https://orcid.org/0000-0003-2767-1579
Abstract
The authors have been working to improve the crack tip opening displacement (CTOD) evaluation standard as a fracture parameter for the cleavage-type brittle fracture critical condition of carbon steel. In 2016, WES1108, Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement, which is the CTOD test standard in Japan, was revised, and subsequently, the CTOD calculation formula of ISO 15653:2010, Metallic Materials – Method of Test for the Determination of Quasistatic Fracture Toughness of Welds, was revised in 2018, focusing on the study of the formula that constitutes the basis of the standard. Similar to the original British Standards equation, the proposed CTOD calculation formula consists of a small-scale yield (SSY) term and a plastic term, but in the SSY term, the two-dimensional (2D) stress intensity factor (SIF) is used. The authors focused on the incorrectness of this treatment derived from the difference between 2D and three-dimensional (3D). Here, two accurate relationships have been explored through systematic finite element method analyses; one is the correlation of the 3D SIF values in the mid-thickness plane and 2D SIF, and the second is the relationship between the actual 3D SIF in mid-thickness and the CTOD in mid-thickness. The KI ratio (K3D/K2D) sharply coincides with the value 1.11, as inferred in several previous pieces of research in the idealistic infinite plate with a crack. However, if the ligament size is finite as in the actual fracture toughness test, the KI ratio drops significantly from 1.11, and in some cases, the KI ratio is less than 1. By unifying these findings, a new precise CTOD formula has been established. Lastly, the study inferred that the error of the calculation formula is improved, especially in small thickness regions, as compared with the current standard proposed in 2016 and 2018 by the authors.
Issue Section:
Technical Papers
References
1.
Wells
A. A.
, “Unstable Crack Propagation in Metals: Cleavage and Fast Fracture
,” in Crack Propagation Symposium
, vol. 2 (Cranfield
, UK
: The College of Aeronautics
, 1961
).2.
Metallic Materials – Unified Method of Test for the Determination of Quasistatic Fracture Toughness
, ISO 12135:2016 (Geneva, Switzerland: International Organization for Standardization
, 2016
).3.
Methods for Crack Opening Displacement (COD) Testing
(Superseded, Withdrawn), BS 5762:1979 (London: The British Standards Institution
, 1979
).4.
Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement
(Superseded), ASTM E1290–02 (West Conshohocken, PA
: ASTM International
, approved December 10, 2002
), https://doi.org/10.1520/E1290-025.
Tagawa
T.
, Kayamori
Y.
, Ohata
M.
, Yamashita
Y.
, Handa
T.
, Kawabata
T.
, Tsutsumi
K.
, Yoshinari
H.
, Aihara
S.
, and Hagihara
Y.
, “Difference between ASTM E1290 and BS 7448 CTOD Estimation Procedures
,” Welding in the World
54
, nos. 7–8
(July 2010
): R182
–R188
, https://doi.org/10.1007/BF032635046.
Kirk
M. T.
and Dodds
R. H.
, “J and CTOD Estimation Equations for Shallow Cracks in Single Edge Notch Bend Specimens
,” Journal of Testing and Evaluation
21
, no. 4
(1993
): 228
–238
, https://doi.org/10.1520/JTE11948J7.
Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement
, WES1108 (Tokyo, Japan: The Japan Welding Engineering Society
, 1995
).8.
Kawabata
T.
, Tagawa
T.
, Sakimoto
T.
, Kayamori
Y.
, Ohata
M.
, Yamashita
Y.
, Tamura
E.
, et al., “Proposal for a New CTOD Calculation Formula
,” Engineering Fracture Mechanics
159
(2016
): 16
–34
, https://doi.org/10.1016/j.engfracmech.2016.03.0199.
Metallic Materials – Method of Test for the Determination of Quasistatic Fracture Toughness of Welds
, ISO 15653:2010 (Geneva, Switzerland: International Organization for Standardization
, 2018
).10.
Larsson
S. G.
and Carlsson
A. J.
, “Influence of Non-singular Stress Terms and Specimen Geometry on Small-Scale Yielding at Crack Tips in Elastic-Plastic Materials
,” Journal of Mechanics and Physics of Solids
21
, no. 4
(July 1973
): 263
–277
, https://doi.org/10.1016/0022-5096(73)90024-011.
Anderson
T.
, Fracture Mechanics
, 4th ed. (Boca Raton, FL
: CPC Press
, 2017
).12.
Shih
C. F.
, “Relationships between the J-Integral and the Crack Opening Displacement for Stationary and Extending Cracks
,” Journal of the Mechanics and Physics of Solids
29
, no. 4
(August 1981
): 305
–326
, https://doi.org/10.1016/0022-5096(81)90003-X13.
Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures
, BS 7910:2019 (London: The British Standards Institution, 2019
).14.
Sih
G. C.
, “A Review of the Three-Dimensional Stress Problem for a Cracked Plate
,” International Journal of Fracture Mechanics
7
(March 1971
): 39
–61
, https://doi.org/10.1007/BF0023648215.
Bažant
Z. P.
and Estenssoro
L. F.
, “Surface Singularity and Crack Propagation
,” International Journal of Solids and Structures
15
, no. 5
(1979
): 405
–426
, https://doi.org/10.1016/0020-7683(79)90062-316.
Benthem
J. P.
, “The Quarter-Infinite Crack in a Half Space; Alternative and Additional Solutions
,” International Journal of Solids and Structures
16
, no. 2
(1980
): 119
–130
, https://doi.org/10.1016/0020-7683(80)90029-317.
Shah
R. C.
and Kobayashi
A. S.
, “Effect of Poisson’s Ratio on Stress Intensity Magnification Factor
,” International Journal of Fracture
9
(1973
): 360
–362
, https://doi.org/10.1007/BF0004922318.
