Experimental Study on Interaction of Low Cycle Fatigue and Accumulative Plastic Damage of AH32 Steel in Uniaxial Cyclic Loading

DONG Qin,YANG Ping,Xü Geng,JIANG Wei

(1.Key Laboratory of High Performance Ship Technology(Wuhan University of Technology),Ministry of Education,Wuhan 430063,China;2.School of Transportation,Wuhan University of Technology,Wuhan 430063,China)

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.The ship structure in the service period is actually in the alternating stress state,when it is subjected to large alternating load,the stress concentration area will produce fatigue crack.In the case of overload caused by severe sea condition,the crack growth rate in the stress concentration area is accelerated and the bearing capacity is reduced,which leads to the rupture of ship structure.It is known that two kinds of failure modes,low cycle fatigue failure due to crack propagation and accumulative plastic damage due to large plastic strain resulting in loss of ductility will take place simultaneously.The existing research[1]shows that most overall fractures of ship hulls are the coupling interaction result of low cycle fatigue and accumulative plastic damage.Therefore,it is meaningful to study the low cycle fatigue of ship hull structure considering the effect of accumulative plastic damage from the aspect of risky safety assessment.

The accumulative plastic damage,which occurs in the components subjected to asymmetric cyclic stressing,refers to accumulation of inelastic deformation progressing cycle by cycle.Early in 1950,the concept of accumulative plastic damage of ship structure was put forward by researchers,but it has not been paid enough attention.In 1970,Coffin[2]had suggested that the accumulative plastic strain would cause additional damage and could result in reduced fatigue life[3-4].In 1990,Mansour and Yang[5]had pointed out that in the calculation of plastic design method and damage rate,the influence of accumulative plastic damage should be considered seriously.In the winter of 1980,a large transport vessel of Japan(L×B×D=216.4 m×31.7 m×17.3 m,15 years old)was subjected to severe sea conditions in Noyasaki,resulting in the ship hull break down overall.The accident caused Japanese researchers to reconsider the accumulative plastic damage of ship hull structure,and carried on a lot of research work[6-10].Huang[11]considered that the overload caused by severe sea condition in service period would result in a new plastic deformation in the dangerous section of ship structure,and the accumulation of plastic deformation and the propagation of fatigue crack under cyclic loading could reduce the bearing capacity of ship’s dangerous section.Therefore,in the condition that the amplitude of cyclic load is smaller than the ultimate bending moment,the ship structure will be unsafe and result in failure.Since the low cycle fatigue failure-accumulative plastic damage interaction is very important in the design and assessment of structure component,it has been studied experimentally and theoretically by some researchers recently.Isobe[12]investigated the effect of accumulative plastic damage on fatigue strength,to rationalize its ultimate strain as a design criterion.Kang[13-15]and Yang[16-17]conducted a series of low cycle fatigue-accumulative plastic damage interaction tests under uniaxial cyclic loading for SS304 stainless steel,42Cr-Mo steel and carbon steel 45,respectively.The experimental results showed that the final fatigue failure life and accumulative plastic strain depended greatly on mean stress,stress amplitude and stress ratio,and stress-based fatigue failure model was proposed to predict the fatigue life,accounting for the effect of accumulative plastic damage.Sinaha and Ghosh[18]proposed a fatigue failure model based on accumulative plastic damage for high strength low alloy.Fatemi and Yang[19]presented a review on the accumulative plastic damage and fatigue life evaluation models.The accuracy of these predictive models for accumulative plastic damage needs to be examined further.However,the existing experimental results have revealed that the interaction between low cycle fatigue and accumulative plastic damage differs from various materials.It is necessary to investigate the interaction between low cycle fatigue and accumulative plastic damage for other materials.

Therefore,the interaction between low cycle fatigue and accumulative plastic damage of AH32 steel is tested under asymmetrical uniaxial cyclic loading in this work.The effect of mean stress,stress amplitude and stress ratio on the final low cycle fatigue crack propagation life and accumulative plastic strain are investigated.Then,the coupling interaction between low cycle fatigue and accumulative plastic damage is discussed in detail.Finally,a fatigue failure model is presented to predict the fatigue life of the material,taking account of the accumulative plastic damage occurred.

