1、Prediction Method of Dwell-Fatigue Crack GrowthBehavior of New Titanium AlloyWANG Ke1,SUN Zheng-yi1,HUANG Xiang-yu2,LI Yong-zheng1(1.School of Naval Architecture and Ocean Engineering,Jiangsu University of Science and Technology,Zhenjiang 212003,China;2.China Classification Society Fuzhou Branch,Fuz
2、hou 350007,China)Abstract:This paper presents the test of the dwell-fatigue crack growth behavior of a new titanium alloy for the pressure shell of deep-sea manned submersibles.The dwell-fatigue crack growth rate atload ratio R=0.3 with different temperatures,and load ratio R=0.03 with different wav
3、eforms were obtained.Based on the existing titanium alloy dwell-fatigue crack growth prediction model,the dwell-fatigue crack growth rate under different temperatures and waveforms was predicted.The results showthat the prediction model selected in this paper can be applied for prediction of the dwe
4、ll-fatiguecrack growth behavior of new titanium alloys,and it can accurately predict the dwell-fatigue crackgrowth rate at different temperatures.After correction,it can also accurately predict the dwell-fatiguecrack growth rate under different waveforms.Key words:new titanium alloy;temperature;wave
5、form;dwell-fatigue crack rate predictionCLC number:TG111.8Document code:Adoi:10.3969/j.issn.1007-7294.2023.06.0080 IntroductionDeep-sea manned submersibles,as a platform for the exploration and collection of marine resources,undoubtedly have a very important position in the development of deep-sea r
6、esources.Asa kind of engineering equipment whose working environment is in the extreme environment of deepseas,the safety of deep-sea manned submersibles is also the research focus of researchers at homeand abroad.Over the past decade,the study on submersibles has increased steadily1.The most import
7、ant component of a manned submersible is undoubtedly the pressure structure of the mannedcompartment,whose material is mainly titanium alloy2.Previously,Ti64 and Ti6211 titanium alloys were used for the pressure-resistant structure of submersibles before Ti64 ELI titanium alloywas used to replace Ti
8、6211 titanium alloy in the United States.At present,all the materials oflarge-depth manned spherical shells are Ti64(ELI).Ti-6Al-4V titanium alloy is usually suitablefor 6500-7000 m class submersibles,not suitable for full ocean depth submersibles18.Therefore,tomeet the operational requirements of t
9、he deep-sea manned submersibles,China needs to develop titanium alloy materials with higher strength.The new titanium alloy studied in this paper is a high-strength titanium alloy designed for the pressure shell of deep-sea manned submersibles,whose第27卷第6期船舶力学Vol.27 No.62023年6月Journal of Ship Mechan
10、icsJun.2023Article ID：1007-7294（2023）06-0877-11Received date:2022-12-01Foundation item:Supported by the National Natural Science Foundation of China(51709134;52071161)Biography:WANG Ke(1979-),female,associate professor,E-mail:;SUN Zheng-yi(1994-),male,master student.dive-work-floatoperating mode is
11、similar to an aircraft stakeoff,cruise,and landoperatingmode.It is considered that the submersibles are affected by the dwell-fatigue during service.Therefore,to study the fatigue crack growth behavior of manned submersible pressure shells,it is necessary to study the dwell-fatigue crack growth beha
12、vior of titanium alloy.Many experts and researchers have carried out experimental studies on dwell-fatigue crack growth.In the 1970s,the RB211 engine provided by RR Company had a fan disk made of nearly-type IMI685 alloy that failed prematurely in service.Through the accident investigation,people re
13、alized that titanium alloys have dwell-fatigue problems3.In 1977,Postans4conducted experimentson IMI685 titanium alloys with different microstructures at room temperature,they found the loadwas kept at the maximum load for 5 minutes,the directional microstructure crack growth rate ofIMI685 increased
14、 significantly.In 2009,Whittaker and Evans5conducted relevant experimentalstudies on the dwell sensitivity of three titanium alloys types,Ti-6Al-4V,IMI685 and IMI834,andthe dwell-fatigue at room temperature greatly reduced the fatigue life.Wang and Cui6conducteddwell-fatigue crack growth rate tests
15、for Ti-6Al-4VELI titanium alloys at different dwell times,and found that:(1)as the dwell time increases,the failure cycle of titanium alloys during dwell-fatigue will decrease;(2)when the dwell time is less than 120 s,it has the greatest impact on fatiguelife;(3)when thisthresholdis exceeded,the dwe
16、ll-fatigue life tends to be constant.Everaertsand Gontcharov7conducted an experimental study on Ti-6Al-4V to study the dwell effect on thefatigue crack growth rate,and their research results show that the loading reduces the fatigue life ofTi-6Al-4V,and that the 30 s dwell time strain accumulation o
17、f Ti-6Al-4V is significantly fasterthan the 120 s dwell time19.For the new titanium alloy,this paper introduces the status quo of the dwell-fatigue crackgrowth prediction model and considers the influence of the waveform.The dwell-fatigue crackgrowth rate tests under different temperatures and wavef
