Composite beams and young's modulus

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SUMMARY

The discussion focuses on calculating the Young's modulus of a composite material made from a polymer and glass fibers. The polymer has a Young's modulus of 2 GPa and yield stress of 50 MPa, while the glass fibers have a Young's modulus of 70 GPa and fracture at 1400 MPa. The volume fraction of fibers is 40%, leading to a calculated composite Young's modulus of 29.2 GPa using the equation E = xE_f + (1-x)E_m. The second part of the problem involves determining the stress on the matrix when the composite yields, which requires further analysis beyond the initial calculations.

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ABoul
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Homework Statement



"A polymer, with Young’s modulus 2GPa and yield stress 50MPa, is reinforced by
uniaxially aligned glass fibres which have Young’s modulus 70GPa and fracture at
1400MPa. The volume fraction of fibres is 40%.


(a) Calculate Young’s modulus for the composite in the direction of the fibres.
(b) The composite is loaded parallel to the fibres. What would be the stress on the
matrix when the composite yields ?"


Homework Equations





The Attempt at a Solution



(a) E = xE_f + (1-x)E_m
E = 0.4(70e9) + 0.6(2e9) = 29.2 GPa

firstly, i don't know if the above is right. also, i have o clue how to do part (b).
 
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i tried using the E from part (a) in the equation for yield stress, but this didn't work. any help would be greatly appreciated.
 

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