elastic strain tensile modulus
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: oONOLTZOo
Type : Classeur 3.0.1
Page(s) : 1
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Mis en ligne Uploaded: 10/10/2024 - 12:51:41
Uploadeur Uploader: oONOLTZOo (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4245403
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.26 Ko KB
Mis en ligne Uploaded: 10/10/2024 - 12:51:41
Uploadeur Uploader: oONOLTZOo (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4245403
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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A ceramic-matrix composite is made with an aluminium oxide(Al2O3) matrix and continuous silicon-carbide-fibre reinforcement with all theSiC fibres in one direction. The composite consists of 30 vol% of SiC fibres.If isostrain conditions exist, calculate the tensile modulus of the compositein the direction of the fibres. If a load of 8 MN is applied to the compositein the direction of the fibres, what is the elastic strain in the composite ifthe surface area over which the load is applied is 55 cm2? E Al2O3 = 350 GPa and E SiC = 340 GPa To calculate the tensile modulus of the ceramic-matrixcomposite and the elastic strain when a load is applied, we can use the rule ofmixtures and basic stress-strain relationships. Given Data: Volume fraction of SiC fibers, Vf = 30% = 0.30 Volume fraction of Al2O3 matrix, Vm=1Vf=10.30=0.70 Modulus of Al2O3, E(Al2O3) =350 GPaE(Al2O3) =350GPa Modulus of SiC, ESiC=340 GPa Applied load, F=8 MN=8 * 10 ^6 N Surface area, A=55 cm^2= 55 * 10^ 4 m^2 = 5.5 * 10^ 2 m Step 1: Calculate the Tensile Modulus of the Composite Using the rule of mixtures for the tensile modulus of thecomposite in the direction of the fibers: Ec=Vf * ESiC + Vm * EAl2O3E Substituting the values: Ec= (0.30*340 GPa)+(0.70 * 350 GPa) Ec=(102 GPa)+ (245 GPa) Ec=347 Step 2: Calculate the Stress in the Composite The stress à can be calculated using the applied load andthe surface area: Ã=F/A Substituting the values: à = 8*10^6 N / 5.5 × 10 2 m^2 = 145.45 Step 3: Calculate the Elastic Strain in the Composite The elastic strain õ can be calculated using Hooke's law: e= à Ec Converting Ec to MPa for consistency: Ec=347 GPa= 347 * 10^3 MPa Now calculating the strain: e= 145.45 MPa/ 347 * 10^3 MPa = 0.000419 Final Results The tensile modulus of the composite is approximately: 347 gpa The elastic strain in the composite when an 8 MN load is applied is approximately: 0.000419 Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
A ceramic-matrix composite is made with an aluminium oxide(Al2O3) matrix and continuous silicon-carbide-fibre reinforcement with all theSiC fibres in one direction. The composite consists of 30 vol% of SiC fibres.If isostrain conditions exist, calculate the tensile modulus of the compositein the direction of the fibres. If a load of 8 MN is applied to the compositein the direction of the fibres, what is the elastic strain in the composite ifthe surface area over which the load is applied is 55 cm2? E Al2O3 = 350 GPa and E SiC = 340 GPa To calculate the tensile modulus of the ceramic-matrixcomposite and the elastic strain when a load is applied, we can use the rule ofmixtures and basic stress-strain relationships. Given Data: Volume fraction of SiC fibers, Vf = 30% = 0.30 Volume fraction of Al2O3 matrix, Vm=1Vf=10.30=0.70 Modulus of Al2O3, E(Al2O3) =350 GPaE(Al2O3) =350GPa Modulus of SiC, ESiC=340 GPa Applied load, F=8 MN=8 * 10 ^6 N Surface area, A=55 cm^2= 55 * 10^ 4 m^2 = 5.5 * 10^ 2 m Step 1: Calculate the Tensile Modulus of the Composite Using the rule of mixtures for the tensile modulus of thecomposite in the direction of the fibers: Ec=Vf * ESiC + Vm * EAl2O3E Substituting the values: Ec= (0.30*340 GPa)+(0.70 * 350 GPa) Ec=(102 GPa)+ (245 GPa) Ec=347 Step 2: Calculate the Stress in the Composite The stress à can be calculated using the applied load andthe surface area: Ã=F/A Substituting the values: à = 8*10^6 N / 5.5 × 10 2 m^2 = 145.45 Step 3: Calculate the Elastic Strain in the Composite The elastic strain õ can be calculated using Hooke's law: e= à Ec Converting Ec to MPa for consistency: Ec=347 GPa= 347 * 10^3 MPa Now calculating the strain: e= 145.45 MPa/ 347 * 10^3 MPa = 0.000419 Final Results The tensile modulus of the composite is approximately: 347 gpa The elastic strain in the composite when an 8 MN load is applied is approximately: 0.000419 Made with nCreator - tiplanet.org
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