*4.1. Multi-Layer Structure of Injection-Molded Parts* 4.1.1. Skin-Core Structures Investigated by PLM

The typical skin-core structures of the molded parts were obtained by morphology investigation with PLM along the thickness direction under different process conditions, as shown in Figure 5. The thicknesses of the layers changed with each different molding process, as shown in Table 1. The upper skin layer of each injection-molded part was near to the stationary side with heating rods.

**Figure 5.** Polarized micrographs of parts under different processes.

**Table 1.** The thickness of each layer under different processes.


The thicknesses of the layers were almost symmetrical along the thickness direction in the skin-core structures of the CIM parts. The mold temperature of the stationary side was the same as that of the moving side. Therefore, the temperature distribution of polymer in the cavity was symmetrical and introduced symmetrical skin-core structures.

The thicknesses of the layers were obviously asymmetrical in the skin-core structures of the RHCM parts, introduced by the different temperatures between the stationary side and the moving side of the mold. Since the upper skin layer of the part was near the stationary side with heating rods, the thicknesses of the upper layers were smaller than those of the lower layers. The thicknesses of the upper skin layer and the lower skin layer in RHCM90 were 221 and 289 µm, respectively, a change by 30.8%. The thicknesses of the upper shear layer and the lower shear layer in RHCM90 were 252 and 491 µm, respectively, a change by 94.8%. The thickness variation in the upper and lower shear layers was three times greater than that in the upper and lower skin layers. The asymmetrical distribution of the layer thicknesses will introduce greater warpage.

#### 4.1.2. Crystallinity of Each Layer

The position range of each layer in the molded parts was divided according to the crystal morphology observed in PLM. The distances *x* from the upper surface of the sample were set as the positions of certain layers to conduct the WAXD investigation, and 0.1, 0.4, 1.2, 2.0, and 2.4 mm were considered to be the positions of the upper skin layer, upper shear layer, core layer, lower shear layer, and lower skin layer, respectively. The crystallinity diffraction pattern of each layer obtained by WAXD is shown in Figure 6. The crystallinity of each layer could be calculated from the crystallinity diffraction pattern using X'Pert HighScore Plus. The calculated results of the crystallinities are shown in Table 2.

**Figure 6.** Crystallinity diffraction pattern of parts with different molding conditions by WAXD: (**a**) CIM, (**b**) RHCM60, (**c**) RHCM90.


**Table 2.** Crystallinity of each layer under different processes.

The crystallinities of the layers were almost symmetrical along the thickness direction in the skin-core structures of the CIM parts, with the same pattern as the thicknesses of the layers. The crystallinity increased from 35.10% in the lower skin layer to 43.50% in the core layer, a change by 23.9%.

The crystallinities of the layers were asymmetrical in the skin-core structures of the RHCM parts, also with the same pattern as the thicknesses of the layers. The crystallinity in RHCM90 increased from 38.15% to 47.51% in the lower skin layer vs. in core layer, a change by 24.5%. The crystallinity difference of the RHCM parts was smaller than that of the CIM parts. However, the crystallinity in the lower skin layer was much smaller than that in the upper skin layer. The crystallinity changed by 12.0% from that in the upper skin layer to that in the core layer, which is only half of the value from in the lower skin layer to that in core layer. The asymmetrical distribution of crystallinities would also introduce greater warpage.

#### *4.2. Temperature Histories of Polymer*

The temperature histories of polymer in the layers were obtained by conducting a heat transmission simulation on the representative position, and the results are shown in Figure 7.

**Figure 7.** Simulated temperature histories in the thickness direction under different processing conditions: (**a**) CIM, (**b**) RHCM60, and (**c**) RHCM90.

Figure 7a shows that the temperature histories are symmetrical along the thickness direction of the parts in CIM due to the temperature of the stationary side being the same as that of the moving side. Meanwhile, in RHCM, the temperature histories of polymer in the layers are asymmetrical along the thickness direction. The asymmetry increases with the increase in mold temperature, and the difference in the temperature histories between different layers will also increase. In RHCM60, the temperature difference at the ejecting time (the specific time is 30 s) between the upper and lower skin layers is 10 ◦C. In RHCM90, the temperature difference at the ejecting time between the upper and lower skin layers increases to 20 ◦C. The core layer temperature will also increase with the increase in heating temperature. The temperature of the core layer at the ejecting time in CIM is about 80 ◦C, but those in RHCM60 and RHCM90 increase to 90 and 95 ◦C, respectively. The higher temperatures will introduce higher crystallinities, as shown in Section 4.1.

#### *4.3. Warpage Prediction*

The multi-layer structures always appear in the molded parts along the thickness direction due to the inhomogeneous temperature history. The different crystal morphology of each layer introduces different mechanical properties. The layers with different mechanical properties will complicate the warpage of the part. Stratification is the most distinguishable feature in the inhomogeneous distribution of process parameters in molten polymer during molding and the microstructure in the molded parts after molding. However, the effect of stratification is ignored in the usual warpage simulation. The warpage prediction was conducted with and without the influence of crystallinity to verify the significance of the introduction of the model describing the elastic modulus with the influence of temperature and crystallinity. In the prediction without the influence of crystallinity, the elastic modulus was a function of temperature. The predicted results with different molding conditions are shown in Figure 8, where results with crystallinity are shown in Figure 8a–c and results without crystallinity are shown in Figure 8d–f. The maximum value of warpage appears very near to one of the corners of the parts. Numbers 1, 2, 3, and 4 are used to mark the different corners for further discussion.