18、orms were carried out to study the effect onthe dwell-fatigue crack growth behavior.Finally,the modified model was used to predict the loadfatigue crack growth rate under different temperatures and different waveforms,and the accuracy ofthe prediction model was verified.1 Experimental detail and pre
19、diction model1.1 Research materialThe material selected is a new titanium alloy material used in full ocean depth manned submersibles.There are some differences in composition and mechanical properties between the new titanium alloy and Ti-6Al-4V.Tab.1 gives the composition of the new titanium alloy
20、 and Ti-6Al-4V.The yield strength level is 1000 MPa.And the new titanium alloy fracture toughness at roomtemperature isKIC=91.8MPamwhile the Ti-6Al-4V fracture toughness isKIC=62.278MPam.Tab.1 Chemical composition of titanium alloy(wt%)TiNew titanium alloyTi-6Al-4VO0.110.11N0.0070.01H0.00190.002C0.0
21、060.01Al6.036.10Fe0.150.12V1.004.10878船舶力学第27卷第6期1.2 Experimental detailThe test sample selected in this paper is a densetensile sample(CT sample)with the characteristics of along crack propagation path,small size,and simpleclamping method.The thickness of the sample selectedis B=12.5 mm,and the wid
22、th of the sample is W=50 mm.The specific dimensions of the sample are shown in Fig.1.Waveform 1 of the dwell-fatigue crack growth rateof the new titanium alloy under different load ratio R=0.3,test temperature T=-20,0,20,dwell time t=30 s is shown in Fig.2.Waveform 2 of dwell-fatigue crack growth ra
23、te of the new titanium alloy under different loadratio R=0.03,test temperature T=20,the dwell time t1=0 s,30 s,60 s under maximum stress andthe dwell time t2=0 s,60 s,120 s under minimum stress is shown in Fig.3.1.3 Prediction modelIn 1980,Munz9divided the dwell-fatigue into two parts,namely the dwe
24、ll-fatigue part andthe fatigue part,so his proposed model was divided into two parts as follows:dadN=()dadNtriang+()dadNK=Kmaxt(1)In 2014,Wang10proposed a dwell-fatigue crack growth rate prediction model consideringsmall crack effects based on the fatigue crack growth rate prediction model consideri
25、ng small crackeffects.The dwell-fatigue crack growth rate model was a linear summation of fatigue and dwells offatigue.Wang considered the dwell time effect on the dwell-fatigue crack growth rate,and introduced the dwell timethold.At the same time,a physical quantity featuring the influence of the m
26、aximum holding stress level on the crack growth rate11was introduced.The model is shown as follows:dadN=A1K-()KthR-Kths()1-e-k(ad)-Kthsm11-()Kmax/KCn1+A2thold()max-R()Y-R K1-()KmaxKCn2m2(2a)K=()1-R Kmax=Kmax-Kmin(2b)Fig.1 Size of CT sampleFig.2 Loading Waveform 1 of dwell-fatigue crack growth rate t
27、estat different temperaturesFig.3 Loading Waveform 2 of dwell-fatigue crack growth rate test underdifferent waveforms第6期WANG Ke et al:Prediction Method of Dwell-Fatigue 879Kmax=YmaxaF(2c)The experimental results show that the waveform has no significant effect on the dwell-fatiguecrack growth rate o
28、f the new titanium alloy in the Paris area.The extension of the waveform will increase the dwell-fatigue crack growth rate of the new titanium alloy,and this effect will becomemore and more significant with the increase ofK.To study the influence of the waveforms on thefatigue crack growth rate,the
29、effect of maximum stress dwell time and the minimum stress dwelltime was considered.The prediction model only considered the effect of the dwell time under maximum stress and did not consider the effect of the dwell time under minimum stress.Therefore,theprediction model needs to be revised.Based on
30、 the prediction model shown in Eq.(2),consideringthe effect of the waveform on the dwell-fatigue crack growth rate of the new titanium alloy,thedwell timetholdis divided into two parts:the dwell timethold1under maximum stress and the dwelltimethold2under minimum stress,as shown in Eq.(3).thold=thold
31、1+thold2(3)At the same time,it is known from the test results that the influence of the waveform is relatedto the range of the stress intensity factorK.The overall influence trend is a dynamic process,sotheK/KICterm is introduced to characterize the influence of the waveform.The modified model issho
32、wn as follows:dadN=A1K-()KthR-Kths()1-e-k()ad-Kthsm11-()Kmax/KICn1+A2()thold1+thold2KKICmax-RY-R K1-()KmaxKICn2m2(4)whereA1is the material and environmental constants related to fatigue cyclic loading,(MPa-mm1m/2);m1is the slope of the crack growth rate curve related to fatigue cyclic loading;n1is t
33、he parameterthat characterizes the affect ability ofKmax/Kminof fatigue cycle;Kmaxis the maximum stress intensityfactor,(MPam);Kminis the minimum stress intensity factor,(MPam);KCis the material fracturetoughness,(MPam);Fis the elastic-plastic correction factor at the crack tip;A2is the materialand
