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Damage Tolerance Assessment Branch MSFC Engineering Directorate 1 Workshop on Life Prediction Methodology and Validation for Surface Cracks Investigations into Deformation Limits for SSY and LSY for Surface Cracks in Tension 5/23/2007 Phillip Allen & Doug Wells NASA MSFC Damage Tolerance Team – EM20

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 2 Try to understand the current solutions to the 2-D problem Compare with current length scale requirements in ASTM E 399 and E 1820 How do we determine the proper deformation limits for surface cracks?.... Our Proposed Method to Understand or Bound the Problem: Step 1: Revisit the 2-D Length Scale Problem a rara rbrb 2-D Plane Strain Boundary Layer Solution (Gives exact solution for crack tip stress field in infinite body) Effect of constraint on crack tip plastic zone size and orientation K, T R>>r p small strain analysis

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 3 For valid K IC, and Implicit requirement on B Length Scale Requirements in Current ASTM E08 Standards E399 – C(T) a = crack length B = thickness W = width b 0 = W-a For valid K IC, and For valid J C, (crack instability without stable tearing) For valid J IC, (crack instability proceeded by stable tearing) For J determination (ensures positive constraint) E1820 – C(T), SEN(B)

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 4 Can the 3-D surface crack front at some distance from the free surface in a finite body be approximated by a plane strain boundary layer solution? What is the influence of the stress tangential to the crack front, t ? (Analogous to thickness requirements in E399 and E1820) What influence does the free surface behind the crack tip have for the shallow crack problem? Step 2: Evaluate Finite Boundary 3-D Surface Crack Problem r a r b r a r b Stresses gradually decrease below SSY values as plasticity becomes uncontained K, T R>>r p

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 5 1/C J ( ys ) 1/C K ( ys ) A D C B E A SSY, K or J dominance, 1 parameter LSY, J dominance, 1 parameter SSY, K or J with constraint, 2 parameters LSY, J with constraint, 2 parameters B C D E Constraint Influenced Collapse, Alternative methods Example: E399 KIc test Example: E1820 JIc test Examples: E740 KIe tests Increasing Deformation Constraint measure Constraint condition equivalent to T = Q = 0 Loading trajectories K- or J- J- J K or J K or J dominance, only 1 parameter required K or J dominance not achieved due to lack of constraint, 2 parameters required to describe fields Collapse At initiation of ductile tearing in a test sample or structure, the crack tip conditions will fall into one of the 5 regions A-E in the constraint/deformation diagram below. Evaluate the constraint ( ) and the deformation limits (C) at the onset of ductile tearing to determine the applicable region for assessment of crack tip conditions. 1/C = J/( l ys ) Small Scale Yielding Large Scale Yielding

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 6 Deformation Limit Study for E740 Determine reasonable deformation limits to compare to r a and r b to characterize test result Proposed deformation limits based on SSY Valid, LSY Valid, Point (x e,B) m Point (x, y ) r a a B Point (x int,0) 2c r b Check at initiation of tearing If prior to initiation of tearing then classify as plastic collapse

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 7 Modified Boundary Layer FEMs Plane strain boundary conditions 20 node bricks WARP3D analysis Linear Plus Power Law Matl Model Apply displacement field as function of K, T Vary T/ ys, K, T R>>r p T/ ys = 0.0 T/ ys = -0.9 T/ ys = 0.9 = r* In this work 0 = ys E/ ys = 400, n = 10

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 8 C(T) a/w = 0.5; E/ ys = 400; n = 10 Plane strain boundary conditions 20 node bricks WARP3D analysis Linear Plus Power Law Matl Model for

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 9 C(T) a/w = 0.5, E/ ys = 400, n = 10 Reference Solution Comparison by T-Stress C J = 31 r* = 2 r* = 4 r* = 6 r* = 8 5% deviation curve (typ) Assume 5% deviation from MBL open as limit of LSY validity a in deformation scale can be r a or r b. The minimum dimension is the limiting case. r a = r b for this r* = 2

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 10 C(T) a/w = 0.5, E/ ys = 400, n = 10 Reference Solution Comparison by Q C J = r* = 4

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 11 C(T) a/w = 0.5, E/ ys = 400, n = 10 J total vs. J elastic Comparison C k = 110 Assume 10% deviation from elastic K prediction as limit of SSY validity

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 12 C(T) a/w = 0.5, E/ ys = 400, n = 10 Reference Solution Comparison by T-Stress – Another look at Deform. Limits SSY, K, J el LSY, J Plastic Collapse C J = 31 C K = 110 C K-E399 = 1100 E399, K I C, Note: this value is a function of E/ ys Traditional definition of SSY, at T = 0, r* = 2 LSY SSY Plastic Collapse

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 13 Point (x e,B) m Point (x, y ) r a a B Point (x int,0) 2c r b 20 node bricks WARP3D analysis Linear Plus Power Law Matl Model a/B = 0.50, a/c = 1.0 SC(T) FEMs

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 14 SC(T) Test conducted at NASA MSFC 2219-T87, E/ ys = 190, n = 10 Sample description: W = 3.00 in. B = in. 2c = in. a = in. a/c = 0.92 a/B = 0.61 Test conditions, results: 70F Monotonic load to crack initiation Initiation force = kip Tearing present 180 deg General tear length = in. Maximum tear length = in.

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 15 = 18 degrees or 2 / = 0.2 SC(T) Test conducted at NASA MSFC Location of Tearing Initiation

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 16 Reference Solution Comparison by T-Stress 2 / = 0.19 SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/ ys = 190, n = 10 C J 50 Initiation of ductile tearing in SC(T) test

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 17 Reference Solution Comparison by Q 2 / = 0.19 SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/ ys = 190, n = 10 C J 50 Initiation of ductile tearing in SC(T) test

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 18 J total vs. J elastic Comparison 2 / = 0.19 SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/ ys = 190, n = 10 C k = 110 Initiation of ductile tearing in SC(T) test

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 19 SSY Deformation Limit Determination

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 20 LSY Deformation Limit Determination E 1820 J IC E 1820 J C

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 21 Deformation Limit Study for E740 Determine reasonable deformation limits to compare to r a and r b to characterize test result Proposed deformation limits based on SSY Valid, LSY Valid, If prior to initiation of tearing then classify as plastic collapse

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 22 SC(T) Test Evaluation per E740 Plots on pp also indicate that SSY should be valid for initiation of ductile tearing. Likely need to increase value for C K, to ensure that J /J K < 1.2, especially for materials with low E/ ys.

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 23 Deformation Limit Comparison Increasing Load May need to modify C K limit for materials with low E/ ys.

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Damage Tolerance Assessment Branch MSFC Engineering Directorate 24 Deformation Limit Study for E740 - Questions What are reasonable deformation limits to compare to specimen dimensions to characterize test results? Can we use deviation from J el solution to determine limits for SSY (K or J el valid solution)? Is a 5% deviation from J-T MBL solution a valid cut off point for LSY validity? Is this just in the noise in test data? Should our deformation limits be a function of E/ ys, n, or other? Which material variables have the strongest influence on deformation limits? Should we use different deformation limits to compare to crack size (r a ) and ligament length (r b )? How do r* distances compare to process zone sizes for ductile tearing? Is r* = 2 the right place to focus or other?

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