From Figure 8a–f, it can be seen that the total predicted warpage ranges of the parts under different conditions are −0.02~3.29, −0.07~13.00, −0.02~18.40, −0.01~3.11, −0.01~8.07, and −0.01~13.40 mm, respectively. The results show that the warpage is influenced by the crystallinity, and the predicted warpage with crystallinity is larger than that without crystallinity, especially in the parts molded using the RHCM process. The maximum values of warpage in the CIM parts are 3.29 and 3.11 mm with and without crystallinity, respectively, a change by 5.8%. The maximum values of warpage of the RHCM60 parts are 13.00 and 8.07 mm, a change by 61.1%. The maximum values of warpage of the RHCM90 parts are 18.40 and 13.40 mm, a change by 37.3%. Therefore, bigger errors will occur if crystallinity is not considered in warpage prediction of the crystalline parts molded by the RHCM process.

The predicted warpage increases as the heating temperature increases, and the warpage with crystallinity is more sensitive to heating temperature than that without crystallinity. The maximum value of warpage with crystallinity gradually increased from 3.29 mm for the CIM to 18.40 mm for the RHCM90, an increase of 459.3%. The maximum value of warpage without crystallinity gradually increased from 3.11 mm for the CIM to 13.40 mm for the RHCM90, an increase of 330.9%.

#### *4.4. Comparation of Warpages of Experiment and Prediction*

The parts were molded under the aforementioned conditions, and warpages were measured by a 3D laser scanner. The parts and the scanned results are shown in Figure 9. The maximum warpage also appears at one of the corners of the parts. Numbers 1, 2, 3, and 4 are used to mark the different corners for further discussion, with the same marking method as in the prediction.

**Figure 8.** The total predicted warpage results of the parts (unit: m): (**a**–**c**) prediction with crystallinity; (**d**–**f**) prediction without crystallinity. (**a**,**d**) CIM; (**b**,**e**) RHCM60; (**c**,**f**) RHCM90.

**Figure 9.** Warpage information of real parts measured by a 3D laser scanner under different molding conditions: (**a**) CIM, (**b**) RHCM60, (**c**) RHCM90.

The maximum values of warpage are shown in Figure 10, including the data of experiments and predictions with crystallinity and without crystallinity. The predicted warpage with crystallinity is much closer to the experimental warpage. The average errors of the four corners between the predicted warpage and average experimental warpage

are 0.23, 0.44, and 0.81 mm, respectively, in CIM, RHCM60, and RHCM90, with respective deviations of 7.0%, 3.5%, and 4.4%. The maximum errors are 0.35, 1.30, and 2.12 mm, respectively, with deviations of 10.1%, 10.0%, and 11.2%. The difference is mainly due to the crystallinity of each layer in the simulation. The crystallinities of each layer in the model were obtained by measuring the corresponding positions of molded parts with WAXD. However, the crystallinity measured with WAXD cannot accurately represent the actual crystallinity of the layer. In addition, experimental errors, characterization errors, etc., which have an impact on the distribution of the model's multiple layers and the mechanical properties of each layer during warpage prediction.

**Figure 10.** The maximum values of warpages of experiment and prediction: (**a**) CIM, (**b**) RHCM60, (**c**) RHCM90.

The predicted warpage without crystallinity deviates more from the experimental warpage in the parts molded by the RHCM process than that with crystallinity. The average errors of warpage prediction of CIM are 0.23 and 0.22 mm with and without crystallinity, respectively, with a difference of 4.5%. The small difference is mainly due to the symmetrical distribution of thickness and crystallinity. However, the difference is much greater between the warpage prediction with and without crystallinity for parts molded by the RHCM process. The average errors of the warpage prediction of RHCM60 are 0.44 and 4.71 mm with and without crystallinity, respectively, with a difference of 970.5%. Additionally, the average errors of warpage prediction of RHCM90 are 0.81 and 5.00 mm, with a difference of 517.3%. They are mainly introduced by the asymmetrical distribution of thickness and crystallinity, as discussed previously.

#### **5. Conclusions**

This paper presented a novel method for predicting the warpage of crystalline parts molded using the RHCM process. A multi-layer model was established based on the stratification in the polymer temperature during molding and in the microstructure of parts after molding. A model was introduced to describe the mechanical properties with the influence of temperature and crystallinity. Finally, experimental warpage was measured using a 3D scanner to verify the predicted warpage. According to the results obtained in this study, the following conclusions can be drawn: (1) The microstructure and temperature are symmetrical along the thickness direction in CIM and are asymmetrical in RHCM. (2) The predicted warpage is influenced by the crystallinity, and the warpage predicted with crystallinity is larger than that predicted without crystallinity, especially in the parts molded by RHCM. (3) The predicted warpage increases as the heating temperature increases, and the warpage with crystallinity is more sensitive to heating temperature than that without crystallinity. (4) The predicted warpage with crystallinity is much closer to the experimental warpage than that without crystallinity, which shows that it is very important to consider crystallization in warpage prediction. (5) The proposed method can predict the warpage of crystalline parts molded by RHCM, and its predicted results agree well with the warpage measured on molded parts using a 3D scanner. In general, the proposed method is accurate and effective. It is a potential candidate technology for the quantitative prediction of the warpage of plate parts and for optimizing the molding process for manufacturing.

**Author Contributions:** J.L. and S.J. proposed the method of warpage prediction; S.J. conceived and designed the experiments; X.X. and B.Z. were responsible for injection molding experiments; J.B. and W.L. were responsible for the PLM and WAXD testing of molded parts; J.B. and X.P. were responsible for the simulation analysis; S.J. analyzed the results; J.L. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation (grant no.51875525) and by the Natural Science Foundation of Zhejiang Province (grant nos. LY20E050100, LY19E050004, and LY19E050009).

**Acknowledgments:** The authors would like to acknowledge the financial support from the National Natural Science Foundation (grant no.51875525) and by the Natural Science Foundation of Zhejiang Province (grant nos. LY20E050100, LY19E050004, and LY19E050009).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

