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19 pages, 2671 KB  
Article
Effects of Two Tempering Treatments at Different Temperatures on Microstructure and Room/High-Temperature Wear Resistance of H13 Steel
by Weiwei Song, Yongbin Liu, Shan Tang, Mengyuan Dai and Zhijun Wu
Materials 2026, 19(12), 2585; https://doi.org/10.3390/ma19122585 - 16 Jun 2026
Viewed by 176
Abstract
As a typical Cr-Mo-V series hot work die steel, H13 steel is widely used in hot extrusion dies under harsh service conditions. Tempering is a vital post-quenching process for regulating microstructural evolution and comprehensive mechanical properties. Since relevant systematic comparative studies remain insufficient, [...] Read more.
As a typical Cr-Mo-V series hot work die steel, H13 steel is widely used in hot extrusion dies under harsh service conditions. Tempering is a vital post-quenching process for regulating microstructural evolution and comprehensive mechanical properties. Since relevant systematic comparative studies remain insufficient, industrial-grade H13 steel was adopted in this work. Specimens were quenched at 1000 °C, followed by single tempering at 520 °C and double tempering at 580 °C. Their microstructure, microhardness, and wear resistance at 25 °C and 580 °C were characterized, and the underlying mechanisms were analyzed. The results show that single tempering at 520 °C produces tempered martensite and finely dispersed carbides with secondary hardening behavior. Its microhardness reaches 590.83 HV, resulting in the best wear resistance at both room and high temperatures. Double tempering at 580 °C causes carbide coarsening, and the microhardness slightly declines to 580.60 HV. Although toughness is enhanced and residual stress is fully released, wear resistance deteriorates. This study optimizes the tempering parameters for H13 steel, provides technical support for die production, and offers theoretical guidance for the technical upgrading of the hot work die steel industry. Full article
(This article belongs to the Section Metals and Alloys)
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11 pages, 225 KB  
Review
Modelling Relationships Between Extrusion Conditions and Quality Attributes of Expanded Snacks
by Danyang Ying
Foods 2026, 15(12), 2118; https://doi.org/10.3390/foods15122118 - 12 Jun 2026
Viewed by 202
Abstract
Expanded snack extrusion is governed by tightly coupled interactions among raw material composition, moisture, barrel temperature, screw speed, feed rate, screw configuration, die geometry, and energy input. These variables affect not only final responses such as expansion ratio, bulk density, hardness, crispness, and [...] Read more.
Expanded snack extrusion is governed by tightly coupled interactions among raw material composition, moisture, barrel temperature, screw speed, feed rate, screw configuration, die geometry, and energy input. These variables affect not only final responses such as expansion ratio, bulk density, hardness, crispness, and water absorption or solubility indices, but also intermediate state variables including specific mechanical energy (SME), melt temperature, die pressure, melt viscosity, and bubble growth dynamics. As a result, modelling has become essential for product design, process optimisation, and scale-up. This review critically evaluates the major classes of models used to describe process–structure–quality relationships in the extrusion of expanded snacks. The literature shows that empirical regression and response surface methodology (RSM) remain the most widely applied tools because they are experimentally efficient and easy to interpret. However, mixture-process designs are more appropriate when formulation and operating variables are changed simultaneously, while phenomenological and mechanistic approaches provide better physical insight into expansion and structure development. More recently, machine-learning and interpretable artificial intelligence approaches have demonstrated strong predictive capability when large, well-curated datasets are available. Across model families, a consistent theme is that operating variables act on final product quality through intermediate process state variables rather than independently. On that basis, this review proposes a practical hybrid framework for expanded snack extrusion: a mixture-process quadratic model augmented with SME, die pressure, melt temperature and shear-related state variables, and structured in three levels linking (i) controllable inputs to state variables, (ii) state variables to measurable quality attributes, and (iii) quality attributes to a gold-standard product target or sensory-control criterion. Such a model offers a realistic balance between predictive performance, physical interpretability, experimental burden, and industrial usefulness, while also providing a clear pathway toward future digital twin and machine-learning-enabled optimisation. Full article
(This article belongs to the Section Food Engineering and Technology)
22 pages, 20141 KB  
Article
Influence of Process Parameters on the Forming Quality and Metal Flow Characteristics of the Billet During Hot Extrusion of an Automotive Luggage Rack
by Anna Cheng, Xuedao Shu, Dewei Zhang, Haijie Xu, Chang Shu, Khamis Essa and Zbigniew Pater
Metals 2026, 16(6), 637; https://doi.org/10.3390/met16060637 - 9 Jun 2026
Viewed by 205
Abstract
Automotive roof racks are important lightweight accessories for vehicles, and their extrusion performance is affected by the coupled effects of material hot deformation behavior, die flow resistance and billet surface layer transport. In this study, Al-0.9Mg-0.6Si alloy samples were subjected to hot compression [...] Read more.
