Rheological Behavior and Processing of High-Performance Engineering Polymers

1. Introduction

The recent developments in the field of rheological analysis and high-performance processing of polymers have led to enhanced design and application of these materials in different engineering applications. PEEK-based nanocomposites have been developed for high-efficiency electromagnetic wave absorption over a wide temperature range, demonstrating their potential for advanced functional and high-performance engineering applications [1]. Polyaryletherketone (PAEK) materials have been developed and are now being used in additive manufacturing with higher thermal resistance and mechanical strength that are appropriate for advanced manufacturing techniques [2]. The concept of compatibilization is essential for improving the mechanical, morphological and rheological properties of polyethylene/polypropylene blends modified by maleic anhydride-grafted polyethylene in a number of studies [3]. In the same way, polyamide 6 containing cellulose nanocomposites are a material with improved mechanical properties and processability on the industrial scale for melt processing [4]. Rheological and dynamic mechanical properties of polymers in fused deposition modeling have been studied to gain insights in the printing quality and adhesion between layers [5]. For industrial uses, some rigid-chain polymers like aromatic polyamides are the subject of research, as they possess superior strength and thermal stability [6].

Moreover, PEEK exhibits excellent mechanical strength, adhesive performance, and biocompatibility, making it suitable for high-performance engineering and biomedical applications [7]. The influence of Fused Deposition Modeling (FDM) 3D printing parameters on the mechanical properties and microstructure of Carbon Fiber (CF)/PEEK and Glass Fiber (GF)/PEEK composites was investigated, showing that processing conditions significantly affect strength and structural performance of printed thermoplastic composites [8]. The study of Ultra-High Molecular Weight Polyethylene (UHMWPE) fiber formation by the gel-spinning method has yielded a greater understanding of polymer physics and processing mechanisms [9]. Recent studies have demonstrated that material extrusion-based 3D printing techniques can be modified to successfully manufacture functional gradient PEEK components with improved structural performance and process adaptability [10]. Furthermore, grafting and long-chain branching of the polyamide 6 have improved the crystallization, foaming and mechanical properties of the material [11]. The incorporation of ceramic fillers in polymer composites has now enhanced the thermal conductivity and rheological properties, in particular for thermal interface materials [12]. At the same time, sustainable and high performance materials have become more interesting by the use of bio-based and functional additives. The use of materials derived from lignin as alternatives for plastics has increased interest in this material, and it has been identified as a potential material for the additive manufacturing industry for sustainable material development [13].

Although considerable advances have been made in the area of rheological modelling, polymer blending and high-performance composite processing, there are still some challenges with the current methods, including incomplete linkage between rheology and processing behaviour, inability to accurately predict under industrial conditions and limited integration of simulation with experimental validation. Most studies concentrate on property enhancement and not on a material–process–performance relationship, thus reducing confidence in their reliability in actual manufacturing situations. The proposed framework addresses these gaps with a comprehensive characterization of the rheological properties, modelling at different temperatures, and CAD–FEA based process simulation for realistic prediction of polymer behaviour. This study is different from traditional approaches as it creates a coupled approach between material properties, flow behavior and process parameters in a single predictive approach. The novelty is the integration of advanced rheological models, injection molding simulation and structural analysis of PEEK parts. This allows for optimization of the processing parameters with mechanical and thermal reliability. The proposed approach offers a comprehensive and scalable high-performance polymer design approach for industrial applications.

1.1. Organization of Paper

The rest of this paper is organized as follows:

• ✓ The related works in polymer rheology and high-performance engineering materials is presented in Section 2.
• ✓ The research gaps explored in this study are presented in section 3.
• ✓ Section 4 describes the proposed methodology such as material selection, rheological modeling, processing simulation and FEA.
• ✓ The results and discussions are presented in Section 5, which includes the rheological behavior, thermal–mechanical properties, and results of simulations.
• ✓ Section 6 concludes the study and discusses future research directions for improving polymer processing and performance.

2. Related Works

Gul et al., [14] developed thermally conductive PEEK composites using twin-screw extrusion, rheological analysis, thermal characterization, and conductivity measurements; however, the study is limited by high filler loading complexity and lack of scalability validation in diverse manufacturing conditions. Rodzén et al., [15] studied PEKK crystallization in Fused Filament Fabrication (FFF) using temperature control and kinetics analysis; however, limited by lack of scalability and parameter optimization. Sabet et al., [16] analyzed composite and nanocomposite polymers using advanced manufacturing processes like polymerization, additive manufacturing and mechanical/thermal characterization, but the study has some limitations in terms of scalability and lack of long-term testing. Jiang et al., [17] developed Polybutylene Adipate Terephthalate (PBAT)/ Thermoplastic Starch (TPS) biodegradable composites using a two-step blending process with Epoxidized Soybean Oil (ESO) compatibilization, characterized by Fourier Transform Infrared Spectroscopy (FT-IR), Gel Permeation Chromatography (GPC), and mechanical testing; however, the study is limited by cost concerns and lack of long-term biodegradation analysis.

