A continuous and aligned fiber-reinforced composite having a cross-sectional area of 1130 mm2is subjected to an external tensile
load. If the stresses sustained by the fiber and matrix phases are 156 MPa and 2.75 MPa, respectively, the force sustained by the fiber phase is 74,000 Nand the total longitudinal strain is1.25x 10-3, determine (a)the force sustained by the matrix phase, (b)the modulus of elasticity of the composite material in the longitudinal direction, and (c)the moduli of elasticity for the fiber and matrix phases.
1 answer:
Answer:
(a) The force sustained by the matrix phase is 1802.35 N
(b) The modulus of elasticity of the composite material in the longitudinal direction Ed is 53.7 GPa
(c) The moduli of elasticity for the fiber and matrix phases is 124.8 GPa and 2.2 GPa respectively
Explanation:
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Solution :
i. Slip plane (1 1 0)
Slip direction -- [1 1 1]
Applied stress direction = ( 1 0 0 ]
τ = 50 MPa ( Here slip direction must be perpendicular to slip plane)
τ = σ cos Φ cos λ
τ = σ cos Φ cos λ
∴
σ = 122.47 MPa
ii. Slip plane --- (1 1 0)
Slip direction -- [1 1 1]
τ = σ cos Φ cos λ
∴
σ = 122.47 MPa
iii. Slip plane --- (1 0 1)
Slip direction --- [1 1 1]
τ = σ cos Φ cos λ
∴
σ = 122.47 MPa
iv. Slip plane -- (1 0 1)
Slip direction ---- [1 1 1]
τ = σ cos Φ cos λ
∴
σ = 122.47 MPa
∴ (1, 0, -1). (1, -1, 1) = 1 + 0 - 1 = 0