Investigation of film–substrate interfacial characteristics of polymer parts fabricated via in-mold decoration and microcellular injection molding process

The appearance quality of foamed polymer parts can be improved by introducing high-appearance quality decorative films. However, the interfacial bonding characteristics of film that penetrated the surface of the substrate are few studied. In this paper, the foamed polypropylene (PP) parts with decoration films penetrated on the surface were prepared by the in-mold decoration and microcellular injection molding (IMD/MIM) process. The interfacial characteristics of the IMD/MIM parts were investigated experimentally through peeling tests and interfacial morphology. Based on the finite volume method, the coupled heat transfer model was established to calculate the temperature field in IMD/MIM process by taking into account the coupled heat transfer between polymer melt, film, and mold. The thermal response in the IMD/MIM process was numerically analyzed. The results show that the higher temperature on the polymer melt–film interface corresponds to relatively higher crystallinity and larger crystallite size and also favors the forming of the β-form crystal, which is beneficial to higher adhesion strength. The IMD/MIM parts can obtain a firm film–substrate adhesion and a uniformly strong bond between the film and the substrate.


Introduction
The concept of microcellular plastics was first propounded by the team of Nam Suh [1] at the Massachusetts Institute of Technology (MIT). Thanks to the massive cells inside the foamed plastics, the density of materials can be significantly reduced. Compared with conventional injection molding (CIM) parts, the micro-foams can yield an effective reduction in the use of raw materials and consequent costs to a great extent [2]. Besides, foamed plastics also feature high thermal stability, high specific strength, good thermal and acoustic insulation, and excellent cushioning properties [3][4][5][6]. However, in the microcellular injection molding (MIM) process, the internal cells turned to the surface of the mold cavity at the melt-filling stage, which then formed bubble marks on the surface of the parts. The greatly affected surface quality further restricted the wider application of MIM technology in turn [7,8].
To solve the poor surface quality problem of MIM parts, scholars have carried out lots of investigations, among which it is previously proved that a layer of insulation film pasted onto the mold during the injection molding process was a relatively easier way to achieve molded parts with the good surface [9][10][11][12][13]. The in-mold decoration (IMD) process cannot only improve the surface quality of MIM plastics, but also play a key role in broadening the application field of CIM for the manufacturing of esthetic parts or coated decorative film pieces, as well as soft-touch materials or anti-scratch parts [14,15]. Besides, the IMD is a one-step process without the need for extra post-processing such as over-molding [16,17] and thermal sprayed coating [18][19][20], which also realizes a reduction in manufacturing time and cost. To simultaneously endow plastic parts with weight reduction and good surface, the combined in-mold decoration and microcellular injection molding process were introduced for preparing foamed parts successfully meeting the aforementioned requirements [10]. Different from the above process for in-mold labeling, parts with decorated film pieces penetrated on the surface can be fabricated via the integrated IMD/MIM technology, which is not yet reported. Then the challenge comes forward toward the interfacial properties between the resin substrate and the inserted film since sufficient and lasting interfacial strength is required for normal usage. Previously conducted research focusing on the parts molded by filminsert injection molding (FIM, also known as a kind of inmold decoration) elucidated the effect of molding condition [21], crystallization [22][23][24], substrate molecular weight [25], film thickness [25], and molecular orientation [24] on the film-substrate interfacial adhesion. Hu et al. [26] verified that interface temperature changes during the cooling period were of immense significance to the interface crystallinity and the resulting film-substrate interfacial adhesion. Although the thermal effect from an inserted film of IMD has been studied [9,14,15], detailed investigations on the dynamic interface temperature of integrated IMD/MIM remain to be revealed.
To clarify the influence mechanism of interface temperature on the interfacial adhesion of IMD/MIM parts, it is essential to understand the heat transfer behavior at the interface during the integrated IMD/MIM process. But experimentally tracking the polymer-film interface temperature is quite hard to implement for the intricate and transient three-dimensional temperature field of the IMD/ MIM process. Hence, the numerical simulation [27] is an effective alternative method to expound on the mechanism of the dynamic interface temperature effect on the interfacial bonding strength between the foamed substrate and the inserted film.
In the melt-filling stage of IMD/MIM, the melt-flowing behavior dominantly holds sway over the interface temperature, for the asymmetric temperature distribution induced by the presence of film [14]. As a consequence, the filled melt at the cooling process undoubtedly gets affected as well, which then shows a substantial impact on the polymer melt crystallization and diffusion. The heat transfer behavior at the interfaces of mold-polymer and melt-film-mold is so essential during the filling and cooling stage that the calculation accuracy desperately needs to be guaranteed [15]. In this case, establishing a reasonable heat transfer algorithm becomes the key to the numerical simulation.
The previous works in the literature proved the feasibility of the implicit coupled heat transfer algorithm in calculating the temperature field of the IMD/MIM at the filling stage [28]. In the implicit domain coupling algorithm (IDCA) [8,[27][28][29], the energy discretization equations of the fluid domain (polymer melt) and solid domain (mold and film) can be assembled into one matrix equation which can be solved by a linear solver with a faster convergence speed. As for the cooling stage, previous simulations usually ignored the heat loss during the filling stage and applied the original melt temperature as the initial cooling temperature [26], which could lead to a discrepancy between the simulated results and facts, since the heat transfer between melt and mold took place every moment during the melt flowing. Moreover, the influence of the solidification of the polymer melt on the heat transfer during the cooling procedure is also not neglectable.
To solve the abovementioned problem and reveal the effect mechanism of interface temperature on the interfacial characteristics of IMD/MIM parts, a mathematical model of coupled heat transfer between multiphase fluid and mold and film solid based on the finite volume method is established in this paper. During the melt-filling stage, the IDCA method was employed to simultaneously calculate the temperature field of the melt, mold, and film. Then the ultimate calculated results were set as the initial state of the cooling process. For the phase change process of the gradual cooling melt, the discretization with time hybrid explicit/implicit technique was adopted to calculate the dynamic temperature [30], which was based on the "new source" method [31]. In addition, the influence of melt-film interface temperature on the crystallization and film-substrate interfacial adhesion of IMD/MIM parts was analyzed.