Xiong et al., [18] developed mathematical prediction models using DSC and tensile analysis to study crystallization and mechanical properties of PEEK/CF–PEEK; however, limited by model accuracy constraints and lack of complex processing condition validation. Maloney et al., [19] reviewed FFF processing of PEEK and PEKK focusing on process–structure–property relationships without a specific predictive model; however, limited by lack of experimental validation and insufficient analysis of PEKK processing behavior. Lucio et al., [20] studied polyurethane curing kinetics by rotational viscometry, dynamic rheometry and kinetic modeling (first-order, autocatalytic, isoconversional); but practical industrial processing validation and scalability analysis are not studied. Lee et al., [21] developed a set of Conjugated Polymer (CP)-based ones with supramolecular/photochemical crosslinking and thermal–mechanical characterization, which still lacks in large-scale recycling validation and long-term performance assessment.

Gavande et al., [22] manufactured a polymer blend of UHMWPE, also with melt blending, rheological study and mechanical/thermal characterization, but with limited mechanical/elongation properties and without large-scale processing validation. Li et al., [23] investigated the effect of hot compression molding parameters on PEEK using experimental analysis without a predictive model; however, limited by lack of advanced modeling and real-time process optimization. Herzog et al., [24] established analytical surrogate models to simulate the melt conveying in single-screw extrusion, but the approximations assumptions made in the study and the resulting approximate accuracy limit the applicability under the very complex real industrial conditions. Baniasadi et al., [25] developed biobased Polyamide–Functionalized Graphene Oxide (PA–FGO) nanocomposites using in situ polymerization, rheological testing, and mechanical/electrical characterization; however, the study is limited by low filler concentration range and lack of large-scale processing validation.

The previous studies showed remarkable advances in polymer composites, rheological analysis, nanocomposites, biodegradable materials, and simulation of processing by the methods of extrusion, in-situ polymerization, rheometry, thermal analysis, and numerical simulation. Most of the existing ones are, however, limited by their high processing complexity, limited optimization of the filler, limited industrial-scale validation, inadequate long-term performance analysis, and reduced accuracy of simplified models or experiments-only models under actual processing conditions. The proposed work will address these challenges by combining detailed rheological characterization, selection of optimized processing parameters and advanced simulation-based analysis using CAD and FEA software tools. This hybrid method allows for a precise material characterization, increases scalability and enables a reliable performance evaluation in realistic injection molding conditions for high-performance engineering polymers.

3. Problem Statement

High-performance semicrystalline polymers during 3D printing showed strong dependency on crystallization control, but lacked consistent control strategies across PEKK and PEEK grades, leading to unstable mechanical performance and limited process repeatability in additive manufacturing applications [15]. Prediction of crystallinity and mechanical behavior under non-isothermal molding was addressed, but existing models were limited by accuracy constraints under varying cooling rates and lacked robustness for complex reprocessing conditions in CF/PEEK systems [18]. Process–structure–property relationships in FFF-based PEKK and PEEK were explored, but insufficient quantitative modeling and limited processing window optimization restricted their applicability for reliable industrial-scale additive manufacturing [19]. Mechanical behavior of PEEK plates under different hot compression molding conditions was analyzed, but the study lacked predictive simulation integration and did not fully capture multi-parameter interactions affecting final material performance [23].

The suggested approach overcomes these challenges by combining rheological characterization, process simulation based on CAD models, and multiphysics analysis performed by FEA, to provide realistic prediction of the behavior of the material in the actual processing conditions. This experimental–computational strategy helps to achieve a heightened degree of scalability, accuracy of the model, and reliable performance prediction of high performance engineering polymers in industrial applications.

3.1. Objectives

• Investigate the rheological behavior and processing characteristics of PEEK for high-performance aircraft bearing applications to understand its flow and deformation behavior under industrial conditions.
• Utilize PEEK as the selected material for aircraft bearing systems, considering its superior thermal stability, mechanical strength, and suitability for high-load engineering applications.
• Evaluate the material through systematic Material Characterization, Rheological Testing, and Rheological Model Fitting to determine its thermal properties, flow behavior, and predictive rheological parameters.
• Simulate the complete manufacturing process using Injection Molding Simulation, CAD-based PEEK bearing modeling, and FEA to analyze flow behavior, structural integrity, and thermo-mechanical performance.

4. Proposed Methodology

The proposed methodology is a systematic approach to analyse the rheological behavior and processing performance of high-performance engineering polymers, applied to the processing of aircraft bearing application, with PEEK. PEEK is first chosen for its excellent thermal, mechanical and chemical properties for use in the aerospace industry, and then processed in a controlled material preparation process that includes hot air oven drying to eliminate moisture and avoid defects during molding. Then material characterization is conducted to assess various thermal properties (Tg, Tm, stability), mechanical strength, density and crystallinity, to ensure suitability for high-performance applications. Rheological testing then takes place via use of rotational and capillary rheometers to study viscosity, shear stress, and viscoelastic properties under various conditions. The experimental results are also fitted to the Power Law, Cross and Carreau–Yasuda equations in order to accurately model the flow behavior. Injection molding simulation is performed to predict the melt flow, filling behavior, pressure and temperature distribution under given injection molding conditions. A detailed CAD model of the PEEK bearing is created and coupled with simulation to study the flow patterns, filling time and defect formation. Finally, FEA is used to assess the structural, thermal and thermo-mechanical performance, such as stress distribution, deformation and temperature variation, to get a comprehensive understanding of the material behavior and to ensure the optimal design and processing conditions. Figure 1 shows the proposed methodology framework.

