vol fractions rule of mix
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: oONOLTZOo
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.90 Ko KB
Mis en ligne Uploaded: 10/10/2024 - 11:04:54
Uploadeur Uploader: oONOLTZOo (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4245327
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.90 Ko KB
Mis en ligne Uploaded: 10/10/2024 - 11:04:54
Uploadeur Uploader: oONOLTZOo (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4245327
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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a ceramic-matrix composite (CMC) is made with continuous SiCfibres embedded in a reaction-bonded silicon nitride (RBSN) matrix with all theSiC fibres aligned in one direction. Assuming isostrain conditions, what is thevolume fraction of the SiC fibres in the composite if the composite has atensile modulus of 250 GPa? E SiC = 395 GPa and E RBSN= 155 GPa. To find the volume fraction of the SiC fibers in theceramic-matrix composite (CMC) under isostrain conditions, we can use the ruleof mixtures for composites in the longitudinal direction. The tensile modulusof the composite Ec isgiven by: Ec = Vf* Ef + Vm * Em where: Ec = modulus of the composite Vf = volume fraction of the fibers Ef = modulus of the fibers (SiC) Vm = volume fraction of the matrix (RBSN) Em = modulus of the matrix Since Vf + Vm =1, we can express Vm as 1 Vf . Given Data Ec=250 GPa Ef=395 GPa (for SiC fibers) Em=155 GPa (for RBSN matrix) Substituting VmV_mVm Substituting Vm into the equation gives us: Ec = Vf * Ef + (1Vf) * Em Rearranging the Equation Expanding and rearranging the equation: Ec = Vf* Ef + Em Vf * Em Ec = Vf (Ef Em )+ Em Ef Em = Ec Em / Vf Solving for VfV_fVf Now, we can isolate VfV_fVf : Vf = EcEm / Ef Em Substituting the Values Vf= 250 GPa 155 GPa/ 395 GPa 155 GPa = 0.3958 = 39.6% Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
a ceramic-matrix composite (CMC) is made with continuous SiCfibres embedded in a reaction-bonded silicon nitride (RBSN) matrix with all theSiC fibres aligned in one direction. Assuming isostrain conditions, what is thevolume fraction of the SiC fibres in the composite if the composite has atensile modulus of 250 GPa? E SiC = 395 GPa and E RBSN= 155 GPa. To find the volume fraction of the SiC fibers in theceramic-matrix composite (CMC) under isostrain conditions, we can use the ruleof mixtures for composites in the longitudinal direction. The tensile modulusof the composite Ec isgiven by: Ec = Vf* Ef + Vm * Em where: Ec = modulus of the composite Vf = volume fraction of the fibers Ef = modulus of the fibers (SiC) Vm = volume fraction of the matrix (RBSN) Em = modulus of the matrix Since Vf + Vm =1, we can express Vm as 1 Vf . Given Data Ec=250 GPa Ef=395 GPa (for SiC fibers) Em=155 GPa (for RBSN matrix) Substituting VmV_mVm Substituting Vm into the equation gives us: Ec = Vf * Ef + (1Vf) * Em Rearranging the Equation Expanding and rearranging the equation: Ec = Vf* Ef + Em Vf * Em Ec = Vf (Ef Em )+ Em Ef Em = Ec Em / Vf Solving for VfV_fVf Now, we can isolate VfV_fVf : Vf = EcEm / Ef Em Substituting the Values Vf= 250 GPa 155 GPa/ 395 GPa 155 GPa = 0.3958 = 39.6% Made with nCreator - tiplanet.org
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