1 Experimental procedure

The test material used in this investigation is AH32 steel,and its chemical composition is(weight percentage,%)C 0.18,Mn 1.4,Al 0.02,Si 0.32,P 0.04,S 0.04,Nb 0.02.The testing specimens were notched plates,whose dimensions were 360 mm in length and 50 mm in width,the notch radius is 2.4mm.The specimens were treated by solution heat treatment at 525℃for 2 h and then aircooled.The test device was MTS322-250 kN fatigue testing machine,shown in Fig.1.Each specimen was tested under load control and the experimental data were collected by the control system of the machine.The axial strain was measured by a tensile extensometer with a 10mm gauge length,±1 mm range,and 0.01%extensometer strain control accuracy.The strain rates of cyclic straining and stress rates of cyclic stressing were prescribed as 0.004/s and 250 MPa/s,respectively.All tests were conducted under uniaxial straining and uniaxial stressing at room temperature and sine waveform loading was used in the tests.

In the paper,the definition of accumulative plastic strain in a cycle is introduced:

where εmaxand εminare the maximum and minimum axial strain in each cycle measured by the extensometer.Meanwhile,the accumulative plastic strain evolution rate is defined as dεa/dN,and N is the number of cycles.

2 Experimental results and discussions

2.1 Monotonic tensile test

Monotonic tensile test was performed to obtain the basic properties for AH32 steel,and the stress-strain curve is shown in Fig.2.The measured values of elastic modulus and yielding strength are 206 GPa and 345 MPa for AH32 steel.

2.2 Uniaxial cyclic straining test

Before the tests of interaction between accumulative plastic damage and low cycle fatigue for AH 32 steel were carried out,the tests of symmetrical uniaxial cyclic straining with different strain amplitudes(0.3%,0.4%,0.5%,0.6%and 0.8%,respectively)were conducted at room temperature.The strain rate of cyclic straining was prescribed as 0.004/s,and the curve of responded stress amplitude vs.the number of cycles is shown in Fig.3.It can be seen from Fig.3 that the cyclic softening/hardening properties of AH32 steel depends on the applied strain amplitude.When the applied strain amplitude is smaller than 0.5%,the responded stress amplitude increases gradually in the initial stage and presents apparent cyclic hardening behavior.Then cyclic softening occurs after about 25 cycles,followed by a stable state after hundreds of cycles.While when the applied strain amplitude is larger than 0.5%,the responded stress amplitude initially increases more quickly and then tends to stabilize,which is characterized by obvious cyclic hardening behavior.

Fig.2 Monotonic tensile stress-strain curve for AH32 steel

Fig.3 Curve of responded stress amplitude vs.number of cycles

2.3 Low cycle fatigue-accumulative plastic damage interaction

A series of uniaxial load tests of low cycle fatigue and accumulative plastic damage for AH32 steel were carried out over different mean stress,stress amplitude and stress ratio till the low cycle fatigue failure occurred.The relationship between accumulative plastic strain and number of cycles is shown in Fig.4,corresponding to the loading cases with different mean stress,where stress amplitude is constant.It can be seen from the figure that the accumulative plastic strain increases with the number of cycles while its increasing rate decreases and then achieves a non-zero stable value with the increasing number of cycles.It is observed that the accumulative plastic strain and its increasing rate increases monotonically with increasing the mean stress.This is because the higher mean stress produces a larger accumulative plastic damage,resulting in a loss of the ability of the material to resist deformation,and finally leading to a rapid increase of evolution rate of accumulative plastic strain untill the specimen is destroyed.This is similar to that obtained in Ref.[20].The Fig.5 shows the accumulative plastic strain vs.number of cycles under different stress amplitude,while mean stress is a constant.It is seen that the accumulative plastic strain and its increasing rate increase monotonically with the increase of stress amplitude,and the larger the stress amplitude,the larger the final accumulative plastic strain.