4.1. Material Selection

High-performance thermoplastics are chosen due to their excellent mechanical, thermal and chemical characteristics, which support difficult engineering tasks. Of these, PEEK is selected for its outstanding performance properties. PEEK is a semi-crystalline high performance engineering polymer that has high thermal stability, good mechanical properties and resistance to chemical and wear degradation.

These are the key features that have led to the choice of PEEK:

• Good thermal stability at high temperature
• Excellent mechanical strength and stiffness
• Excellent wear and chemical resistance
• Suitability for aerospace applications such as aircraft bearing components

The properties make PEEK very attractive for use in aerospace application being favoured for aircraft bearing and other components. Additionally, its high-temperature resistance and load-bearing capacity guarantee its reliability and durability in industrial settings.

4.2. Material Preparation

Pre-processing of polymer before manufacturing is known as material preparation. This is primarily involves removing moisture and impurities to avoid defects in the production process, which occurs at high temperatures. Figure 2 shows the material preparation process of PEEK using a hot air oven drying.

The first step is to gather the PEEK pellets in their raw state, which can have moisture absorbed by the ambient air. This is eliminated by putting the pellets in a hot air oven and drying them under controlled conditions for 4 hours at 150°C. In the oven, heated air is constantly circulated around the pellets to help distribute heat evenly and to help the moisture evaporate. The higher the temperature, the more moisture is absorbed by the PEEK pellets and is thus removed from the product. This process guarantees the complete drying of the polymer giving defect-free material for further processing. The water removal is important to prevent defects like voids, bubbles and thermal degradation in the subsequent injection molding process, improving the overall material stability and product quality.

4.3. Material Characterization

Material characterization is the process of systematically identifying the thermal, mechanical and physical properties of a material to gain understanding of its behavior under various conditions. This step ensures that the material selected is suitable in terms of performance parameters for processing and use.

4.3.1. Thermal Analysis

The thermal properties of the PEEK material is investigated using the Differential Scanning Calorimetry (DSC) and the Thermogravimetric Analysis (TGA). The glass transition temperature (Tg) and melting temperature (Tm) are used to determine thermal transitions of the polymer and used DSC method. TGA is employed to assess the thermal stability by monitoring the material’s weight loss against temperature, which will indicate the degradation behavior at high temperatures.

4.3.2. Mechanical Properties

The mechanical characterization is performed to evaluate the strength and stiffness of the material. The tensile strength is determined to find the maximum amount of stress that a material can resist before failing, and the elastic modulus is determined to understand the resistance of the material to the applied load.

4.3.3. Physical Properties

Physical characterization includes determining the density of the material, which gives information about the compactness and mass distribution. The density is an important factor in the structural performance and efficiency of materials.

4.3.4. Crystallinity Analysis

This is done by the crystallinity analysis to assess the extent of ordered molecular structure in the polymer. The crystallinity will depend greatly on the degree of crystallinity, which is determined by applying the following Eqn (1):

$$X_c={\displaystyle \frac{\mathsf{\Delta }{H}_m}{\mathsf{\Delta }{H}_m^0}}\times 100$$

(1)

In this equation, $X_c$ is the degree of crystallinity, $\mathsf{\Delta }{H}_m$ is the measured melting enthalpy, $\mathsf{\Delta }{H}_m^0$ is the theoretical melting enthalpy. This analysis provides critical insight into the structure–property relationship of the material.

4.4. Rheological Testing

This is conducted to measure the shearing and deformation characteristics of the molten PEEK material. The rheological measurements are carried out in a rotational and capillary rheometers that can be used to analyze the flow properties of polymer melts across the entire range of shear rates. PEEK material is heated to its melting point or above so it will be fully molten before it is tested.

Flow Behavior Analysis: The primary rheological parameters measured include viscosity (η) and shear stress as a function of shear rate. These parameters provide insight into the resistance of the material to flow under applied forces. The variation of viscosity with shear rate is analyzed to determine the shear-thinning behavior of the polymer melt, which is a critical factor in processing performance.

Frequency Sweep Analysis: Tests are performed to assess the material’s viscoelastic properties under oscillatory conditions. The analysis can be used to understand the material response in terms of storage modulus and loss modulus over frequencies, and give further information on molecular dynamics and structural stability during deformation.

4.5. Rheological Model Fitting

Rheological model fitting is a way to obtain a mathematical model of the experimentally obtained flow behavior and enable the description of the viscosity–shear rate relationship of the polymer melt. By doing so, it is possible to predict the material response when subjected to various processing parameters. The models which are widely used are the Power Law model, the Cross model and Carreau–Yasuda model.

1. Power Law Model:

Describe the non-Newtonian (shear-thinning or shear-thickening) flow behavior of polymer melts. It explains how the viscosity of a material changes with respect to the applied shear rate during flow. This law is defined as Eqn (2):

$$\eta =K{\dot{\gamma }}^{n-1}$$

(2)

Here $\eta$ denotes viscosity, $\dot{\gamma }$ denotes shear rate, $K$ denotes consistency index, $n$ denotes flow behavior index.

