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Comparison of ElasticPlastic Surface Crack Solutions

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Life Prediction Methodology and Validation for Surface Cracks. Comparison of Elastic-Plastic Surface Crack Solutions. Chris Wilson and Eric Quillen ... – PowerPoint PPT presentation

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Title: Comparison of ElasticPlastic Surface Crack Solutions


1
Comparison of Elastic-Plastic Surface Crack
Solutions
  • Chris Wilson and Eric Quillen
  • Department of Mechanical Engineering
  • Tennessee Technological University
  • Cookeville, TN

2
Overview
  • Introduction
  • Past Through Crack Validation Work
  • The Problem with Surface Cracks
  • Geometric Complexity
  • Mechanical Behavior
  • Effect of Idealization on Results
  • Elastic-Plastic J-Solutions
  • Finite Elements Typically
  • Modeling Assumptions
  • Comparisons, Conclusions, and Recommendations

3
J -integral
  • EPFM parameter
  • Rices path independent line integral
  • Energy and stress intensity parameter
  • Ramberg-Osgood power law

4
EPRI Handbook Format
Total J taken as sum of elastic and plastic parts
(figure from Anderson).
5
EPRI Handbook Format
6
EPRI Handbook Approach
7
Previous Through Crack Validation Work
  • Objective
  • Validate existing solutions
  • EPRI handbook method
  • Reference stress method
  • Ramberg-Osgood constants estimation
  • Geometries
  • Center-cracked tensile (CCT)
  • Single-edge notched tensile (SENT)
  • Single-edge notched bend (SENB)
  • Materials
  • Al2024, Al2219, IN100, SS301

8
Material Properties
  • Engineering and true stress-strain curves
  • Determination of n and ? for four materials
    AL2024, AL2219, IN100 and SS301 (5ltnlt25)
  • Empirical Formulae
  • Constant volume method
  • Barsom and Rolfe
  • Curve fitting technique
  • All data from yield to ultimate stress (RO-1)
  • Plastic data near yield stress (RO-2)
  • Plastic data near ultimate stress (RO-3)
  • Incremental plasticity and actual stress-strain

9
Through Crack Conclusions
  • Original EPRI solutions for shallow cracks in CCT
    plane strain questionable
  • Excellent agreement of new results with Shih and
    Needleman results for SENT plane strain
  • For SENB plane strain, no firm conclusion
  • RSM and EPRI results agree within 5, except for
    a/w0.125 with n gt 13
  • Constant volume method overestimates Jpl

10
On to Surface Cracks
a crack depth c half crack width t
thickness w half specimen width (W2w) h half
specimen height (H2h)
Important ratios a/c, a/t, c/w, h/w
11
Need for Validation No Newman-Raju
Many different solutions before settling with
Newman-Raju family of solutions (figure from
Sanford)
12
The Problem Mechanical Behavior
  • Varying Constraint Around Crack Boundary
  • Changes in Singularity Order
  • Constitutive Models

Ramberg-Osgood Power Law
13
The Problem Modelling Idealization
  • Crack Shape Evolution Beyond Elliptical Shapes
  • Real Materials Arent Typically Ramberg-Osgood
  • Deformation Plasticity vs. Real Behavior

14
Crack Shape Evolution
Inconel 718 Tension Specimen (Hudak, et al. NASA
CR 4318)
15
Tunnelling
Aluminum 2219-T851 Tension Specimen (Carter,
Canda and Blind, ASTM STP 1060)
16
Overview
  • Introduction
  • Past Through Crack Validation Work
  • Problems with Surface Cracks
  • Geometric Complexity
  • Mechanical Behavior
  • Effect of Idealization on Results
  • Elastic-Plastic J-Solutions
  • Finite Elements Typically
  • Modeling Assumptions
  • Comparisons, Conclusions, and Recommendations

17
Elastic-Plastic J-Solutions
  • Finite Elements Dominate the Scene
  • Common Modeling Assumptions
  • Ramberg-Osgood Material
  • Deformation Plasticity
  • Small Strain Theory
  • No Effect of Hydrostatic Pressure on Yield
  • Elliptical Cracks
  • Tension, Bending, or Pressure

18
Some J-Solutions
  • Yagawa and Kitajima 1992
  • Sharobeam and Landes 1995, 1999
  • McClung, et al. 1999
  • Incremental plasticity to model fully plastic
  • a/t 0.2, 0.5, 0.8
  • a/c 0.2, 0.6, 1.0
  • h/w 1
  • Lei 2003
  • Deformation plasticityfully plastic (? 10?y)
  • h/w 4

19
New Work
  • Used
  • FEA-Crack
  • ABAQUS
  • 20-Noded, Not 8-Noded Elements
  • Explored
  • Fully Plastic Region
  • Specimen Height
  • Mesh Refinement
  • Revisited
  • Elastic Solution
  • Symmetry

20
Fully Plastic Region
Partial Layer 1
LayerCR
Layer 2
Layer 1
21
Mesh Refinement
3x crack-front nodes
17-45 crack-front nodes
22
Summary of Results
  • Fully plastic region size had no effect on the
    resulting J-integrals
  • Specimen height had no significant effect on the
    J-integral (lt5)
  • Coarse and refined meshes gave the same result
  • Large changes in h1 found at surface (always) and
    at depth (sometimes) for 1/4-symmetry models

23
Mesh Refinement (a/t 0.2, a/c 0.2)
24
Comparison for a/t 0.2, a/c 0.2
25
Comparison for a/t 0.2, a/c 1.0
26
Comparison for a/t 0.8, a/c 0.2
27
Elastic Solution for a/t 0.2, a/c 0.2
28
Elastic Solution for a/t 0.2, a/c 0.6
29
Elastic Solution for a/t 0.8, a/c 0.6
30
1/2-Symmetry vs. 1/4-Symmetry
31
Tied vs. Untied Nodes a/t 0.2, a/c 0.2
32
Conclusions
  • Fully Plastic Results
  • McClung et al. and Lei compared relatively well
    with the current FEMs
  • Surface and depth spikes were present
  • Anomaly at 3rd and 4th angles resulted in large
    percent differences in some models
  • K and Elastic J-integral Results
  • Newman-Raju comparison was good for shallow
    cracks
  • Surface and depth spikes were present again
  • Consensus SolutionNot Yet, But Close

33
Recommendations
  • Investigate the surface and depth phenomenon
  • Investigate the anomaly at the third or fourth
    angle
  • Investigate mesh refinement and element type (and
    integration scheme)
  • Expand to study bending or use same meshes for
    corner cracks in tension or bending
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