1. THE EVOLUTION AND APPLICATION OF THREE-DIMENSIONAL STRESS-INTENSITY 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
Workshop on Life Prediction Methodology
and Validation for Surface Cracks
23 May 2007
Norfolk, VA

2. OUTLINE 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

3. EMBEDDED ELLIPTICAL CRACK TO AN APPROXIMATE SURFACE CRACK SOLUTIONff
Green & Sneddon (1950) Irwin (1962)

4. METHODS 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

5. THE SURFACE-CRACK PROBLEM2w

6. SEMI-CIRCULAR SURFACE CRACK UNDER REMOTE TENSION
Newman (1979)

7. SEMI-ELLIPTICAL SURFACE CRACK UNDER
REMOTE TENSION
Newman (1979)

8. THE BOUNDARY-LAYER EFFECT
Crack
Lose of square-root singularity Free surface
Hartranft & Sih (1970)
Benthem & Koiter (1973)

9. EFFECT OF FE MESH REFINEMENT ON NORMALIZED STRESS-INTENSITY FACTORS
Raju & Newman (1979)

10. CRACK CONFIGURATIONS ANALYZED WITH FEA
UNDER REMOTE TENSION OR BENDING LOADS 2w 2w 2w 2r 2w w 2r
Raju & Newman ( )

11. SURFACE CRACK AT A HOLE UNDER TENSION
Newman & Raju (1981)

12. ILL-SHAPED ELEMENT MESH PROBLEM CORNER CRACK AT A HOLE UNDER TENSION
Tan et al (1988)

13. STRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTIC
CORNER CRACKS
Bakuckas (1999)

14. CORNER CRACK(S) AT AN OPEN-HOLE UNDER REMOTE TENSION AND BENDING LOADS
Raju and Newman ( )
FEA (h-version)
~10,000 dof (0.5 < r / t < 2)
Fawaz and Andersson ( )
FEA (p-version)
100,000+ dof (0.1 < r / t < 10) 2w

15. } } Corner Crack at Hole under Tension: a/c = 1 and f = 0 & 90o Major
discovery }
w = 6 r }
w = 400 r

16. } } Corner Crack at Hole under Bending: a/c = 1 and f = 0 & 90o
w = 6 r
Major
discovery }
w = 400 r

17. Corner Crack at Hole under Tension: a/c = 1.0 and a/t = 0.5

18. Corner Crack at Hole under Tension: a/c = 1.0 and a/t = 0.95

19. APPLICATION TO FATIGUE-CRACK GROWTH
Plane-strain behavior
Crack
Plane-stress behavior Free surface
Jolles & Tortoriello (1983)
Newman & Raju (1984)

20. PLANE-STRESS-TO-PLANE-STRAIN CONVERSION
DKfs = bR DK

21. OFFSET ANGLES TO AVOID BOUNDARY LAYER

22. PREDICTION OF SURFACE-CRACK-AT-HOLE SHAPE AND CRACK-GROWTH BEHAVIOR

23. APPLICATION TO FRACTURE
(Surface crack in D6ac steel under bending loads)

24. FRACTURE OF SURFACE AND THROUGH CRACKS

25. CONCLUDING REMARKS
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).
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.
Three-dimensional stress-intensity factor solutions have improved the fatigue-crack growth predictions for complex crack configurations.
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.