Materials
The polymer substrate employed in the experiment was modified polypropylene (PP) with the brand AIP-1927, provided by Jinfa Technology Co., LTD. The physical blowing agent was supercritical nitrogen (SCF-N 2 ), provided by Wuhan Xiangyun Industry Co., Ltd. The mold was made of P20 steel. The PP film, with a thickness of 0.25 mm, is provided by Shenzhen Jinghua Film Technology Co., Ltd. To make the simulation more accordant with the fact, the thermal conductivity of PP film was primarily measured using the thermal constant analyzer.

The integrated IMD/MIM process
The schematic diagram of the integrated in-mold decoration and microcellular injection molding (IMD/MIM) process is vividly depicted in Fig. 1. The polymer film is attached to one side of the mold wall before injection molding, with adhesive tape used at both ends to avoid the slide of film, as shown in Fig. 1a. Especially for peeling specimens, one of the film halves is adhered to thin-layer polyimide film to obtain a nonstick region for the easy peeling of the film from the substrate. The left part of Fig. 1. shows the process of producing the polymer/supercritical fluid (SCF) singlephase solution, which is formed by the mixed molten polymer and introduced SCF-N 2 under the stirring of the screw. In Fig. 1b, the polymer/SCF single-phase solution pushed by the screw is injected into the cavity, and fountain flow emerges at the melt front. The hot melt will partially melt the film as the melt flows. The thermodynamic instability caused by the high-pressure drop favors the nucleation and growth of cells. Due to the presence of film, the heat transfer is changed causing the asymmetric temperature distribution on two sides of the polymer melt. Figure 1c shows the completion of melt filling, and then the internal cells continue to grow until the melt solidifies. As the cooling process proceeds, the hot polymer melt solidifies at different rates on the film side and the non-film side for the heat retardation induced by the polymer film. And then between the partially molten film and melt, there forms the adhesion of the film to the substrate. Finally, trimming the excess edges, the IMD/MIM samples are obtained as seen in Fig. 1d. From the SEM of impact fracture morphology, no obvious interfacial boundary indicates a strong bonding strength between the film and the substrate.
The injection molding machine (HDX50) and the highpressure gas compressor (GBL-200/3500) were used to experiment with IMD/MIM injection molding process. The basic parameters were set as follows: injection rate 60 g/s, injection pressure 70 MPa, melt temperature 220 °C, mold temperature 20 °C, coolant temperature 20 °C, physical foaming agent (N 2 ) content 0.5%, back pressure 10 MPa, cooling time 30 s, gas injection pressure 17.5 MPa, and gas injection time 3 s. In addition, a holding pressure of 35 MPa and a holding time of 12 s were applied in preparing the IMD/IM parts without the foaming process.

