problem 15.11 (a) verify that equation 15.11, the expression for the ratio of fiber load to matrix load (ff/fm), is valid.

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13-12-2022
Mathematics

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problem 15.11 (a) verify that equation 15.11, the expression for the ratio of fiber load to matrix load (ff/fm), is valid.

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Tutorconsortium423 Tutorconsortium423 · Answer 1 · 2022-12-18T20:01:50+01:00

The formula (ff/fm) for the relationship between fiber load and matrix load is correct.

what is fiber load of matrix load ?

The load transfers from the matrix to the fiber and vice versa happen through the fiber-matrix interfacial region, which is a crucial component of composites. The majority of authors are in favor of weak interfaces as a way to boost fracture toughness. Crack-bridging and fiber pullout are given the toughening designation.

But, Vm=Am/Ac,

which, upon rearrangement gives Ac/Am=1 /Vim

. Also, from Equation 16.10a,Ec=EmVm+EfVf, which, when substituted for Ec into the previous expression, yields Ff Fm=EmVm+EfVfEmVm-1=EmVm+EfVf-EmVmEmVm=EfVfEmVm

The formula (ff/fm) for the relationship between fiber load and matrix load is correct.

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