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TECHNICAL PAPERS

Shallow Flaws Under Biaxial Loading Conditions—Part II: Application of a Weibull Stress Analysis of the Cruciform Bend Specimen Using a Hydrostatic Stress Criterion

[+] Author and Article Information
Paul T. Williams, B. Richard Bass, Wallace J. McAfee

Oak Ridge National Laboratory, Oak Ridge, TN 37831e-mail: williamspt@ornl.gov

J. Pressure Vessel Technol 123(1), 25-31 (Oct 23, 2000) (7 pages) doi:10.1115/1.1344235 History: Received January 01, 2000; Revised October 23, 2000
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References

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Bass, B. R., Keeney, J. A., and McAfee, W. J., 1995, “Assessment of the Fracture Behavior of Weld Material from a Full-Thickness Clad RPV Shell Segment,” Fatigue and Fracture Mechanics in Pressure Vessels and Piping, ASME Pressure Vessel and Piping Conference, Honolulu, HI, 304 , pp. 299–311.
McAfee, W. J., Bass, B. R., and Bryson, J. W., Jr., 1997, “Development of a Methodology for the Assessment of Shallow-Flaw Fracture in Nuclear Reactor Pressure Vessels,” ASME Pressure Vessel and Piping Conference, Orlando, FL, 346 , pp. 85–94.
Pennell, W. E., Bass, B. R., Bryson, J. W., Jr., Dickson, T. L., and Merkle, J. G., 1996, “Preliminary Assessment of the Effects of Biaxial Loading on Reactor Pressure Vessel Structural-Integrity-Assessment Technology,” Proc. 4th ASME/JSME International Conference in Nuclear Engineering, New Orleans, LA.
McAfee, W. J., Bass, B. R., Bryson, J. W., Jr., and Pennell, W. E., 1995, “Biaxial Loading Effects on Fracture Toughness of Reactor Pressure Vessel Steel,” USNRC Report NUREG/CR-6273 (ORNL/TM-12866), Oak Ridge National Laboratory, Oak Ridge, TN.
Theiss, T. H., et al., 1993, “Initial Results of the Influence of Biaxial Loading on Fracture Toughness,” USNRC Report NUREG/CR-6036 (ORNL/TM-12349), Oak Ridge National Laboratory, Oak Ridge, TN.
Bass, B. R., Bryson, J. W., Jr., Theiss, T. H., and Rao, M. C., 1994, “Biaxial Loading and Shallow-Flaw Effects on Crack-Tip Constraint and Fracture Toughness,” USNRC Report NUREG/CR-6132 (ORNL/TM-12498), Oak Ridge National Laboratory, Oak Ridge, TN.
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Bass, B. R., McAfee, W. J., Williams, P. T., and Pennell, W. E., 1998, “Evaluation of Constraint Methodologies Applied to a Shallow-Flaw Cruciform Bend Specimen Tested under Biaxial Loading Conditions,” Fatigue, Fracture, and High Temperature Design Methods in Pressure Vessels and Piping, ASME/JSME Joint Pressure Vessels and Piping Conference, San Diego, CA, 365 , pp. 11–25.
Bass,  B. R., McAfee,  W. J., Williams,  P. T., and Pennell,  W. E., 1999, “Fracture Assessment of Shallow-Flaw Cruciform Beams Tested under Uniaxial and Biaxial Loading Conditions,” Nucl. Eng. Des., 188, pp. 259–288.
Williams, P. T., Bass, B. R., and McAfee, W. J., 1999, “Application of the Weibull Methodology to a Shallow-Flaw Cruciform Bend Specimen Tested under Biaxial Loading Conditions,” ASTM 31st National Symposium on Fatigue and Fracture Mechanics, Cleveland, OH.
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Figures

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PTS loading produces biaxial stresses in an RPV wall with one of the principal stresses aligned parallel with the tip of the constant-depth shallow surface flaw
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Cruciform shallow-flaw biaxial fracture toughness test specimen
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Stress-strain behavior for Plate 14 RPV steel
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Finite-element quarter-model of cruciform beam specimen: (a) detailed view of the shallow-flaw region, (b) complete mesh layout
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Weibull stresses normalized by the yield stress σ0, with (a) maximum principal stress, and (b) hydrostatic stress as the equivalent stress at J=100 kJ/m2
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Weibull probability density distributions of shallow-flaw (a/W=0.1) cruciform toughness data at −5°C
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Weibull parameter estimation by G-R-D: (a) mapping to SSY Weibull stress space: (1:1) and (0:1) mappings for m=10.6, and (b) estimated β(x:1) as a function of trial m
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Sensitivity of maximum principal (opening mode) stress to biaxiality: stress profiles along the normalized distance ahead of cruciform crack tip for J≈130 kJ/m2
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Sensitivity of hydrostatic (σH) stress to biaxiality: stress profiles along the normalized distance ahead of cruciform crack tip for J≈130 kJ/m2
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Cumulative failure probabilities for uniaxial (0:1) loading using a three-parameter Weibull model plotted in Weibull coordinates for m=10.6
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Cumulative failure probabilities for biaxial (1:1) loading using a three-parameter Weibull model plotted in Weibull coordinates for m=10.6
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(a) J versus σw trajectories for uniaxial (0:1) and biaxial (1:1) loading for m=10.55, and (b) biaxial scaling curve for m=10.6

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