Reducing the Sink Marks of a Crystalline Polymer using External Gas-Assisted Injection Molding

External gas-assisted injection molding (EGAIM) has been used to reduce the sink marks of amorphous polymer products, but that of crystalline polymer products has not yet been reported. EGAIM of a crystalline polymer product was investigated in this study, and the influences of process parameters on the sink marks were discussed based on experiments. An isotactic polypropylene (iPP) product was fabricated by EGAIM under different process conditions. A uniform design was applied as an experimental design to investigate the influences of the process parameters on the sink marks. A regression equation was established to describe the quantitative relationship between the important parameters and sink marks in which a data-processing method was applied to determine the optimal value of at significant level to reduce the possibility of omission of some important parameters. e results show that EGAIM was effective in reducing the sink marks in these iPP products, and the most important parameters were the cooling time, gas pressure, and gas time. is study also provides the quantitative relationship between the important parameters and sink marks as reference for the research of EGAIM on crystalline polymer.

EGAIM is more complicated than the conventional injection molding (CIM) because of the introduction of gas. Gas with certain pressure is injected between the cavity surface of the mold and the solidified polymer formed during filling, a er the cavity was filled by polymer. e gas pressure is maintained until the cooling process is terminated. e pressure on the solidified polymer pushes it to move and deform, which compensate the polymer shrinkage caused by temperature decrease during packing and cooling and reduce the sink marks. e advantages and complexity of EGAIM have attracted the attention of researchers. Chen et al. [19] investigated the packing effects of EGAIM on the shrinkage and sink marks of plastic parts (ABS) under various rib designs and compared them with those of CIM. e results showed that EGAIM could further reduce the part shrinkage when the gas pressure and gas-packing time were both increased. Su et al. [20] also reduced the ghost marks in plastic parts of PA using EGAIM. Moreover, the quality of the parts was improved by increasing the mold temperature, melt temperature, injection speed, and pressure, although some limitations were experienced. Jiang et al. [21] discussed the relationship between the process parameters and part quality of ABS using the single-factor test method and developed a physical model that described the influence of gas-melting interaction on the sink marks [22]. e aforementioned studies focused on amorphous polymer products and did not explore the application of EGAIM to crystalline polymer products. Crystalline polymers are an important component in industrial production [23], aerospace [24], and pharmaceutical production [25]. In addition, the shrinkage of crystalline polymers is usually more obvious than that of amorphous polymers [26], and the sink marks of crystalline polymer products are usually larger than those of amorphous polymer products. erefore, investigating the application of EGAIM to crystalline polymer products is important. In the present study, an iPP product was manufactured using EGAIM, and the influences of the process parameters on the sink marks of the iPP products were discussed. A regression equation was established to investigate the quantitative influence based on the experimental results in which a data-processing method was applied to determine the optimal value of at significant level to reduce the possibility of omission of some important parameters. To verify the reduction of the sink marks of these iPP products by EGAIM, experiments with or without gas were carried out under an optimal condition, as calculated by the regression equation.

Experiments
A semi-crystalline iPP (T30S, Zhenhai Branch of Sinopec Corp., China) product was used in this study, and its parameters were as follows: melt flow index of 2.5 g/10 min, melting point of 167°C, density of 0.91 g/cm 3 , and isotactic index of more than 94%. An injection molding machine (MA3800/2250, Haitian International Holdings Ltd., China) was used to manufacture the products with dimensions of 150 mm × 100 mm × 3 mm. A er filling at a later time (delay time), an inert gas ( 2 ) with certain pressure was injected between the solidified polymer and cavity surface of the moving mold using a nitrogen pressure controller (C8-01, Beijing Chn-Top Machinery Group Co., Ltd., China). e sink marks of the crystalline polymer products were measured by a dial indicator (A0-12.7, Shanghai Siwei Instrument Manufacturing Co., Ltd., China), which has a measurement range of 12.7 mm and accuracy of 0.001 mm. e locations of gate, gas injections and measuring point are shown in Figure 1.
To study the efficiency of EGAIM on the reduction of sink marks in the crystalline polymer products, almost all of the process parameters were considered, including the material temperature, injection pressure, injection speed, packing pressure, packing time, cooling time, gas pressure, gas time, and delay time. e uniform design focuses on the uniform distribution of test points within the test range to obtain the largest available information with the least number of tests.

