is filled with carbonated drinks. A Second example represents the one-liter bottle base picked from Publix Supermarket in Atlanta. Fig. 3a shows the dark field image. By comparing Figs. 3a and 2a the interferometric patterns
Fig. 3. One-liter Bottle Base A (a) Dark-field image (b) Distribution of Biaxial Center distance (mm) and stress (MPa) (c) Maximum Shear Stress (MPa) Plot (d) Three dimensional maximum shear stress plot.
12
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
(a)
(b)
(b)
(a)
Fig. 4. One-liter Bottle Base B (a) Dark-field image (b) Distribution of Biaxial Center distance (mm) and stress (c) Maximum Shear Stress (MPa) Plot (d) Three-dimensional maximum shear stress plot.
Table 1 Summary of bottle base stresses measured experimentally. Bottle base
Avg Stress around GATE in MPa
No of biaxial Points
Avg Stress at Biaxial points in MPa
Avg Distance of Biaxial Points in mm
500 ml 1.0 L: A 1.0 L: B
25.16 17.3 14.256
10 5 5
29.22 11.4 16.12
11.72 6.6 9.4
are completely different. Fig. 3b shows a bar chart of the secondary biaxial point distances and the stress at these locations. This further confirms stress distribution are also different. In this bottle base we observe biaxial centers around the gate area but not near to the transition zone. We see the higher stress value in the transition area in the radial direction for this base and it is clearly visible from the three-dimensional plot shown in Fig. 3d. Stress asymmetry is clearly seen in this bottle base. Fig. 4 shows another one-liter bottle base from Publix supermarket in Atlanta. In this case we see a different interferometric pattern as compared to Fig. 3. Both are one-liter bottles but the stresses in the respective bottle bases vary. Both the bottle bases are petaloid in shape but in the case of Bottle Base B, higher stresses are observed at the feet of the bottle. The distance of the biaxial center locations from the gate center also varies. The stress maps provide an understanding of the distribution of stresses in the bottle base and its symmetry in all the directions from the gate center.
Symmetry is expected if the bottle is blown with uniform processing parameters. Table 1 summarizes the data of the three bottle bases.
4. Conclusions Maximum shear stress can be experimentally measured and the quantitative and qualitative data provide useful information on the process conditions of the bottles. Photoelastic measurements provide a picture of how stresses are distributed on the bases and can provide a guidance on how stresses are related to stress cracking and the process parameters. Comparing two one liter bottles, the average stresses at biaxial stretching location varied from 16 to 11 MPa, distances varied from 9.4 to 6.6 mm. Symmetry of the bottle base may also be important. This tool can be useful in comparing the stresses from mold to mold as a stress monitoring tool, and
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
within the mold bottle to bottle to keep the blowing process under control. One can easily find the differences in stress, location of biaxial centers when the blow molding process parameters are varied. This system can easily be installed as an inline inspection tool to check the quality for each bottle immediately after blowing from the injection blow molding process. This measurement adds value to the Finite element simulations of bottles, where one can compare the simulated stress distributions and improve their model. References [1] Marcus P. Injection blow molding method.US Patent 3,776,991; 1973. [2] Gittner F, Glaser A, Kotke KD. US Patent 4,177,239; 1979. [3] Schmidt FM, Agassant JF, Bellet M. Experimental study and numerical simulation of the injection stretch/blow molding process. Polym Eng Sci 1998;38(9):1399–412.
13
[4] Pham XT, Thibault F, Lim LT. Modeling and simulation of stretch blow molding of polyethylene terephthalate. Polym Eng Sci 2004;44(8):1460–72. [5] Ramesh K. Digital photoelasticity advanced techniques and application. Springer; 2000. [6] Prasath RGR, Skenes K, Danyluk S. Comparison of phase shifting techniques for measuring in-plane residual stress in thin, flat silicon wafers. J Electron Mater 2013:1–8. [7] Skenes K, Prasath RGR, Danyluk S. Residual stress, thermomechanics & infrared imaging, hybrid techniques and inverse problems, vol. 8, conference proceedings of the society for experimental mechanics series, 2014. p. 79–85. [8] Ramji M, Prasath RGR. Sensitivity of isoclinic data using various phase shifting techniques in digital photoelasticity towards generalized error sources. Opt Lasers Eng. [9] Ramji M, Ramesh K. Adaptive Quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models. Strain 2010;46(2):184–94.
