XU Geng,YAN Ren-jun,YAO Guo-quan,DONG Qin

(a.Key Laboratory of High Performance Ship Technology;b.School of Transportation,Wuhan University of Technology,Wuhan 430063,China)

Theoretical and Experimental Study on CTOD for Notch Plate Under Low Cycle Fatigue

XU Genga,b,YAN Ren-juna,b,YAO Guo-quanb,DONG Qina,b

(a.Key Laboratory of High Performance Ship Technology;b.School of Transportation,Wuhan University of Technology,Wuhan 430063,China)

Abstract:This paper aims to study the crack tip opening displacement(CTOD)for notch plate under large scale yielding.An analytical model is presented to determine CTOD for notch plate based on the theory of elastic-plastic fracture mechanics.Moreover,an experimental campaign in high strength steel AH36,performed in the low cycle fatigue regime,was performed on specimens with pre-cracks.The effect of stress ratio,stress amplitude and mean stress on CTOD were investigated.

Key words:low cycle fatigue;CTOD;experimental study;high strength steel

0 Introduction

The fatigue strength of ship’s structure has very important significance on the safety and survivability.Along with the increasing in ship dimensions and more use of high-strength steel in recent years,the stress and deformation of ship structures are so high and large,which result in prominent problem demanding prompt solution in the development of large-scale ships.Crack tip opening displacement(CTOD)and J integral are the major parameters to describe the resistance to crack propagation of ductile structural materials[1].However,at the load controlled experiments the results show that J integral was unable to correlate the low cycle fatigue crack growth rates.Therefore,studying and establishing assessment methods of CTOD under cyclic loading are of great practical significance.

The CTOD is less frequently used but it holds a direct physical meaning and can be measured directly in an experiment together with the crack opening/closing level.Furthermore,CTOD can be determined numerically for applications.Jiang[2]analyzed CTOD of ship stiffened plate based on Dugdale model and found out the influence rule caused by external load,stiffness ratio and other factors.Finite element method[3-8]is one of the efficient ways in studying elastic-plastic fracture problems,thus it is widely used in various kinds of fracture assessments.It is used to study CTOD and other relative parameters through calculation of crack tip stress-field and displacement-field.The CTOD has in fatigue crack growth investigations often connected with a micro-mechanical examination of the striation spacing on the fracture sur-face.Neumann[9]and Kikukawa et al[10]made quantitative observations on fatigue crack growth rates in combination with CTOD.In 1984,Tanaka et al[11]put forward a thorough investigation on the crack tip displacement as a fatigue crack growth mechanism.Both load and displacement controlled fatigue experiments were conducted for three different materials.However,no direct proportionality was observed between the fatigue crack growth rate and CTOD.

The present work presents an analytical model to determine the crack tip opening displacement for notch plate subjected to cyclic loading.A series of experiments were conducted to study the effect of stress ratio,stress amplitude and mean stress on CTOD.

1 Theoretical analysis

Shih[12]proposed an equation between the cyclic crack tip opening displacement and cyclic J-integral for notch plate subjected to uniaxial loading:

In the viewpoint of Kumar et al[14]and Heitmann et al[15],△J can be attributed by the sum of an elastic(small scale yielding)and a plastic(large scale yielding)approximately.For I crack with crack length a in a flat specimen under plane stress,one obtains:

where△σ and△εpare the stress and plastic strain range respectively.Crack closure is taken into account by the use of the effective stress range △σeff=σmax-σopin the elastic part of△J.σmaxand σopare the maximum and crack opening stress,respectively.The crack opening stress σop,which can either be estimated with empirical formulas or taken from numerical calculations.Here,the crack opening stress equation by Newman[16]is used,then the crack opening stress is obtained as follows:

of the material is usually defined as the average value between the material yielding and ulti-mate strength for convenience.

2 Experimental investigation

2.1 Material and campaign overview

The steel employed for testing is AH36 steel.The steel AH36,is a high strength steel which is widely used in the ship and ocean engineering in China,was employed to the tests,where the basic mechanics properties of material are showed in Tab.1.Chemical composition(in%wt)of this material is:C 0.18,Si 0.43,Mn 1.4,P 0.02,S 0.013 and Nb 0.018.In order to study CTOD for notch plate under low cycle fatigue,three different loading conditions were considered:The first,keep the maximum stress unchanged and take different stress ratio,second,keep the stress amplitude unchanged and take different mean stress,and third,keep mean stress unchanged and take different stress amplitude.

Tab.1 The mechanics properties of AH36

2.2 Experimental setup

The fatigue crack growth experiments were made on 12 mm thick low cycle fatigue standard specimen(notch plate)with other dimensions shown in Fig.1.The total length L=360 mm,the total width W=50 mm,the radius of notch R=2.4 mm,the precrack length a=1 mm.In order to remove nucleation time from the experiments,before testing,all the specimens were precracked.

