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

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THE SURFACE-CRACK PROBLEMTHE SURFACE-CRACK PROBLEM

2w

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SEMI-CIRCULAR SURFACE CRACK UNDER SEMI-CIRCULAR SURFACE CRACK UNDER REMOTE TENSIONREMOTE TENSION

Newman (1979)

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SEMI-ELLIPTICAL SURFACE CRACK UNDERSEMI-ELLIPTICAL SURFACE CRACK UNDERREMOTE TENSIONREMOTE TENSION

Newman (1979)

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THE BOUNDARY-LAYER EFFECTTHE BOUNDARY-LAYER 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 STRESS-INTENSITY FACTORSNORMALIZED STRESS-INTENSITY FACTORS

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

Raju & Newman (1979-1986)

2r

2r

w

2w

2w 2w

2w

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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)

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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)

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STRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTICSTRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTICCORNER CRACKSCORNER CRACKS

Bakuckas (1999)

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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

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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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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

}

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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

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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

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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

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Kfs = R K

PLANE-STRESS-TO-PLANE-STRAIN CONVERSIONPLANE-STRESS-TO-PLANE-STRAIN CONVERSION

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OFFSET ANGLES TO AVOID BOUNDARY LAYER OFFSET ANGLES TO AVOID BOUNDARY LAYER

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PREDICTION OF SURFACE-CRACK-AT-HOLE SHAPE PREDICTION OF SURFACE-CRACK-AT-HOLE SHAPE AND CRACK-GROWTH BEHAVIORAND CRACK-GROWTH BEHAVIOR

2r

2w

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

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FRACTURE OF SURFACE AND THROUGH CRACKS FRACTURE OF SURFACE AND THROUGH CRACKS

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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.