Automotive roof racks are important lightweight accessories for vehicles, and their extrusion performance is affected by the coupled effects of material hot deformation behavior, die flow resistance and billet surface layer transport. In this study, Al-0.9Mg-0.6Si alloy samples were subjected to hot compression tests at 350–500 °C and strain rates of 0.01–10 s−1. The corrected true stress–true strain data were used to establish and validate an Arrhenius-type constitutive model, which was then implemented in HyperXtrude to simulate the hot extrusion of an automotive roof rack profile. The hot working map showed that the main rheological instability region was located at high strain rates, and the preferred processing window was 437–500 °C and 0.01–0.6 s−1. EBSD analysis showed that hot compression refined the microstructure relative to the initial average grain size of 173.147 μm, and the most uniform grain size distribution was obtained at 500 °C and 0.1 s−1. The ODF results indicated strengthened {111}<121> and <110>//TD texture components after compression. The finite-element results showed that the standard deviation of outlet velocity (SDV), used here as an index of outlet flow uniformity, increased with ram speed, billet preheating temperature and die preheating temperature, but decreased with increasing container temperature. Finally, grain size and texture measurements from butt discard samples were compared with simulated surface layer flow paths, supporting the predicted difference between simple axial flow and complex recirculating flow near the die. Full article
(This article belongs to the Special Issue Rolling and Forming of Alloys and Steels)
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31 pages, 10884 KB  
Article
Influence of Vibration-Assisted MIG Weld Cladding on the Reconditioning of Hot Extrusion Punches
by Mihai Alexandru Luca, Dorin-Ioan Catana, Dana Luca Motoc and Mircea Horia Tierean
J. Manuf. Mater. Process. 2026, 10(5), 173; https://doi.org/10.3390/jmmp10050173 - 14 May 2026
Viewed by 576
Abstract
Hot extrusion tools operate under severe thermal and mechanical conditions, which significantly limit their service life. During operation, the punch and die absorb large amounts of heat from the hot billet while being subjected to high pressures and intense friction, leading to severe [...] Read more.
Hot extrusion tools operate under severe thermal and mechanical conditions, which significantly limit their service life. During operation, the punch and die absorb large amounts of heat from the hot billet while being subjected to high pressures and intense friction, leading to severe abrasive wear and progressive hardness reduction. In practice, the punch generally exhibits a shorter service life than the die. The present study proposes a technological solution for reconditioning worn extrusion punches using vibration-assisted welding (VAW). A wear-resistant layer was deposited by MIG welding using DUR 600 filler material, while mechanical vibrations were introduced through a vibrating welding table. The applied vibration regime consisted of a frequency of 50 Hz–108 Hz and acceleration components of ax = 30–60 m/s2 and az = 35–70 m/s2. The experimental investigations included macroscopic analysis, hardness and microhardness measurements, microstructural observations, and SEM-EDS line scanning analysis of the dilution zone between the cladding material and the base metal. The results suggest that vibration-assisted welding may influence the microstructural characteristics, hardness distribution, and dilution behavior of the cladded layer. The vibrated specimens exhibited higher hardness values in the range of 702 to 908 HV5–10. Under the investigated conditions, the process did not require additional hardening treatment, and only a stress-relief annealing stage was applied. The proposed VAW approach appears to be a promising option for the reconditioning of hot extrusion tools; however, further investigations are required to validate its performance under industrial conditions. Full article
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22 pages, 839 KB  
Article
Numerical Investigation of Die Swell Behavior in EPDM Rubber Extrusion: Effects of Compound Formulation and Processing Conditions
by Yancai Sun, Haoran Wang, Jingtao Jiang, Kongshuo Wang, Wenjuan Bai, Dianming Chu, Ranran Jian, Peiwu Hou, Yan He and Wenzhong Deng
Polymers 2026, 18(9), 1122; https://doi.org/10.3390/polym18091122 - 1 May 2026
Viewed by 1251
Abstract
Die swell is the dominant source of dimensional deviation in rubber profile extrusion. Because it is driven by recoverable elastic strain, a purely viscous baseline flow field cannot reproduce its speed dependence; a viscoelastic correction is required. This study presents, to the best [...] Read more.