2. Cross Model:

The Cross Model is one of the advanced rheological models which is used to describe the viscosity curve of polymer melt in a wide range of shear rates, including low shear and high shear regions. It reflects a transition between the Newtonian region at low shear rates and shear-thinning region at high shear rates. This model is represented in Eqn (3):

$$\eta ={\displaystyle \frac{{\eta }_0}{1+(k\dot{\gamma }{)}^m}}$$

(3)

Where ${\eta }_0$ indicates zero-shear viscosity, $\left(k\dot{\gamma }\right)$ indicates dimensionless term, $m$ indicates dimensionless flow parameter.

3. Carreau–Yasuda Model:

Explain the complete flow behaviour of polymer melts in the low, intermediate and high shear regions. It is more accurate than simpler models because it models Newtonian and shear-thinning behavior. This is represented in Eqn (4):

$$\eta ={\eta }_{\mathrm{\infty }}+\left({\eta }_0-{\eta }_{\mathrm{\infty }}\right)/{\left[1+(\lambda \dot{\gamma }{)}^a\right]}^{{\displaystyle \frac{n-1}{a}}}$$

(4)

In this equation, ${\eta }_{\mathrm{\infty }}$ represents infinite-shear viscosity, $\lambda \dot{\gamma }$ represents dimensionless parameter, $a$ represents yasuda parameter, $n$ denotes flow behavior index, ${\displaystyle \frac{n-1}{a}}$ represents controls slope of shear-thinning region.

4.6. Injection Molding Simulation

It is a numerical study of molten polymer behavior during a melting process inside a mold used to predict the polymer processing responses and to optimize the processing parameters before the polymer production. The choice of processing method for the PEEK material is injection moulding, as suitable for high-performance parts. The main parameters of processing are determined: melt temperature 360-400°C, mold temperature 160-200°C and injection pressure. All of these parameters have a significant impact on flow behavior, filling time and final part quality. To accurately describe the molten polymer flow during injection molding, the generalized momentum conservation Navier–Stokes equation for incompressible non-Newtonian flow is used in Eqn (5):

$$\rho \left({\displaystyle \frac{\partial \mathrm{v}}{\partial t}}+\mathrm{v}\cdot \nabla \mathrm{v}\right)=-\nabla p+\nabla \cdot \tau +\mathrm{F}$$

(5)

Here $\rho$ is the density of molten polymer, $\mathrm{v}$ is the velocity vector of flow, t is the time, p is the pressure inside mold cavity, $\tau$ is the shear stress tensor, $\mathrm{F}$ is the body force. The simulation analyzes melt flow progression, filling patterns, pressure distribution, and temperature variation during injection. These results help in optimizing processing conditions, preventing defects such as air traps and incomplete filling, and ensuring uniform mold filling with improved part quality and process efficiency.

4.7. PEEK Bearing CAD Modeling

The process includes the development of accurate 3D geometric model of the bearing part in order to simulate and analyse the material flow and the behaviour during injection molding. This step allows the accurate visualization and prediction of the behavior of the molten polymer in the mold cavity. Figure 3 shows the CAD-based injection molding simulation workflow.

The first step in the PEEK bearing CAD modeling process is to develop a detailed three dimensional geometric model of the aircraft bearing part using the proper CAD software, with all of the critical dimensions, shapes and design features correctly defined. Following this, the material properties of PEEK such as its rheological and thermal properties are assigned to the model to achieve realistic simulated behavior of the material and to accurately represent the flow of the molten polymer in the mould cavity. The developed model is then divided into finite elements by using a meshing process, and finer mesh is used in the areas that are important for the simulation to increase the accuracy of the simulation. This is followed by melt flow simulation to study the behavior of the molten PEEK flow through the mold to gain insight into the flow and distribution pattern of the material. From this simulation, the filling time needed to fill the entire cavity of the mold is calculated, an important step in optimizing production time. Further, pressure distribution analysis is performed to understand the pressure distribution inside the mold that can help to find the high-pressure zone of the mold and the possible defects. Lastly, the temperature distribution during the flow and cooling phases are studied to ensure uniform solidification and eliminate various thermal defects which increase the quality and reliability of the final product.

4.8. FEA

FEA is a numerical simulation method to analyze the structural and thermal properties of a component by breaking it up into smaller elements and solving the governing physical equations. Based on the CAD geometry, a finite element model of the PEEK bearing component is built. The model is broken down into small elements and suitable boundary conditions like loads, temperature and constraints are added to the model to mimic practical operating conditions.

1. Structural Analysis

The mechanical performance of the bearing is assessed using structural analysis when loads are applied. The stress distribution within the component is calculated using Eqn (6):

$$\sigma ={\displaystyle \frac{F}{A}}$$

(6)

Here $\sigma$ indicates stress, $F$ indicates applied force, $A$ indicates cross-sectional area. The equivalent stress is often represented using the Von Mises criterion, this is defined in Eqn (7):

$${\sigma }_v=\sqrt{{\displaystyle \frac{{\left({\sigma }_1-{\sigma }_2\right)}^2+{\left({\sigma }_2-{\sigma }_3\right)}^2+{\left({\sigma }_3-{\sigma }_1\right)}^2}{2}}}$$

(7)

In this equation, ${\sigma }_v$ is the von Mises stress, ${\sigma }_1,{\sigma }_2,{\sigma }_3$ are the principal stresses.

