Differential Poisson contraction

An additional radial stress, i(a,z), acts at the interface that arises from the differential Poisson contraction between the fiber and the matrix when the matrix is subjected to an axial tension at remote ends. q (a,z) is obtained from the continuity of tangential strain at the interface (i.e. e (a,z) = e (a,z)) (Gao et al., 1988)... 

The normalized FAS and IFSS are shown in Fig. 4.17. Both the FAS and IFSS distributions are higher for larger values of residual clamping stress, go, (in absolute terms) for a given fiber length. Varying the coefficient of friction, p, would have similar effects on the stress distributions. The predominant effect of differential Poisson contraction between the fiber and matrix is obvious, particularly in Fig. 4.17(b), where the IFSS values at the fiber ends are several-fold the values obtained in the center. 

The radial (compressive) stress, qo, is caused by the matrix shrinkage and differential thermal contraction of the constituents upon cooling from the processing temperature. It should be noted that q a, z) is compressive (i.e. negative) when the fiber has a lower Poisson ratio than the matrix (vf < Vm) as is the normal case for most fiber composites. It follows that q (a,z) acts in synergy with the compressive radial stress, 0, as opposed to the case of the fiber pull-out test where the two radial stresses counterbalance, to be demonstrated in Section 4.3. Combining Eqs. (4.11), (4.12), (4,18) and (4.29), and for the boundary conditions at the debonded region... 

We note that homogeneous material, HT = 0.33 T. The magnitude of HT depends on the relationship between m and /x2 and on angle 8. Equation 2 has been solved for a number of interesting cases, with results shown in Table I. Table I shows that the elastic inclusion does increase the hydrostatic tension maximum above the 0.33 T level in a homogeneous material, that a void increases hydrostatic tension more than a rubber particle, and that a hard inclusion increases hydrostatic tension more than a void. These results assume adhesion of sphere to... 

Mechanical properties of the composite materials were tested by a hydraulic-driven MTS tensile tester manufactured by MTS Systems Corporation, Minneapolis, Minnesota. A strain-rate of 5x 10 5 s 1 was used. During deformation, the linear actuactor position was monitored and controlled by a linear variable differential transformer (LVDT), while strain was measured using MTS-brand axial and diametral strain-gauge extensometers. The axial extensometer serves to measure the tensile deformation in the direction of loading while the diametral extensometer serves to measure the compressive deformation at 90° to the loading axis due to Poisson s contraction. All tensile tests were performed at 23 °C and in accordance to ASTM D3518-76. 

---