tensile modulus stress and elastic strain
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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 - 11:05:49
Uploadeur Uploader: oONOLTZOo (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4245328
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.28 Ko KB
Mis en ligne Uploaded: 10/10/2024 - 11:05:49
Uploadeur Uploader: oONOLTZOo (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4245328
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? 58 Al2O3 = 350 GPa and 58 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: õ= à Ec Converting Ec to MPa for consistency: Ec=347 GPa= 347 * 10^3 MPa Now calculating the strain: õ= 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? 58 Al2O3 = 350 GPa and 58 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: õ= à Ec Converting Ec to MPa for consistency: Ec=347 GPa= 347 * 10^3 MPa Now calculating the strain: õ= 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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