2. Thermal Analysis

This is done to check the temperature distribution in the component under operation. Fourier’s law is used to characterize the behavior of heat transfer, which is represented in Eqn (8):

$$\mathrm{q}=-k\nabla T$$

(8)

Where $q$ is the heat flux vector, $k$ is the thermal conductivity, $\nabla T$ is the temperature gradient.

3. Thermo-Mechanical Analysis

It combines structural and thermal effects to analyse material behaviour under multiple thermal and mechanical loading. Thermal expansion is considered using Eqn (9):

$$\sigma =E(ϵ-\alpha \Delta T)$$

(9)

Here $\sigma$ denotes stress, $E$ denotes young’s modulus, $ϵ$ denotes total strain, $\alpha \Delta T$ denotes thermal strain component. This is a comprehensive deformation, stress and failure analysis performed by combining the two analyses.

5. Experimental Setup

Establishes the organized sequence, equipment, parameters, and procedures to run simulations or experiments to analyze them. This includes establishing testing conditions, choosing test equipment, establishing parameters, and conducting simulations or experiments to obtain reliable results.

5.1. System Configuration

The hardware and software environment that is used to run simulations, modeling and analysis in the study is referred to as system configuration. The detailed hardware and software specifications used for the realization of the computational and simulation tasks are presented in Table 1. The MATLAB toolboxes and functions used for simulation, model fitting, statistical validation and visualization are summarized in Table 2.

5.2. Performance Evaluation Metrics

Evaluate the overall performance and quality of the material and process through the evaluation of the results of the rheological, thermal, mechanical, processing and simulation tests.

5.2.1. Rheological Metrics

Rheological metrics are used to characterize the flow characteristics of polymer melts by examining the relationship between the shear stress, shear rate, and viscosity during processing conditions.

➢

Viscosity (η): The resistance of a material to flow, that is, how easily the molten polymer flows during the injection molding process. Where $\eta$ is the viscosity, $A\mathrm{e}\mathrm{x}\mathrm{p}$ is the pre-exponential function, $E$ is the activation energy for flow, $RT$ is the temperature effect.

➢

Shear thinning index (n): Represents the change in viscosity of a material with shear rate and aids classification of the flow behaviour of a polymer melt. This is expressed in Eqn (10):

$$n={\displaystyle \frac{d\mathrm{l}\mathrm{n}\tau }{d\mathrm{l}\mathrm{n}\dot{\gamma }}}$$

(10)

Here $n$ indicates flow behavior index, $\tau$ indicates shear stress, $\dot{\gamma }$ indicates shear rate, $d\mathrm{l}\mathrm{n}$ indicates log scale.

5.2.2. Thermal Metrics

Analyse the temperature dependent behaviour of polymers through transitions, melting and degradation properties in relation to the thermal loading.

➢

Glass transition temperature (Tg): Temperatures at which the polymer transitions from a rigid glassy state to a flexible rubbery state as measured by change in heat capacity from DSC. This is denoted in Eqn (11):

$$T_g={\displaystyle \frac{d{C}_p}{dQ}}$$

(11)

Where $T_g$ denotes glass transition temperature, $d{C}_p$ denotes heat capacity of the material, $dQ$ denotes heat flow supplied to the material.

➢

Melting temperature (Tm): Temperature at which the crystalline part of the polymer is melted (as detected by the maximum heat flow during DSC). This is defined in Eqn (12):

$$T_m=\mathrm{Temperature}\mathrm{at}\mathrm{peak}\left({\displaystyle \frac{dQ}{dt}}\right)$$

(12)

Here $T_m$ indicates melting temperature, $Q$ indicates heat flow, $t$ indicates time, ${\displaystyle \frac{dQ}{dt}}$ indicates rate of heat flow.

➢

Thermal degradation temperature (Td): Temperatures at which polymer begins to decompose, determined from TGA analysis peak of maximum mass loss coefficient. It is represented in Eqn (13):

$$T_d=\mathrm{Temperature}\mathrm{at}\mathrm{m}\mathrm{a}\mathrm{x}\left({\displaystyle \frac{dm}{dt}}\right)$$

(13)

Where $T_d$ is the thermal degradation temperature, $m$ is the mass of the material, ${\displaystyle \frac{dm}{dt}}$ is the rate of mass loss.

5.2.3. Mechanical Metrics

Evaluate the strength and stiffness of materials by analyzing their response to applied forces and deformation.

➢

Tensile strength: A material’s strength is the maximum stress that it can endure (without failing) when it is being stressed. This is expressed in Eqn (14):

$${\sigma }_u={\displaystyle \frac{F_{\mathrm{m}\mathrm{a}\mathrm{x}}}{A_0}}$$

(14)

Here ${\sigma }_u$ indicates ultimate tensile strength, $F_{\mathrm{m}\mathrm{a}\mathrm{x}}$ indicates maximum applied force before fracture, $A_0$ indicates original cross-sectional area.

➢

Elastic modulus: Elastic modulus is a measure of the stiffness of material, which is resistance to elastic deformation when subjected to stress. This is expressed in Eqn (15):

$$E={\displaystyle \frac{d\sigma }{dϵ}}$$

(15)

In this equation $E$ is the elastic modulus, ${\displaystyle \frac{d\sigma }{dϵ}}$ is the slope of stress–strain curve.

