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Keywords = automatic fiber placement

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17 pages, 13381 KiB  
Article
Vacuum Chamber Infusion for Fiber-Reinforced Composites
by Benjamin Grisin, Stefan Carosella and Peter Middendorf
Polymers 2024, 16(19), 2763; https://doi.org/10.3390/polym16192763 - 30 Sep 2024
Cited by 2 | Viewed by 2223
Abstract
A new approach to an automatable fiber impregnation and consolidation process for the manufacturing of fiber-reinforced composite parts is presented in this article. Therefore, a vacuum chamber sealing machine classically used in food packaging is modified for this approach—Vacuum Chamber Infusion (VCI). Dry [...] Read more.
A new approach to an automatable fiber impregnation and consolidation process for the manufacturing of fiber-reinforced composite parts is presented in this article. Therefore, a vacuum chamber sealing machine classically used in food packaging is modified for this approach—Vacuum Chamber Infusion (VCI). Dry fiber placement (DFP) preforms, made from 30 k carbon fiber tape, with different layer amounts and fiber orientations, are infused with the VCI and with the state-of-the-art process—Vacuum Assisted Process (VAP)—as the reference. VCI uses a closed system that is evacuated once, while VAP uses a permanently evacuated open system. Since process management greatly influences material properties, the mechanical properties, void content, and fiber volume fraction (FVF) are analyzed. In addition, the study aims to identify how the complexity of a resin infusion process can be reduced, the automation potential can be increased, and the number of consumables can be reduced. Comparable material characteristics and a reduction in consumables, setup complexity, and manufacturing time by a factor of four could be approved for VCI. A void content of less than 2% is measured for both processes and an FVF of 39% for VCI and 45% for VAP is achieved. Full article
(This article belongs to the Special Issue Manufacturing of Polymer-Matrix Composites)
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28 pages, 3366 KiB  
Review
Towpreg—An Advanced Composite Material with a Potential for Pressurized Hydrogen Storage Vessels
by Anka Trajkovska Petkoska, Blagoja Samakoski, Bisera Samardjioska Azmanoska and Viktorija Velkovska
J. Compos. Sci. 2024, 8(9), 374; https://doi.org/10.3390/jcs8090374 - 21 Sep 2024
Cited by 5 | Viewed by 3677
Abstract
Hydrogen is one of the critical components to address global challenges such as climate change, environmental pollution and global warming. It is a renewable source of energy that has many advantages compared to other renewables. Even though it may not be a “silver [...] Read more.
Hydrogen is one of the critical components to address global challenges such as climate change, environmental pollution and global warming. It is a renewable source of energy that has many advantages compared to other renewables. Even though it may not be a “silver bullet” solution for the polluted world, there is still a big expectation that it can solve some of the energy crisis and challenges in the transportation, domestic and industry sectors. This study reviews the latest advancements in materials science, especially in the composite materials used for energy storage/transportation tanks. Special attention is given to towpreg material structures as the most promising ones for hydrogen storage. Various types of storage vessels are reviewed with emphasis on the most advanced type IV and type V vessels for energy (hydrogen) storage. The manufacturing processes, mainly filament winding (FW) and automatic fiber placement (AFP), are reviewed with their pros and cons. The sustainability aspects for the most promising hydrogen technologies, limitations and future challenges are also discussed. Full article
(This article belongs to the Special Issue Composite Materials for Energy Management, Storage or Transportation)
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15 pages, 6289 KiB  
Article
Automated Foreign Object Detection for Carbon Fiber Laminates Using High-Resolution Ultrasound Testing
by Rifat Ara Nargis, Daniel P. Pulipati and David A. Jack
Materials 2024, 17(10), 2381; https://doi.org/10.3390/ma17102381 - 16 May 2024
Cited by 4 | Viewed by 1596
Abstract
Carbon fiber laminates have become popular in the manufacturing industry for their many desirable properties, like good vibration damping, high strength-to-weight ratio, toughness, high dimensional stability, and low coefficient of thermal expansion. During the manufacturing process, undesirable foreign objects, such as peel-ply strips, [...] Read more.
