Stress Intensity Factor Plasticity Correction for Flaws in Stress Concentration Regions Page: 4 of 13
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STRESS INTENSITY FACTOR PLASTICITY CORRECTION FOR FLAWS IN
STRESS CONCENTRATION REGIONS
Edward Friedman
William K. Wilson
Bechtel Bettis, Inc.
Bettis Atomic Power Laboratory
West Mifflin, PAABSTRACT
Plasticity corrections to elastically computed stress intensity
factors are often included in brittle fracture evaluation procedures.
These corrections are based on the existence of a plastic zone in the
vicinity of the crack tip. Such a plastic zone correction is included in
the flaw evaluation procedure of Appendix A to Section XI of the
ASME Boiler and Pressure Vessel Code. Plasticity effects from the
results of elastic and elastic-plastic explicit flaw finite element
analyses are examined for various size cracks emanating from the root
of a notch in a panel and for cracks located at fillet radii. The results
of these calculations provide conditions under which the crack-tip
plastic zone correction based on the Irwin plastic zone size
overestimates the plasticity effect for crack-like flaws embedded in
stress concentration regions in which the elastically computed stress
exceeds the yield strength of the material. A failure assessment
diagram (FAD) curve is employed to graphically characterize the
effect of plasticity on the crack driving force. The Option 1 FAD
curve of the Level 3 advanced fracture assessment procedure of British
Standard PD 6493:1991, adjusted for stress concentration effects by a
term that is a function of the applied load and the ratio of the local
radius of curvature at the flaw location to the flaw depth, provides a
satisfactory bound to all the FAD curves derived from the explicit flaw
finite element calculations. The adjusted FAD curve is a less
restrictive plasticity correction than the plastic zone correction of
Section XI for flaws embedded in plastic zones at geometric stress
concentrators. This enables unnecessary conservatism to be removed
from flaw evaluation procedures that utilize plasticity corrections.
INTRODUCTION
Brittle fracture evaluation procedures as given, for example, in
Section XI of the ASME Boiler and Pressure Vessel Code (ASME,
1998) or the British Standard PD 6493, 1991 use linear elastic stress
intensity factors for crack configurations in simple geometries to
characterize the crack driving force for crack-like flaws located in
regions of more complex geometry. In particular, the stress intensity
factor solutions applied to surface flaws in such geometries are often
those for surface cracks in finite thickness flat plates or in cylindrical
shells. This approach is often called the implicit method since thestress intensity factor is determined implicitly from (1) the stress
distribution existing at the crack location but calculated in the absence
of the crack, and (2) a stress intensity factor solution for a structure
whose geometry may not resemble that of the region in which the
crack is located. An example of this is a stress concentration region
such as a notch or a fillet radius. The stress intensity factor calculation
directly accounts for neither the geometry of the structure nor the
source or nature of the loading that drives the crack. Explicit
procedures such as energy release rate or domain integral methods that
utilize finite element models with cracks included explicitly in the
model accommodate the interaction of the crack, the component
geometry, and the loading. This interaction can be especially
important when distinguishing between cracks driven by primary
loading, such as pressure, and secondary loading, such as thermal or
residual stresses.
The effects of plasticity in flaw evaluation procedures are often
expressed in terms of a plastic zone correction factor (see, for
example, ASME, 1998) which is predicated on the assumption that the
flaw is located in a region whose behavior is elastic if the flaw did not
exist. Furthermore, in the presence of the crack-like flaw, a plastic
zone existing in the vicinity of the crack tip simulates the plasticity
effect. The size of the plastic zone is presumed to be small relative to
the crack size or any other characteristic dimension. An effective
crack size is then defined as the sum of the actual crack size and the
distance from the crack tip to the center of the plastic zone (i.e., the
plastic zone radius). For a material that does not strain harden, the
plastic zone radius under these conditions is approximated by the
distance ahead of the crack tip in which the elastically calculated stress
component acting normal to the crack surface exceeds the yield stress.
This is described, for example, in Kanninen and Popelar (1985).
Consider now the case of a flaw contained within a region in
which the stresses calculated in the absence of the flaw exceed the
yield stress of the material while the surrounding structure remains
elastic. Thus the entire system behaves elastically, except for the
localized stress concentration region which undergoes plastic strain.
In this case, the higher stressed zone is subject to a strain concentration
due to "elastic follow-up" of the stiffer or lower stressed regions.
Such a strain concentration may exist, for example, at the radius of a
fillet or the root of a notch. Under sufficiently high magnitudes of
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Friedman, E. & Wilson, W.K. Stress Intensity Factor Plasticity Correction for Flaws in Stress Concentration Regions, article, February 1, 2000; West Mifflin, Pennsylvania. (https://digital.library.unt.edu/ark:/67531/metadc703655/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.