Keywords

1 Introduction

The demand for microstructures continues to grow. It needs to improve the manufacturing process for fabricating the microcomponents at lower cost and with short production time. Hot embossing (HE) is a conventional and mature process for manufacturing small-scale devices on a large scale. Poly(methyl methacrylate) (PMMA) and polycarbonate (PC) are mainly used as processing materials in HE [1].

Cheng et al. [2] have developed a micro-scale HE process using an innovative injection-molding press and an instrumented mold for a PMMA plate to produce microfluidic systems slightly above the glass transition temperature (\({T}_{g}\)). Wang et al. [3] optimized various parameters in HE processing and obtained a filling accurately and efficiently. Kasztelanic et al. [4] employed the HE process to develop the optical devices. Their work was aimed at optimizing the process to eliminate product defects. Deshmukh et al. [5] employed the simulation to analyze the replication accuracy of micro-structured components by optimizing HE processing parameters. Worgull et al. [6] employed Moldflow to simulate mold filling and applied ANSYS to modeling demolding to reduce defect in the replicated micro-structured components obtained by the HE process.

A large number of experimental tests have been carried out to analyze the behavior of amorphous thermoplastic polymers and to identify their properties within the forming range applied. Cheng et al. [7] employed thermo-mechanical compression tests to identify by inverse strategy the properties of polymers with various physical constitutive behavior models. The behavior law described by the two-layer viscoplastic (TLVP) model dedicated to viscoelastic behavior is composed of elastoplastic and viscoelastic branches and was employed for the forming simulation process by Charkaluk et al. [8]. Abdel-Wahab et al. [9] investigated the plastic, elastic, and viscous properties with the same TLVP model. The PMMA material parameters were identified by an inverse method based on various thermo-mechanical experiment tests.

In this paper, the HE process for producing microchannels in PMMA and PC was investigated numerically with the TLVP model. Thermo-mechanical compression tests were carried out to identify material behavior parameters for the selected polymers. HE simulation was carried out to determine the influence of material parameters on mold filling efficiency.

2 Description of HE Process and TLVP Model

2.1 Description of HE Process

HE process is one of the polymer replication processes for elaborating the microstructures for the production runs of microcomponents in small and medium series [10]. Figure 1 shows the steps of the HE process to elaborate micro-scale components (molding, cooling, demolding). The process involves pressing a polymer plate into a structural mold, the tooling of which is regulated to a temperature higher than \({T}_{g}\) of the material used. Holding time and pressure were required to allow the polymer to fill all the structures in the mold. Once the mold and plate have been cooled, the replicated structural plate is removed from the mold, as it has sufficient rigidity to be recovered [11].

Fig. 1
figure 1

Schematic picture of the HE technique

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The main advantage of HE is the possibility to manufacture devices with various patterns thanks to its easy operation, high accuracy, mass production, short cycle time, and cost-effective. The HE is employed to produce different geometries in microscales such as circular patterns; threadlike lines and hexagonal shapes [12]. HE process can be used to replicate the geometries from simple (triangular, rectangular with shape repetition…) to complex shapes (microfluidic, MEMS…).

2.2 Description of TLVP Model

It was used to describe the behaviors of elastic viscoplastic in the range of forming temperatures used in the embossing process. It considers the elastic, plastic, and viscous deformations of the polymeric material, as shown in Fig. 2. It has already been implemented in the Abaqus® finite element software. All the parameters have been identified by the inverse method based on the experimental database of thermocompression tests, to provide the behavior of PMMA and PC.

Fig. 2
figure 2

One-dimensional idealization of the TLVP model [13]

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The total modulus is calculated as K = Kp + Kv, where \({K}_{p}\) and \({K}_{v}\) are the elastic modulus of the elastoplastic and the elastic modulus of the viscoelastic, respectively. The proportion of elasticity in the viscoelastic relative to total elasticity f is expressed by the following relationship:

$$f=\frac{K-{K}_{p}}{K}$$
(1)

The total stress \(\sigma \) is obtained by the addition of the viscous stress \({\sigma }_{v}\) and stress \({\sigma }_{p}\) expressed by the following relationship:

$$\sigma ={\sigma }_{p}+{\sigma }_{v}$$
(2)

The elastic strain \({\varepsilon }^{el}\) is divided into a viscoelastic part \({\varepsilon }_{v}^{el}\) and elastoplastic part \({\varepsilon }_{p}^{el}\):

$${\varepsilon }^{el}=f{\varepsilon }_{v}^{el}+(1-f){\varepsilon }_{p}^{el}$$
(3)

The total strain \(\varepsilon \) contains the elastic \({\varepsilon }^{el}\), plastic strains \({\varepsilon }^{pl}\) and the viscous strain \({\varepsilon }^{v}\) which is expressed by the following relationship:

$$\varepsilon ={\varepsilon }^{el}+f{\varepsilon }^{v}+(1-f){\varepsilon }^{pl}$$
(4)

3 Results of Experimental Characterization Tests

Uniaxial thermo-mechanical compression tests were carried out to identify the material parameters of the viscoplastic constitutive behavior by using the inverse method and the method of least squares. The plastic parameters of the polymers are identified from stress–strain curves at two testing temperatures for PMMA and PC polymers. All the obtained plastic parameters are summarized in Table 1.