Carbon fiber laminates have become popular in the manufacturing industry for their many desirable properties, like good vibration damping, high strength-to-weight ratio, toughness, high dimensional stability, and low coefficient of thermal expansion. During the manufacturing process, undesirable foreign objects, such as peel-ply strips, gloving material, and Kapton film, can be introduced into the part which can lead to a localized weakness. These manufacturing defects can function as stress concentration points and oftentimes cause a premature catastrophic failure. In this study, a method using high-resolution pulse-echo ultrasound testing is employed for the detection and quantification of the dimensions of foreign object debris (FOD) embedded within carbon fiber laminates. This research presents a method to create high-resolution C-scans using an out of immersion tank portable housing ultrasound scanning system, with similar capabilities to that of a full immersion system. From the full-waveform dataset, we extract the FOD depth and planar dimensions with an automatic edge detection technique. Results from several carbon fiber laminates are investigated with embedded foreign objects that are often considered undetectable. Results are presented for FOD identification for two different shapes: circles with diameters ranging from 7.62 mm to 12.7 mm, and 3-4-5 triangles with hypotenuses ranging from 7.6 mm to 12.7 mm. CT imaging is used to confirm proper FOD placement and that the FOD was not damaged or altered during manufacturing. Of importance for the ultrasound inspection results, in every single case studied, the FOD is detected, the layer depth is properly identified, and the typical error is less than 1.5 mm for the primary dimension. Full article
(This article belongs to the Special Issue Non-Destructive Testing (NDT) of Advanced Composites and Structures)
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17 pages, 6951 KiB  
Article
Robot-Assisted Manufacturing Technology for 3D Non-Metallic Reinforcement Structures in the Construction Applications
by Danny Friese, Lars Hahn, Hung Le Xuan, Johannes Mersch, Tobias Neef, Viktor Mechtcherine and Chokri Cherif
Buildings 2023, 13(11), 2748; https://doi.org/10.3390/buildings13112748 - 31 Oct 2023
Cited by 3 | Viewed by 2053
Abstract
Of all industrial sectors, the construction industry accounts for about 37% of carbon dioxide (CO2) emissions. This encompasses the complete life cycle of buildings, from the construction phase to service life to component disposal. The main source of emissions of climate-damaging [...] Read more.
Of all industrial sectors, the construction industry accounts for about 37% of carbon dioxide (CO2) emissions. This encompasses the complete life cycle of buildings, from the construction phase to service life to component disposal. The main source of emissions of climate-damaging greenhouse gases such as CO2, with a share of 9% of global emissions, is the production of ordinary cement as the main binder of concrete. The use of innovative approaches such as impregnated carbon yarns as non-corrosive reinforcement embedded in concrete has the potential to dramatically reduce the amount of concrete required in construction, since no excessive concrete cover is needed to protect against corrosion, as is the case with steel reinforcement. At the same time, architectural design options are expanded via this approach. This is achieved above all using novel robotic manufacturing technologies to enable no-cut direct fiber placement. This innovative technological approach to fabricating 2D and 3D biologically inspired textiles, including non-metallic structures for textile-reinforced concrete (TRC) components, will promote an automatable construction method that reduces greenhouse gas emissions. Furthermore, the impregnated yarn which is fabricated enables the production of load-adapted and gradual non-metallic reinforcement components. Novel and improved design strategies with innovative reinforcement patterns allow the full mechanical potential of TRC to be realized. The development of a robotic fabrication technology has gone beyond the state of the art to implement spatially branched, biologically inspired 3D non-metallic reinforcement structures. A combined robotic fabrication technology, based on the developed flexible 3D yarn-guiding and impregnation module and a 3D yarn fixation module, is required to implement this sophisticated approach to fabricate freely formed 3D non-metallic reinforcement structures. This paper presents an overview of the development process of the innovative technological concept. Full article
(This article belongs to the Special Issue Research on the Performance of Non-metallic Reinforced Concrete)
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12 pages, 5157 KiB  
Article
Design of Variable Stiffness Trajectories with Cubic Ferguson Curve
by Deli Zhang, Kai Wang and Xiaoping Wang
Materials 2023, 16(21), 6866; https://doi.org/10.3390/ma16216866 - 26 Oct 2023
Cited by 1 | Viewed by 1479
Abstract
To design a class of full cover trajectories that satisfy curvature limitations and enhance the buckling load of constructed laminates, a variable stiffness laminate is proposed by applying the cubic Ferguson curve. First, the traditional explicit form of the cubic Ferguson curve is [...] Read more.
