Please solve this mechanical engineering materials course question 16.16It is desired to produce an aligned carbon fiber-epoxy matrix composite having a longitudinaltensile strength of 750 MPa. Calculate the volume fraction of fibers necessary if (1) theaverage fiber diameter and length are 1.2 × 102 mm and, 1 mm, respectively; (2) the fiberfracture strength is 5000 MPa; (3) the fiber-matrix bond strength is 25 MPa; and (4) thematrix stress at fiber failure is 10 MPa.

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Answered: 16.16 It is desired to produce an…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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16.12 In an aligned and continuous carbon fiber- reinforced nylon 6,6 composite, the fibers are to carry 97% of a load applied in the longitudinal direction. (a) Using the data provided, determine the vol- ume fraction of fibers required. (b) What is the tensile strength of this com- posite? Assume that the matrix stress at fiber fail- ure is 50 MPa (7250 psi). Modulus of Elasticity [GPa (psi)] Tensile Strength [MPa (psi)] 260 (37 x 10°) 2.8 (4.0 × 10°) Carbon fiber 4000 (580,000) Nylon 6,6 76 (11,000)
A discontinuous fibre reinforced composite consists of 20mm long carbon fibres in a polymer matrix. The volume fraction of the composite is 0.5, interfacial shear strength 5MPa and the critical fibre length 2.5mm. The fibre modulus is 250GPa and strain to failure 1.5%. The matrix modulus is 3.5GPa and failure strain 10%. If the ultimate fibre strength = 3500MPa, calculate the average failure stress in the composite. Answer: 2584
b. i. Calculate the tensile modulus of elasticity of a unidirectional Kevlar-49 fibers epoxy composite material that contains 63% by volume of Kevlar 49 fibers and is stressed under isostrain conditions. The Kevlar 49 fibers have a tensile modulus of elasticity of 189.8 GPa and the epoxy matrix a tensile modulus of elasticity of 3.8 GPa.
On the basis of fiber length and orientation, which of the following results to an 'isotropic' properties of fiber-reinforced composites. Continuous and aligned Discontinuous and randomly oriented Discontinuous and aligned
Problem 4 Calculate the tensile modulus of elasticity of a unidirectional carbon-fiber-reinforced-plastic composite material that contains 64 percent by volume of carbon fibers and is stressed under isostrain conditions. The carbon fibers have a tensile modulus of elasticity of 54.0 × 10° psi and the epoxy matrix a tensile modulus of elasticity of 0.530 x 10° psi.
A composite with a vinyl ester (VE) matrix contains 2 vol% CNTS with the following characteristics: 1= 7 um, d= 50 nm, di = 4 nm, and EcCNT = 900 GPa. The modulus of the VE matrix is 1.9 GPa. %3D c. Find the Major Poisson's ratio for this composite using strength of materials approach. d. Find the in-plane shear modulus for this composite using strength of materials approach.
16.D5 It is necessary to fabricate an aligned and dis- O continuous carbon fiber-epoxy matrix composite having a longitudinal tensile strength of 1900 MPa (275,000 psi) using 0.45 volume fraction of fibers. Compute the required fiber fracture strength as- suming that the average fiber diameter and length are 8 x 10-3 mm (3.1 x 10-4 in.) and 3.5 mm (0.14 in.), respectively. The fiber-matrix bond strength is 40 MPa (5800 psi), and the matrix stress at fiber failure is 12 MPa (1740 psi).
A discontinuous fibre reinforced composite consists of 20mm long carbon fibres in a polymer matrix. The volume fraction of the composite is 0.5, interfacial shear strength 5MPa and the critical fibre length 2.5mm. The fibre modulus is 250GPa and strain to failure 1.5%. The matrix modulus is 3.5GPa and failure strain 10%. Calculate the tensile strength of the composite in the fibre direction. Answer: 3564
3. The geometry of the reinforcing phase in a composite greatly determines the overall properties. Polycarbonate has a Modulus of Elasticity=2.2 GPa, Tensile Strength-62.5 MPa. Carbon Fiber has a Modulus of Elasticity=228 GPa, Tensile Strength=3.5 GPa. For a 40 vol% carbon fiber and a 60 vol% polycarbonate matrix composite, compute the Tensile Strength and Young's Modulus for the composite for the following situations. Assume longitudinal loading. a. Continuous and aligned fibers b. Discontinuous and aligned fibers with I> le where 1 = 101, (K = 1). c. Discontinuous and aligned fibers with I< le where I= 0.51, (K = 1). d. Which of these composites is the strongest? Which is the stiffest (has the highest Young's Modulus)?
What is the tensile strength of a composite fibre when its diameter is 20 microns and its critical fibre length is 30 microns? The strength between the fibre and matrix is 150 MPa.
(B) Composite consists of polyester as a matrix reinforced by glass fiber. If the composite have cross- sectional area is (250 mm') and stress of (50 MPa) is applied in this longitudinal direction. 1-Compute the weight fraction of fibers and matrix. 2-Compute the magnitude of the load carried by each of fiber and matrix phase. Note:- Modulus of Elasticity (GPa) Material Density (g/cm³) Polyester 1.38 3.4 Glass Fiber 2.58 69 Composite 2.1
A composite sample of carbon reinforced epoxy has dimensions of 12 in x 12 in x 0.25 in and mass of 1.8 lb. The carbon fibers have a modulus of elasticity of 50(106) lb/in² and a density of 0.069 lb/in³. The epoxy matrix has modulus of elasticity of 0.61(106) lb/in² and a density of 0.042 lb/in³. What is the volume fraction of (a) the carbon fibers and (b) the epoxy matrix in the sample? Assume there are no voids in the sample. What is the predicted value for the modulus of elasticity (c) in the longitudinal direction and (d) the perpendicular to the carbon fibers?

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