Die swell is the dominant source of dimensional deviation in rubber profile extrusion. Because it is driven by recoverable elastic strain, a purely viscous baseline flow field cannot reproduce its speed dependence; a viscoelastic correction is required. This study presents, to the best of our knowledge, the first controlled comparison of a Carreau–Arrhenius baseline flow field against a fractional-order viscoelastic correction for carbon-black-filled EPDM across an industrial speed window. The viscoelastic correction (PyCFD-FMM) is a post-processing fractional-order viscoelastic swell correction built on the shared non-isothermal Polyflow Carreau–Arrhenius flow field, derived from a six-mode fractional Maxwell model parameterized from dynamic mechanical analysis via the Laun rule and closed through the Tanner recoverable-strain theory. Three carbon-black-filled EPDM compounds (Shore A 60–80) were extruded at four screw speeds (15–30 rpm) under instrumented conditions. Experimentally, swell ratios of 1.12–1.15 increase monotonically with screw speed (Fisher-combined p=0.007; measurement repeatability CV 0.27% across n=4 replicates per condition). The purely viscous baseline output gives a decreasing apparent swell–speed trend—opposite to experiment—whereas PyCFD-FMM recovers the correct increasing trend for all compounds. Under single-anchor hold-out evaluation at 20/25/30 rpm, the non-anchor MAPE decreases from 0.99% for the baseline flow-field output to 0.30% (PyCFD-FMM); an anchor-sensitivity check over all four rpm choices keeps the compound-averaged non-anchor MAPE within 0.27–0.39% and preserves the correct slope sign in every case. Swell decomposition into geometric baseline and net correction factor (BPyCFD=Bgeom×fcorr) confirms that the viscous baseline flow field captures flow-geometry effects but carries no elastic memory. Within the tested window, the viscoelastic correction meets a dual-gate criterion—correct slope sign and reduced non-anchor MAPE—which the purely viscous baseline cannot satisfy by construction. Full article
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41 pages, 8196 KB  
Article
Process and Structure Modeling of Architected Thermoplastic Composites Using Shape Forming Elements
by Rebecca H. Olanrewaju, Yuefeng Jiang, Thao D. Nguyen and David O. Kazmer
Polymers 2026, 18(9), 1098; https://doi.org/10.3390/polym18091098 - 30 Apr 2026
Viewed by 409
Abstract
Architected polymer composites use spatially organized phases to achieve targeted property combinations. Shape forming elements (SFEs) are modular coextrusion die inserts that impose internal architectures by reshaping multiple melt streams. This study evaluates three SFE designs (Jacks, I-Beam, and Barn Door) that position [...] Read more.
Architected polymer composites use spatially organized phases to achieve targeted property combinations. Shape forming elements (SFEs) are modular coextrusion die inserts that impose internal architectures by reshaping multiple melt streams. This study evaluates three SFE designs (Jacks, I-Beam, and Barn Door) that position a liquid crystalline polymer (LCP) and an amorphous polyamide (APA) in distinct core–shell configurations. Polymer clay prototyping and ANSYS Polyflow simulations were used to screen flow behavior, followed by extrusion at two puller speeds and characterization via optical microscopy and tensile testing. Microscopy revealed that abrupt area transitions and viscosity contrast disrupt encapsulation and distort designed features. Regression analysis showed that LCP content governs stiffness and strength, while higher puller speed enhances reinforcement through molecular orientation. Cross sectional geometries were quantified using interfacial perimeter, moments of inertia, and polar dispersion ratios, and correlated to tensile performance. Increased interfacial length reduced modulus, strength, and ductility. Modulus improved with LCP orientation and confinement, strength increased when LCP was placed at vertical extremities, and elongation was maximized by horizontally distributing LCP within a thick APA shell. These results demonstrate that SFEs enable tunable tradeoffs between stiffness, strength, and ductility. Full article
(This article belongs to the Section Polymer Composites and Nanocomposites)
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28 pages, 46303 KB  
Article
Volumetric Control vs. Pneumatic Pressure: A Comparative Analysis of Extrusion in 3D Bioprinting
by Doru-Daniel Cristea, Eduard Liciu, Andreea Trifan and Corneliu Bălan
Micromachines 2026, 17(5), 521; https://doi.org/10.3390/mi17050521 - 24 Apr 2026
Viewed by 454
Abstract
Extrusion-based bioprinting faces significant challenges in achieving the shape fidelity and internal porosity necessary for cell viability, often hindered by subjective assessment methods. This study investigated the relationship between rheological properties and print quality using a natural polymer biomaterial ink composed of 12% [...] Read more.
