2 Two composites are fabricated with silica fibers vr 46 and

2. Two composites are fabricated with silica fibers (vr 46%) and matrices A and B, whose stress-strain curves are shown in Fig. 3-41, page #126. The Silica fibers are elastic up to failure and have properties as shown in Table 1-1, page #8. Assuming that the composites are stressed parallel to the unidirectional Silica fibers, calculate (a) The composite stress at 1% and 3% strains for each composite and (b) The minimum and critical fiber volume fractions for both composites

Solution

Use E = E1* V1 + E2 *V2

Upto 1%, the composite modulus is   E (silica) *.46 + E(matrix) * .54 = 35.165 GPa

After 1%, modulus for Matrix B compositeis 34.22 + .54*( 35/.08) = 34.46

For MAtrix A, E=Esilica since Matrix B suffers elastic failure

at 1% strain, stress for each composite

E e = 35.165*.01 =351.65 Mpa

at 3%: for Matrix B composite: 34.46*.02 = 689.2.6MPa, for Matrix A composite E =Esi

Overall stress: (351.65+ 689.2) =1040.85 MPa

For Matrix A; formula does not hold, stress is borne by fibers alone.

Minimum and critical vol fractions:

Vcrit = amount of fiber that is enough to match the composite modulus

Vmin = vol fraction that determines transition for the matrix

Vmin = ( matrix failure stress- transitionstress)/( fiber stress+ matrix fstress-matrix transition stress)

calculations giv 0.16 and 0.47