To design a class of full cover trajectories that satisfy curvature limitations and enhance the buckling load of constructed laminates, a variable stiffness laminate is proposed by applying the cubic Ferguson curve. First, the traditional explicit form of the cubic Ferguson curve is redefined as polar coordinates, two connected Ferguson curve segments with three extra parameters are applied to describe full cover trajectories, and the effects on trajectories introduced by these modifications are discussed. Then, the finite element method is used to introduce parameters for analyzing the buckling load of the designed variable stiffness laminates. Numerical experiments show that automatic fiber placement (AFP) trajectories described by the cubic Ferguson curve can automatically reach C1 continuity and can be locally modified by adjusting the introduced parameters. Compared with traditional constant stiffness laminates, the variable stiffness laminates designed using the proposed method exhibit a higher buckling load and better stability. Full article
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13 pages, 8618 KiB  
Article
Bonding of Low-Melting Polyaryletherketone onto Polyamide 6: A Concept for Molds for Automated Fiber Placement
by Fynn Atzler, Lukas Raps, Jonathan Freund, Samuel Tröger and Simon Hümbert
J. Compos. Sci. 2023, 7(9), 371; https://doi.org/10.3390/jcs7090371 - 5 Sep 2023
Cited by 3 | Viewed by 1923
Abstract
Automated fiber placement (AFP) is a method to manufacture complex composite parts in an automatable and scalable process. Thermoplastic in situ AFP has received more attention in recent years for its use in high-performance, aerospace applications that use low-melting polyaryletherketone (LM-PAEK) composites. Although [...] Read more.
Automated fiber placement (AFP) is a method to manufacture complex composite parts in an automatable and scalable process. Thermoplastic in situ AFP has received more attention in recent years for its use in high-performance, aerospace applications that use low-melting polyaryletherketone (LM-PAEK) composites. Although in situ AFP is a promising technology for the automated and economical manufacturing of composites, the production of a mold is still a considerable expense. Using large-scale additive manufacturing, molds can be manufactured in a short time frame for a fraction of the cost of traditional molds. By using polyamide 6 (PA6), a polymer incompatible with LM-PAEK, a bond can be created, which holds a laminate in the desired form during production and allows for demolding. Due to the thermoplastic nature of PA6, a mold can be manufactured using large-scale, extrusion-based additive manufacturing. This study investigates the suitability of 3D-printed molds composed of PA6 for the AFP of CF/LM-PAEK laminates. To this end, peel tests and shear tests were conducted to investigate the influence of the process temperature, the area of heating and the consolidation pressure on the bond of these incompatible polymers. A shear strength of up to 2.83 MPa and a peel strength of up to 0.173 N·mm−1 were achievable. The principal suitability of PA6 as a mold material for the AFP of CF/LM-PAEK was demonstrated. Full article
(This article belongs to the Topic Advanced Carbon Fiber Reinforced Composite Materials)
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13 pages, 1461 KiB  
Article
Artifacts’ Detection for MRI Non-Metallic Needles: Comparative Analysis for Artifact Evaluation Using K-Means and Manual Quantification
by Marwah AL-Maatoq, Melanie Fachet, Rajatha Rao and Christoph Hoeschen
Magnetochemistry 2023, 9(3), 79; https://doi.org/10.3390/magnetochemistry9030079 - 7 Mar 2023
Cited by 6 | Viewed by 2658
Abstract
Interventional biopsy needles need to be accurately localized to the target tissue during magnetic resonance imaging (MRI) interventions. In this context, severe susceptibility artifacts affect the visibility of structures in the MR images depending on the needle’s material composition. In particular, standard needles [...] Read more.
Interventional biopsy needles need to be accurately localized to the target tissue during magnetic resonance imaging (MRI) interventions. In this context, severe susceptibility artifacts affect the visibility of structures in the MR images depending on the needle’s material composition. In particular, standard needles for the spinal cord made of nickel-titanium alloys (NiTi) generate massive susceptibility artifacts during MRI. Consequently, this does not allow the precise placement of the needle to the target. The aim was to prove that using a non-metallic material for the needle can significantly reduce the appearance of artifacts. Hence, this work used a new combination of non-metallic materials based on an enforced fiber bundle as an inner core with different outer hollow sheets to fabricate seven prototypes of interventional spinal needles to optimize their visualization in MRI scans. Susceptibility artifacts for the non-metallic needles were evaluated in MRI images by an automatic quantification based on a K-means algorithm and compared with manual quantification. The width and length of the artifacts were measured for each needle. The non-metallic needles showed significantly lower artifacts in comparison to the standard needle. K-means provided the capability for detecting needle artifacts in MRI images, facilitating qualitative and quantitative assessment of MRI artifacts. Full article
(This article belongs to the Special Issue NMR Spectroscopy and Imaging in Biological Chemistry and Medicine)
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16 pages, 4372 KiB  
Article
Research on Defect Detection in Automated Fiber Placement Processes Based on a Multi-Scale Detector
by Yongde Zhang, Wei Wang, Qi Liu, Zhonghua Guo and Yangchun Ji
Electronics 2022, 11(22), 3757; https://doi.org/10.3390/electronics11223757 - 16 Nov 2022
Cited by 8 | Viewed by 3169
Abstract
Various surface defects in automated fiber placement (AFP) processes affect the forming quality of the components. In addition, defect detection usually requires manual observation with the naked eye, which leads to low production efficiency. Therefore, automatic solutions for defect recognition have high economic [...] Read more.