Extrusion-based bioprinting faces significant challenges in achieving the shape fidelity and internal porosity necessary for cell viability, often hindered by subjective assessment methods. This study investigated the relationship between rheological properties and print quality using a natural polymer biomaterial ink composed of 12% gelatin, 5% alginate, and 1% carboxymethylcellulose. We conducted a comparative analysis between traditional pneumatic systems and screw-driven volumetric extrusion, utilizing a suite of quantitative metrics: Spreading Ratio (SR), Printability Index (Pr), Uniformity Ratio (UF), Collapse Angle (θ), and evaluated porosity. Our results demonstrate that the screw-driven system’s positive displacement mechanism provides superior control over filament morphology by enabling precise volumetric modulation. While the pneumatic system exhibited a high SR of 1.82 and the lowest porosity at 59.92%, the screw-driven system allowed for “under-extrusion” to compensate for viscoelastic die swell. Reducing the flow rate to 50% in the screw system lowered the SR to 1.09, nearly matching the nozzle diameter, and increased porosity to 76.46%. Furthermore, the screw-driven system achieved an ideal Pr of 1.0, whereas the pneumatic system produced distorted, rounded pores with a Pr of 1.57. The findings indicate that screw-driven extruders can decouple line complex rheology from the printing process, allowing for finer spatial resolution and better pore interconnectivity. Full article
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25 pages, 3443 KB  
Article
Rheology-Guided and CFD-Integrated Analysis of Non-Isothermal Gelation Kinetics in a Three-Stage Cooling Die for Soy Protein Concentrate Extrusion
by Timilehin Martins Oyinloye and Won Byong Yoon
Gels 2026, 12(4), 339; https://doi.org/10.3390/gels12040339 - 17 Apr 2026
Viewed by 382
Abstract
Soy protein concentrate (SPC) undergoes continuous thermal and structural changes during passage through a cooling die, yet these changes are often interpreted using viscosity-based descriptions that do not explicitly account for structural development rate (SDR). This study developed a rheology-guided framework to analyze [...] Read more.
Soy protein concentrate (SPC) undergoes continuous thermal and structural changes during passage through a cooling die, yet these changes are often interpreted using viscosity-based descriptions that do not explicitly account for structural development rate (SDR). This study developed a rheology-guided framework to analyze SPC behavior in a three-stage cooling die by integrating isothermal and non-isothermal rheological characterization with computational fluid dynamics (CFD). SPC samples containing 76, 78, and 80% moisture were evaluated using strain sweep, frequency sweep, viscosity, time sweep, and temperature sweep tests. Lower moisture promoted stronger structure development, higher viscosity, and faster gelation. For the 76% moisture sample, peak SDR increased from 6.66 Pa/s at 50 °C to 22.46 Pa/s at 100 °C, while the time to peak decreased from 937 to 360 s. During non-isothermal cooling, the major structure development occurred in the 80–50 °C interval, where ΔG′ reached 4902.54 Pa at 76% moisture. CFD analysis showed that the gelation-kinetics-based model predicted both pressure and extrudate temperature more accurately than the viscosity-based model. Pressure RMSE ranged from 8.57 to 14.43 kPa for the kinetic model, compared with 11.31 to 22.39 kPa for the viscosity model. These results demonstrate that the three-stage cooling die should be interpreted as a coupled thermal, flow, and structure-development domain. Full article
(This article belongs to the Special Issue Design, Fabrication, and Applications of Food Composite Gels)
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24 pages, 4530 KB  
Article
Granulate-to-Filament: An Extrusion-Mixed PLA–Human Bone Material System for 3D-Printed Bone Scaffolds
by Jonas Neijhoft, Hela Weslati, Volker Eras, Jan Brune, Maximilian Leiblein, Santiago Bianconi, Nicolas Söhling, Lewin Busse, René Verboket, Johannes Frank, Ingo Marzi and Dirk Henrich
J. Funct. Biomater. 2026, 17(4), 187; https://doi.org/10.3390/jfb17040187 - 11 Apr 2026
Viewed by 811
Abstract
Fused filament fabrication (FFF) enables patient-specific scaffolds for critical-size bone defects, but most filaments are bioinert and difficult to functionalize at high particulate loadings due to segregation, agglomeration, clogging, and diameter instability. We developed a mechanism-guided extrusion toolkit to stabilize polylactic acid (PLA) [...] Read more.