Characterization
The thermal conductivity of the PP film was measured using the thermal constant analyzer (TPS2500S, Hot Disk, Sweden) with the method of the transient plane source.
The adhesion strength between the film and substrate was gauged by a 180° peeling test using the electromechanical universal testing machine (MTS SYSTEMS CMT6104, China). The 180° peeling test was conducted with a peeling rate of 50 mm/min at room temperature. During the peel test, the free end of the film (initially adhered with polyimide tape, which was removed before testing) and the substrate were gripped for a length of 10 mm before peel initiation, as depicted in Fig. 2. To avoid the experimental error caused by the test contingency, at least five samples were tested under the test condition and the average value of them was taken as the experimental result.
The X-ray diffraction spectra of the IMD/MIM parts were obtained by an X-ray diffractometer (D8 ADVANCE, BRUKER AXS, Germany) using the Cu-K α radiation wavelength (λ = 1.54056 Å). The scanning range was from 10° to 80°, and the operating conditions were 40 kV and 40 mA.
The microscopic structure of the film-substrate interface of peeled samples was observed using a JSM-IT300 (JEOL Ltd., Tokyo, Japan) scanning electron microscope (SEM).

Governing equation
The actual injection molding process is rather complicated, and many potential factors concerning the physical field may affect the numerical results. To better simulate the changing temperature field of the IMD/MIM process, the calculation needs to be simplified with the following assumptions: (1) polymer melt, air, and SCF are all incompressible non-Newton fluid; (2) no chemical reaction occurs in the IMD/MIM process; (3) the flow type is laminar and surfaces of cavity wall are non-slip wall; (4) the force of gravity and surface tension and the radiant heat are ignored; and (5) physical and thermal properties of melt, mold, and film are considered constant. According to the above assumptions, the governing equations for coupled heat transfer between the multiphase fluid and solid are given as follows:

Mass equation is expressed as
where U is the velocity field and ∇⋅ is the divergence operator.

Momentum equation is expressed as
where f and are the density and the kinematic viscosity of the multiphase fluid, P is the pressure field and t is time, and is the stress rate tensor of the multiphase system, which can be expressed as

Energy equation of the multiphase fluid domain is expressed as
where T f , C f , k f are the temperature field, the specific heat capacity, and the thermal conductivity of the multiphase fluid, respectively. ̇ is the modulus of the strain rate tensor and can be expressed as

Energy equation of the mold solid domain is expressed as
where M , T M , C M , k M are the density, the temperature field, the specific heat capacity, and the thermal conductivity of the mold, respectively.

Energy equation of the film solid domain is expressed as
where m , T m , C m , k m are the density, the temperature field, the specific heat capacity, and the thermal conductivity of the film, respectively.
At the cooling stage, in consideration of the solidification behavior of the polymer melt, a source term is added to the energy equation of the multiphase fluid domain, comprising the heat absorption and the heat dissipation due to phase change: where T s is the solidification temperature of the polymer melt.

Interface tracking method
The coupled level set and volume-of-fluid (CLSVOF) method [32] is adopted in this study to simulate the polymer melt-gas interface dynamics, which tracks the interface by the LS function and conserves the mass by the VOF function as a complement. The LS function ( ) is defined as the signed normal distance from the cell center to the interface. is zero for the cell center located on the interface and positive and negative for that in the liquid phase and the gas phase, respectively, which equals the following expression as where d is the distance to the interface and can be solved with the following conservative equation The VOF function is defined as the phase fraction occupied by the polymer melt phase fraction α and air phase fraction 1-α in each grid cell of the multiphase fluid domain. is zero for the cell occupied only by the gas phase and unity for the cell occupied only by the liquid phase, whereas, for the cell located on the interface of the liquid phase and gas phase, is a value between zero and unity, which is defined as for cell center in the gas phase 0, for cell center on the interphase d, for cell center in the liquid phase 0, for cell center in the gas phase 0 < < 1, for cell center on the interphase 1, for cell center in the liquid phase The phase fraction of each phase can be solved using the following governing equation Physical property in the interface can be solved by the arithmetic mean of the physical property parameters i of each phase [27] and expressed as where n denotes the number of phases in the mesh element and i represents C p , k , , and , respectively.

