Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Equivalent Distributed Stress Analysis of a Semi-Circular Surface Crack
Zwe Letyar Htut*, Naoki OSAWA*, Satoyuki TANAKA**, Phyo Myat Kyaw**Graduate School of Engineering, Osaka University, Suita, Osaka, Japan**Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima, JapanABSTRACT

Symbols

Elastic-Plastic Fracture Mechanics (EPFM) parameters (plastic zonesize, rp and Crack Tip Opening Displacement, CTOD) of a semi-circularsurface crack are estimated by two-dimensional analysis based on
Equivalent Distributed Stress (EDS) concept. EDS is determined by anEDS analysis system based on spline interpolation and Generalized
matrix Inversion (EDSGI) developed in this study. Surface crack’s ‘a-K’
relationship is analyzed by Interaction Integral Method (IIM) with
precise Crack Face Traction (CFT) integral implemented in publicdomain Finite Element (FE) code of WARP3D. In the analyses of Crack
Cohesive Force (CCF)’s a-K relationship, SIF for CFT stress partiallyapplied on an element face is integrated by ultra-high order Gaussianquadrature. The rp and CTOD estimated by two-dimensional EDS
analyses almost agree with those calculated by three-dimensional
Elastic-Plastic Finite Element Analysis (EPFEA). This demonstrates theeffectiveness of EDS concept and the developed EDS analysis system
for surface cracks.

[A]ac{coef}
E
[E]
[E+]
fP(x)
fY(x)
g(ξ,x)
g*(ξ,x)KPKYmnn̄NNaP

KEYWORDS: Crack, Equivalent distributed stress, Stress intensity
factor, Generalized matrix inversion, Crack cohesive force

NOMENCLATURE

rpt(x)tY(x)VLAcronyms
CCF
CFT
CCT
COD
CTOD
EDS
EDSGI

Crack Cohesive Force (MPa)
Crack Face Traction (MPa)Center Crack Tension (MPa)
Crack Opening Displacement (mm)Crack Tip Opening Displacement (mm)Equivalent Distributed Stress (MPa)EDS analysis system which is based on Spline interpolation
and Generalized matrix Inversion
EPFEA Elastic-Plastic Finite Element Analysis
EPFM Elastic-Plastic Fracture Mechanics
FCPFatigue Crack Propagation
FLM
Fictitious crack face Loading Method
LEFM Linear Elastic Fracture Mechanics
RHS
Right Hand SideSIF
Stress Intensity Factor (MPa mm0.5)

VR{w(q)}xa-K relation matrix
Fictitious crack’s half-length (mm)Real crack length (mm)Coefficient vector
Young’s Modulus (N/mm2)
m × n̄ matrix
Moore-Penrose general inverse matrix
EDS for external loading (MPa)EDS for crack cohesive force (MPa)Weight function of target crack when a pair of unit point load
traction is applied at x = ξ on the crack face of crack length, aWeight function of center crack for the target crack
SIF due to external loading (MPa mm0.5)
SIF due to CCF calculated by FLM at the fictitious crack tip(MPa mm0.5)
Number of rows of matrix [A]Number of columns of matrix [A]Number of independent coefficients
Number of spline interpolation divisions
Number of SIF evaluation points
Remote tensile loading (MPa)
Plastic zone size (mm)
CFT (MPa)
CCF (MPa)
Fictitious crack opening displacement calculated by EPFEA(mm)Real crack opening displacement calculated by EPFEA (mm)A vector which is equal to √𝜆(𝑞) , q = 1,…,n̄Coordinate along the crack face for two-dimensional centercrack and thickness direction for three-dimensional surface
crack (mm)Greek Symbols
α, β, γ, δ Spline interpolation coefficientsεP
Plastic strain
θCrack bodyθ*Uncracked bodyκ(q)Singular value of [E]λPlastic constraint factor

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