Fused filament fabrication (FFF) enables patient-specific scaffolds for critical-size bone defects, but most filaments are bioinert and difficult to functionalize at high particulate loadings due to segregation, agglomeration, clogging, and diameter instability. We developed a mechanism-guided extrusion toolkit to stabilize polylactic acid (PLA) filaments containing human demineralized bone matrix (DBM) or cortical granulate (CG) up to 70 wt%. PLA was ground, dried, silicone pre-coated, and compounded with DBM or CG (25/40/70 wt%) using starve-fed extrusion, sequential extrusion, and post-die mixing to maintain stable diameters. FFF produced disks and tubes. MSC adhesion was assessed by SEM. qPCR (control vs. osteogenic medium) quantified RUNX2, ALP, BGLAP, COL1A, VEGF, IL-6, MAPK8. Tubes underwent three-point bending. The toolkit yielded printable, dimensionally stable filaments at 25–70 wt% with uniform dispersion and surface-exposed filler. Both composites increased early mesenchymal stromal cells (MSC) adhesion versus PLA. RUNX2 was increased on DBM40 versus PLA. VEGF was elevated on CG25 (DBM40 trend). Under osteogenic medium, IL-6 and MAPK8 were generally reduced. Mechanics were loading-dependent: CG25 exceeded CG70 and DBM25, while DBM40/70 recovered stiffness versus DBM25. A mechanism-guided extrusion toolkit enables high-loading PLA–DBM/CG filaments with excellent printability and material-specific biological and mechanical advantages over PLA. Full article
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15 pages, 2607 KB  
Article
Aluminum Extrusion Simulation Using Finite Elements
by Dimitrios Skarvelakis and Georgios E. Stavroulakis
Eng 2026, 7(3), 138; https://doi.org/10.3390/eng7030138 - 19 Mar 2026
Viewed by 1406
Abstract
The complexity of an extrusion die profile is determined by its geometry. Various metrics such as the complexity index, shape factor, and form factor are used to quantify how geometric intricacy affects production costs, die life, energy consumption, product quality, and overall manufacturability. [...] Read more.
The complexity of an extrusion die profile is determined by its geometry. Various metrics such as the complexity index, shape factor, and form factor are used to quantify how geometric intricacy affects production costs, die life, energy consumption, product quality, and overall manufacturability. Bearing geometry plays a critical role in controlling metal flow and tool life in aluminum extrusion. In this study, a simulation-based investigation is performed to investigate the influence of bearing geometry on extrusion behavior using the finite element method. Two extrusion dies are examined: A single-cavity die with uniform bearing geometry and a dual-cavity die with controlled bearing geometry modification in one cavity. The results show that the bearing modification in the dual-cavity die causes severe flow imbalance, with exit velocity deviations. This imbalance leads to localized pressure amplification, increased thermal gradients, and stress concentration in critical die regions. In contrast, the single-cavity die, due to its simple geometry, exhibits uniform flow, stable pressure evolution, and low tool stress. These findings demonstrate the high sensitivity of multi-cavity extrusion dies to bearing geometry and highlight the importance of simulation-driven die design for achieving balanced flow and improved tool performance. Full article
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17 pages, 5694 KB  
Article
Rheology for Wood Plastic Composite Extrusion Part 2: Process Simulation and Experimental Verification
by Krzysztof J. Wilczyński, Kamila Buziak, Andrzej Nastaj, Adrian Lewandowski and Krzysztof Wilczyński
Polymers 2026, 18(6), 744; https://doi.org/10.3390/polym18060744 - 19 Mar 2026
Cited by 1 | Viewed by 949
Abstract
Rheological data of wood plastic composites (WPCs) are not readily present in many of the common scientific databases. For this reason, designing the processing of WPCs, e.g., extrusion, is difficult or even impossible, and it is often necessary to conduct research on your [...] Read more.