Data-Processing Method
Regression analysis is a set of statistical processes that estimates the relationship between the parameters and results. More specifically, regression analysis helps us understand how the typical values of parameters change when any one of the results is varied [28]. One of the most important steps in regression analysis is the determination of optimal value at significant level , which directly determines whether parameters are introduced into the regression equation. In general, significant level 훼 = 0.05 is commonly used in statistics [29]. However, some important parameters are sometimes omitted in injection molding. us, a data-processing method was applied in this study to establish the optimal value of at significant level , which would reduce the possibility of omission of some important parameters. e data in the uniform table need to be dealt with by this processing method. A uniform table was designed using a uniform design to reduce the number of experiments. e uniform table consists of ( = 1, 2, …, ) experiments, ( = 1, 2, …, ) parameters, and (recorded as , where 푗 = 푃 + 1 ) results. e value of parameter in the th experiment is , and result is recorded as 푗(푃+1) , as listed in Table 2.
Correlation coefficient accurately describes the reliability between the parameters and results. e value of is positively correlated with the reliability between the parameters and results, as expressed in Equation. (1) [30] where and are the sum of the products of the mean deviation and sum of squares of the deviation from the mean, respectively. is the average value of ( = 1, 2,…, P+1, = 1, (2) [31].
Generally, should be calculated for every parameter in the regression analysis and is compared with pre-determined at significant level to determine whether the parameter is retained or not. In this study, the important parameters were obtained by comparing the correlation coefficients that should be included in the regression analysis. If the commonly used significant level, i.e., = 0.05, in the statistics is applied to the regression analysis in EGAIM, some important parameters might be omitted. us, this study introduced a method for modifying significant level and corresponding .
In this work, the data processing can be summarized by the following steps.
Step 1. A set of significant level in a certain range and corresponding are obtained using the critical value table of the distribution.
Step 2. e values of the important parameters are calculated using Equation (3) [32],where subscript represents the selected important parameters using the comparison of the correlation coefficients.
Step 3. Minimum is compared with using Equation (4). If minimum is less than , cannot ensure that the important parameters are included in the regression equation. If minimum is larger than or equal to , is suitable for the regression analysis.
e matrix of the correlation coefficients is shown in the form of a heat map by combining Equations (1) and (2) to intuitively express the relationship between the parameters and sink marks, as shown in Figure 2. In the heat map, red and blue represent the positive and negative effects, respectively, and the number and shade of the colors indicate the correlation between the abscissa and ordinate. e value of the correlation coefficient between the gas time and sink marks is the largest value, which reaches −0.71. us, gas time is the most important parameter in EGAIM, and the negative sign indicates that the relationship between the gas time and sink marks is positive. e longer the gas time is, the smaller is the sink-mark value. e correlation coefficients of the cooling time and gas pressure are also large, which reach 0.32 and −0.23, respectively. erefore, the gas time, cooling time, and gas pressure are important in the sink marks of the crystalline polymer products. e value of the correlation coefficient between the delay time and gas pressure is also large, which reaches 0.27. us, the influence of the delay time and gas pressure should not be neglected. e determination of the important parameters establishes a basis for exploring the Step 4. Correspondingly, this condition results in many suitable values based on Step (2), but not all values are optimal . To improve the accuracy, maximum is considered as the optimal value from a large number of suitable values. e aforementioned data-processing method provides the basis for selecting at significant level by comparing it with of the important parameters, which reduces the possibility of omission of some important parameters in the regression equation and improves the accuracy of this equation.

Correlation Coefficients of the Parameters.
e sink marks of the crystalline polymer products measured by the dial indicator are listed in Table 3.

Advances in Polymer Technology
To obtain the quantitative relationship between the parameters and sink marks, the square term of the parameters and the interaction among the parameters were considered in the regression equation. e regression equation was investigated using the comparison between and = 1.4, as expressed in Equation (5), e ratio of variation to the total variation for Equation (5) was described by the important coefficient 2 , which is a measure of the degree of fit. When 2 more approaches unity, the response model fits the actual data better. e value of 2 in Equation (5) is 85.37%, which is acceptable. e regression equation of the sink marks in EGAIM was obtained according to the analysis of the correlation coefficients, which revealed the quantitative relationship between the important parameters and sink marks of the crystalline polymer products in EGAIM.