Contents lists available at ScienceDirect
Manufacturing Letters journal homepage: www.elsevier.com/locate/mfglet
Letters
Stress monitoring of PET beverage bottles by Digital Photoelasticity R.G.R. Prasath a,⇑, Thomas Newton b, Steven Danyluk a,b a b
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA Polaritek Systems Inc, 1640 Powers Ferry Road, Building 27, Suite 301, Marietta, GA 30067, USA
a r t i c l e
i n f o
Article history: Received 11 December 2017 Accepted 16 December 2017 Available online 18 December 2017 Keywords: Inspection Monitoring Residual stresses Biaxial and uniaxial stretching
a b s t r a c t Polyethylene Terephthalate (PET) is used in many packaging applications. PET is especially important in the carbonated soft drink industry, where the pressure of carbonation and the imposed and residual stresses in the bottle bases can sometimes lead to cracking, and failures. In the process of bottle blowing, residual stresses are created and remain in the bottle base as a result of the uniaxial and biaxial stretching in these regions. It is advantageous to measure these residual stresses and the mode of stretching, which may be related to the failure characteristics of the bottle bases. Photoelasticity can be used to examine these residual stresses in the sidewalls and bases of bottles. This work reports on a residual stress measurement tool for the bottle blowing industry. Ó 2017 Society of Manufacturing Engineers (SME). Published by Elsevier Ltd. All rights reserved.
1. Introduction For the past several years, Polyethylene Terephthalate (PET) has been widely used for packaging of carbonated beverages, drinking water and other liquids. PET’s demand for packaging in the beverage and bottled water industries is increasing due to its strength, light weight and recyclability. PET bottles are made by traditionally known injection blow molding processes [1]. In this process, a preform is heated then inserted into the blow mold chamber as it is simultaneously blown using high pressure air. The bottle is blown until stretched to the walls of the cold mold [2,3]. Once the material freezes it retains its shape and the finished bottle is removed from the mold. In the blowing operation PET undergoes molecular reorientation which causes the formation of residual stress in the material [4]. In addition to this, residual stresses are also modified by creep, shrinking and aging. Stresses retained due to the blow molding process influences the stress crack resistance once the bottle is filled with carbonated beverages at 60 psi. This residual stress plays a major role in affecting the performance of the filled beverage bottles along with other factors like the presence of micro voids, cracks and crystallinity. It would be very helpful to predict the stress crack resistance based on measurement of the residual stress at blown bottle bases and preform bases. So far attempts have been made to develop Finite element models to predict the bottle stresses. Translucent PET has birefringence property that allows for a measure of the residual stress by photoelasticity. This
⇑ Corresponding author. E-mail address: [email protected] (R.G.R. Prasath).
paper reports on how birefringence can be used when light transmits through the thickness of PET. Photoelasticity refers to the transmission of polarized white light and its influence by birefringence. Polarized light passing through a birefringent material will display retardation between the ordinary and extra-ordinary light rays. Fast and slow rays will be aligned to the stress. This technique is non-contact and provides the information of principal stress difference (isochromatics) and principal stress direction (isoclinics) in the form of fringe contours [5]. With the availability of high resolution digital cameras, recording of images is straight-forward and is called digital transmission photoelasticity where the information of isochromatics (N) and isoclinics (h) at every pixel over the model domain is obtained [6]. Phase shifting and polarization stepping techniques [7] have also been developed to measure the isochromatic and isoclinic parameters from the experimentally recorded digital images. Further, the developments in the intensity-based phase shifting/ polarization stepping techniques allows for low retardation measurements applicable for residual stress measurements when external loading of the specimen is not present. In this paper the ten-step method has been used for recording the images. Ramji and Prasath [8] have done an error analysis to find the effectiveness of the ten-step methodology over photoelastic parameter estimation and they recommended the ten-step method for accurate photoelastic parameter estimation. This paper outlines one example of the 10-step photoelastic retardation to measure residual stresses in unpressurized bottle bases. The systematic statistical analysis of stress data gives us the confidence in understanding the stress crack resistance and bottle failures.
https://doi.org/10.1016/j.mfglet.2017.12.010 2213-8463/Ó 2017 Society of Manufacturing Engineers (SME). Published by Elsevier Ltd. All rights reserved.
