Page 322 - Engineered Interfaces in Fiber Reinforced Composites

Chapter I. Improvement of transverse fracture toughness with interface control 303

where the coefficients are:

(7.4)

(1 + s4 - 2Vi)( 1 + Vi) Ei
s2 = + (1 + Vf)(l - 2vf)- ,
s4 - 1 Em

t2
s4= (I+--) ?

E, v and a are the Young’s modulus, Poisson ratio and CTE, respectively, and the
subscript i refers to the interlayer or coating. The residual stress at the fiber/matrix
interface, Cai7 for the composite without an interlayer can be obtained for Ei = E,,
vi = v, and ai = a, in Eq. (7.2). Figs. 7.14 and 7.15 present the results which are
calculated using the properties of a CFRP given in Table 7.3, and the stresses are
normalized with the compressive stress oa, = -10.7MPa which is obtained without
an interlayer. The residual stresses, o,i and oci, decrease parabolically with
increasing interlayer thickness when the coating is more compliant than the matrix.
Further reductions in these residual stresses were realized with increasing CTE of the
interlayer, mi. This result is explained by the fact that the compressive stress induced
by the shrinkage of the stiff matrix is effectively balanced by the greater shrinkage of
the compliant interlayer. This means that the thicker the coating layer, the greater is
the counterbalance against matrix shrinkage.
When the Young’s modulus of the interlayer is the same as the matrix material,
Le., Ei/& = 1, and ai is high, oai is almost equivalent to that obtained without an
interlayer, regardless of the interlayer thickness, t/a. On the contrary, aci decreases
drastically with increasing interlayer thickness and mi, becoming negative (Le. tensile
stress) at the right-hand bottom comer of Fig. 7.14(b). It is worth noting that aai is
always greater than oci in absolute terms, regardless of Young’s modulus ratio,
Ei/E,, the difference increasing with ai and t/a. This finding agrees well with the
results from finite element analysis shown in Fig. 7.11 such that the interfacial shear
stress is always higher at the fiber/coating interface than at the coating/matrix
interface for a constant external stress. The Young’s modulus of the interlayer is a
very important parameter which governs the magnitude of the residual stresses in
the composites. Both the residual stresses, oai and oci, increase significantly within a
very small range of low modulus ratio, Ei/E,, followed by a more gradual increase
with further increase in Ei/E,, depending on CTE and thickness of the interlayer. In