Various surface defects in automated fiber placement (AFP) processes affect the forming quality of the components. In addition, defect detection usually requires manual observation with the naked eye, which leads to low production efficiency. Therefore, automatic solutions for defect recognition have high economic potential. In this paper, we propose a multi-scale AFP defect detection algorithm, named the spatial pyramid feature fusion YOLOv5 with channel attention (SPFFY-CA). The spatial pyramid feature fusion YOLOv5 (SPFFY) adopts spatial pyramid dilated convolutions (SPDCs) to fuse the feature maps extracted in different receptive fields, thus integrating multi-scale defect information. For the feature maps obtained from a concatenate function, channel attention (CA) can improve the representation ability of the network and generate more effective features. In addition, the sparsity training and pruning (STP) method is utilized to achieve network slimming, thus ensuring the efficiency and accuracy of defect detection. The experimental results of the PASCAL VOC and our AFP defect datasets demonstrate the effectiveness of our scheme, which achieves superior performance. Full article
(This article belongs to the Special Issue Convolutional Neural Networks and Vision Applications, Volume II)
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22 pages, 5822 KiB  
Article
Evolutionary Strategy for Practical Design of Passive Optical Networks
by Leonardo Pereira Dias, Alex Ferreira Dos Santos, Helder Alves Pereira, Raul Camelo De Andrade Almeida, William Ferreira Giozza, Rafael Timóteo De Sousa and Karcius Day Rosario Assis
Photonics 2022, 9(5), 278; https://doi.org/10.3390/photonics9050278 - 20 Apr 2022
Cited by 7 | Viewed by 4246
Abstract
Passive optical networks (PONs) are an important and interesting technology for broadband access as a result of the growing demand for bandwidth over the past 10 years. An arduous and complex step in the design of such networks involves determining the placement of [...] Read more.
Passive optical networks (PONs) are an important and interesting technology for broadband access as a result of the growing demand for bandwidth over the past 10 years. An arduous and complex step in the design of such networks involves determining the placement of equipment, optical fiber cables and several other parameters relevant to the proper functioning of the network. In this paper, we propose an evolutionary strategy to optimize the infrastructure design of PONs by using genetic algorithm technique. This meta-heuristic is capable of elaborating fast, automatic and efficient solutions for the design and planning of PONs. Our proposal has been developed using real maps, aiming to minimize deployment costs and time spent to carry out PON projects, achieving pre-defined quality criteria. We considered, in our simulations, two scenarios (non-dense and dense), four possible topologies and two regions of interest. The non-dense consists of a scenario in which subscribers are distributed in a dispersed manner in the region of interest. The dense has a considerably higher number of subscribers distributed in a very close way to each other. Based on the obtained results, the potential of our proposal is quite clear, as well as its relevance from a technical, economic, and commercial point of view. Full article
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30 pages, 4529 KiB  
Article
Buckling Analysis and Optimization of Stiffened Variable Angle Tow Laminates with a Cutout Considering Manufacturing Constraints
by Wei Zhao and Rakesh K. Kapania
J. Compos. Sci. 2022, 6(3), 80; https://doi.org/10.3390/jcs6030080 - 4 Mar 2022
Cited by 17 | Viewed by 3749
Abstract
Variable angle tow laminates (VAT) and stiffeners are known to redistribute the in-plane load distribution and tailor the buckling mode shapes, respectively, for improving structural performance. To leverage the benefits of using VAT laminates in the practical applications, in the present paper, we [...] Read more.