5.2.4. Processing Metrics

Analyze parameters which control the mold filling, pressure and manufacturing efficiency during polymer manufacturing to evaluate flow behavior and manufacturing performance.

➢

Melt flow index (MFI): Refers to the ease with which the molten polymer flows under normal conditions. This is represented in Eqn (16):

$$\mathrm{M}\mathrm{F}\mathrm{I}={\displaystyle \frac{600\times m}{t}}$$

(16)

Where $m$ is the mass of extruded polymer, $t$ is time,$600$ is conversion factor (10 min = 600 s).

➢

Filling time: The time taken to fill the mold cavity with molten polymer. This is defined in Eqn (17):

$$t_f={\displaystyle \frac{L}{v}}$$

(17)

In this equation, $t_f$ denotes filling time, $L$ denotes flow length, $v$ denotes flow velocity.

➢

Injection pressure: Calculates the moulding force for producing the moulded polymer. This is expressed in Eqn (18):

$$P={\displaystyle \frac{12\eta LQ}{h^{3}W}}$$

(18)

Here $P$ indicates injection pressure, $Q$ indicates volumetric flow rate, $h$ indicates channel thickness, $w$ indicates channel width.

5.2.5. FEA Metrics

Use FEA to analyse a component’s response to simulated loading and operating conditions to assess its structural, thermal and deformation behaviour.

➢

Von Mises stress: Equivalent stress that can be used to predict yielding of material under complex loading. This is expressed in Eqn (19):

$${\sigma }_v=\sqrt{3.J_2}$$

(19)

Where ${\sigma }_v$ denotes Von Mises stress, $J_2$ denotes Second invariant of deviatoric stress tensor.

➢

Total deformation: Describes how much the component is displaced when a load is applied. This is represented in Eqn (20):

$$\delta ={\displaystyle \frac{FL}{AE}}$$

(20)

Here $\delta$ represents deformation, $F$ represents applied force, $L$ represents original length, $A$ represents cross-sectional area, $E$ represents Young’s modulus.

➢

Temperature distribution: Describes the change of temperature in the component with time. This is defined in Eqn (21):

$${\displaystyle \frac{\partial T}{\partial t}}=\alpha {\nabla }^{2}T$$

(21)

Where ${\displaystyle \frac{\partial T}{\partial t}}$ denotes rate of change of temperature with respect to time, $\alpha$ denotes thermal diffusivity, ${\nabla }^{2}T$ denotes the laplacian of temperature.

1.3. Results

The results show that PEEK has a high degree of thermal stability, mechanical strength and shear-thinning properties which are appropriate for high performance applications. The validation of flow behavior under processing conditions by the rheological analysis and model fitting is accurate. The efficient mold filling, uniform pressure distribution and optimized design performance are demonstrated with injection molding and CAD simulations. Finally, FEA and statistical validation ensures reliability, minimal deformation and high accuracy even for practical engineering applications.

5.3.1. Material Preparation Results

Pre-processing in this section includes heating the PEEK material to remove absorbed moisture prior to further processing. It guarantees process stability, free of defects like voids, bubbles and degradation at high temperature processing.

The drying process parameters of PEEK are displayed in Table 3, which displays the controlled thermal conditions to which PEEK needs to be subjected to remove moisture before processing. The findings have confirmed that the drying treatment process can successfully decrease moisture content from 0.120% to 0.00099%, the moisture-free polymer is helpful for high quality manufacturing application.

The moisture-free PEEK material that is poured after drying occurs is modeled as a 3D solid geometry, as seen in Figure 4. The uniform structure ensures defect-free material for further processing, due to the successful moisture removal. This is a validation of the efficiency of material drying in enhancing the quality and stability of the materials.

5.3.2. Material Characterization Results

This section is to evaluate systematically the thermal, mechanical and physical properties of the selected polymer in order to understand its behavior under processing and service conditions. It offers fundamental input parameters like transition temperatures, strength parameters and properties of structure needed for simulating and analyzing their performance correctly.

As can be seen in Table 4, PEEK has high thermal stability, making it an ideal material for use at high temperatures. The results demonstrate the ability of PEEK to retain structural integrity, which is enabled by its high melting and degradation temperatures.

The material properties and geometric dimensions of the PEEK specimen for analysis are exhibited in the detailed Table 5. The values reflect high mechanical properties and heat stability, suitable for structural and high-performance engineering applications.

The DSC curve of PEEK (Figure 5 (a)) depicts the glass transitions and melting characteristics and the melting temperature (Tm) is clearly visible as the endothermic peak. This confirms that the material is of semi-crystalline nature and its thermal transition properties. The thermal stability of PEEK is demonstrated in Figure 5 (b) by the lack of weight loss to high temperatures, followed by an accelerated loss of weight. This means that the material has a high thermal resistance and is suitable for use in high-temperature applications. Figure 5 (c) shows the DSC curve of PEEK highlighting its glass transition at 143 °C, cold crystallization at 185 °C, and sharp melting peak at 343 °C.

5.3.3. Rheological Testing Results

Explain the assessment of the deformation and flow behaviour of PEEK, relating to its viscoelastic properties (storage modulus, loss modulus, viscosity and shear response). This analysis enables to understand the material’s flow behavior and processability in conditions such as injection molding.