Viscosity model
In the mathematical model established in this study, the viscosity of air and SCF are considered constants. The viscosity of the polymer melt is calculated with a modified cross-WLF viscosity model [33]: where 0 and represent the zero-shear viscosity and dynamic viscosity, respectively. The n , * , D 1 ,D 2 ,D 3 ,A 1 , and A 2 are coefficients related to the materials.

Boundary condition
Taking the IMD/MIM injection mold of flexural samples as an example, a generalized setting method of boundary conditions is proposed to numerically analyze the heat transfer of the IMD/MIM process, which consist of the multiphase fluid domain, mold solid domain, and film solid domain.
In Table 1, the boundary conditions of the mold solid domain are listed, where n is the normal vector of the boundary surface, h a is the convective heat transfer coefficient between air and mold, and T a is the temperature of the air. Since the hot melt is air-cooled during the entire injection molding process and no cooling liquid medium exists in the cooling channel, the convective heat transfer coefficient of the cooling channel wall surface is set the same as that of the outer wall surface of the mold.
In Table 2, the boundary conditions of the multiphase fluid domain are listed, where U in and T in are the inlet velocity and inlet temperature of the polymer melt at the melt-filling stage. At the beginning of the cooling stage, U in turns zero, and the initial temperature is set as the temperature at the end of melt filling, i.e., T e−f . Γ coupled is a coupled heat transfer boundary condition of the mold cavity wall.
In Table 3, the boundary conditions of the film solid domain are listed. Since the surfaces of the film walls are fully coupled walls, the coupled heat transfer boundary conditions are set with the film.

Calculation method
The mathematical model established in this study was discretized by the finite volume method. The coupled algorithm was employed to solve the Navier-Stokes equations of the multiphase fluid flow. The heat transfer between the mold, the film, and the polymer melt typically belongs to a problem of fluid-solid coupled heat transfer. To better address this problem, the IDCA method was adopted in this study for the calculation of the coupled heat transfer between the multiphase fluid domain and the solid domain of mold and film. For the phase change heat transfer of the polymer melt due to solidification behavior, the discretization with time hybrid explicit/implicit technique was adopted to calculate the dynamic temperature, which was based on the "new source" method.

Model validation
To validate the feasibility of the aforementioned mathematic model in calculating the heat transfer of the IMD/MIM process, the corresponding simulation was conducted in this study to capture the interface temperature according to the experiment by Kurt et al. [34]. In addition, the geometric model, processing conditions, and material properties were set nearly the same as that in the actual experiment. Then the simulation results of temperature history were compared with the experimental results at the same monitoring point on the mold cavity surface. Figure 4 shows the comparison of the simulation results in this study and the experimental results detected by Kurt et al. at the melt temperature of 200 ℃. The geometric model constructed in Fig. 4a corresponds to Kurt's experimental object. Figure 4b shows the simulation results and the comparison of the monitoring interface temperature between simulation results and measured results at the melt temperature of 200 ℃. It can be seen that the simulated results agree well with the experimental results on the whole. Some minor differences can also be     Table 4, the maximum and minimum temperatures of the experiment and simulation at the monitoring point are compared when the melt temperature is 200 ℃. The relative errors of the maximum temperature and the minimum temperature between the simulation results and the experimental results are 1.02% and 2.58%, respectively (not exceeding 5%). From Fig. 4b and Table 4, the feasibility of the mathematical model and the calculating algorithm established above is validated.

