Fracture toughness and R -Curve behavior of laminated brittle-matrix composites
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I.
INTRODUCTION
IN recent years, several intermetallic compounds have been developed with many desirable properties for potential use in structural and aerospace applications;[1] these properties include high melting points (typically ;15007C to 20007C), low densities (typically 4 to 8 g/cm3), and good creep resistance.[2–5] However, the disadvantage of these materials is that they are often very brittle due to a high resistance to dislocation motion resulting from their relatively complex, ordered crystal structures. For example, in comparison to toughnesses of ;50 to 100 MPa=m shown by traditional Ti- and Ni-based alloys, intermetallics such as Nb3Al and MoSi2 typically display fracture toughness, Kc, values below ;4 MPa=m; in fact, even in the more ‘‘ductile’’ compounds such as g-TiAl, intrinsic toughnesses are typically ;10 MPa=m. To improve the low intrinsic toughnesses of intermetallics, extrinsic toughening techniques that invoke crack-tip shielding mechanisms are often used in alloy and microstructural development. Such mechanisms, which include crack bridging via ductile or brittle reinforcements, primarily act behind the crack tip and locally screen the crack from the applied (far-field) driving force.[6,7] Using ductile reinforcements, the principle is to promote crack-particle interactions to create bridging ligaments in the crack wake, which deform plastically and impart closing tractions on the crack faces.
D.R. BLOYER, Postdoctoral Researcher, and R.O. RITCHIE, Professor, are with the Department of Materials Science and Mineral Engineering, University of California, and the Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 947201760. K.T. VENKATESWARA RAO, formerly Research Engineer with the Department of Materials Science and Mineral Engineering, University of California, is Manager of R&D, Vascular Intervention Group, Guidant Corporation, Santa Clara, CA 95052. Manuscript submitted December 9, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
Under small-scale bridging (SSB) conditions,* the in*Small-scale bridging conditions apply where the bridging tractions act over a distance that is small relative to the crack length and in-plane specimen dimensions; in this regime, Gb is independent of crack length and specimen geometry. With larger bridging zones, the traction contribution is a function of crack length and geometry; this is referred to as large-scale bridging (LSB).
crease in fracture energy due to ductile reinforcements, Gb, can be formulated in terms of the physical properties of the reinforcement and interface by relating it to a nondimensional work of rupture, x:[8,9,10] u*
x5
/r
* ss( / ) z d( / ) u
0
r
u
r
[1]
0
where s(u) is the stress-displacement function of the bridging tractions; u* is the displacement at failure of the bridging ligament; and s0 and r are, respectively, the flow stress and characteristic dimension of the reinforcement, such that[8] Gb 5 f z r z s0 z x
[2]
where f is the volume fraction of reinforcement intercepted by
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