The rheological properties of PEEK are given in Table 6, with the storage modulus indicating the elastic properties of the material and the loss modulus indicating the viscous properties. The results show a balanced viscoelastic behavior, which is indicative of the good energy storage and dissipation properties under deformation.

As seen in Figure 6 (a), the viscosity curve has a downward trend for PEEK at different temperatures, which means that PEEK is shear thinning at these temperatures. This means that the polymer melt has enhanced flowability during processing at high shear rates. The non-Newtonian flow behavior of PEEK is demonstrated in Figure 6 (b) of the shear stress vs shear rate curve, with a linear increase. This means that a higher shear rate would result in more stress for the processing, as this is significant for control.

5.3.4. Rheological Model Fitting Results

The section compares the shear rate–viscosity relationship for the experimental data with the predictions of various constitutive models. It is useful for the identification of the most important model that describes the non-linear flow behaviour of the polymer melt under various processing conditions.

The experimental values and several models, such as Power Law, Cross, Carreau–Yasuda, were compared over a wide shear rate range as shown in Figure 7. The Carreau–Yasuda model is able to give a close prediction of the polymer flow behavior as compared to the experimental data and shows higher accuracy in predicting the non-linear viscosity variation.

Figure 8 shows the flow behavior index values for different models, which are less than 1, confirming the shear-thinning nature of PEEK. The consistency between the models indicates stable rheological behavior and reliable prediction of processing performance.

5.3.5. Injection Molding Simulation Results

Modeling melt flow, filling and pressure distribution in the cavity to determine the suitability of the material for efficient and defect-free processing.

In the mold cavity, the flow front and filling time distribution are displayed in Figure 9 (a) and it represents the filling process of the molten PEEK. The uniform gradient shows the efficient and complete filling behavior. The pressure contour distribution throughout the mold is shown in Figure 9 (b) which reveals the areas of high and low injection pressure. This is useful for determining the critical zones and optimizing the processing conditions to prevent defects.

5.3.6. CAD Modeling Results

Describes the geometric representation and meshed structure of the PEEK bearing to provide accurate material flow, stress distribution and thermal simulation.

Figure 10 displays the 3D CAD model of an aerospace bearing made of PEEK, which has a cylindrical shape with two surfaces labeled F2 and F6 for orientation and analysis purposes. The coordinate axes are used to give the spatial reference for the simulation, which is important to represent the flow and the stress distribution. Based on this model, it is used as the basis of injection molding and FEA to assess structural and thermal performance.

The finite element mesh structure of PEEK material is shown in Figure 11, the block is divided into elements to make it possible to simulate the stress and thermal behavior. The colour scale shows the variation of a physical property (such as stress or strain) from cell to cell in the mesh. This visualisation is used as a basis for the correct FEA of PEEK parts in practical operating conditions.

5.3.7. FEA Results

Evaluates the structural, thermal and thermo-mechanical response of the PEEK bearing to determine stress distribution, deformation and the temperature change in its operation.

Figure 12 (a) presents the Von Mises stress distribution throughout the component, with red indicating the areas of maximum stress concentration, and blue indicating the areas of minimum stress. The total deformation contour is shown in Figure 12 (b), with red areas corresponding to high deformation and blue areas to low deformation. The temperature distribution contour in Figure 12 (c) depicts the variation of temperature within the structure, ranging from cooler blue areas to warmer yellow areas.

The combined thermal and mechanical stresses are displayed in Figure 13 (a) with red areas representing high stresses and blue areas representing low stresses of the bearing. Figure 13 (b) illustrates the shape of the deformation of the bearings when under load, the red areas indicating maximum bending, and the blue areas indicating minimal deformation.

5.3.8. Statistical Validation

The statistical validation assesses the accuracy and reliability of the predicted results by comparing the predicted results with the expected results, based on error metrics and correlation measures.

Table 7 shows the statistical analysis of stress and deformation, the mean value represents the overall performance and the deviation from the mean value represents the variation of the results. The low RMSE and MAE values confirm high prediction accuracy of the model. Strong correlation and excellent model reliability are shown with high R2 values (0.97).

5.4. Discussion

The results have shown that the proposed framework was able to capture the rheological behavior, thermal stability, and mechanical performance of PEEK that are suitable for its application in high performance engineering fields. Moisture free condition for material preparation stage, which would definitely improve the quality of processing, and avoid defects. Thermal and mechanical characterization were also performed and shows that PEEK has high stability and strength, thus suitable for an application as a bearing in the aerospace sector. The Carreau–Yasuda model is used to accurately predict the non-linear flow properties, with strong shear thinning behavior as revealed by rheological testing and model fitting, which leads to reliable processing insights. Injection molding simulation reveals uniform flow and optimized pressure distribution, which show the efficient molding of the mold and the reduction of the formation of defects. CAD modelling and FEA results give an understanding of structural integrity and where stress, deformation and temperature distributions are within acceptable limits ensuring the reliability of the component being used under operational conditions. Last but not least, the statistical validation, indicated by high R² values and low error measures, ensures the accuracy and robustness of the proposed approach.

