A composite material is made from a 7075-T6 aluminum matrix with 50 % uniaxial alumina fibers. The yield strength of the aluminum is 500 MPa, and the elastic modulus is 70 GPa. The tensile strength of the alumina fibers is 1.4 GPa, and the elastic modulus is 380 GPa.
(a) Calculate the strain where the first change in elastic modulus occurs for this composite material in an axial tensile test.
(b) Calculate the composite stress where the change in elastic modulus occurs.
(a) First it is necessary to determine the strain at fracture for the fibers and the strain at yield for the matrix: The strain in the fibers at fracture is
(b) The stress in the metal matrix at fracture of the fibers is calculated from the elastic modulus of the metal matrix of 70 GPa and the strain at fracture of the fibers of 0.0037
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