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

2. 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)

3. 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)

4. 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

5. 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

6. 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

7. 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*

8. 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

9. 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

10. C(T) a/w = 0.5, E/sys = 400, n = 10 Reference Solution Comparison by Q
CJ = 49
@ r* = 4

11. 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

12. 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

13. 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

14. 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.

15. SC(T) Test conducted at NASA MSFC Location of Tearing Initiation
f = 18 degrees or 2 f / p = 0.2

16. 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

17. 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

18. 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

19. SSY Deformation Limit Determination

20. LSY Deformation Limit Determination
E 1820 JC
E 1820 JIC

21. 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

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 CK, to ensure that Jf/JK < 1.2, especially for materials with low E/sys.

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

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 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?