On macroscopic and microscopic analyses for crack initiation and crack growth toughness in ductile alloys
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I.
INTRODUCTION
Blunting line
THE fracture
toughness of a material is conventionally assessed in terms of the critical value of some crack tip field characterizing parameter at the initiation of unstable crack growth. In plane strain, for example, under smallscale yielding (ssy) conditions, the critical value of the linear elastic stress intensity factor, K~c, is generally determined at the onset of crack extension, and can be referred to as the "toughness. ''~ With appreciable nonlinearity in the load-displacement curve, however, the (crack initiation) toughness is measured in terms of the critical value of the J - i n t e g r a l , Jlc, 2'3 or the crack tip opening displacement, ~ or 8i, 4 For ssy conditions, these parameters are explicitly related in terms of the flow stress, Co, and the elastic (Young's) modulus E, i.e.: K~ E'
Jlc = --
1 c~
-~ - - ~ i O ' o ,
dj R
~
JR
/.i"
C ock
growth
1
~_~
initiation -1~
9
Experimental data
Crack blunting ~_
CRACK EXTENSION, &o Fig. 1--JR(Aa) resistance curve of J vs crack extension Aa, showing definition of Ji = J,c at initiation of crack growth where the blunting line intersects the resistance curve.
[1]
where E ' = E in plane stress and E/(1 - v 2) in plane strain, and c~ is a proportionality factor of order unity, dependent upon the yield strain (eo = co~E), the work hardening exponent (n), and whether plane stress or plane strain conditions are assumed. 5 Although in "brittle" structures, catastrophic failure or instability is effectively coincident with this onset of crack extension, in the presence of sufficient crack tip plasticity crack initiation is generally followed by a region of stable crack growth. Under elastic-plastic conditions (or plane stress, linear elastic conditions), such subcritical crack advance has been macroscopically characterized in terms of crack growth resistance curves, i.e., the JR (Aa) and 8R (Aa) R curves (Figure 1). 6,7'8 Crack growth toughness is now assessed in terms of the slope of the resistance curve, which R. O. RITCHIE, Professor, is with the Lawrence Berkeley Laboratory and the Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720. A.W. THOMPSON is Professor, Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University, Pittsburgh, PA 15213. Manuscript submitted December 31, 1983.
METALLURGICALTRANSACTIONS A
/
in the J approach can be evaluated in terms of the nondimensional tearing modulus (TR = E / c ~ " dJ/da), 7 or in the CTOD approach in terms of the crack tip opening angle (CTOA = d ~ / d a ) , 8'9 where: E dJ E d6 CTOA TR - - - - - = -. c~ da Co da Yield Strain
[2]
Whereas crack initiation toughness values (i.e., Klc, J~c, etc.) are by far the most widely measured and quoted, it has been noted in high toughness ductile materials, for example, that stable ductile crack growth can occur at J values some 5 to 10 or more times the initial J~c value prior to instability, 1~ e.g., Figure 2. Furthermore, microstructural influenc
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