Rheological data of wood plastic composites (WPCs) are not readily present in many of the common scientific databases. For this reason, designing the processing of WPCs, e.g., extrusion, is difficult or even impossible, and it is often necessary to conduct research on your own to obtain the proper data. In the first part of the paper, studies of WPCs’ rheology have been performed in laboratory and production conditions. Tests in laboratory conditions have been conducted based on High-Pressure Capillary Rheometry (HPCR), using the Melt Flow Index (MFI). Tests in production conditions (on-line) have been performed by measuring the extrusion die pressure and extrusion throughput. The MFI’s viscosity and on-line viscosity results have been assessed against those of HPCR. In the second part of the paper, the viscosity data and models have been used for extrusion process simulations. Experimental studies of the process have been performed, and the experimental results have been used for evaluating the models applied. It was found that the two-point MFI method of determining viscosity and the on-line tests may be a reasonable alternative in the absence of HPCR data. The MFI method using the power-law model is fast and easy to apply and allows for analytical solutions to many processing problems. A significant advantage of on-line tests is that they are performed under real flow conditions of the tested material rather than laboratory conditions that do not take into account the material processing history. Full article
(This article belongs to the Special Issue Advances in Wood and Wood Polymer Composites)
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22 pages, 3926 KB  
Article
Computational Design of Fat Marbling Formation in Plant-Based Meat: Coupled CFD and Image Analysis of Oil Transport During Co-Extrusion
by Timilehin Martins Oyinloye and Won Byong Yoon
Appl. Sci. 2026, 16(6), 2704; https://doi.org/10.3390/app16062704 - 12 Mar 2026
Cited by 1 | Viewed by 445
Abstract
This study developed and evaluated an integrated experimental–computational framework to quantify coconut-oil transport and marbling stabilization in soy protein concentrate (SPC) during static holding and co-extrusion with a cooling die. Temperature-sweep rheology and Differential Scanning Calorimetry (DSC) identified the main gelation transition at [...] Read more.
This study developed and evaluated an integrated experimental–computational framework to quantify coconut-oil transport and marbling stabilization in soy protein concentrate (SPC) during static holding and co-extrusion with a cooling die. Temperature-sweep rheology and Differential Scanning Calorimetry (DSC) identified the main gelation transition at 65–78 °C, with oil shifting gelation to higher temperatures and increasing enthalpy, supporting an exit/cooling target of 70–75 °C. Static drop tests at 100 °C for 60 s were analyzed by depth-resolved imaging and coupled with a single-phase CFD model to inversely calibrate an effective diffusion coefficient for coconut oil in SPC (Dref = 4.86 × 10−18 m2/s). A viscosity-coupled fractional Stokes–Einstein relationship then gave temperature-dependent effective diffusivities of 1.89 × 10−18 to 4.86 × 10−18 m2/s over 60–100 °C, indicating reduced oil mobility during cooling. Additional static time-temperature comparisons suggested limited redistribution beyond ~50 s. Co-extrusion simulations and product imaging further indicated that staged hot-zone residence followed by rapid cooling can help stabilize oil domains into marbling-like structures. The framework can support selection of cooling-die temperatures, residence times, and oil-injection conditions. Future work should extend the framework by linking marbling microstructure with sensory performance, oxidative stability, and sensitivity analysis of key transport parameters. Full article
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14 pages, 1716 KB  
Article
Anisotropic Extrudate Swell from a Slit Die: A Velocity-Centre Hypothesis and Numerical Verification
by Guangdong Zhang, Xinyu Hao and Linzhen Zhou
Polymers 2026, 18(5), 652; https://doi.org/10.3390/polym18050652 - 7 Mar 2026
Viewed by 532
Abstract
While anisotropic extrudate swell in polymer processing is fundamentally driven by physical viscoelastic recovery, this paper proposes a theoretical framework to explicitly isolate and map the purely geometric and kinematic components of this phenomenon. Serving as a mathematical proof-of-concept, a multi-velocity-centre hypothesis is [...] Read more.
