Role of interface properties on the toughness of brittle matrix composites reinforced with ductile fibers
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The incorporation of ductile fibers in brittle matrices can lead to a significant increase in fracture resistance. The increase in toughness that derives from crack bridging is governed by the properties of the matrix/fiber interface and the ductility of the fibers. The current study addresses the role of interface sliding stress on the toughness of brittle composites reinforced with ductile fibers. The debond length is explicitly related to the interface sliding stress and the properties of the fiber. It is then incorporated into a geometrical model to simulate the bridging tractions versus crack opening under condition of continuous debonding. The implications on the effect of interfaces on the resistance curve are discussed.
I. INTRODUCTION 1 3
It is now well documented " that ceramics and intermetallics can be substantially toughened by the incorporation of ductile particles. The toughness usually derives from crack-bridging, crack-trapping,4 crackshielding,5 or a combination of the above,6 depending on the morphology of the ductile phase. In the case of isolated reinforcements, such as fiber reinforced composites, the main toughening mechanism has been shown to be crack-bridging.1"3 The increase in strain energy release rate attributed to bridging is,7
r(u)du
AG =
(1)
where / is the area fraction of ductile phases intercepted by the crack, a is the bridging stress, and u is the crack opening (Fig. 1). The toughness provided by the bridging ligaments is thus fully characterized from the stressstretch relation, cr(u), that governs ligament deformation. Equivalently, AG can be expressed as a function of a dimensionless parameter, the work of rupture, ^, 7 ' 8 AG =
(2)
with
II. BACKGROUND TO THE MODEL u'/R
J
a
where cr0 is the reinforcement uniaxial yield stress, and R its radius. The work of rupture is a function of the ductility of the reinforcement and of the matrixreinforcement interfacial properties.2-9 Previous experimental2'6 and theoretical studies8 revealed that debonding increases the work of rupture. This behavior is illustrated in the study of Mataga8 where the bridging ligaments were assumed to be ductile cylinders of aspect ratio, /*//?. The effect of various debond lengths was discretely simulated by varying the cylinder aspect ratio, and the constraint exerted by a rigid matrix was simulated by constraining both ends from shrinking radially (Fig. 2). The finite element calculations showed that in the case of a short aspect ratio, the nominal axial stress in the reinforcement reaches large values due to the constraint exerted by the surrounding rigid matrix. In contrast, for a long aspect ratio the peak stress is lower but the plastic stretch is increased, thereby producing an overall increase in the work of rupture, x- The purpose of the present study is to rationalize the influence of interface properties on the debond length and on the a(u) response by using a physical model representative of the bridging behavior for weakly bonded fibers.
(70
U
(3)
'This work was completed while
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