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

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.

[1]Hutchinson J W.Fundamentals of the phenomenological theory of nonlinear fracture mechanics[J].J Appl.Mech.,1982,49:103-197.

[2]Jiang Cuixiang.Research on fracture and crack arrest in ship structures[D].Wuhan:Huazhong University of Science and Technology,2005.

[3]Potirniehe G P,Daniewiez S R.Analysis of crack tip plasticity for microstructuralIy small cracks using crystal plasticity theory[J].Eng.Fraet.Meeh.,2003,70:1623-1643.

[4]Wu F W,Ibrahim R N,Das R,et al.Fracture toughness for CNT specimens from numerieally obtained critical CTOD values[J].Theor.Appl.Fract.Meeh.,2009,52:50-54.

[5]Chen Jingjie.Strength analysis method research of cracked ship structure[D].Dalian:Dalian University of Technology,2011.

[6]Chen Jingjie,Huang Yi.A study on evaluation method of crack tip reverse plastic zone size for the center cracked steel plate model under tension-compression cyclic loading[J].Engineering Fracture Mechanics,2015(133):138-151.

[7]Dong Qin,Yang Ping,Deng Junlin,Wang Dan.The theoretical and numerical research on CTOD for ship plate under cyclic loading considering accumulative plastic strain[J].Journal of Ship Mechanics,2015,19(12):1507-1516.

[8]Dong Qin,Yang Ping,Xu Geng,Deng Junlin.Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345[J].International Journal of Fatigue,2016,89:2-10.

[9]Neumann P.Coarse slip model of fatigue[J].Acta Metall,1969,17(9):1219-1225.

[10]Kikukawa M,Jono M,Adachi M.Direct observation and mechanisms of fatigue crack propagation[M].In:ASTM STP 675.American Society for Testing and Materials,1979:234-253.

[11]Tanaka K,Hoshide T,Sakai N.Mechanics of fatigue crack propagation by crack-tip plastic blunting[J].Engng Fract Mech,1984,19(5):805-825.

[12]Shih C F.Relationship between the J-integral and the crack opening displacement for stationary and extending cracks[J].Mech Phys Solids,1981,29(4):305-326.

[13]Shih C F.Tables of Hutchinson-Rice-Rosengren singular field quantities[R].Tech.rep.Brown University Report MRL E-147,1983.

[14]Kumar V,German M D,Shih C F.An engineering approach for elastic-plastic fracture analysis[R].Tech.rep.Report NP-1931 on Project 1237-1 for Electric Power Research Institute,Palo Alto,California,1983.

[15]Heitmann H H,Vehoff H,Neumann P.Advances in fracture research 84[M].In:Valluri SR,et al.,editor.Proc of ICF6,vol.5.Oxford and New York:Pergamon Press Ltd.,1984:3599-3606.

[16]Newman J C.A crack opening stress equation for fatigue crack growth[J].International Journal of Fatigue,1984,24:131-135.

低周疲勞下船體缺口板的裂紋尖端張口位移理論及試驗(yàn)研究

徐 庚a，b， 嚴(yán)仁軍a，b， 姚國全b， 董 琴a，b
（武漢理工大學(xué)a.高性能船舶技術(shù)教育部重點(diǎn)實(shí)驗(yàn)室；b.交通學(xué)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。基于彈塑性斷裂力學(xué)理論，建立了循環(huán)載荷下船體缺口板CTOD理論模型。進(jìn)而，對于船用高強(qiáng)度鋼AH36進(jìn)行低周疲勞試驗(yàn)研究，對于影響裂紋尖端張口位移的參數(shù)，如應(yīng)力比、應(yīng)力幅和平均應(yīng)力進(jìn)行了深入探討。

低周疲勞；CTOD；試驗(yàn)研究；高強(qiáng)度鋼

U661.4

A

國家自然科學(xué)基金資助（51479513）；中央高校科研資助基金（2016-YB-014）

徐 庚（1988-），男，武漢理工大學(xué)交通學(xué)院博士研究生，E-mail：xugeng_1988@163.com；嚴(yán)仁軍（1962-），男，武漢理工大學(xué)交通學(xué)院教授，E-mail：renjun_yan@163.com；姚國全（1986-），男，武漢理工大學(xué)交通學(xué)院實(shí)驗(yàn)研究員；董 琴（1988-），女，武漢理工大學(xué)交通學(xué)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.