**1. Introduction**

Rapid heat cycle molding (RHCM) is a special injection molding technology used to mold parts with a high surface quality without extending the cycle time [1]. Some defects in the plastic parts produced by conventional injection molding (CIM) can be solved by RHCM, such as flow mark, silver mark, jetting mark, weld mark, exposed fibers, short shot, etc. [2]. However, RHCM is not a nostrum for all the defects in injection-molded parts. Warpage is one of the defects that cannot be solved by RHCM [3].

Warpage is a distortion where the shape or dimension of a molded part deviates from that of the intended design [4]. It is caused by the residual stresses in the molded part after ejection, which mainly result from the non-uniform shrinkage of the polymer in different positions of the molded part [3]. Unfortunately, non-uniform shrinkage is inevitable due to the inhomogeneous temperature history of polymer in different positions, inhomogeneous pressure distribution, etc. [5]. In particular, in injection-molded crystalline parts, the inhomogeneous condition of polymer will introduce more complex crystallization than in static crystallized parts. The complex crystallization will introduce more complicated shrinkage and greater warpage [6,7].

Some researchers have discussed the influences of the processing parameters on the warpage of CIM parts through experiments [8–12], and the warpage has been optimized based on experimental results [13–17]. These works have provided guidance to reduce the warpage of injection-molded parts. However, the guidance is usually not universal to all parts. The prediction of warpage by computer will solve the issue of universality. Some

**Citation:** Li, J.; Bei, J.; Liu, W.; Xia, X.; Zhou, B.; Peng, X.; Jiang, S. Warpage Prediction of RHCM Crystalline Parts Based on Multi-Layers. *Polymers* **2021**, *13*, 1814. https://doi.org/ 10.3390/polym13111814

Academic Editors: Célio Bruno Pinto Fernandes, Salah Aldin Faroughi, Luís L. Ferrás, Alexandre M. Afonso

Received: 1 May 2021 Accepted: 27 May 2021 Published: 31 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

methods have been introduced and developed to predict the warpage of CIM parts [18–20], and some of them have been introduced into commercial software, such as Moldflow and Moldex 3D. The large warpage is considered as the main defect of RHCM parts [21]. Unlike the conventional injection molding (CIM) process, the RHCM process employs a dynamic mold temperature control strategy based on rapid mold heating and cooling [22]. In RHCM, the mold temperature is heated to a relatively high preset value before melt injection and remains constant during the filling and packing phases. On gate solidification, the mold is rapidly cooled to allow the solidification and the demolding of the polymer part [23], as shown in Figure 1. The different temperature histories in the mold introduce various thermal and shear histories to the polymer. 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. The different crystal morphology of each layer introduces different mechanical properties. The layers with different mechanical properties will complicate the warpage of RHCM parts. The warpage prediction of RHCM parts is difficult because Moldflow cannot set multi-layer material and crystallinity. Therefore, it will be very meaningful to propose a prediction method to accurately predict the warpage of crystalline parts molded using the RHCM process.

**Figure 1.** The RHCM process.

In this paper, a prediction method is proposed to calculate the warpage of RHCM parts based on multi-layers, according to the common skin-core structure in the molded parts [3] and the layer distribution of pressure and temperature along the thickness during the molding process. The thicknesses of the multi-layers were determined as the thicknesses of the skin-core structure in the molded parts, measured using a polarizing microscope (PLM). A model was introduced to describe the elastic modulus with the influence of temperature and crystallinity [24]. Finally, the predicted results were compared with the warpage information of the parts obtained using a 3D laser scanner.

#### **2. Experimental**

#### *2.1. Part Preparation*

A semi-crystalline iPP (T30S, Zhenhai branch of Sinopec Corp, Ningbo, China) was used to mold parts. The parameters of the polymer were as follows: melt flow index (MFR) of 2.5 g/10 min, melting point of 167 ◦C, density of 0.91 g/cm<sup>3</sup> , and an isotactic index greater than 94%. An injection molding machine (MA3800/2250, Haitian International Holdings Ltd., Ningbo, China) was employed to produce CIM and RHCM parts with a size of 280 × 180 × 2.5 mm, as shown in Figure 2.

