Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional
In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence o...
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2024-09-01
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| author | Mario Versaci Filippo Laganà Francesco Carlo Morabito Annunziata Palumbo Giovanni Angiulli |
| author_facet | Mario Versaci Filippo Laganà Francesco Carlo Morabito Annunziata Palumbo Giovanni Angiulli |
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| description | In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity. |
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| language | English |
| publishDate | 2024-09-01 |
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| spelling | doaj-art-3d46b8621b784e8da5e2fef88b36a0dc2025-08-20T01:55:38ZengMDPI AGMathematics2227-73902024-09-011218285410.3390/math12182854Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy FunctionalMario Versaci0Filippo Laganà1Francesco Carlo Morabito2Annunziata Palumbo3Giovanni Angiulli4Department of Civil, Energetic, Environmental and Material Engineering, Mediterranea University, Via Zehender, I-89122 Reggio Calabria, ItalyHealth Science Department, “Magna Graecia” University of Catanzaro, I-88100 Catanzaro, ItalyDepartment of Civil, Energetic, Environmental and Material Engineering, Mediterranea University, Via Zehender, I-89122 Reggio Calabria, ItalyMIFT Department, University of Messina, Via F. D’Alcontres 31, I-98122 Messina, ItalyDepartment of Information Engineering, Infrastructures and Sustainable Energy, Mediterranea University, Via Zehender, I-89122 Reggio Calabria, ItalyIn this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.https://www.mdpi.com/2227-7390/12/18/2854ECdefects in CFRPelectrical conductivity tensorLax–Milgram theoremsolution stability2D maps of magnetic flux density amplitude |
| spellingShingle | Mario Versaci Filippo Laganà Francesco Carlo Morabito Annunziata Palumbo Giovanni Angiulli Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional Mathematics EC defects in CFRP electrical conductivity tensor Lax–Milgram theorem solution stability 2D maps of magnetic flux density amplitude |
| title | Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional |
| title_full | Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional |
| title_fullStr | Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional |
| title_full_unstemmed | Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional |
| title_short | Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional |
| title_sort | adaptation of an eddy current model for characterizing subsurface defects in cfrp plates using fem analysis based on energy functional |
| topic | EC defects in CFRP electrical conductivity tensor Lax–Milgram theorem solution stability 2D maps of magnetic flux density amplitude |
| url | https://www.mdpi.com/2227-7390/12/18/2854 |
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