Finite element model
To figure out the influencing mechanism of the interface temperature on the film-substrate interfacial properties of the IMD/MIM parts, the standard flexural sample was taken as the object in this simulation. The geometric model and corresponding boundary conditions were set up as depicted in Fig. 5. The previously established coupled heat transfer model was adopted to calculate the temperature field of the IMD/MIM process. Because of the phase change of solidification during the cooling period, the melting/solidification model was added to accurately characterize the heat transfer behavior as a compliment. In the numerical simulation, the viscosity of the polymer melt was calculated by Eqs. (16)- (19), and the parameters related to the material were listed in Table 5. The other physical parameters of the materials are presented in Table 6, and the related processing parameters were set the same as that in the physical experiment. Figure 6 shows the temperature histories of the polymer melt, mold, and film obtained by numerical simulation. The mesh in the figure is divided into the multiphase fluid   These points with subscripts 1, 2, and 3 are 30 mm, 50 mm, and 70 mm away from the mold sprue, respectively. "PF" represents the point located on the interface of polymer melt and film, "PM" represents the point located on the interface of polymer melt and mold, and "MF" represents the point located on the interface of mold and film. Figure 7 presents the temperature histories of the monitoring points on the interfaces. As shown in Fig. 7a, the temperature of the polymer melt-film interface at three monitoring points shares the same changing trend, firstly rising quickly, then climbing sharply after a brief slow increase, and finally decreasing. The surface layer polymer is defined as the first heat source heating the mold cavity surface. When the hot polymer melt flows through the monitoring point, the temperature begins to rise quickly. The partially molten film absorbs some heat, which may account for the brief slow increase of the temperature. The sharp increase in the temperature is due to the further heating of the core polymer melt acting as a second heat source. It is also obvious that the maximum and minimum temperatures at point PF1 are higher than that of points PF2 and PF3. In addition, the temperature rises with a larger rising rate and drops with a lower decreasing rate from point PF1 to point PF3, which is because of the thermal dissipation during melt flow and the solidification behavior of the polymer melt.  It can be seen from Fig. 7b and c that the temperature on the polymer melt-mold interface and film-mold interface was lower than 30 ℃ due to the efficient cooling system. A distinct difference appears that the temperature on the polymer melt-film interface is much higher than that on the polymer melt-mold interface. This is because the existence of the film reduces the heat transfer coefficient on the film-side melt, and the great heat retardation causes the temperature on the film side much higher than that of the non-film side. Besides, at the same monitoring point, the temperature of the polymer melt-mold interface is much higher than that of the film-mold interface, which verifies the heat retardation effect induced by the film.

Crystallization
To figure out the influencing mechanism of temperature on the interfacial properties, the crystallization was characterized by X-ray diffraction (XRD). The XRD results of interfaces A, B, and C are given in Fig. 8. The characteristic crystal planes of the α-form crystal of the PP molecules are (110), (040), (130), (111), and (131) planes, which correspond to the diffraction angles 2θ = 14.0°, 16.8°, 18.4°, 21.2°, and 22.0°, respectively. And the characteristic crystal plane (300) for the β-form crystal is characterized at the diffraction angles 2θ = 15.9°. The diffraction intensity of interface A is much stronger than that of interfaces B and C at the characteristic crystal plane (300).
The relative content of the β-crystals k was evaluated by the following expression [35] as where A (300) is the area of the (300) diffraction peak and A (110) , A (040) , and A (130) are the areas of the (110), (040), and (130) diffraction peaks, respectively. The relative content of the β-form crystal of the IMD/ MIM samples on interfaces A, B, and C is shown in Table 7. The β-form crystals in PP are significantly affected by the thermal history during processing. The slower heating rate is conducive to the transformation of β-α crystalline phases in PP, which results in the decrease of β-crystal content. The results show that k of the interface and A is slightly higher than that of interfaces B and C, which is consistent with the thermal response of the polymer melt-film interface in Fig. 7a.
The crystallite size was calculated with Debye-Scherrer formula [35]: where d is the average crystallite size, K is the Scherrer constant ( K =0.89), is the wavelength of the incident X-rays ( = 0.154056 nm), B is the full width at half maximum of the diffraction peak, and is the diffraction angle.
The Gaussian method was used to deconvolute the XRD peaks to obtain the relative crystallinity index. And the overall crystallinity X c was calculated with the following expression [36] as where A cryst and A amorp are the fitted areas of the crystal and the amorphous peaks, respectively. Figure 9 presents the crystallinity and crystalline size of IMD/MIM samples on interfaces A, B, and C. It can be seen that the crystallinity and crystalline size share the same changing trend with the interface temperature. Higher interface temperature corresponds to higher crystallinity and crystalline size. A higher interface temperature leads to a faster crystallization rate, which is preferred for higher crystallinity. Since the higher temperature contributes to lower melt viscosity, the molecular segment moves faster, diffuses rapidly toward the nucleus, and get easily organized and deposited, which favors the growth of crystals. As a consequence, the crystallinity and crystalline size turn out to be larger at a higher interface temperature.

