# Modeling of a Process Window for Tailored Reinforcements in Overmolding Processes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. A Model for the Transverse Flow of Composite Inserts

## 3. Constitutive Equations for Squeeze Flow of Two Layered Power-Law Fluids

## 4. Solution and Model Validation

#### 4.1. Resulting Solution and Dimensionless Numbers of the Model

_{1}, π

_{2}, and π

_{3}in Equations (8)–(10).

_{1}, in Equation (8) is the ratio of the actual layer heights, representing a key design parameter for the part design. The second dimensionless number, π

_{2}, in Equation (9) is the ratio of the consistency index ratios, representing a key design parameter for the material selection. The third dimensionless number, π

_{3}, in Equation (10) incorporates global parameters, such as the overall dimensions of the setup and the closing speed as a processing parameter.

#### 4.2. Model Validation—Flow Fields

#### 4.3. Effect of Newtonian and Non-Newtonian Layer Combinations

## 5. Implications for the Application of Tailored Reinforcement Inserts

#### 5.1. Flow Behavior of Pseudo-Plastic Inserts

_{1}and the pressure gradient indicate that the flow is similar to the single-layer flow of the insert. The velocity profile remains entirely within the layer height, and the resistance corresponds to the insert’s single-layer flow resistance. The overmolding layer interacts with the shear layer of the insert and is solely dragged, as shown by the lower pressure gradient compared to a single-layer setup.

#### 5.2. Processing Window Resutling from Part and Material Designs

#### 5.3. Model-Based Optimization of Process and Part Design

#### 5.4. Comparison to Applications and Experimental Results

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 1.**A schematic representation of a squeeze flow setup consisting of two circular-shaped adjacent fluid layers with different flow properties and heights between two moving rigid plates.

**Figure 2.**A schematic representation of a radial velocity profile for two adjacent fluid layers with their representative layer heights and coordinate systems.

**Figure 3.**Dimensionless radial velocity by the dimensionless position in z for fluid layer 1 and fluid layer 2 with the line of symmetry for both flow fields for two different consistency index ratios.

**Figure 4.**Ratio of the radii of two pseudo-plastic and two Newtonian fluid layers as a ratio of their consistency indices.

**Figure 5.**The height change of the two fluid layers scaled by their height change in a single-layer setup as a ratio of their consistency indices with the indication of three flow zones.

**Figure 6.**Pressure gradient of the two fluid layers scaled by their pressure gradient in a single layer setup (

**top**) and their representative height scaled by the total height (

**bottom**) as a ratio of their consistency indices with the indication of three flow zones.

**Figure 7.**Ratio of the radii for the combination of a pseudo-plastic and a Newtonian fluid layer at different height ratios as a ratio of their consistency indices with the indication of three flow zones and a process window.

**Figure 8.**Schematic representation of an overmolding setup with an overmolding layer and an insert, where the insert consists of a molten and a solidified layer.

**Figure 9.**Schematic representation of an overmolding setup with an overmolding layer and an insert, where part of the insert height is covered by a tool.

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**MDPI and ACS Style**

Picard, P.K.W.; Osswald, T.A.; Zaremba, S.; Drechsler, K.
Modeling of a Process Window for Tailored Reinforcements in Overmolding Processes. *J. Compos. Sci.* **2024**, *8*, 65.
https://doi.org/10.3390/jcs8020065

**AMA Style**

Picard PKW, Osswald TA, Zaremba S, Drechsler K.
Modeling of a Process Window for Tailored Reinforcements in Overmolding Processes. *Journal of Composites Science*. 2024; 8(2):65.
https://doi.org/10.3390/jcs8020065

**Chicago/Turabian Style**

Picard, Philipp K. W., Tim A. Osswald, Swen Zaremba, and Klaus Drechsler.
2024. "Modeling of a Process Window for Tailored Reinforcements in Overmolding Processes" *Journal of Composites Science* 8, no. 2: 65.
https://doi.org/10.3390/jcs8020065