Table 1 Set of values for the parameters identified for the two materials studied
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The value of the parameter \(f\) is determined using Eq. (1). The parameters identified for the materials studied in the elastic–viscoplastic model are summarized in Table 2.

Table 2 TLVP model parameters at Tg + 20 °C
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4 Results of Numerical Simulation

The aim of the study is to optimize the efficiency of cavity filling during the HE process. Two-dimensional axisymmetric geometric representing the compression of the polymer plate in the structural mold is employed in the simulation of forming process, see Fig. 3. Elastic, elastoplastic, and elastic–viscoplastic behaviors are considered with the TVLP model in the simulation. It was carried out with different parameters identified in Tables 1 and 2 at two temperatures with different imposed displacements (0.07, 0.12, and 0.17 mm). Numerical simulation was carried out for both polymers (PMMA, PC) in order to determine the von Mises stresses as well as to study the influences of the material properties on the mold filling rate.

Fig. 3
figure 3

Description of the 2D model studied

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4.1 Results and Discussions of Mold Filling Ratio for PC and PMMA

The simulation results for PC of the HE process at Tg + 20 °C in terms of mold filling rate are shown in Fig. 4. The filling rate increases with the imposed displacement of the mold. The mold is 95% filled with the elastic–viscoplastic behavior applied on the polymer substrate. This indicates that viscous behavior plays a very important role in filling the micro-cavity during shaping.

Fig. 4
figure 4

Evolution of cavity filling ratio during simulation as a function of imposed displacements and constitutive behaviors for PC

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Filling of the mold with the combination of PC’s elastic, plastic, and viscous properties at Tg + 20 °C is studied by numerical simulation during the HE process, see Fig. 5. The value of von Mises stress is homogeneous with different imposed displacements. As a conclusion, the cavity-filling ratio increased with the imposed displacement. When the maximal imposed displacement of 0.17 mm is performed, the simulation result shows that the micro-cavity was almost completely filled. Based on the filling simulation results obtained at the same imposed displacement (0.17 mm), the case of elastic–viscoplastic behavior generates the higher filling ratio than that of elastic behavior.

Fig. 5
figure 5

Von Mises stress for PC during HE process with TLVP model at Tg + 20 °C versus imposed displacements: a 0.07, b 0.12, and c 0.17

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This result demonstrates that the micro-cavity was almost completely filled when the elastic, plastic, and viscous behaviors were considered with the TVLP model during the simulation of the HE process in the micro-scale.

The simulation results for PMMA with the elastic and elastic–viscoplastic behaviors of the HE process at Tg + 20 °C in terms of mold filling rate are shown in Table 3. The cavity filling ratio increased with the imposed displacement and the elastic–viscoplastic behavior generated an increase in the filling ratio compared to the elastic proprieties.

Table 3 Evolution of cavity filling ratio during simulation with different imposed displacements and constitutive behavior laws for PMMA
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4.2 Effect of Temperature on Mold Filling Ratio for PC

The cavity filling ratio of PC substrate is investigated with various embossing temperatures to analyze its effect on the filling rate, shown in Fig. 6. It shows a comparison of filling rate as a function of temperature and imposed displacement, taking into account elastic–viscoplastic properties. The filling ratio increases slightly with temperature during the shaping of micro-structured component.

Fig. 6
figure 6

Effect of temperature on cavity filling ratio versus different imposed displacements for PC with elastic–viscoplastic behavior

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5 Conclusions

The aim of this current work was to study the influence of behavior laws on the filling efficiency for the shaping of PMMA and PC by using the HE process at micro-scale. The TLVP model was employed to model the elasto-viscoplastic property.

The elastic, plastic, and viscous parameters were identified using the inverse method, based on the evolution of the true stress–strain curves obtained from the results of uniaxial thermal mechanical compression at different temperatures.

A filling rate of 99% was obtained taking into account the elasto-viscoplastic property, which means that the viscous property of PMMA influences the filling rate. For the PC, the polymer substrate is better filled with higher temperatures in the HE process.