THETHE EVOLUTIONEVOLUTION ANDAND APPLICATIONAPPLICATION OFOF THREE-THREE-DIMENSIONALDIMENSIONAL STRESS-INTENSITYSTRESS-INTENSITY FACTORSFACTORS
J. C. Newman, Jr.Mississippi State University
Starkville, MS
I. S. RajuNASA Langley Research Center
Hampton, VA
S. A. FawazU. S. Air Force Academy
Colorado Springs, CO
Workshop on Life Prediction Methodologyand Validation for Surface Cracks
23 May 2007Norfolk, VA
Surface Crack - # 2
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
Surface Crack - # 3
EMBEDDED ELLIPTICAL CRACK TO ANEMBEDDED ELLIPTICAL CRACK TO ANAPPROXIMATE SURFACE CRACK SOLUTIONAPPROXIMATE SURFACE CRACK SOLUTION
f
Green & Sneddon (1950) Irwin (1962)
Surface Crack - # 4
METHODS OF SOLUTION FOR FINITE-BODY PROBLEMSMETHODS OF SOLUTION FOR FINITE-BODY PROBLEMS
• Engineering Estimates
• Alternating Methods
• Line-Spring Model
• Boundary-Element Methods
• Finite-Element Methods COD methods
J-Integral or energy methods
Nodal-force method
Surface Crack - # 5
THE SURFACE-CRACK PROBLEMTHE SURFACE-CRACK PROBLEM
2w
Surface Crack - # 6
SEMI-CIRCULAR SURFACE CRACK UNDER SEMI-CIRCULAR SURFACE CRACK UNDER REMOTE TENSIONREMOTE TENSION
Newman (1979)
Surface Crack - # 7
SEMI-ELLIPTICAL SURFACE CRACK UNDERSEMI-ELLIPTICAL SURFACE CRACK UNDERREMOTE TENSIONREMOTE TENSION
Newman (1979)
Surface Crack - # 8
THE BOUNDARY-LAYER EFFECTTHE BOUNDARY-LAYER EFFECT
Lose of square-root singularity Free surface
Hartranft & Sih (1970)Benthem & Koiter (1973)
Crack
Surface Crack - # 9
EFFECT OF FE MESH REFINEMENT ON EFFECT OF FE MESH REFINEMENT ON NORMALIZED STRESS-INTENSITY FACTORSNORMALIZED STRESS-INTENSITY FACTORS
Raju & Newman (1979)
Surface Crack - # 10
CRACK CONFIGURATIONS ANALYZED WITH FEACRACK CONFIGURATIONS ANALYZED WITH FEAUNDER REMOTE TENSION OR BENDING LOADSUNDER REMOTE TENSION OR BENDING LOADS
Raju & Newman (1979-1986)
2r
2r
w
2w
2w 2w
2w
Surface Crack - # 11
SURFACE CRACK AT A HOLE UNDER TENSION SURFACE CRACK AT A HOLE UNDER TENSION
Newman & Raju (1981)
K = S (a/Q)1/2 F(, a/c, a/ t, c/ r, c/ w)
Surface Crack - # 12
ILL-SHAPED ELEMENT MESH PROBLEM ILL-SHAPED ELEMENT MESH PROBLEM CORNER CRACK AT A HOLE UNDER TENSION CORNER CRACK AT A HOLE UNDER TENSION
Tan et al (1988)
Surface Crack - # 13
STRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTICSTRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTICCORNER CRACKSCORNER CRACKS
Bakuckas (1999)
Surface Crack - # 14
CORNER CRACK(S) AT AN OPEN-HOLE UNDER REMOTECORNER CRACK(S) AT AN OPEN-HOLE 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 (a/Q)1/2 F(, a/c, a/ t, c/ r, c/ w)
2w
Surface Crack - # 15
Corner Crack at Hole under Tension: a/c = 1 and Corner Crack at Hole under Tension: a/c = 1 and = 0 & 90 = 0 & 90oo
Majordiscovery
w = 6 r
w = 400 r
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Surface Crack - # 16
Corner Crack at Hole under Bending: a/c = 1 and Corner Crack at Hole under Bending: a/c = 1 and = 0 & 90 = 0 & 90oo
Majordiscovery
w = 6 r
w = 400 r
}
}
Surface Crack - # 17
Corner Crack at Hole under Tension: a/c = 1.0 and a/t = 0.5 Corner Crack at Hole under Tension: a/c = 1.0 and a/t = 0.5
Surface Crack - # 18
Corner Crack at Hole under Tension: a/c = 1.0 and a/t = 0.95 Corner Crack at Hole under Tension: a/c = 1.0 and a/t = 0.95
Surface Crack - # 19
APPLICATION TO FATIGUE-CRACK GROWTH APPLICATION TO FATIGUE-CRACK GROWTH
Plane-stress behavior Free surface
Jolles & Tortoriello (1983)Newman & Raju (1984)
Plane-strain behavior
Crack
Surface Crack - # 20
Kfs = R K
PLANE-STRESS-TO-PLANE-STRAIN CONVERSIONPLANE-STRESS-TO-PLANE-STRAIN CONVERSION
Surface Crack - # 21
OFFSET ANGLES TO AVOID BOUNDARY LAYER OFFSET ANGLES TO AVOID BOUNDARY LAYER
Surface Crack - # 22
PREDICTION OF SURFACE-CRACK-AT-HOLE SHAPE PREDICTION OF SURFACE-CRACK-AT-HOLE SHAPE AND CRACK-GROWTH BEHAVIORAND CRACK-GROWTH BEHAVIOR
2r
2w
Surface Crack - # 23
APPLICATION TO FRACTUREAPPLICATION TO FRACTURE(Surface crack in D6ac steel under bending loads) (Surface crack in D6ac steel under bending loads)
Surface Crack - # 24
FRACTURE OF SURFACE AND THROUGH CRACKS FRACTURE OF SURFACE AND THROUGH CRACKS
Surface Crack - # 25
CONCLUDING REMARKSCONCLUDING REMARKS
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-Andersson finite-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.
