Workshop on Life Prediction Methodology and Validation for Surface CracksInvestigations into DeformationLimits for SSY and LSY forSurface Cracks in Tension5/23/2007 Phillip Allen & Doug Wells NASA MSFC Damage Tolerance Team – EM20
K, T a ra rb R>>rp 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 Effect of constraint on crack tip plastic zone size and orientation small strain analysis 2-D Plane Strain Boundary Layer Solution (Gives “exact” solution for crack tip stress field in infinite body)
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)
Stresses gradually decrease below SSY values as plasticity becomes uncontained K, T rfb rfa R>>rp rfa rfb 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?
A SSY, K or J dominance, 1 parameter Loading trajectories E A D C B B LSY, J dominance, 1 parameter C SSY, K or J with constraint, 2 parameters D LSY, J with constraint, 2 parameters E Constraint Influenced Collapse, Alternative methods 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 Collapse 1/CJ(E/sys) J J-j 1/CK(E/sys) Increasing Deformation K or J K-j or J-j K or J dominance not achieved due to lack of constraint, 2 parameters required to describe fields jo j K or J dominance, only 1 parameter required • = Constraint measure jo = Constraint condition equivalent to T = Q = 0 Example: E399 KIc test Example: E1820 JIc test Examples: E740 KIe tests
rfb m Point (xe,B) Point (xf, yf) B a rfa f Point (xint,0) 2c 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 , If prior to initiation of tearing then classify as plastic collapse
K, T R>>rp 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, 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*
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
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
C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by Q CJ = 49 @ r* = 4
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
C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by T-Stress – Another look at Deform. Limits LSY SSY Plastic Collapse Traditional definition of SSY, at T = 0, r* = 2 Plastic Collapse SSY, K, Jel LSY, J E399, KIC, CJ = 31 CK-E399 = 1100 CK = 110 Note: this value is a function of E/sys
rfb m Point (xe,B) Point (xf, yf) B a rfa f Point (xint,0) 2c SC(T) FEMs • 20 node bricks • WARP3D analysis • Linear Plus Power Law Mat’l Model a/B = 0.50, a/c = 1.0
SC(T) Test conducted at NASA MSFC 2219-T87, E/sys = 190, n = 10 • Sample description: • W = 3.00 in. • B = 0.375 in. • 2c = 0.494 in. • a = 0.229 in. • a/c = 0.92 • a/B = 0.61 • Test conditions, results: • 70F • Monotonic load to crack initiation • Initiation force = 54.95 kip Tearing present 180 deg General tear length = 0.006 in. Maximum tear length = 0.013 in.
f = 18 degrees or 2 f / p = 0.2 SC(T) Test conducted at NASA MSFC Location of Tearing Initiation
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
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
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
LSY Deformation Limit Determination E 1820 JC E 1820 JIC
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
SC(T) Test Evaluation per E740 Plots on pp 16-18 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.
Deformation Limit Comparison Increasing Load May need to modify CK limit for materials with low E/sys.
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?