**Figure 2.** Shape and dimensions of the experimental part.

The same RHCM mold was used in this study as in an earlier study [25]. Electrical heating rods and cooling tunnels were deployed in the stationary mold, which could be rapidly heated by electric heating before filling and cooled by circulating water after filling. Meanwhile, the moving mold only had regular cooling tunnels. The heating of the electrical heating rods was controlled by an MTS-32II mold heating temperature controller (Beijing CHN-TOP Machinery Group Co Ltd., Beijing, China), the heating rods and heating temperature controller were all turned off. Parts were molded under the following process conditions: melt temperature of 220 ◦C, injection pressure of 90 MPa, packing pressure of 50 MPa, cooling time of 30 s, and coolant temperature at room temperature (20 ◦C). CIM was conducted at room temperature. Room temperature is usually 20 or 25 ◦C according to the literature [22,25–27]. Combined with the actual room temperature, the mold temperature was 20 ◦C in this study. The iPP used in this experiment was a fast crystallizing polymer, and its crystallization temperature ranged from 20 to 120 ◦C [28,29]. The mold temperature was determined by the microscopic morphological structure, which had a significant difference between 60 and 90 ◦C [25,27]. The stratification in the microstructure of parts can be better observed and analyzed. Combined with the room temperature at the time of the experiments, the mold temperatures containing large differences were determined to be 20, 60, and 90 ◦C; the parts molded under 60 and 90 ◦C were marked as RHCM60 and RHCM90, respectively.

#### *2.2. Polarizing Microscope Experiment*

Samples with dimensions of 8 × 8 × 2.5 mm were taken from the center of the molded parts, as shown in Figure 3. The location was determined mainly by avoiding the weld mark. Thin slices of specimens were cut along the thickness direction of samples and observed using a polarizing microscope (U-FMP, Olympus Corporation, Tokyo, Japan). The thickness of each layer was investigated on the PLM results along the thickness direction.

#### *2.3. WAXD Experiment*

Wide-angle X-ray diffraction (WAXD) was employed to determine the crystallinity of each layer. The samples were polished with coarse and fine sandpaper to the location range of each layer. WAXD was conducted on an X-Pert PRO X-ray diffraction instrument (PANalytical B. V., Almelo, The Netherlands) with an X-ray source of *Kα* radiation from a Cu target (λ = 0.154056 nm), a voltage of 40 kV, and a current of 40 mA. Its diffraction angle 2*θ* ranged from 10◦ to 40◦ . The crystallinities were calculated using X'Pert HighScore Plus.

#### *2.4. 3D Scanning*

The warpages of the molded parts were measured using a 3D laser scanner (Faroarm, Faro, FL, USA). The surface of the part was set as the reference plane and the thickness direction of the part was set as the *z* direction. The warpage was defined as the difference between the maximum value in the *z* direction of the molded part and the reference plane.

Five parts molded under the same molding conditions were chosen to be scanned, and the average of the warpages was taken as the measured warpage for discussion. The measured warpage was compared with the prediction results to verify the accuracy of the prediction method.

**Figure 3.** Experimental sample.

#### **3. Methodology**

Shear stratification and temperature stratification usually appear in a polymer during injection molding [30], and multi-layer structures always appear in the molded parts along the thickness direction [31]. A multi-layer structure is always introduced by the fountain flow due to the thin-walled, large-plane part characteristics. In the fountain flow, the temperature and shear of the polymer usually show stratification distribution. The solid area, liquid melt area, and two-phase area of the polymer will appear in the cavity during the filling process [30]. The whole polymer presents five areas along the thickness direction, namely the upper solid area, upper two-phase area, liquid melt area, lower two-phase solid area, and lower solid area. Additionally, skin-core structures will appear in the parts molded by CIM and RHCM [30–32].

