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. 

More recently, Stang and Shah (1986) derived a debond criterion based on a compliance analysis, and Wells and Beaumont (1985) took into account the effect of the Poisson contraction of the fiber and non-linear friction in the debonded region. 

This is discussed in standard tests on elasticity, and the anisotropic case in Lekhnitskii171. The simplest assumption is that of the Bernoulli-Euler theory in which plane sections remain plane and Poisson contraction is ignored. Young s modulus measured by the deflection of a simply supported beam under three point bending is given by... 

Consider now a portion of the surface of a stressed body (Fig. 16-5). Principal stresses and 02 are parallel to the surface, and 03 is zero. However, 63, the strain normal to the surface, is not zero. It has a finite value, given by the Poisson contractions due to 0j and 02 ... 

In the thin sheet, at the tip of the stressed crack, the thickness of the specimen decreases because of the Poisson contraction plane stress conditions occur at the crack tip. 

Stress distribution Poisson s ratio D A DILLARD Poisson contraction and stress distribution... 

Plane stress conditions are assumed, ignoring complications arising from different Poisson contractions in the bonded region and single adherend regions. 

Figure 3.9 Representation of fibre and matrix in the vicinity of a crack. The Poisson contractions have been grossly exaggerated for clarity (after Kelly and Zweben [20])...

A. Kelly and C. Zweben, Poisson contraction in aligned fibre composites showing pull-out , J. Mater. Sci. 11,1976, 582-587. 

---