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

Low cycle fatigue crack growth behavior of hull plates based on accumulative plastic damage
Mengyuan Rong, Qin Dong,Jiankang Lei
School of Naval Architecture,Ocean and Energy Power Engineering., Wuhan University of Technology
Wuhan, Hubei,China

INTRODUCTION

ABSTRACTOur foreign trade has flourished in recent years, and its dependence onmarine environment and resources has increased substantially.
Developing marine economy and building a “maritime power” havebecome an inevitable choice for our economy to reach a new level. The
trend of large-scale development of ships is inevitable. In thedevelopment process of large-scale ships, the stress and deformation ofship structures are so high and large, which causes the low cycle fatigue
damage of ship structure to be paid more and more attention. In recentyears, many scholars have done a lot of research on this.
Paris P C (1961) proposed the classic formula describing the fatigue
crack growth rate in 1961, which provided conditions for describing
the fatigue fracture problem. Thereafter, many scholars such as Wells
A A (1963), Rice J R (1968) used new control parameters to analyze
crack propagation behavior based on Paris approach. However, as anempirical formula, the Paris formula does not explain the material
fatigue crack growth mechanism from the perspective of mechanism
research. At the same time, as a parameter based on the theory of linear
elastic mechanics, stress intensity factor amplitude is usually used forlinear elastic fracture and small-scale yield problems, but obviously notapplicable to the LCF problems that mainly extend in the plastic zoneof the material. It can be seen that the crack growth rate formula basedon linear elastic mechanics will not be suitable for describing theelastic-plastic stress-strain field under LCF loadings.
To solve this problem, in recent years, many scholars had introduced alarge number of elastic-plastic fracture mechanics parameters todescribe the LCF crack growth rate, mainly including plastic strain
amplitude (𝜀𝑝𝑎 ) ( Shmada H 1981;Dowling N E 1976), cyclic J integral(Δ𝐽) (Ehaddad M H 1980; Heung B P 1996), reverse plastic zone size(Zhang J 2005;Liaw P K 1981), plastic dissipation energy (Dover W D1973), crack tip opening displacement (CTOD) (Chen J J 2011), etc.,
which provide a theoretical basis for the in-depth study of LCF crack
growth behavior. However, there are still some certain deficiencies. (1)The plastic strain amplitude 𝛥𝜀 mostly relies on the analysis of thetest results to get the relationship with the LCF crack growth rate. Thereare less research in theory about 𝛥𝜀 to characterize the crack growthmechanism. (2) The cyclic J-integral is not clearly defined and difficult
to calibrate in the test. It is only commonly used in calculation, andcannot be applied to unloading conditions. (3) The reverse plastic zone
size and the plastic dissipation energy are based on finite element
methods (FEM) to establish the relationship with the LCF crack growthrate without a rigorous theoretical basis. In contrast, the CTOD is easy
to be measured in the test, and can effectively characterize the plastic
deformation of the crack tip with less limitations. The CTOD can beused in not only the growth of linear elastic cracks, but also elasticplastic conditions, large-scale yielding and full yielding scenarios.
Wells A A(1963) first proposed the concept of CTOD, many scholars
had conducted in-depth research on CTOD theory. Many scholars(Dugdale D S 1960; Cottrell A H 1963; Shi Y W 1998) proposed theCTOD calculation model in linear elastic state. Shimanuki H (2007)

The failure of ship structure is usually caused by the combined actionof LCF failure and accumulative plastic damage. In this paper, a CTOD
theoretical model of LCF cracks considering accumulative plastic
failure under cyclic loading is established. The LCF crack growthexperiment under different loading conditions was carried out toinvestigate the effects of stress ratio and maximum load on the CGR.
Finally, the CGR characterized by CTOD was obtained by fitting theexperimental results. The research work in the paper shows that CTOD
based on accumulative plastic damage can better characterize the LCFcrack growth rate.

KEY WORDS: CTOD ； Accumulative plastic damage ； Crackpropagation；Low cycle fatigue；experimental study

NOMENCLATURE
𝐾𝑚𝑎𝑥∆𝐾𝑟𝑟0𝜇𝐸
∆𝜎 𝑒
∆𝜀 𝑒
∆𝜎 𝑝
∆𝜀 𝑝𝜎𝑦′𝑟𝑦′
𝑟𝑦𝑛′𝑘′
𝑅
𝜶𝒔𝜀𝑟
∆𝛿
∆𝐽𝑎𝑊
𝛼、𝑛𝑑𝜎𝑌𝜀𝑌LCFCTOD
FEM
CTCGR

Maximum Stress intensity factor
Stress intensity factor amplitude
The distance from the crack root to the crack tip
Crack tip passivation radius
Poisson’s ratio
Young's modulus
Cyclic elastic stress amplitude
Cyclic elastic strain amplitude
Cyclic plastic stress amplitude
Cyclic plastic strain amplitude
Cyclic yield strength
Size of cyclic plastic zone at crack tip
Size of monotone plastic zone at crack tip
Cyclic hardening index
Cyclic hardening coefficient
Stress ratio
Back stress
Deviatoric stress tensor
Accumulative plastic strain
Cyclic crack tip opening displacement
Cyclic j-integral
Crack length
Plate width
Hardening index
Function of hardening exponent n
Yield stress
Yield strain
Low cycle fatigue
Crack tip opening displacement
Finite element method
Compact tension
Crack growth rate

3124