THE THE EVOLUTION EVOLUTION AND AND APPICATION APPICATION OF OF THREE THREE - - DIMENSIONAL DIMENSIONAL STRESS STRESS - - INTENSITY INTENSITY FACTORS FACTORS J. C. Newman, Jr. Mississippi State University Starkville, MS I. S. Raju NASA Langley Research Center Hampton, VA S. A. Fawaz U. S. Air Force Academy Colorado Springs, CO The George R. Irwin Centennial Conference University of Maryland 18-20 March 2007 College Park, MD
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THE EVOLUTION AND APPICATION OF THREE- DIMENSIONAL STRESS ... · APPICATION OF THREE-DIMENSIONAL STRESS-INTENSITY FACTORS. ... Starkville, MS. I. S. Raju. NASA Langley Research Center.
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The George R. Irwin Centennial ConferenceUniversity of Maryland
18-20 March 2007College Park, MD
Irwin 100th Conference - # 2
George Rankin IrwinGeorge Rankin Irwin
Irwin 100th Conference - # 3
OUTLINE OF PRESENTATIONOUTLINE OF PRESENTATION
• Embedded Elliptical Crack
• Methods of Solution for Finite-Body Problems
• The Surface-Crack Problem• The Boundary-Layer Effect• Surface and Corner Crack(s) at a Hole• Application to Fatigue-Crack Growth• Application to Fracture• Concluding Remarks
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EMBEDDED ELLIPTICAL CRACK TO ANEMBEDDED ELLIPTICAL CRACK TO ANAPPROXIMATE SURFACE CRACK SOLUTIONAPPROXIMATE SURFACE CRACK SOLUTION
πGreen & Sneddon (1950) Irwin (1962)
fφ
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METHODS OF SOLUTION FOR FINITEMETHODS OF SOLUTION FOR FINITE--BODY PROBLEMSBODY PROBLEMS
THE BOUNDARYTHE BOUNDARY--LAYER EFFECTLAYER EFFECT
Lose of square-root singularity Free surface
Hartranft & Sih (1970)Benthem & Koiter (1973)
Crack
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EFFECT OF FE MESH REFINEMENT ON EFFECT OF FE MESH REFINEMENT ON NORMALIZED STRESSNORMALIZED STRESS--INTENSITY FACTORSINTENSITY FACTORS
2 φ / π0.0 0.2 0.4 0.6 0.8 1.0
1.00
1.05
1.10
1.15
1.20
8 Wedge model10 Wedge model14 Wedge model
Semi-circular crack:a / c = 1a / t = 0.2
K
S √πa/Q
Estimatedboundaylayer
Raju & Newman (1979)
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CRACK CONFIGURATIONS ANALYZED WITH FEACRACK CONFIGURATIONS ANALYZED WITH FEAUNDER REMOTE TENSION OR BENDING LOADSUNDER REMOTE TENSION OR BENDING LOADS
2r
2r
w
2w
2w2w
2w
Raju & Newman (1979-1986)
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SURFACE CRACK AT A HOLE UNDER TENSION SURFACE CRACK AT A HOLE UNDER TENSION
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
K
S √πa/Q
2 φ / π
a / c = 1
a / c = 0.2
Shah
Raju-Newman
Raju-Newman
Shah
Newman-Raju Equation
r / t = 1a / t = 0.5
Newman & Raju (1981)
K = S (πa/Q)1/2 F(φ, a/c, a/ t, c/ r, c/ w)
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ILLILL--SHAPED ELEMENT MESH PROBLEM SHAPED ELEMENT MESH PROBLEM CORNER CRACK AT A HOLE UNDER TENSION CORNER CRACK AT A HOLE UNDER TENSION
φ, degrees
0 30 60 900.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Model A (ill-shaped elements)Model B (new mesh)
Model C
Newman-Raju Equation
Force Method:
VCCT Method:
K
S √πa/Q
r / t = 1a / c = 1a / t = 0.2
Tan et al (1988)
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STRESSSTRESS--INTENSITY FACTORS FOR QUARTERINTENSITY FACTORS FOR QUARTER--ELLIPTICELLIPTICCORNER CRACKSCORNER CRACKS
Parametric angle, φ , degrees
0 30 60 902.0
2.5
3.0
3.5
BEM
Equation(Newman-Raju)
WFM(3D)FEM(DIM)
Plate surface Hole surface
FADD(3D)
FEAM
FEM(GIL,J)
5%
r/t = 2; r/w = 0.2a/c = 0.8; a/t = 0.2
K
S √πa/Q
Bakuckas (1999)
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CORNER CRACK(S) AT AN OPENCORNER CRACK(S) AT AN OPEN--HOLE UNDER REMOTEHOLE UNDER REMOTETENSION AND BENDING LOADSTENSION AND BENDING LOADS
• Raju and Newman (1979-86)FEA (h-version)~10,000 dof (0.5 < r / t < 2)
• Fawaz and Andersson (2000-04)FEA (p-version)100,000+ dof (0.1 < r / t < 10)
K = S (πa/Q)1/2 F(φ, a/c, a/ t, c/ r, c/ w)
2w
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Fawaz & Andersson Crack Configurations Analyzed and Fawaz & Andersson Crack Configurations Analyzed and SelectedSelected Values for Tension and Bending EvaluationsValues for Tension and Bending Evaluations
1. Advancements in computers and highly-refined finite-element models have been used to develop more accurate stress-intensity factors for three-dimensional crack configurations – but more analyses and improved equations are needed over a wide range of loading and crack configuration parameters (such as very shallow and very deep cracks).
2. The Newman-Raju equations have been found to be fairly accurate over a wide range in crack configurations, but the new Fawaz-Anderssonfinite-element solutions for a corner-crack-at-a-hole under remote tension or bending loads have resulted in more accurate equations.
3. Three-dimensional stress-intensity factor solutions have improved the fatigue-crack growth predictions for complex crack configurations.
4. Three-dimensional stress-intensity factor solutions and local crack-front constraint variations have allowed the correlation of fracture for surface and through cracks under both tension and bending loads.