Fig.4 Curve of accumulative plastic strain vs.cyclic numbers with different mean stress and constant stress amplitude

Fig.5 Curve of accumulative plastic strain vs.cyclic numbers with different stress amplitude and constant mean stress

The final accumulative plastic strain is obtained from the experimental results to express the low cycle fatigue-accumulative plastic damage interaction.Figs.6-7 show its relationship to mean stress and stress amplitude,respectively.From Fig.6,it can be observed that the final accumulative plastic strain increases apparently with the increasing mean stress.From Fig.7,it is shown that the final accumulative plastic strain increases with the increase of stress amplitude,while the increasing stress amplitude slightly influences the value of final accumulative plastic strain.It implies that the effect of mean stress on accumulative plastic damage is more significant than that of stress amplitude,which is corresponding to that accumulative plastic damage occurs under cyclic loading with non-zero mean stress.

The accumulative plastic damage behavior of AH32 steel is also investigated in the cyclic stressing with constant peak stress and different stress ratios,and the results with constant peak stress 250 MPa and 270 MPa are shown in Fig.8(a)and(b)respectively.It can be seen from Fig.8 that the maximum accumulative plastic strain occurs at the stress of-0.92 and-0.93 with constant peak stress 250 MPa and 270 MPa,respectively,and increasing stress ratio leading to decreased accumulative plastic strain.

Fig.7 Relation of final accumulative plastic strain to stress amplitude

Fig.8 Curve of accumulative plastic strain vs.cyclic number with different stress ratio and constant peak stress

The interaction between low cycle fatigue and accumulative plastic damage to stress ratio is shown in Fig.9.It is observed from Fig.9 that when the peak stress is a constant,the increase of stress ratio results in a smaller final accumulative plastic strain,and the maximum final accumulative plastic strain occurs at the stress ratio of near-0.9 for peak stress 250 MPa and 270 MPa.It can be seen from Fig.9 that the increase of peak stress causes a larger final accumulative plastic strain.

Fig.9 Relation of final accumulative plastic strain to stress ratio

The experimental results show in the work that the accumulative plastic strain increases with the number of cycles untill the specimen fails and its rate decreases but not be zero in the cyclic stressing.This means that in fact the shakedown of accumulative plastic damage for AH32 steel will not occur in the range of prescribed stress levels in this work.

2.4 Low cycle fatigue life

The low cycle fatigue life of AH32 steel is tested in asymmetrical uniaxial cyclic stressing,and the relations of low cycle fatigue life to mean stress,stress amplitude and stress ratio are shown in Figs.10-12.To compare with experimental results,the predicted low cycle fatigue life by the model presented in the next section is plotted in the figures as solid points.The effect of mean stress on the fatigue life of AH32 steel can observed in Fig.10,it is concluded that the fatigue life monotonically decreases with the increasing of mean stress,and the longest fatigue life occurs in the cyclic stressing with mean stress of 5 MPa.It means that the accumulative plastic damage produced in the asymmetrically cyclic stressing results in additional damage,and then reducing the fatigue life.It can also be seen from Fig.10 that when the mean stress is larger,increasing mean stress results in an increased accumulative plastic strain rate,and then the failure of the material is mainly controlled by such large accumulative plastic strain.Therefore,the fatigue life of AH32 steel decreases with the increasing of mean stress.When the mean stress is lower,after certain cycles the accumulative plastic strain rate decreases to a constant,and then the failure of the material is mainly controlled by the low cycle fatigue.Therefore,it can be concluded that the fatigue life of AH32 steel is reduced due to the accumulative plastic strain produced in the asymmetrically cyclic stressing,and such interaction should be considered in the study of the structure subjected to cyclic stressing with nonzero mean stress.

Fig.10 Relation of fatigue life to mean stress

Fig.11 Relation of fatigue life to stress amplitude

The effect of stress amplitude on the low cycle fatigue life of AH32 steel under uniaxial cyclic stressing is more pronounced.It is seen from Fig.11 that the low cycle fatigue life monotonically decreases with the increasing of stress amplitude,since the increasing stress amplitude results in the larger final accumulative plastic strain,therefore the fatigue life correspondently decreases.The experimental results with different stress ratios are plotted in Fig.12.It can be concluded that the fatigue life of AH32 steel is apparently influenced by stress ratio,the low cycle fatigue life increases with stress ratio when the maximum stress keeps unchanged,and that the low cycle fatigue life with larger maximum stress is shorter than that with smaller one when the stress ratio is almost the same.It can be seen that when the stress ratio is in the range of-0.96 to-0.75,a larger accumulative plastic strain will be produced under the uniaxial cyclic stressing as shown in Fig.8.Therefore,the fatigue life of AH32 steel in the stress ratio range of-0.96 to-0.75 is apparently influenced by the detrimental effect of accumulative plastic strain.