These existing studies (Gul et al., [14] and Herzog et al., [24]) show that the thermal conductivity of the material has been enhanced and the thermo-mechanical behavior predicted with good accuracy by using extrusion-based processing and surrogate modeling techniques, but with high processing complexity and limited validation in real manufacturing scenarios. In contrast, the proposed framework incorporates advanced experimental characterization, experimental rheological modeling, injection molding simulation, CAD-based design and FEA analysis into a single streamline approach that subsequently allows for better prediction of flow, structure, and thermal properties. This is a combination of two things which makes the system more reliable, reduces the number of processing defects and also gives a complete solution with a scalable model for practical industrial applications, outperforming the limitations found in the existing works.

5.4.1. Limitation

• Limited experimental validation under practical industrial manufacturing conditions
• Computationally dependent for simulation, which results in more time and resources needed

6. Conclusion

This study successfully investigates the rheological behavior and processing characteristics of PEEK for high-performance aircraft bearing applications through a novel integrated experimental-computational framework. The proposed methodology uniquely combines four key components—material characterization, rheological testing with multi-model fitting, injection molding simulation, and multiphysics FEA—into a coupled predictive approach that bridges the critical gap between laboratory-scale material analysis and industrial-scale processing optimization.

The major findings and novel contributions of this work are summarized as follows:

• Comprehensive material characterization confirmed PEEK’s exceptional thermal stability (Tg = 143 °C, Tm = 343 °C, Td = 575 °C) and mechanical strength (tensile strength = 95 MPa, elastic modulus = 3.60 GPa), validating its suitability for demanding aerospace bearing applications.
• Rheological testing revealed pronounced shear-thinning behavior, with viscosity decreasing significantly with increasing shear rate across all tested temperatures, demonstrating enhanced processability under high-shear injection molding conditions.
• Comparative rheological model fitting established the Carreau-Yasuda model as the most accurate predictor of PEEK’s non-linear flow behavior (R² = 0.97), outperforming Power Law and Cross models, providing a robust mathematical foundation for processing simulation.
• The key novelty of this work—the integrated rheology-simulation framework—enabled accurate prediction of mold filling behavior, pressure distribution, and temperature profiles during injection molding, with simulation results confirming homogeneous flow patterns and optimized processing conditions.
• Multiphysics FEA incorporating thermo-mechanical coupling (σ = E(ε - αΔT)) provided comprehensive assessment of bearing performance under operational loads, with von Mises stress analysis and deformation patterns remaining within acceptable limits for aerospace applications.
• Rigorous statistical validation confirmed the reliability of the proposed framework, with low error metrics (RMSE: 0.6854 MPa for stress, 0.003220 mm for deformation; MAE: 0.4850 MPa for stress, 0.002037 mm for deformation) and high correlation coefficients (R² = 0.97), demonstrating excellent predictive accuracy.

The significant novelty of this work compared to existing literature lies in: (a) the seamless integration of experimental rheological characterization with advanced multiphysics simulation, creating a truly coupled material-process-performance prediction platform; (b) the application of comprehensive model comparison to identify the optimal rheological model for PEEK under injection molding conditions; (c) the thermo-mechanical coupling in FEA that captures the combined effects of thermal expansion and mechanical loading on bearing performance; and (d) the quantitative statistical validation that establishes the framework’s reliability and transferability to other high-performance polymer systems.

The proposed framework has practical implications in industrial manufacture, including less trial-and-error in tuning processing parameters, higher manufacture efficiencies due to fewer defects through prediction of possible defects, improved part quality and reliability for aerospace applications; the approach can be expanded for other high-performance polymers or with complex geometries.

6.1. Future Work

While this study establishes a robust foundation for integrated polymer processing analysis, several promising directions for future research emerge:

• Advanced Material Development: Investigate PEEK-based hybrid polymers and nanocomposites incorporating functional fillers (e.g., carbon nanotubes, graphene, hexagonal boron nitride) to enhance thermal conductivity, mechanical strength, and multifunctional performance for next-generation aerospace applications.
• Artificial Intelligence Integration: Introduce AI/ML based predictive models (on neural networks or support vector regression (SVR)) for accelerated rheological parameter prediction, on-line processing condition optimisation and reduced computation cost of multiphysics simulations.
• Process Optimization: The developed framework can further be extended in optimising injection moulding parameters (melt temperature, mould temperature, injection pressure and cooling rate) to multiple industrial applications for the products such as automotive, biomedical and electronic components, apart from bearings.
• Multi-Material Systems: Expand the methodology to multi-material and functionally graded PEEK components, addressing the growing demand for tailored property distributions in advanced engineering structures.
• Long-Term Performance Assessment: Integrate fatigue analysis, creep behavior and environmental degradations such as moisture absorption, UV exposure and chemical resistance into FEA simulation for long-term durability and service life prediction of PEEK components under actual operating conditions.
• Experimental Validation Under Industrial Conditions: Conducting detailed experimental trials with actual manufacturing conditions to further validate the predictive capabilities of the proposed framework and make it robust for industrial use.
• Sustainability Integration: Consider environmentally-responsible PEEK processing routes: recycling, bio-based precursors, and less energy-demanding manufacture. Meet sustainability goals while maintaining high-performance characteristics.

In summary, this work delivers a comprehensive, validated, and industrially relevant framework for high-performance polymer processing, significantly advancing the state-of-the-art in integrated experimental-computational materials engineering. The demonstrated methodology produces immediate benefits for the manufacture of PEEK bearings and could be translated as a platform for application across other advanced polymer processing challenges and designs.