Peeling test
The peel test results of the IMD/IM parts and IMD/MIM parts are given in Fig. 10. It shows that the IMD/MIM parts require greater peeling force than IMD/IM parts, which means the stronger bonding strength of the film-substrate interface via the IMD/MIM process. According to the three kinds of force-displacement curves by Leong et al. [25], it is obvious that the distinct saw-teeth-like curve in Fig. 10 indicates the peeling failure belongs to a cohesive type. The presented "stick-slip" phenomenon can be explained in two aspects. On the one hand, the film-substrate interfacial strength is strong enough so that the film surface, the substrate, or both could yield a critical level. When exceeding the critical level, the severance emerges in the yielded regions, and then the crack continues extending rapidly and brittlely. On the other hand, once the yielded region on the interface has severed, the high stiffness of the film imparts itself the ability to "spring back," which abruptly halts the crack propagation and leads to a sudden drop of the peeling force as a consequence. Then the peeling force would build up again at the next propagation of the crack. It should be noticed that the film would undergo plastic deformation and lose the ability to "spring back" during the peeling process when at extremely high interfacial strength. An obvious distinction can be observed the peel force of the IMD/MIM parts is relatively higher than that of the IMD/IM parts. It is preliminarily hypothesized that bubble marks formed by the migration of internal cells to the mold cavity surface at the melt-filling stage play a dramatic impact on this improvement of peel force. Since surface roughness was proved to be the most important factor in terms of adhesion strength [17], the increased surface roughness of the nominal surface of the substrate is conducive to better film-substrate bonding strength. To better characterize the relationship between temperature and interface adhesion, three corresponding interfaces are chosen to calculate the average peel strength in the given area.
The interfacial bonding strength of the sample can be calculated according to the following expression [26]: where P represents the peeling force;B is the width of the bonding interface; and denotes the peeling angle. Figure 11 shows the average peel strength of the peeled areas on interfaces A, B, and C of IMD/IM parts and IMD/ MIM parts. The quantitative comparison shows that the average peel strength of IMD/MIM parts is relatively stronger The average peel strength of the peeling area on interfaces A, B, and C of the IMD and IMD/MIM parts than that of the IMD/IM parts on the interfaces, which may be due to the rougher "surface" of the substrate caused by the migration of internal cells to the interface between film and polymer melt. Figure 11 also elucidates that the peeling strength gradually decreases from interface A to interface C, which agrees well with the change in interface temperature and crystallization. The reason is that the higher temperature melts the film surface more and then forms a thicker diffusion entanglement layer, thus increasing the interfacial strength. And it also illustrates the significance of crystallization on the interfacial strength that the grain damage during the peeling test can absorb more energy than the amorphous structure leading to higher adhesion strength.