Variable angle tow laminates (VAT) and stiffeners are known to redistribute the in-plane load distribution and tailor the buckling mode shapes, respectively, for improving structural performance. To leverage the benefits of using VAT laminates in the practical applications, in the present paper, we discuss buckling load maximization conducted for a stiffened VAT laminated plate with a central cutout considering VAT laminate manufacturing constraints. Three representative boundary conditions as seen in the aerospace structures are considered: in-plane axial displacement, in-plane pure shear, and in-plane pure bending displacements. Two common manufacturing constraints, the one on the automatic fiber placement (AFP) manufacturing head turning radius and the other on the tow gap/overlap, while fabricating VAT laminates are considered in the laminate design. These two manufacturing constraints are modeled by controlling the fiber path radius of curvature and tape parallelism in optimizing the fiber path orientations for the VAT laminates. Stiffener layout and fiber path angle for the VAT laminated plates are both considered in the buckling load maximization study. To avoid using a fine mesh in modeling the stiffened VAT laminates with a cutout when employing the finite element analysis during the optimization, the VAT laminated plate and the stiffeners are modeled independently. The displacement compatibility is enforced at the stiffener–plate interfaces to ensure that the stiffeners move with the plate. Particle swarm optimization is used as the optimization algorithm for the buckling load maximization study. Optimization results show that, without considering AFP manufacturing constraints, the VAT laminates can increase the buckling loads by 21.2% and 12.4%, respectively, comparing to the commonly used quasi-isotropic laminates and traditionally straight fiber path laminates for the structure under the in-plane axial displacement case, 19.7% and 12.5%, respectively, for the in-plane shear displacement case, and 62.1% and 26.6%, respectively, for the in-plane bending displacement case. The AFP manufacturing constraints are found to have different impacts on the buckling responses for the VAT laminates, which cause the maximum buckling load to be 9.3–10.1%, 3.0–3.2%, and 23.2–29.8% less than those obtained without considering AFP manufacturing constraints, respectively, for the present studied model under in-plane axial, shear, and bending displacements. Full article
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23 pages, 8133 KiB  
Article
Study of Allowable Interlaminar Normal Stress Based on the Time–Temperature Equivalence Principle in Automated Fiber Placement Process
by Rui Xiao, Jiaqi Shi and Jun Xiao
Polymers 2021, 13(23), 4180; https://doi.org/10.3390/polym13234180 - 29 Nov 2021
Cited by 3 | Viewed by 2368
Abstract
Automatic fiber placement (AFP) is a type of labor-saving automatic technology for forming composite materials that are widely used in aviation and other fields. In this process, concave surface delamination is a common defect, as existing research on the conditions for this defect [...] Read more.
Automatic fiber placement (AFP) is a type of labor-saving automatic technology for forming composite materials that are widely used in aviation and other fields. In this process, concave surface delamination is a common defect, as existing research on the conditions for this defect to occur is insufficient. To predict the occurrence of this defect, the concept of allowable interlaminar normal stress is proposed to define its occurrence conditions, and based on this concept, probe tests are carried out using the principle of time–temperature equivalence. Through the laying speed/allowable normal stress curve measured in the probe experiment, the physical meaning of allowable normal stress is discussed. At the same time, the measured curve is quantitatively analyzed, combined with viscoelastic theory and the molecular diffusion reptation model, and the dominating effect in the formation of a metal/prepreg layer and prepreg/prepreg layer is determined. Finally, the experimental data are used to guide the parameter selection in an automatic placement engineering case and prove its correctness. Full article
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18 pages, 52753 KiB  
Article
Numerical and Experiment Studies of Different Path Planning Methods on Mechanical Properties of Composite Components
by Dongli Wang, Jun Xiao, Xiangwen Ju, Mingyue Dou, Liang Li and Xianfeng Wang
Materials 2021, 14(20), 6100; https://doi.org/10.3390/ma14206100 - 15 Oct 2021
Cited by 2 | Viewed by 2097
Abstract
The purpose of this paper is to study the effects of different trajectory planning methods on the mechanical properties of components. The scope of the research includes finite element simulation calculation and experimental tests of the actual structure. The test shall be carried [...] Read more.