Fig.12 Relation of fatigue life to stress ratio

It can be concluded from the experimental results that the accumulative plastic strain produced under the uniaxial asymmetrically cyclic stressing is detrimental to the low cycle fatigue life of AH32 steel,which will greatly reduce the fatigue life.Therefore,it is better to express the low cycle fatigue life of AH32 steel by considering the interaction effect of low cycle fatigue vs.accumulative plastic damage.

3 The low cycle fatigue failure model

Since the experimental results show that the accumulative plastic damage produced in the asymmetrically cyclic stressing results in additional damage,and then reducing the fatigue life,thus it is assumed that the total damage in the process of low cycle fatigue is consists of two parts,i.e.,low cycle fatigue damage represented by maximum stress and accumulative plastic damage characterized by accumulative plastic strain rate.Then for low cycle fatigue damage,the SWT(Smith-Watson-Topper)parameter method to predict fatigue life will be adopted.It is shown that SWT parameter method is capable of predicting low cycle fatigue life under cyclic stressing.For the accumulative plastic damage,the influence of accumulative plasticity on fatigue life under asymmetrically cyclic stressing is included in the failure approach by introducing a correction term which contains accumulative plastic strain rate.Based on the above-mentioned instructions,a new low cycle fatigue failure model is constructed as follows:

where Nfis fatigue life,Nffis failure cyclic number controlled by low cycle fatigue,Nfais failure cyclic number controlled by accumulative plastic damage,σmaxis maximum stress,εais strain amplitude, σf′is fatigue strength coefficient, εf′is fatigue ductility coefficient,b is fatigue strength exponent,c is fatigue ductility exponent, ε˙ais accumulative plastic strain rate,κaand β are material parameters.For AH32 steel, σf′=1 152 MPa, εf′=0.086,b=-0.126,c=-0.34,κa=45 268,β=-1.528.

As expounded above,the fatigue life of the material under asymmetrically cyclic stressing is the linear superposition of low cycle fatigue life and accumulative plastic damage.It should be noted that although the accumulative plastic strain produced in the asymmetrically cyclic stressing will reduce the fatigue life,the fatigue life of the material in the cyclic stressing with non-zero mean stress is still longer than that in symmetrically cyclic stressing with the same maximum stress due to larger stress ratio.Figs.9-11 show the relationship of experimental results and corresponding predicted fatigue life by the model in various loading cases.It can be seen from these figures that a good comparison has been found between predictions and experimental results for AH32 steel,and the influence of mean stress,stress amplitude and stress ratio on fatigue life can be well presented by the predicted model.

4 Conclusions

A series of low cycle fatigue-accumulative plastic damage interaction tests of AH32 steel under uniaxial cyclic stressing were conducted.Based on the experimental observations,the major conclusions are obtained as follows:

(1)The accumulative plastic strain produced in the uniaxial asymmetrically cyclic stressing results in additional damage,then shorten the low cycle fatigue life of AH32 steel.The low cycle fatigue life decreases monotonically with the increasing of mean stress and stress amplitude.However,the fatigue life increases as stress ratio increases since the larger final accumulative plastic strain produced in the stress ratio range of-0.96 to-0.75.

(2)The final accumulative plastic strain increases apparently with the increasing mean stress and stress amplitude,and the effect of mean stress on accumulative plastic damage is more significant than that of stress amplitude,which is corresponding to that accumulative plastic damage occurs under cyclic loading with non-zero mean stress.The maximum final accumulative plastic strain occurs at the stress ratio of near-0.9 for peak stress 250 MPa and 270 MPa.

(3)When the mean stress is larger,increasing mean stress results in an increased accumulative plastic strain rate,and then the failure of the material is mainly controlled by such large accumulative plastic strain.However,when the mean stress is lower,the material fails due to low cycle fatigue.