She
C.
and Guo
W.
, “The Out-of-Plane Constraint of Mixed-Mode Cracks in Thin Elastic Plates
,” International Journal of Solids and Structures
44
, no. 9
(May 2007
): 3021
–3034
, https://doi.org/10.1016/j.ijsolstr.2006.09.00219.
Hutař
P.
, Ševčík
M.
, Náhlík
L.
, Zouhar
M.
, Seitl
S.
, Knésl
Z.
, and Fernández-Canteli
A.
, “Fracture Mechanics of the Three-Dimensional Crack Front: Vertex Singularity versus out of Plain Constraint Descriptions
,” Procedia Engineering
2
, no. 1
(April 2010
): 2095
–2102
, https://doi.org/10.1016/j.proeng.2010.03.22520.
He
Z.
, Kotousov
A.
, Fanciulli
A.
, Berto
F.
, and Nguyen
G.
, “On the Evaluation of Stress Intensity Factor from Displacement Field Affected by 3D Corner Singularity
,” International Journal of Solids and Structures
78–79
(January 2016
): 131
–137
, https://doi.org/10.1016/j.ijsolstr.2015.09.00721.
Garcia-Manrique
J.
, Camas
D.
, and Gonzalez-Herrera
A.
, “Study of the Stress Intensity Factor Analysis through Thickness: Methodological Aspects
,” Fatigue & Fracture of Engineering Materials & Structures
40
, no. 8
(August 2017
): 1295
–1308
, https://doi.org/10.1111/ffe.1257422.
Garcia-Manrique
J.
, Camas-Peña
D.
, Lopez-Martinez
J.
, and Gonzalez-Herrera
A.
, “Analysis of the Stress Intensity Factor along the Thickness: The Concept of Pivot Node on Straight Crack Fronts
,” Fatigue & Fracture of Engineering Materials & Structures
41
, no. 4
(April 2018
): 869
–880
, https://doi.org/10.1111/ffe.1273423.
Murakami
Y.
, Stress Intensity Factors Handbook
, vols. 1–2 (Oxford, UK: Pergamon Press, 1987
).24.
Pook
L. P.
, “A 50-Year Retrospective Review of Three-Dimensional Effects at Cracks and Sharp Notches
,” Fatigue & Fracture of Engineering Materials & Structure
36
, no. 8
(August 2013
): 699
–723
, https://doi.org/10.1111/ffe.1207425.
Berto
F.
, Lazzarin
P.
, and Wang
C. H.
, “Three-Dimensional Linear Elastic Distributions of Stress and Strain Energy Density ahead of V-Shaped Notches in Plates of Arbitrary Thickness
,” International Journal of Fracture
127
(June 2004
): 265
–282
, https://doi.org/10.1023/B:FRAC.0000036846.23180.4d26.
Kawabata
T.
, Tagawa
T.
, Kayamori
Y.
, Ohata
M.
, Yamashita
Y.
, Kinefuchi
M.
, Yoshinari
H.
, et al., “Plastic Deformation Behavior in SEB Specimens with Various Crack Length to Width Ratios
,” Engineering Fracture Mechanics
178
, no. 1
(June 2017
): 301
–317
, https://doi.org/10.1016/j.engfracmech.2017.03.02927.
Kawabata
T.
, Tagawa
T.
, Kayamori
Y.
, Ohata
M.
, Yamashita
Y.
, Kinefuchi
M.
, Yoshinari
H.
, et al., “Applicability of New CTOD Calculation Formula to Various a0/W Conditions and B×B Configuration
,” Engineering Fracture Mechanics
179
, no. 15
(June 2017
): 375
–390
, https://doi.org/10.1016/j.engfracmech.2017.03.02728.
Kawabata
T.
, Tagawa
T.
, Kayamori
Y.
, Mikami
Y.
, Kitano
H.
, Kiuchi
A.
, Kanna
S.
, et al., “Investigation on η and m Factors for J Integral in SE(B) Specimens
,” Theoretical and Applied Fracture Mechanics
97
(October 2018
): 224
–235
, https://doi.org/10.1016/j.tafmec.2018.08.01329.
Kawabata
T.
, Kayamori
Y.
, and Tagawa
T.
, “A Proposal of the Crack Tip Opening Displacement Calculation Formula and Its Conversion Factor to J-Integral in C(T) Specimens
,” Materials Performance and Characterization
9
, no. 5
(October 2020
): 608
–626
, https://doi.org/10.1520/MPC2019019630.
Srawley
J. E.
, “Wide Range Stress Intensity Factor Expressions for ASTM E399 Standard Fracture Toughness Specimens
,” International Journal of Fracture
12
, no. 3
(June 1976
): 475
–476
, https://doi.org/10.1007/BF0003284431.
Dassault Systems
Abaqus/Standard, Version 6.14-1
(Vélizy-Villacoublay, France: Dassault Systems, 2014
).32.
Berto
F.
, Lazzarin
P.
, and Kotousov
A.
, “On Higher Order Terms and Out-of-Plane Singular Mode
,” Mechanics of Materials
43
, no. 6
(June 2011
): 332
–341
, https://doi.org/10.1016/j.mechmat.2011.03.00433.
Berto
F.
and Lazzarin
P.
, “Multiparametric Full-Field Representations of the In-Plane Stress Fields ahead of Cracked Components under Mixed Mode Loading
,” International Journal of Fatigue
46
(January 2013
): 16
–26
, https://doi.org/10.1016/j.ijfatigue.2011.12.004
This content is only available via PDF.
All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ASTM International.
You do not currently have access to this content.
