Presentation on theme: "Workshop on Life Prediction Methodology and Validation for Surface Cracks Investigations into Deformation Limits for SSY and LSY for Surface Cracks in."— Presentation transcript:
1Workshop on Life Prediction Methodology and Validation for Surface Cracks Investigations into Deformation Limits for SSY and LSY for Surface Cracks in Tension 5/23/2007Phillip Allen & Doug WellsNASA MSFCDamage Tolerance Team – EM20
2Our 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 ProblemTry to understand the current solutions to the 2-D problemCompare with current length scale requirements in ASTM E 399 and E 1820ararbEffect of constraint on crack tip plastic zone size and orientationK, TR>>rpsmall strain analysis2-D Plane Strain Boundary Layer Solution (Gives “exact” solution for crack tip stress field in infinite body)
4Step 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 uncontainedrfarfbK, TR>>rprfarfb
51/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 YieldingSmall Scale YieldingECollapse1/CJ(E/sys)BJDJ-j1/CK(E/sys)Increasing DeformationK or JCK-j or J-jAK or J dominance not achieved due to lack of constraint, 2 parameters required to describe fieldsjoK or J dominance, only1 parameter requiredjASSY, K or J dominance, 1 parameterLSY, J dominance, 1 parameterSSY, K or J with constraint, 2 parametersLSY, J with constraint, 2 parametersBCDEConstraint Influenced Collapse, Alternative methods= Constraint measurejo = Constraint condition equivalent to T = Q = 0Loading trajectoriesExample: E399 KIc testExample: E1820 JIc testExamples: E740 KIe tests
6Deformation Limit Study for E740 Determine reasonable deformation limits to compare to rfa and rfb to characterize test resultProposed deformation limits based onSSY Valid,Check at initiation of tearingLSY Valid ,fPoint (xe,B)mPoint (xf, yf)rfaaBPoint (xint,0)2crfbIfprior to initiationof tearing then classify as plastic collapse
7Modified Boundary Layer FEMs Plane strain boundary conditions20 node bricksWARP3D analysisLinear Plus Power Law Mat’l ModelApply displacement field as function of K, TVary T/sys,K, TR>>rpIn this work s0 = sysE/sys = 400, n = 10T/sys = 0.9T/sys = 0.0T/sys = -0.9E/sys = 400, n = 10= r*
8C(T) a/w = 0.5; E/sys = 400; n = 10 Plane strain boundary conditions 20 node bricksWARP3D analysisLinear Plus Power Law Mat’l Modelforfor
95% deviation curve (typ) C(T) a/w = 0.5, E/sys = 400, n = 10Reference Solution Comparison by T-Stressr* = 25% deviation curve (typ)r* = 4r* = 6r* = 8CJ = 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
10C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by Q CJ = 49@ r* = 4
11C(T) a/w = 0.5, E/sys = 400, n = 10 Jtotal vs. Jelastic Comparison Ck = 110Assume 10% deviation from elastic K prediction as limit of SSY validity
12C(T) a/w = 0.5, E/sys = 400, n = 10Reference Solution Comparison by T-Stress – Another look at Deform. LimitsTraditional definition of SSY, at T = 0, r* = 2SSYLSYPlastic CollapsePlastic CollapseLSY, JSSY, K, JelE399, KIC,CJ = 31CK-E399 = 1100CK = 110Note: this value is a function of E/sys
13SC(T) FEMs 20 node bricks WARP3D analysis Linear Plus Power Law Mat’l ModelfPoint (xe,B)mPoint (xf, yf)rfaaBPoint (xint,0)2crfba/B = 0.50, a/c = 1.0
14SC(T) Test conducted at NASA MSFC 2219-T87, E/sys = 190, n = 10Sample description:W = 3.00 in.B = in.2c = in.a = in.a/c = 0.92a/B = 0.61Test conditions, results:70FMonotonic load to crack initiationInitiation force = kipTearing present 180 degGeneral tear length = in.Maximum tear length = in.
15SC(T) Test conducted at NASA MSFC Location of Tearing Initiation f = 18 degrees or 2 f / p = 0.2
16SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/sys = 190, n = 10 Reference Solution Comparison by T-Stress2f/p = 0.19Initiation of ductile tearing in SC(T) testCJ ≈ 50
17SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/sys = 190, n = 10 Reference Solution Comparison by Q2f/p = 0.19Initiation of ductile tearing in SC(T) testCJ ≈ 50
18SC(T) a/B = 0.61, a/c = 0.92, 2219-T87, E/sys = 190, n = 10 Jtotal vs. Jelastic Comparison2f/p = 0.19Initiation of ductile tearing in SC(T) testCk = 110
20LSY Deformation Limit Determination E 1820 JCE 1820 JIC
21Deformation Limit Study for E740 Determine reasonable deformation limits to compare to rfa and rfb to characterize test resultProposed deformation limits based onSSY Valid,LSY Valid ,Ifprior to initiationof tearing then classify as plastic collapse
22SC(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.
23Deformation Limit Comparison Increasing LoadMay need to modify CK limit for materials with low E/sys.
24Deformation 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?