Page 142 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechunics of stress transfer 125

(stress) is increased, there is a competition between interface debonding and matrix
crack propagation. This phenomenon of fiber fragmentation has been recently
analyzed by Liu et al.( 1997) using fracture mechanics and a constant average fiber
strength model.

4.3. Fiber pull-out test
4.3.1. Introduction

Theoretical analyses of interfacial debonding and frictional pull-out in the fiber
pull-out test were initially modeled for ductile matrices (e.g. tungsten wiresopper
matrix (Kelly and Tyson, 1965, Kelly, 1966)) assuming a uniform IFSS. Based on
the matrix yielding over the entire embedded fiber length, L, as a predominant
failure mechanism at the interface region, a simple force balance shown in Fig. 4.19
gives the fiber pull-out stress, which varies directly proportionally to the cylindrical
surface area of the fiber

(4.85)
where r, is the matrix shear yield strength, and oe the fiber stress at its embedded
end (with ge = 0 for specimens without such bonding). However, in most practical
composites containing brittle matrix materials, the distribution of IFSS is neither
uniform nor continuous due to the coexistence of the bonded and debonded regions
along the interface. Moreover, the functional dependence of the external stress for

%,I P bonded free
end end
pull out 0 0

0 2 4 6
LI2a

Fig. 4.19. Fiber pull-out stress as a function of embedded fiber length, L/2a, for a tungsten wire embedded
copper matrix composite system. Open symbols for pulled-out specimens; solid symbols for fractured
specimens. After Kelly and Tyson (1965).