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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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Surface Crack - # 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

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Surface Crack - # 3 EMBEDDED ELLIPTICAL CRACK TO AN APPROXIMATE SURFACE CRACK SOLUTION f Green & Sneddon (1950) Irwin (1962)

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Surface Crack - # 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

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Surface Crack - # 5 THE SURFACE-CRACK PROBLEM 2w

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Surface Crack - # 6 SEMI-CIRCULAR SURFACE CRACK UNDER REMOTE TENSION Newman (1979)

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Surface Crack - # 7 SEMI-ELLIPTICAL SURFACE CRACK UNDER REMOTE TENSION Newman (1979)

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

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

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

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Surface Crack - # 11 SURFACE CRACK AT A HOLE UNDER TENSION Newman & Raju (1981)

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

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Surface Crack - # 13 STRESS-INTENSITY FACTORS FOR QUARTER-ELLIPTIC CORNER CRACKS Bakuckas (1999)

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Surface Crack - # 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

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

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

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

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

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

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Surface Crack - # 20 K fs = R K PLANE-STRESS-TO-PLANE-STRAIN CONVERSION

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Surface Crack - # 21 OFFSET ANGLES TO AVOID BOUNDARY LAYER

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Surface Crack - # 22 PREDICTION OF SURFACE-CRACK-AT-HOLE SHAPE AND CRACK-GROWTH BEHAVIOR 2r 2w

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Surface Crack - # 23 APPLICATION TO FRACTURE (Surface crack in D6ac steel under bending loads)

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Surface Crack - # 24 FRACTURE OF SURFACE AND THROUGH CRACKS

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Surface Crack - # 25 CONCLUDING 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.

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