Interfacial morphology
Microscopic evidence of the peeled surfaces is of equal significance to illustrate the degree of interfacial adhesion achieved between film and substrate. Figure 12 shows the SEM interface morphology of IMD/IM and IMD/MIM parts However, for the interfaces of IMD/MIM parts, it can be observed obviously that the exfoliation almost occupies the given area with rarely smooth and flat space. The possible explanations would be that during the melt-filling stage of the IMD/MIM process, the internal cells turn over to the mold cavity to form bubble marks, and the molten film then fills the gap of the marks, thus forming a uniform bond of film and substrate. Nevertheless, the cells might play a similar role with the introduced oligomers [25] which could hinder interaction between longer molecular chains from the substrate with those at the film surface; thus strong, molecular linkages can be scarcely seen in the figure. Evidence can be found in the enlarged pictures that massive tiny voids exist in the exfoliations indicating that the cell itself could also be extracted from the polymer melt and then turned into the mold cavity. This phenomenon can be illustrated by the peeling curve in Fig. 11; the peel force of IMD/MIM parts varies much more tightly between every peak and bottom, whereas that of the IMD/IM parts presents a few sharp increments or deteriorations. Furthermore, it can be seen from the magnified micrographs that the interfaces of both IMD/IM parts and IMD/MIM parts show a gradual flatter or smoother morphology from interface A to interface C, indicating a slightly poorer interfacial adhesion. The closer location of the interface to the sprue corresponds to a more drastic peeling severity. This is a strong indication that interface temperature is the main factor that governs the extent of adhesion. These observations are in good correlation to the peel test results shown in Fig. 10 and Fig. 11. To quantitatively characterize the surface topography of the interfacial regions, the 2D and 3D surface profiles of the IMD/ IM parts and IMD/MIM parts on interfaces A, B, and C are presented in Fig. 13. The maximum and minimum polymer melt-film interface temperature and the interface roughness of the IMD/IM and IMD/MIM parts on interfaces of A, B, and C are given in Fig. 14. The maximum and minimum temperatures of polymer melt-film interface were extracted from the simulated results of temperature history in Fig. 7a. The arithmetic means roughness (Sa) and root mean square roughness (Sq) were used to characterize the surface roughness of the peeled film-substrate interface. Both Sa and Sq were calculated from the 3D optical profiler with a precision of 0.001 μm. It can be noticed that both the surface roughness of IMD/IM parts and IMD/MIM parts on interface A is larger than that on interfaces B and C, which is consistent with the surface morphology. There is also an obvious correspondence that higher interface temperature leads to a rougher peeling surface. Regions with higher temperatures possess more free molecules that can interact and form entanglements across the interface, thus causing stronger interfacial adhesion during peeling and manifesting larger interface roughness after peeling. Besides, the surface roughness of IMD/ MIM parts is higher than that of the IMD/IM parts. It is probably because the cells that migrate to the surface of the melt burst to create bubble marks, and the molten film penetrates wider to fill these marks, thus leading to a firmer interfacial bonding. Figure 15 shows the cellular morphology of the IMD/MIM part along the melt flow direction. It can be seen that large bubbles appeared in the core layer, while small bubbles  16 The IMD /IM parts and IMD/MIM parts formed in the transition layer at sections A, B, and C. The reason may be that the core layer temperature is higher than that in the transition layer causing a lower melt viscosity, which is beneficial to the bubble growth. The number of bubbles both in the core layer and transition layer at section C, which is farthest from the gate, was less than that at sections A and B. As the melt flow distance increased, the heat loss also increased, causing an increase in the melt viscosity. High melt viscosity would limit the growth of bubbles. As the decorative film reduces the heat transfer coefficient between the melt and the mold, the temperature on the film side drops slower than that on the non-film side during the melt-filling stage, which could provide a longer time for the bubble growth. Comparing the bubble morphology on the different sides at sections A, B, and C, the cell densities on the film sides are higher than the non-film sides. In addition, the cell distribution on the film sides is more uniform. It proves that IMD/MIM process can improve the cellular structure of foamed polymers. Figure 16 shows the appearance photograph of the IMD/ IM parts and IMD/MIM parts. It can be seen that the surface of IMD/MIM parts is smooth, while the surface of IMD / IM parts has obvious defects and melt flow marks. Owing to the PP film adhering to the polymer substrate by IMD/ MIM process, the surface quality of foamed polymer parts has improved.

Conclusion
The adhesion of PP film to the foamed PP composite was achieved by IMD/MIM process. The temperature field of the IMD/MIM process was numerically calculated based on a coupled heat transfer model. The established mathematical model by considering the coupled heat transfer between the polymer melt, film, and mold and the latent heat during the solidification of polymer melt can precisely predict the temperature field of the IMD/MIM process. The thermal response analysis and physical experiment results show that there is a good correspondence between temperature, crystallization, and interfacial adhesion. The higher temperature on the polymer melt-film interface corresponds to relatively higher crystallinity and larger crystallite size and also favors the forming of the β-form crystal. Crystallization has a crucial impact on adhesion strength, and larger grain damage during peeling can absorb more energy than amorphous structure leading to higher adhesion strength. Compared with the IMD/IM parts, the IMD/MIM parts can obtain a firmer film-substrate adhesion, and a uniformly strong bond between the film and the substrate was formed. This study provides theoretical support for the interface characteristics of other polymers and films.