Fig.1 Geometry of test specimen

The fatigue crack growth experiments were performed in air and at room temperature by using a computer controlled servo-hydraulic test machine,MTS322 250 kN.The crack lengthwas simultaneously measured by using strain extensometer with a 10 mm gauge length,±1 mm range,and 0.01%extensometer strain control accuracy whose operating temperature ranges from-80℃ to 200℃,as shown in Fig.2.A uniaxial controlled load was used to control the total stress range and a tensile-compression loading with a triangular waveform was used to ensure that the strain rate remained constant in a loop beginning with the tensile load.A 0.5 Hz frequency was chosen based on other low cycle fatigue test results available in the literature.The specimens were tested in cyclic loading,considering the influence of stress ratio,stress amplitude and mean stress.Each test is performed to failure and an average of three measurements under each condition was taken.The real-time information such as time,load,crack tip opening displacement and extensometer strain were recorded.The loading conditions and experimental results of AH36 were summarized in Tab.2.An example of the appearance of the surface was shown in Fig.3.

Tab.2 The loading condition and experimental results of AH36

2.3 Experimental result and discussion

2.3.1 The effect of stress ratio on the CTOD

The stress controlled low cycle fatigue experiment with constant applied peak stress and various stress ratio was carried out under uniaxial cyclic loading.Keep the maximum stress unchanged and different stress ratio R=-1,0,0.1,0.2,it can be seen from Fig.4 that with the increasing of stress ratio,the CTOD is increasing.It is obvious that the stress ratio apparently influences the relationship between CTOD and fatigue life,i.e.,the CTOD rapidly increases with stress ratio at a constant maximum stress.Meanwhile,when the stress ratio is negative,in the initial cycle the CTOD is small,while the stress amplitude is large,so the trend of CTOD changes rapidly.

2.3.2 The effect of mean stress on the CTOD

In order to discuss the impact of mean stress on the CTOD,the stress controlled low cycle fatigue experiment with constant stress amplitude and various mean stress was carried outunder uniaxial cyclic loading.Keep the stress amplitude unchanged and different mean stress σm=10,20,30 MPa,the evolution result of CTOD is shown in Fig.5.Experimental results reveal that for the smaller mean stress applied in the test,the CTOD shows monotonically increasing with the increase of mean stress.The change of CTOD is small in the early cycle,while in the late fatigue life,the CTOD increases violently.

Fig.5 The crack tip opening displacement vs fatigue life for different mean stress

2.3.3 The effect of stress amplitude on the CTOD

In order to discuss the impact of stress amplitude on the CTOD,the stress controlled low cycle fatigue experiment with constant mean stress and various stress amplitude was carried out under uniaxial cyclic loading.Keep the mean stress unchanged and different stress amplitude σa=170,180,190,200 MPa,the evolution results of CTOD is shown in Fig.6.The experimental results show that with the increasing of stress amplitude,the CTOD exhibits monotonically increasing.Tab.2 shows that the stress amplitude has a significant effect on fatigue life under stress controlled cyclic loading,the fatigue life decreases with the increases of stress amplitude.

Fig.6 The crack tip opening displacement vs fatigue life for different stress amplitude

3 Conclusions

In the present work,an analytical model is presented to determine the CTOD for notch plate subjected to cyclic loading.Based on the experimental study of fatigue crack growth of AH36 steel,the following concluding remarks can be drawn:

(1)The study reveals that stress ratio,mean stress and stress amplitude have obvious influence on the relationship of CTOD vs fatigue life.The experimental results reveals that the increasing stress amplitude and mean stress shorten the fatigue life of the material significantly.

(2)The experimental results suggest that with the increasing of stress ratio,the CTOD is increasing while the fatigue life is decreasing.

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低周疲勞下船體缺口板的裂紋尖端張口位移理論及試驗研究

徐 庚a，b， 嚴仁軍a，b， 姚國全b， 董 琴a，b
（武漢理工大學a.高性能船舶技術(shù)教育部重點實驗室；b.交通學院，武漢 430063）

文章旨在研究大范圍屈服下船體缺口板的裂紋尖端張口位移?；趶椝苄詳嗔蚜W理論，建立了循環(huán)載荷下船體缺口板CTOD理論模型。進而，對于船用高強度鋼AH36進行低周疲勞試驗研究，對于影響裂紋尖端張口位移的參數(shù)，如應力比、應力幅和平均應力進行了深入探討。

低周疲勞；CTOD；試驗研究；高強度鋼

U661.4

A

國家自然科學基金資助（51479513）；中央高?？蒲匈Y助基金（2016-YB-014）

徐 庚（1988-），男，武漢理工大學交通學院博士研究生，E-mail：xugeng_1988@163.com；嚴仁軍（1962-），男，武漢理工大學交通學院教授，E-mail：renjun_yan@163.com；姚國全（1986-），男，武漢理工大學交通學院實驗研究員；董 琴（1988-），女，武漢理工大學交通學院博士研究生，E-mail：dongqin19881022@163.com。

10.3969/j.issn.1007-7294.2017.09.007

Article ID： 1007-7294（2017）09-1128-08

Received date：2017-02-25

Foundation item:Supported by the National Natural Science Foundation of China(Grant No.51479153);the Fundamental Research Funds for the Central Universities(Grant No.2016-YB-014)

Biography：XU Geng(1988-),male,doctoral student of Wuhan University of Technology,E-mail:xugeng_1988@163.com;YAN Ren-jun(1962-),male,professor/tutor of Wuhan University of Technology,E-mail:renjun_yan@163.com.