NUREG/CR-5971
UILU-ENG-92-2014
CDNSWC/SME-CR-19-92
Continuum and Micromechanics
Treatment of Constraint in
Fracture
III I
Manuscript Completed: February 1993
Date Published: July 1993
Prepared by
R. H. Dodds, Jr., University of Illinois
C. F. Shih, Brown University
T. L. Anderson, Texas A&M University
University of Illinois at Urbana-Champaign
Department of Civil Engineering, MC-250
205 North Mathews Avenue
Urbana, I161801-2352
Brown University
Division of Engineering
Providence, RI 02912
Texas A&M University
Department of Mechanical Engineering
College Station, TX 77843
Under Contract to:
Naval Surface Warfare Center
Annapolis Detachment, Carderock Division
Code 2814
Annapolis, MD 21402-5067
Preparedfor
Divisionof Engineering
Office of Nuclear Regulatory Research _,q _ _ _'_
U.S. Nuclear Regulatory Commission _]f_?_li_::}_ _"
- ,- Jt.,_ |
Washington, DC 20555-0001 b
NRC FIN B6290 _........, - -
ABSTRACT
Two complementary methodologies are described to quantify the effects of crack-tip stress
triaxiality (constraint) on the macroscopic measures ofelastic-plastic fracture toughness,
J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodolo-
gy,two parameters, J and Q, suffice to characterize the full range ofnear-tip environments
at the onset of fracture. J sets the size scale of the zone of high stresses and large deforma-
tions while Q scales the near-tip stress level relative to a high triaxiality reference stress
state. Full-field finite element calculations show that the J-Q field dominates over physi-
cally significant size scales, i.e., it describes the environment in which brittle and ductile
failure mechanisms are active. The material's fracture resistance is characterized by a
toughness locus, Jc(Q), which defines the sequence of J-Q values at fracture determined
by experiment from high constraint conditions (Q =0) to low constraint conditions (Q < 0).
Toreduce experimental effort needed to construct a J-Q toughness locus, a micromechanics
methodology is described which predicts the toughness locus using crack-tip stress fields
and critical J-values from a few fracture toughness tests. A robust micromechanics model
for cleavage fracture has evolved from the observations of a strong, spatial self-similarity
of crack-tip principal stresses under increased loading and across different fracture speci-
mens. While the spatial variation remains self-similar, the magnitudes of principal
stresses vary dramatically as crack-tip constraint evolves under loading. The microme-
chanics model employs the volume of material bounded within principal stress contours at
fracture to correlate Jc values for different specimens and loading modes. The J-Q descrip-
tion of the crack-tip stress fields predicts the similarity of principal stress contours as
constraint evolves under loading. For an applied J-value, the size, but not the shape, of
principal stress contours is altered by the near-tip, uniform hydrostatic stress states of ad-
justable magnitude characterized by Q. These observations imply that values specified for
metallurgical parameters in the micromechanics model, such as the critical fracture stress
and the distance to the critical particle, have only a weak influence on the relative variation
of fracture toughness, Jt, with constraint for a given material and temperature.
This report explores the fundamental concepts of the J-Q description of crack-tip fields,
the fracture toughness locus and micromechanics approaches to predict the variability of
macroscopic fracture toughness with constraint under elastic-plastic conditions. While
these concepts derived from plane-strain considerations, initial applications in fully 3-D
geometries are very promising. Computational results are presented for a surface cracked
plate containing a 6:1 semi-elliptical, a=t/4 flaw subjected to remote uniaxial and biaxial
tension. Crack-tip stress fields consistent with the J-Q theory are demonstrated to exist
at each location along the crack front. The micromechanics model employs the J-Q descrip-
tion of crack-front stresses to interpret fracture toughness values measured on laboratory
specimens for fracture assessment of the surface cracked plate. The computational results
suggest only a minor effect of the biaxial loading on the crack tip stress fields and, conse-
quently, on the propensity for fracture relative to the uniaxial loading.
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Contents
Section No. Page
Abstract ...................................................................... iii
List of Figures ................................................................ vi
List of Tables ............................................................... viii
1. INTRODUCTION ....................................................... 1
2. J-Q THEORY ........................................................... 4
2.1 Q-Family of Fields-MBL Formulation ............................... 4
2.2 Difference Field and Near-Tip Stress Triaxiality ...................... 5
2.3 Choice of Reference Field ............................................ 7
2.4 Variation of Q with Distance ......................................... 7
2.5 Simplified Forms for Engineering Applications ........................ 8
2.6 Difference Field and Higher-Order Terms of the Asymptotic Series ..... 9
2.7 J-Q Material Toughness Locus ...................................... 10
3. MICROMECHANICAL CONSTRAINT CORRECTIONS ................ 12
3.1 Transgranular Cleavage Mechanism ................................ 12
3.2 Development of the Constraint Corrections ........................... 13
3.3 Application of Constraint Corrections in Fracture Testing ............. 18
3.4 Engineering Use of J-Q Fields in the Micromechanics Model .......... 19
4. SURFACE CRACKS UNDER UNIAXIAL AND BIAXIAL LOADING ..... 23
4.1 Part-Through Surface Crack Model ................................. 23
4.2 Crack Front Stress Triaxiality ...................................... 26
4.3 Matching Structural and Test Specimen Constraint ................... 29
5. CONCLUSIONS ........................................................ 32
6. REFERENCES ............... _ ........................................ 34
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