Polypropylene can be considered an intercalated homogeneous material based on the Eshelby equivalence principle [33] and the Mori–Tanaka method [34]. The crystals produced during crystallization are considered to be inclusions, and the amorphous phase is considered to be the matrix. Furthermore, the multi-layers of the parts are divided according to the crystal morphology of the parts along the thickness direction. The different crystal morphology of each layer introduces different mechanical properties, e.g., modulus and strength [35–37]. The inhomogeneous distribution of mechanical properties and temperature will introduce non-uniform shrinkage and result in warpage of the parts.

A multi-layer model was established to predict the warpage of injection-molded parts, because the stratification is the most distinguishable feature in the inhomogeneous distribution of process parameters in a molten polymer during molding and the microstructure in the molded parts after molding. In the model, the overall shape and dimensions were the same as those of the part. However, the model was divided into five layers along the thickness direction, namely the upper skin layer, upper shear layer, core layer, lower shear layer, and lower skin layer, as shown in Figure 4. The thicknesses of the layers in the model were the same as those of the parts.

**Figure 4.** The multi-layer model with five layers.

Warpages were defined as deformations of the molded parts. The deformations in the multi-layer model were solved using the classical Laminated Plate Theory [38] by Abaqus. The layers with different mechanical properties were treated as layers with different angles during the solving simulation. The crystallinities of each layer in the model were obtained by measuring the corresponding positions of molded parts with WAXD. The mechanical properties of each layer necessary for prediction were calculated using the following model describing the elastic modulus with the influence of temperature and crystallinity [24].

$$\begin{cases} \ E(\theta) = E\_0 \cdot \exp[-b(\theta - \theta\_0)] \\ \quad E\_0 = a \cdot \exp\left(\frac{cw}{1-w}\right) \end{cases} \tag{1}$$

where *θ*<sup>0</sup> is the reference temperature (room temperature); *E*<sup>0</sup> is the elastic modulus at the reference temperature; *a*, *b*, and *c* are material parameters; *w* and *θ* are the crystallinity and service temperature, respectively. The same material was used to mold the part as in our past study, and the parameters were introduced [39].

The complex crystallization is inevitable due to the inhomogeneous temperature history, which will introduce more complicated shrinkage and greater warpage. The internal thermal stress of the part cannot be released by the mold constraint before ejection. The part produces warpage due to internal thermal stress release after ejection. The simulation process was divided into two stages: before ejection and after ejection. In the simulation before ejection, temperature histories were summarized from the simulation results of heat transmission between the polymer and mold. Additionally, the thermal stresses were simulated under shape restriction, where the shape was same as the cavity. In the simulation after ejection, temperature histories were summarized from the simulation results of heat transmission between the polymer and atmosphere, and the deformation was calculated from the thermal strains simulated without deformation restriction.

The simulations before ejection were conducted under the initial conditions with the temperature of the moving mold at 20 ◦C; the temperature of the stationary mold at 20, 60, and 90 ◦C; a melt temperature of 220 ◦C. Thermal load was introduced by the density variations because of the temperature dropping during the molding process, and the density variations were described by a modified two-domain Tait equation of state [20,40–42] in this paper.

$$V(T, P) = V\_0(T)\left\{1 - \mathbb{C}\ln\left[1 + \frac{P}{B(T)}\right]\right\} + V\_1(T, P) \tag{2}$$

where *V*(*T*,*P*) is the specific volume at temperature *T* and pressure *P*; *V*<sup>0</sup> is the specific volume at atmospheric pressure; *C* is a constant, whose value is 0.0894; *B* is the pressure sensitivity of the material.

In the simulation after ejection, the simulation results of the parts in the first stage were introduced as the initial conditions. The thicknesses of each layer were determined by the data measured in PLM, and different mechanical properties were introduced in each layer. The mold restriction was removed, and the parts were cooled at room temperature. Additionally, the centers of the parts were fixed. Thus, the simulation results of warpage were obtained.

#### **4. Results and Discussion**