While anisotropic extrudate swell in polymer processing is fundamentally driven by physical viscoelastic recovery, this paper proposes a theoretical framework to explicitly isolate and map the purely geometric and kinematic components of this phenomenon. Serving as a mathematical proof-of-concept, a multi-velocity-centre hypothesis is proposed. By introducing a semi-empirical, lumped material-flow calibration parameter, the macroscopic diameter swell ratio is mathematically extended to the discrete local flow field of a rectangular slit die. To evaluate its validity, the analytical framework is subjected to a numerical test for kinematic consistency utilizing isothermal, inelastic power-law fluid CFD simulations, thereby separating geometric mapping from complex viscoelastic stress relaxation. Results indicate that analytical predictions show good agreement with CFD data (error < 5%) strictly within the core zone of high-aspect-ratio dies. However, due to the infinite-slit assumption, 3D flow kinematics near die edges induce velocity decay, leading to local deviations that require future empirical corrections. Although comprehensive physical extrusion experiments and non-isothermal viscoelastic coupling are required for industrial deployment, this semi-empirical kinematic mapping provides a foundational mathematical basis that could potentially inform future inverse die-profile design and shape distortion compensation. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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14 pages, 4425 KB  
Article
A Numerical Study on Optimization of Shape and Dimensions for Cold-Extruded Blank of Copper Pin-Type Heat Dissipation Substrates
by Wei Wei, Fakai Chen, Jingbo Gao, Yong Xu, Tengfei Zhang and Wenlong Xie
Materials 2026, 19(5), 962; https://doi.org/10.3390/ma19050962 - 2 Mar 2026
Viewed by 497
Abstract
The thermal dissipation performance of the radiator is crucial for the stable operation of power electronic devices. Due to excellent thermal performance, copper pin-type heat sink substrates are widely adopted. However, the cold extrusion process for heat sink substrates suffers from low material [...] Read more.
The thermal dissipation performance of the radiator is crucial for the stable operation of power electronic devices. Due to excellent thermal performance, copper pin-type heat sink substrates are widely adopted. However, the cold extrusion process for heat sink substrates suffers from low material utilization and high forming loads. To improve material utilization and reduce cold extrusion forming load, four blank shapes (rectangular, trapezoidal, trapezoidal cap, and stepped) were designed using finite-element simulation to investigate the effects of blank shape and placement method with orientation relative to the die cavity on forming quality. Further dimensional optimization was conducted to determine the optimal configuration. The results show that the stepped blank with front orientation exhibits the optimal forming performance, featuring the lowest forming load and the most sufficient pin-fin filling. Compared with back orientation, front orientation achieves higher and more uniform material flow velocity, and significantly reduces forming load. Through dimension optimization, the 7 mm-thick stepped blank is determined as the optimal solution, with the forming load reduced to 15,000 kN (a 35.3% decrease compared to the initial 7.5 mm stepped blank), and both the substrate thickness and pin-fin height meet the design requirements (4.5 mm and 6.5 mm). Experiments verify the feasibility of the optimized scheme, providing technical support for the low-cost, high-quality mass production of copper pin-type heat sink substrates. Full article
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35 pages, 6853 KB  
Article
Experimental and Numerical Investigation of Liquid Nitrogen Die Cooling for Increased Efficiency in Porthole Aluminum Extrusion Dies
by Evangelos Giarmas, Ioannis Theodoridis, Panagiotis Tounis, Tommaso Pinter and Dimitrios Tzetzis
Appl. Sci. 2026, 16(5), 2385; https://doi.org/10.3390/app16052385 - 28 Feb 2026
Viewed by 495
Abstract
Die design plays a critical role in achieving high-quality aluminum extrusion products with optimal efficiency. Porthole dies are widely employed to produce hollow profiles for diverse industrial applications, yet their design parameters significantly influence surface quality, geometry, and productivity. In this study, a [...] Read more.
Die design plays a critical role in achieving high-quality aluminum extrusion products with optimal efficiency. Porthole dies are widely employed to produce hollow profiles for diverse industrial applications, yet their design parameters significantly influence surface quality, geometry, and productivity. In this study, a two-hole porthole die was investigated using both numerical and experimental approaches. The 6060 aluminum alloy (produced in the foundry of Alumil SA, Kilkis, Greece) was selected as the material of focus. Finite Element Analysis was conducted with HyperXtrude™ 2022 software, while experimental trials were performed on a 35 MN extrusion press. To further enhance productivity, a liquid nitrogen cooling system was integrated into the process. The combined numerical and experimental results demonstrated that the redesigned die and the integration of liquid nitrogen cooling significantly improved process performance. Productivity increased by 8.76%, with ram speed rising from 6.8 mm/s to 9.5 mm/s while maintaining dimensional accuracy and stable extrusion conditions. Full article
(This article belongs to the Special Issue Advanced Finite Element Method and Its Applications, Second Edition)
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