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| Composite Materials | ||||||||||||
| ·
The
initial response of the composite to a variable applied force is elastic.
· For an elastic response in the isostrain case (loading parallel to the fibers): εC = ef = em , and the applied load is shared between the fibers and the matrix in proportion to their volume fractions, Vf and Vm. · For a load, P1, applied in the 1-direction: P1 = Pf + Pm , where Pf = σfΑf , and Pm = σmΑm , and Ai is the total area of the component i. · Assuming that the materials obey Hooke's law in the elastic range, the stresses can be written in terms of the strains and Youngs modulus: σi= Ei εi and the area fractions may be converted to volume fractions: Vi = Ai /A. · Substituting into the force expression gives: σC = σfVf + σm Vm , so that: EC1εC = Ef εf Vf + EmεmVm. Recognizing the isostrain constraint gives: EC1 = Ef Vf + Em Vm = Ef Vf + (1 - Vf ) Em |
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