34、environmental constants related to dwell-fatigue cyclic loading,(MPa-mm1m/2);m2is the slopeof the crack growth rate curve related to dwell-fatigue;n2is the parameter that characterizes the affect ability ofKmax/Kminof dwell-fatigue;thold1is the dwell time under maximum stress,s;thold2is thedwell tim
35、e under minimum stress,s;is a physical quantity that characterizes the extent to whichthe maximum loading stress level affects the crack growth rate.2 Research on prediction of dwell-fatigue crack growth rate atdifferent temperatures2.1 Test resultsThe dwell-fatigue crack growth life of the new tita
36、nium alloy is less than the fatigue crack880船舶力学第27卷第6期growth life at 20.The dwell will reduce the fatigue crack growth life of the new titanium alloy.Bycomparing the crack growth rate of fatigue and dwell-fatigue,it can be concluded that the dwell increases the fatigue crack growth rate.This is bec
37、ause the stress intensity factor at the crack tip hasincreased compared with fatigue due to the dwell effect.Evans12-13believes that the microstructurewill affect the sensitivity of the titanium alloy to dwell-fatigue.According to the test results,the temperature has a certain influence on the dwell
38、-fatiguecrack growth life of the new titanium alloy.Overall,the temperature has little effect on life.Stephens14believes that low temperature will reduce the fatigue crack growth rate,but the fracturetoughness,fatigue crack growth life and final crack length will become smaller.For new titanium allo
39、y,the effect of temperature on the dwell-fatigue crack growth life is not obvious.It can be seen from Fig.4 that the temperature has a certain effect on the dwell-fatigue crackgrowth rate.The low temperature decreases the dwell-fatigue crack growth rate.Zheng15believesthat titanium alloys have diffe
40、rent dwell-fatigue phenomena at different temperatures.The mainreason is that low temperature will hinder the movement of dislocations,so that creep during thedwell phase cannot occur.Jun16believes that different microstructures will lead to different dwell-fatigue crack growth behavior of titanium
41、alloys at different temperatures.In the low temperaturestate,the difference between the dwell-fatigue crack growth rate of the new titanium alloy at 0 and-20 is not obvious.The possible reason is that the microstructure of the new titanium alloy isinsufficiently sensitive to temperature changes.As t
42、he range of stress intensity factorKincreases,the dwell-fatigue crack growth rate curve at low temperature will produce a focusK0with thedwell-fatigue crack growth rate curve at room temperature.When the range of stress intensity factorKis greater thanK0,the dwell-fatigue crack growth rate under low
43、 temperature is greater thanthat under room temperature.At the same time,the low temperature will reduce the fracture toughness of the new titanium alloy.Combined with the a-N curve shown in Fig.5,it can be judged thatthe reduction in fracture toughness is the main reason for the reduction in the dw
44、ell-fatigue crackgrowth life under low temperatures.ddFig.5 Life curve of dwell-fatigue crack propagation under different temperatures ofnew titanium alloy materialFig.4 Test results of new titanium alloy dwell-fatigue crack growth rate under differenttemperatures第6期WANG Ke et al:Prediction Method o
45、f Dwell-Fatigue 8812.2 Prediction resultsThe prediction research on the dwell-fatigue crack growth rate of the new titanium alloy atload ratio R=0.3 and different temperatures(20,0,-20)was carried out.Under the premisethat other test parameters remained unchanged,changes in ambient temperature mainl
46、y affected themodel parameters A1and A2.The parameter fitting results at different temperatures are shown inTab.2.The prediction results are close to the test results as shown in Fig.6.When the stress intensity factor range is small,the dwell-fatigue crack growth rate at room temperature is greater
47、than atlow temperature(0,-20).The dwell-fatigue crack growth rate at 0 is slightly greater thanat-20,but the difference is not obvious.As the range of the stress intensity factor gradually increases,there is an intersection between the dwell-fatigue crack growth rate curve at low temperature and roo
48、m temperature.After this point,the dwell-fatigue crack growth rate at 0 and-20 also shows a significant difference.As the temperature decreases,the fracture toughness of the newtitanium alloy gradually decreases.There is a difference between the prediction curve and the testcurve at 0.The possible r
49、eason is that the inherent properties of the material and accidental factors in the low temperature environment affect the sampling accuracy of the extensometer8.But theprediction results more accurately reflect the influence of temperature on the dwell-fatigue crackgrowth rate.Therefore,it can be c
50、onsidered that the revised dwell-fatigue crack growth predictionmodel can accurately predict the dwell-fatigue crack growth rate of the new titanium alloy at different temperatures.Tab.2 Model parameters at different temperaturesR=0.3T=20 T=0 T=-20 A12.810-10KC94.8A12.510-10KC80.93A12.210-10KC75.35n
