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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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**Our Proposed Method to Understand or Bound the Problem: **

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 Try to understand the current solutions to the 2-D problem Compare with current length scale requirements in ASTM E 399 and E 1820 a ra rb Effect of constraint on crack tip plastic zone size and orientation K, T R>>rp small strain analysis 2-D Plane Strain Boundary Layer Solution (Gives “exact” solution for crack tip stress field in infinite body)

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**Length Scale Requirements in Current ASTM E08 Standards**

E399 – C(T) For valid KIC, and Implicit requirement on B E1820 – C(T), SEN(B) a = crack length B = thickness W = width b0 = W-a For valid KIC, and For valid JC, (crack instability without stable tearing) For valid JIC, (crack instability proceeded by stable tearing) For J determination (ensures positive constraint)

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**Step 2: Evaluate Finite Boundary 3-D Surface Crack Problem**

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, st? (Analogous to thickness requirements in E399 and E1820) What influence does the free surface behind the crack tip have for the shallow crack problem? Stresses gradually decrease below SSY values as plasticity becomes uncontained rfa rfb K, T R>>rp rfa rfb

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**1/C = J/(lsys) E 1/CJ(E/sys) B D 1/CK(E/sys) C A jo j Collapse J J-j**

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 (j) 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/(lsys) Large Scale Yielding Small Scale Yielding E Collapse 1/CJ(E/sys) B J D J-j 1/CK(E/sys) Increasing Deformation K or J C K-j or J-j A K or J dominance not achieved due to lack of constraint, 2 parameters required to describe fields jo K or J dominance, only 1 parameter required j 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 = Constraint measure jo = Constraint condition equivalent to T = Q = 0 Loading trajectories Example: E399 KIc test Example: E1820 JIc test Examples: E740 KIe tests

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**Deformation Limit Study for E740**

Determine reasonable deformation limits to compare to rfa and rfb to characterize test result Proposed deformation limits based on SSY Valid, Check at initiation of tearing LSY Valid , f Point (xe,B) m Point (xf, yf) rfa a B Point (xint,0) 2c rfb If prior to initiation of tearing then classify as plastic collapse

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**Modified Boundary Layer FEMs**

Plane strain boundary conditions 20 node bricks WARP3D analysis Linear Plus Power Law Mat’l Model Apply displacement field as function of K, T Vary T/sys, K, T R>>rp In this work s0 = sys E/sys = 400, n = 10 T/sys = 0.9 T/sys = 0.0 T/sys = -0.9 E/sys = 400, n = 10 = r*

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**C(T) a/w = 0.5; E/sys = 400; n = 10 Plane strain boundary conditions**

20 node bricks WARP3D analysis Linear Plus Power Law Mat’l Model for for

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**5% deviation curve (typ)**

C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by T-Stress r* = 2 5% deviation curve (typ) r* = 4 r* = 6 r* = 8 CJ = 31 @ r* = 2 “a” in deformation scale can be rfa or rfb. The minimum dimension is the limiting case. rfa = rfb for this geometry. Assume 5% deviation from MBL sopen as limit of LSY validity

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**C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by Q**

CJ = 49 @ r* = 4

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**C(T) a/w = 0.5, E/sys = 400, n = 10 Jtotal vs. Jelastic Comparison**

Ck = 110 Assume 10% deviation from elastic K prediction as limit of SSY validity

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C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by T-Stress – Another look at Deform. Limits Traditional definition of SSY, at T = 0, r* = 2 SSY LSY Plastic Collapse Plastic Collapse LSY, J SSY, K, Jel E399, KIC, CJ = 31 CK-E399 = 1100 CK = 110 Note: this value is a function of E/sys

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**SC(T) FEMs 20 node bricks WARP3D analysis**

Linear Plus Power Law Mat’l Model f Point (xe,B) m Point (xf, yf) rfa a B Point (xint,0) 2c rfb a/B = 0.50, a/c = 1.0

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**SC(T) Test conducted at NASA MSFC**

2219-T87, E/sys = 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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**SC(T) Test conducted at NASA MSFC Location of Tearing Initiation**

f = 18 degrees or 2 f / p = 0.2

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**SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/sys = 190, n = 10**

Reference Solution Comparison by T-Stress 2f/p = 0.19 Initiation of ductile tearing in SC(T) test CJ ≈ 50

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**SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/sys = 190, n = 10**

Reference Solution Comparison by Q 2f/p = 0.19 Initiation of ductile tearing in SC(T) test CJ ≈ 50

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**SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/sys = 190, n = 10**

Jtotal vs. Jelastic Comparison 2f/p = 0.19 Initiation of ductile tearing in SC(T) test Ck = 110

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**SSY Deformation Limit Determination**

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**LSY Deformation Limit Determination**

E 1820 JC E 1820 JIC

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**Deformation Limit Study for E740**

Determine reasonable deformation limits to compare to rfa and rfb 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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**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 CK, to ensure that Jf/JK < 1.2, especially for materials with low E/sys.

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**Deformation Limit Comparison**

Increasing Load May need to modify CK limit for materials with low E/sys.

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**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 Jel solution to determine limits for SSY (K or Jel 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/sys, n, or other? Which material variables have the strongest influence on deformation limits? Should we use different deformation limits to compare to crack size (rfa) and ligament length (rfb)? 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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