Crack-tip behaviors of stationary and growing cracks in Al-Fe-X alloys: Part I. Near-tip strain field
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I.
INTRODUCTION
F R A C T U R E of a cracked material subjected to a monotonically increasing remote tensile load usually involves these processes: (1) plastic blunting at the crack tip, (2) stable crack growth if the material is ductile, and (3) unstable crack growth. In a recent study, Chan t'l observed that fracture of A1-8Fe-7Ce, AI-8Fe-2Mo-IV, and AI-10.5Fe-2.5V at ambient temperature occurred by unstable propagation of brittle cracks, whose plastic zone, when viewed with light microscopy, was reminiscent of the tensile strip yielding zone assumed in the Barenblatt I2L Dugdale 131 crack model. The brittle fracture behavior prevailed in these alloys despite the fact that fracture occurred via a microvoid process, t'l On the other hand, crack-tip deformation in the A1-8Fe-1.4V-1.7Si alloy was manifested as two localized shear bands inclined to the crack tip. I'l The Kic values of the first three alloys are 10 MPaX/-~ or less, while the latter has a Ktc value of 30 MPaX/m. The high value of K~c in the A1-Fe-V-Si alloy was attributed partly to a thin sheet toughening mechanism, I41which involves crack divider delamination and relaxation of triaxial stresses in the process zone, and partly to the high interfacial debonding strength of the coherent silicide dispersoids. II,41 The crack growth resistance of the A1-Fe-X alloys has also been found to vary with individual alloys; a zero value of the tearing modulus, TR, was observed for the AI-Fe-V, A1-Fe-Ce, and A1-Fe-Mo-V alloys, but a value of TR = 23 was observed for the A1-Fe-V-Si alloy at ambient temperature. The intimate relationship between crack-tip deformation and fracture properties is evident, but factors responsible for the change in the crack-tip deformation behavior in the A1-Fe-X alloys have yet to be identified. It is well established 15'61that the onset of crack growth of a monotonically loaded crack in an elastic-plastic material can be characterized in terms of a critical value of the J integral, I71 J~c, which is related to Kt2 through the KWAI S. CHAN, Principal Engineer, is with the Department of Materials Sciences and Mechanics, Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78228-0510. Manuscript submitted January 6, 1989. METALLURGICAL TRANSACTIONS A
elastic modulus, E, and Poisson's ratio, v, when smallscale yielding prevails. When the conditions for J dominance are met, subsequent stable crack growth can be characterized in terms of a J-resistance curve/s] To meet the J-dominance condition, I91 the crack-tip region within which nonproportional loading, finite strain, and microscopic fracture processes occur, must be well within the region of the small-strain solution dominated by the HRR fields. The HRR strain field is represented by tl~
(
t J
)n/(n+l)
which indicates that the near-tip strains manifest an r -"m+") singularity, where r is the distance from the crack tip, in a material exhibiting power-law hardening (gp = a'eo(6"/~ro)", where gp is the effective plastic strain, 6 is the effective stress, go is the yield
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