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**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

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**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

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**EMBEDDED ELLIPTICAL CRACK TO AN APPROXIMATE SURFACE CRACK SOLUTION**

ff Green & Sneddon (1950) Irwin (1962)

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**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

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**THE SURFACE-CRACK PROBLEM**

2w

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

Newman (1979)

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**SEMI-ELLIPTICAL SURFACE CRACK UNDER**

REMOTE TENSION Newman (1979)

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**THE BOUNDARY-LAYER EFFECT**

Crack Lose of square-root singularity Free surface Hartranft & Sih (1970) Benthem & Koiter (1973)

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**EFFECT OF FE MESH REFINEMENT ON NORMALIZED STRESS-INTENSITY FACTORS**

Raju & Newman (1979)

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**CRACK CONFIGURATIONS ANALYZED WITH FEA **

UNDER REMOTE TENSION OR BENDING LOADS 2w 2w 2w 2r 2w w 2r Raju & Newman ( )

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**SURFACE CRACK AT A HOLE UNDER TENSION**

Newman & Raju (1981)

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**ILL-SHAPED ELEMENT MESH PROBLEM CORNER CRACK AT A HOLE UNDER TENSION**

Tan et al (1988)

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**STRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTIC**

CORNER CRACKS Bakuckas (1999)

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**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

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**} } Corner Crack at Hole under Tension: a/c = 1 and f = 0 & 90o Major**

discovery } w = 6 r } w = 400 r

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**} } Corner Crack at Hole under Bending: a/c = 1 and f = 0 & 90o**

w = 6 r Major discovery } w = 400 r

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**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**

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**APPLICATION TO FATIGUE-CRACK GROWTH**

Plane-strain behavior Crack Plane-stress behavior Free surface Jolles & Tortoriello (1983) Newman & Raju (1984)

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**PLANE-STRESS-TO-PLANE-STRAIN CONVERSION**

DKfs = bR DK

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**OFFSET ANGLES TO AVOID BOUNDARY LAYER**

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

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**APPLICATION TO FRACTURE **

(Surface crack in D6ac steel under bending loads)

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**FRACTURE OF SURFACE AND THROUGH CRACKS**

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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.

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