10
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
2. Methodology Fig. 1 shows the schematic representation of a circular polariscope arrangement used for retardation measurement. A bottle is shown horizontal with the light being transmitted through the neck. A white light source has been used and the polarizer, ana-
lyzer and quarter-wave plates are matched with the wavelength. A JAI colour 3CCD camera is used for recording images. Maxwell’s stress optic law can then be used to find the absolute magnitude of the differences in normal principal stresses by measuring the Fringe number. The stress optic law for the plane stress is given by the equation
Fig. 1. Schematic of experimental setup.
Fig. 2. Half liter Bottle Base (a) Dark-field image (b) Distribution of Biaxial Center distance (mm) and stress (MPa) (c) Maximum Shear Stress (MPa) Plot (d) Three-dimensional maximum shear stress plot.
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
NF r k ; Fr ¼ C t
ð1Þ
d C ¼ h ðr1 r2 Þ 2p k
ð2Þ
r1 r2 ¼ and
N¼
The Maximum Shear Stress, smax ¼ NF2tr is written with the Tresca criterion equivalentwhere d – Relative retardation k – Wavelength of light Fr – Material Stress Fringe value N/mm/fringe C – Relative stress-optic coefficient t – Thickness of the sample The ten-step phase shifting technique [8] has been used for the photoelastic parameter estimation [9] and maximum shear stress calculation. A software program controls the motions and positions of the optical elements and the CCD camera, and the stress calculations are plotted as stress maps. 3. Residual stress measurements in bottle bases There are three types of bottle bases analyzed to show the variation in stresses captured experimentally. These bottles were randomly picked from a commercial supermarket. These stresses vary with shape of the blowing mold, temperature, pre-blow pressure, blow pressure and cooling. Even though the process conditions are not known for the bottles use in this study, the differences in
11
the fringe and stress maps verify that the bottles can be sorted by the measurement. Fig. 2 shows the results of 500 ml PET bottle base. The dark field is shown in Fig. 2a is correlated to the stress maps in Fig. 2c and d. An inspection of Fig. 2a around the Gate center shows that the PET is radially stretched and the circular fringes reveal hoop stress. Beyond this region, the material is stretched biaxially and indicated by ‘X’- shaped fringe feature. White dots marked in Fig. 2a show the location of the biaxial points near to the Gate. In addition, yellow dots show the secondary biaxial locations. Fig. 2b shows a bar chart of the secondary biaxial point distances (radial distance measured from the center of the Gate) and the stress at these locations is helpful in the understanding how the material is stretched during the blow molding. From the stress plots 2c and 2d it is seen that the stresses are a maximum around the gate and also at the locations of the feet. Fig. 2d shows the three dimensional plot of stress gradients of the bottle base. The biaxial center distance at the locations marked with yellow dots varies in this case from location 1 to 5 as 12.09, 11.36, 11.54, 11.39 and 12.20 mm. The measured maximum shear stress at locations 1–5 are 29.9, 28.3, 29.0, 28.7 and 30 MPa. During the blowing operation, it was assumed as these biaxial centers are at equal distance from the Gate and its stress values are same. But due to variations in the process conditions and influence of other factors these values are different. This is the important parameter to measure in terms of symmetry to predict the bottle failure when it is filled with carbonated drinks. A Second example represents the one-liter bottle base picked from Publix Supermarket in Atlanta. Fig. 3a shows the dark field image. By comparing Figs. 3a and 2a the interferometric patterns
Fig. 3. One-liter Bottle Base A (a) Dark-field image (b) Distribution of Biaxial Center distance (mm) and stress (MPa) (c) Maximum Shear Stress (MPa) Plot (d) Three dimensional maximum shear stress plot.