Discussion on the Regression Equation.
e regression equation explores the influence of important parameters quantitative relationship between the parameters and sink marks of the crystalline products in EGAIM.

Establishment of the Regression Equation.
According to the calculation by Equation (3), the values of the cooling time, gas pressure, and gas time, were 3.19, 1.56, and 28.46, respectively. of the interaction of the gas pressure and delay time was 2.03. One of the most important steps in considering the regression equation is to determine at significant level to select the parameters. In general, at significant level should be defined before exploring the regression equation. However, depends on the preferences of different people.
is generally defined in statistics as 0.05, and = 2.9 at significant level = 0.05. If = 2.9 is used to investigate the EGAIM parameters, the cooling and gas times are considered in the regression equation because 퐹 > 퐹 = 2.9. However, the gas pressure is omitted from the equation, which is unacceptable according to the aforementioned discussion. Significant level was thus adjusted to = 0.3 to ensure that all important parameters were included into the regression equation. = 1.4 at = 0.3. All the values of the important parameters were larger than , which avoided omitting the important parameters. Advances in Polymer Technology 6 and the other unimportant parameters were combined according to the uniform design in a certain range, the sink marks of the crystalline polymer under different unimportant parameters are as those listed in Table 4.
e experimental results are shown in Figure 3, and the values of the sink marks under different unimportant parameters fluctuate from the average value and reach 0.097 mm. e difference between the average and predicted values of the regression equation is 0.006 mm and reaches 6.18%, which indicates that the accuracy of the regression equation and the influence of these parameters on the sink marks of crystalline polymer products are almost negligible. e regression equation establishes the quantitative relationship between the important parameters and sink marks of the crystalline polymer products in EGAIM.

Reduction of Sink Marks Using EGAIM.
e aforementioned research obtained the optimal important parameters for the sink marks, including a cooling time of 55 s, gas pressure of 9 Mpa, gas time of 30 s, and delay time of 1 s. the other unimportant parameters were randomly determined from no. 14 in Table 4, and the material temperature, injection pressure, injection speed, packing pressure, and packing time are 220°C, 70 Mpa, 60 mm/s, 60 Mpa, and 5 s, respectively. e sink marks of the crystalline polymer products with or without gas are compared and shown in Figure 4. Figure 4(a) shows that the sink mark of the crystalline polymer products without the gas is 0.365 mm, whereas that with the gas is only 0.085 mm, as shown in Figure 4(b). e difference in the sink marks of the crystalline polymer products with or without gas is 0.280 mm. us, EGAIM significantly reduces the sink marks of the crystalline polymer products. erefore, EGAIM obviously reduces the sink marks of these iPP products. e results provide sufficient evidence for the application of crystalline polymers in EGAIM.
on the sink marks of the crystalline polymer products. e minimum value of the sink marks was obtained by calculating the regression equation, which was equal to 0.103 mm when the cooling time, gas pressure, gas time, and delay time were 55 s, 9 Mpa, 30 s, and 1 s, respectively.
According to the previous research, when the important parameters were defined, the influence of the unimportant parameters on the sink marks of crystalline polymers could be ignored, including the material temperature, injection pressure, injection speed, packing pressure and packing time. When the important parameters were the same as those of the aforementioned values, i.e., the cooling time, gas pressure, gas time, and delay time were 55 s, 9 Mpa, 30 s and 1 s, respectively,

Conclusion
In this study, the application of EGAIM to an iPP product was investigated by experiment. According to the results of this study, the following conclusions can be drawn. (1) EGAIM can significantly reduce the sink marks of these iPP products.
(2) e cooling time, gas pressure, and gas time are important parameters that affect the sink marks of the crystalline polymer products according to the correlation coefficients. (3) e regression equation can correctly predict the sink marks of the crystalline polymer products when the important parameters in EGAIM are constant. In general, this study verifies the effectiveness of EGAIM on reducing the sink marks of crystalline polymer products and provides the quantitative relationship between the important parameters and sink marks of crystalline polymer products in EGAIM.
Data Availability e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.