(4)Based on the experimental results,the low cycle fatigue failure model is proposed to predict the fatigue life of the material accounting for the effect of low cycle fatigue-accumulative plastic damage interaction.The failure model consists of two parts,the low cycle fatigue damage that is obtained by using SWT parameter method,and the effect of accumulative plastic strain on fatigue life occurred in the asymmetrically cyclic stressing that is obtained by introducing a correction term which contains accumulative plastic strain rate into the failure approach.Comparison with the experimental result shows that the model provides a good prediction for AH32 steel.

[1]Hu Y R,Chen B Z.Fatigue reliability analysis of ship and offshore structure[M].Beijing:China Communications Press,1997.(in Chinese)

[2]Coffin L F.The deformation and fracture of ductile metal under superimposed cyclic and monotonic strain[M].ASTM STP 467.American Society for Testing and Materials,1970:53-76.

[3]Rider R J,Harvey S J,Chandler H D.Fatigue and ratcheting interactions[J].International Journal of Fatigue,1995,17(7):507-511.

[4]Xia Z,Kujawski D,Ellyin F.Effect of mean stress and ratcheting strain on fatigue life of steel[J].International Journal of Fatigue,1996,18(5):335-341.

[5]Mansour A,Yang J M,Thayamballi A.An experimental investigation of ship hull ultimate strength[J].Ultimate Strength,1990,98:411-439.

[6]Murray J M.Structural development of tankers[J].European Shipbuilding,1953,3(5):1-5.

[7]Fujita Y,Nomoto T,Yuge K.Behavior of deformation of structural members under compressive and tensile loads(1st report)on the buckling of a column subjected to repeated loading[J].The Japan Society of Naval Architects and Ocean Engineering,1984,156:346-354.

[8]Fukumoto Y,Kusama H.Local instability tests of plate elements under cyclic uniaxial loading[J].Journal of Structural Engineering,1985,111:1051-1067.

[9]Fukumoto Y,Kusama H.Cyclic bending tests of thin-walled box beams[J].Journal of Earthquake Engineering,1985,2(1):141-151.

[10]Yao T,Nikolov P I.Buckling/plastic collapse of plates under cyclic loading[J].The Japan Society of Naval Architects and Ocean Engineering,1990,168:449-462.

[11]Huang Z Q.Some problems in the study of ship strength[J].Wuhan Shipbuilding,1999,3:1-5.

[12]Isobe N,Sukekawa M,Nakayama Y.Clarification of strain limits considering the ratcheting-fatigue strength of 316FR steel[J].Nuclear Engineering and Design,2008,238:347-352.

[13]Kang G Z,Liu Y J.Uniaxial ratcheting and low cycle fatigue failure of the steel with cyclic stabilizing or softening feature[J].Materials and Science Engineering A,2008,472:258-268.

[14]Kang G Z,Liu Y J,Zhao L.Experimental study on ratcheting-fatigue interaction of SS304 stainless steel in uniaxial cyclic stressing[J].Materials and Science Engineering A,2006,435-436:396-404.

[15]Liu Y J,Kang G Z,Gao Q.Stress-based fatigue failure models for uniaxial ratcheting-fatigue interaction[J].International Journal of Fatigue,2008,30:1065-1073.

[16]Yang X J.Low cycle fatigue and cyclic stress ratcheting failure behavior of carbon steel 45 under uniaxial cyclic loading[J].International Journal of Fatigue,2005,27:1124-1132.

[17]Yang X J.A unified time dependent model for low cycle fatigue and ratcheting failure based on microcrack growth[J].Nuclear Engineering and Design,2007,237:1381-1387.

[18]Sinaha S,Ghosh S.Modeling cyclic ratcheting based fatigue life of HSLA steels using crystal plasticity FEM simulations and experiments[J].International Journal of Fatigue,2006,28:1690-1704.

[19]Fatemi A,Yang L.Cumulative fatigue damage and life prediction theories:A survey of the state of the art for homogeneous materials[J].International Journal of Fatigue,1998,20(1):9-34.

[20]Kang G Z,Gao Q,Cai L X,Sun Y F.Experimental study on uniaxial and nonproportionality multiaxial ratcheting of SS304 stainless at room and high temperature[J].Nuclear Engineering and Design,2002,216:13-26.