12
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
(a)
(b)
(b)
(a)
Fig. 4. One-liter Bottle Base B (a) Dark-field image (b) Distribution of Biaxial Center distance (mm) and stress (c) Maximum Shear Stress (MPa) Plot (d) Three-dimensional maximum shear stress plot.
Table 1 Summary of bottle base stresses measured experimentally. Bottle base
Avg Stress around GATE in MPa
No of biaxial Points
Avg Stress at Biaxial points in MPa
Avg Distance of Biaxial Points in mm
500 ml 1.0 L: A 1.0 L: B
25.16 17.3 14.256
10 5 5
29.22 11.4 16.12
11.72 6.6 9.4
are completely different. Fig. 3b shows a bar chart of the secondary biaxial point distances and the stress at these locations. This further confirms stress distribution are also different. In this bottle base we observe biaxial centers around the gate area but not near to the transition zone. We see the higher stress value in the transition area in the radial direction for this base and it is clearly visible from the three-dimensional plot shown in Fig. 3d. Stress asymmetry is clearly seen in this bottle base. Fig. 4 shows another one-liter bottle base from Publix supermarket in Atlanta. In this case we see a different interferometric pattern as compared to Fig. 3. Both are one-liter bottles but the stresses in the respective bottle bases vary. Both the bottle bases are petaloid in shape but in the case of Bottle Base B, higher stresses are observed at the feet of the bottle. The distance of the biaxial center locations from the gate center also varies. The stress maps provide an understanding of the distribution of stresses in the bottle base and its symmetry in all the directions from the gate center.
Symmetry is expected if the bottle is blown with uniform processing parameters. Table 1 summarizes the data of the three bottle bases.
4. Conclusions Maximum shear stress can be experimentally measured and the quantitative and qualitative data provide useful information on the process conditions of the bottles. Photoelastic measurements provide a picture of how stresses are distributed on the bases and can provide a guidance on how stresses are related to stress cracking and the process parameters. Comparing two one liter bottles, the average stresses at biaxial stretching location varied from 16 to 11 MPa, distances varied from 9.4 to 6.6 mm. Symmetry of the bottle base may also be important. This tool can be useful in comparing the stresses from mold to mold as a stress monitoring tool, and
R.G.R. Prasath et al. / Manufacturing Letters 15 (2018) 9–13
within the mold bottle to bottle to keep the blowing process under control. One can easily find the differences in stress, location of biaxial centers when the blow molding process parameters are varied. This system can easily be installed as an inline inspection tool to check the quality for each bottle immediately after blowing from the injection blow molding process. This measurement adds value to the Finite element simulations of bottles, where one can compare the simulated stress distributions and improve their model. References [1] Marcus P. Injection blow molding method.US Patent 3,776,991; 1973. [2] Gittner F, Glaser A, Kotke KD. US Patent 4,177,239; 1979. [3] Schmidt FM, Agassant JF, Bellet M. Experimental study and numerical simulation of the injection stretch/blow molding process. Polym Eng Sci 1998;38(9):1399–412.
13
[4] Pham XT, Thibault F, Lim LT. Modeling and simulation of stretch blow molding of polyethylene terephthalate. Polym Eng Sci 2004;44(8):1460–72. [5] Ramesh K. Digital photoelasticity advanced techniques and application. Springer; 2000. [6] Prasath RGR, Skenes K, Danyluk S. Comparison of phase shifting techniques for measuring in-plane residual stress in thin, flat silicon wafers. J Electron Mater 2013:1–8. [7] Skenes K, Prasath RGR, Danyluk S. Residual stress, thermomechanics & infrared imaging, hybrid techniques and inverse problems, vol. 8, conference proceedings of the society for experimental mechanics series, 2014. p. 79–85. [8] Ramji M, Prasath RGR. Sensitivity of isoclinic data using various phase shifting techniques in digital photoelasticity towards generalized error sources. Opt Lasers Eng. [9] Ramji M, Ramesh K. Adaptive Quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models. Strain 2010;46(2):184–94.