The purpose of this paper is to study the effects of different trajectory planning methods on the mechanical properties of components. The scope of the research includes finite element simulation calculation and experimental tests of the actual structure. The test shall be carried out in the whole load range until the failure of the structure occurs. Taking the composite conical shell as an example, a variable angle initial path generation method of the conical shell surface is proposed, and the parallel offset algorithms based on partition and the circumferential averaging are proposed to fill the surface. Then, finite element analysis is carried out for the paths that satisfy the manufacturability requirements, the analysis results show that the maximum deformation and maximum transverse as well as longitudinal stress of fiber of circumferential averaging variable angle path conical shell are reduced by 16.3%, 5.85%, and 19.76%, respectively, of that of the partition variable angle path. Finally, the strength analysis of conical shells manufactured by different trajectory design schemes is carried out through finite element analysis and actual failure tests. The finite element analysis results are in good agreement with the experimental results of the actual structure. The results show that the circumferential uniform variable angle has good quality, and it is proved that the path planning algorithm that coordinates path planning and defect suppression plays an important role in optimizing placement trajectory and improving mechanical properties of parts. Full article
(This article belongs to the Topic Advances and Applications of Carbon Nanotubes)
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17 pages, 5772 KiB  
Article
Temperature Field in the Heat Transfer Process of PEEK Thermoplastic Composite Fiber Placement
by Zhongliang Cao, Mingjun Dong, Kailei Liu and Hongya Fu
Materials 2020, 13(19), 4417; https://doi.org/10.3390/ma13194417 - 4 Oct 2020
Cited by 17 | Viewed by 3504
Abstract
Under the effect of different process parameters, the temperature field inside the thermoplastic fiber is very complex and directly affects the fusion quality between the resins. Considering the heat transfer behavior of thermoplastic fiber polyether ether ketone (PEEK) as the research object, a [...] Read more.
Under the effect of different process parameters, the temperature field inside the thermoplastic fiber is very complex and directly affects the fusion quality between the resins. Considering the heat transfer behavior of thermoplastic fiber polyether ether ketone (PEEK) as the research object, a mathematical model of heat transfer in the thermoplastic composite fiber placement with the relevant boundary conditions was established. Ansys Parametric Design Language (APDL) was used to generate the finite element model and simulate the transient process, not only to explore the influence of various process parameters on the temperature field, but also to build an online temperature field measurement system. The influence rules of placement process parameters and mold initial temperature with respect to the temperature field in the first layer were obtained. Combining the relationship between heating temperature and placement speed, when the first layer was laid, the placement process temperature could be quickly reached by low speed and high temperature. The temperature data were collected by the online detection system. Compared with the temperature data from the simulation, the error was below 8%, which verified the correctness of the heat transfer model. The academic research results will lay a theoretical foundation for the thermoplastic fiber placement. Full article
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17 pages, 5658 KiB  
Article
Mechanical Simulation of Thermoplastic Composite Fiber Variable-Angle Laminates
by Zhongliang Cao, Dengke Guo, Hongya Fu and Zhenyu Han
Materials 2020, 13(15), 3374; https://doi.org/10.3390/ma13153374 - 30 Jul 2020
Cited by 4 | Viewed by 2497
Abstract
By changing the placement angle of the placement path, the fiber direction can be controlled and adjusted to change the load distribution in the laminate, and the stress and natural frequency performances of the laminate can then be altered to finally obtain laminates [...] Read more.
By changing the placement angle of the placement path, the fiber direction can be controlled and adjusted to change the load distribution in the laminate, and the stress and natural frequency performances of the laminate can then be altered to finally obtain laminates with desired mechanical properties. In this paper, the finite element analysis model of variable-stiffness laminates is established based on the fiber placement reference path defined by the Bezier curve method. Based on the analysis of the mechanical properties of the thermoplastic fiber variable-angle laminates obtained by variable-angle trajectory planning, the changes in the stress and deformation of the thermoplastic fiber variable-angle laminate with the connection point parameter β under a compressive load are analyzed. The influence of the parameter β on the static performances of the variable-angle laminates is studied. The simulation results indicate that the maximum stress of the laminate increases first and then decreases as the parameter β increases and reaches the maximum value when the parameter β is 0.5. The minimum stress also shows the same trend as that of the maximum stress and reaches the minimum value when the connection point parameter β is 0.3. The deformation of the variable-angle laminates varies with the change of the connection point parameter β. The maximum deformation increases at first and then decreases for the laminate with the parameter β increasing and reaches the maximum value when the parameter β is 0.8. The minimum deformation of the laminate decreases initially and then increases as the connection point parameter β increases and reaches the minimum value when the parameter β is 0.6. The deformation gradually decreases from the upper and lower ends to the middle, and the deformation area has a symmetrical form. The initial regular rectangular area gradually changes to an elliptical distribution and the area of maximum deformation gradually decreases. Full article
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