Fatigue behavior of direct laser deposited Ti-6.5Al-2Zr-1Mo-1V titanium alloy and its life distribution model

Xiaofan HE,Tianshuai WANG,Xiaobo WANG,Weigang ZHAN,Yuhai LI

School of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

KEYWORDS Additive Manufacturing;Bimodal Lognormal distribution;Direct Laser Deposition;Fatigue life;Mixed failure behavior

Abstract The present work aims to investigate the fatigue behavior of Direct Laser Deposition(DLD)Ti-6.5Al-2Zr-1Mo-1V titanium alloy under constant amplitude stress.22 pieces of DLD Ti-6.5Al-2Zr-1Mo-1V titanium alloy standard cylinder specimens were tested under a stress level of 800 MPa with a stress ratio of 0.06.Fatigue fractography and fatigue life data were obtained.Through the fracture surface analysis,the specimens were divided into two categories in accordance with the location of crack initiation and defect types.Comparison of fatigue life and behavior between two specimen types was given,which was followed by a discussion about the impact of defect type,size and position on the fatigue life of the specimen.The fatigue test results also show a large variation of fatigue life.To illustrate the statistical characteristics of the fatigue life,probabilistic analysis was performed,and a novel bimodal lognormal model was established.The model has a good fit with the experimental data and can reduce the scatter of the fatigue life significantly.

1.Introduction

Motivated by the need for ‘rapid and flexible manufacturing”from engineering fields,many Additive Manufacturing(AM)processes have been developed in recent years.Among them,Direct Laser Deposition(DLD),also called Laser Engineered Net Shaping(LENS),is a Direct Energy Deposition(DED)technique1with the laser used as the energy source.This technique uses a high-powered laser to fabricate dense components directly from Computer Aided Design(CAD)models via melting the metal powder sent synchronously and depositing the melted powder on the substrate layer by layer.Compared with other AM processes such as Selective Laser Melting(SLM),DLD has the following advantages2:(A)complex parts and molds with declining thin wall,overhanging part,or cavity and inner flow channel can be directly fabricated;(B)heterogeneous material components can be flexibly manufactured;(C)structural damage can be repaired by DLD;(D)DLD can be employed with an extensive range of materials.Due to its extraordinary flexibility in fabricating and designing,DLD shows great potential in engineering manufacturing fields.As titanium alloy usually has poor forming performance,the application of DLD in titanium alloy component and structure manufacturing is particularly attractive.3

DLD process characterized by layer-by-layer depositing leads to variation in microstructure and mechanical properties.4To achieve safety and economy of the DLD and AM-processed components in the service period,there have been considerable researches on mechanical properties and failure behavior.

Previous studies on mechanical properties of DLD titanium alloy generally focused on the static mechanical properties and microstructures under different processing parameters and heat treatments.Many researchers have contributed to different types of DLD titanium alloy investigations.3,5–13

As-built DLD titanium alloys always have mechanical properties no weaker than those wrought materials.Qiu et al.3considered that the as-built Ti-6Al-4V microstructure was characterized by columnar grains with martensitic needle structure and a small fraction of β phase,which resulted in the fine mechanical properties.Carroll et al.9studied the tensile behavior of Ti-6Al-4V component fabricated with DLD and found that the DLD components are commensurate with those of wrought materials.

In many applications,structures are under cyclic loading conditions that induce fatigue failure.The existing literature regarding fatigue property investigation on DLD material tends to concentrate on the impacts of processing parameters,defects,surface qualities and heat treatments.14,15

Defects play a major role on the fatigue life of AM materials.Edward and Ramulu16carried out a fatigue test on Ti-6Al-4V specimens fabricated by Selective Laser Melting(SLM)to investigate the effects of surface quality and fabricating direction on fatigue properties.They concluded that the effects of depositing direction and surface quality are incomparable to those of defects.Their analysis shows that the majority of cracks initiate from defects such as pore and Lack of Fusion(LOF).Wycisk et al.17,18found that different surface treatment methods have similar effects on the fatigue properties of the AM Ti-6Al-4V specimen,which is in accordance with the dominant role of defects on fatigue life.More supporting evidence comes from studies of Xu et al.19and Liu et al.20

Fatigue life is known to have significant variation.To model the variation,a large number of fatigue tests have been conducted,and probabilistic methods have been proposed.Several probabilistic models,such as Lognormal distribution(LG)and Weibull distribution,can be used to describe the fatigue life distribution of traditional metal materials.21–24Experimental results have proved that such models can well reflect the fatigue life distribution.Unlike those traditional metal materials,the special forming processes of AM materials differ from the traditional processes and will inevitably be affected by some unexpected factors,thus resulting in the formation of inner pores,LOFs,and other defects.Although these defects can be somewhat reduced by optimizing process parameters and appropriate heat treatment such as Hot Isostatically Pressing(HIP),it is hardly possible to eliminate all of them.3,13,25,26These defects are usually fatigue sources and randomly distribute in AM materials,which may lead to various failure forms and obvious variation in fatigue life.Prabhu et al.4studied the effect of defects on the fatigue life of Ti-6Al-4V specimens manufactured by DLD and found that the fatigue life of specimens with cracks initiated from the defect at the surface are one order of magnitude lower than that of the inner defect initiation specimens.The existence of defects leads to a greater scatter of the fatigue life of AM materials.Therefore,a major problem to be tackled is how to model the fatigue life variation of AM materials.

Previous studies have shown that the metal materials produced by AMs have defects such as pores and LOFs which may lead to variations in fatigue crack initiation and propagation,resulting in an obvious variation in fatigue life.27To ensure the safety,the fatigue behavior and fatigue life distributions should be investigated through fatigue tests.However,in the existing literature,little research has dealt with this issue and a few relevant studies preferred the methods for traditional materials.There are generally 5–10 pieces of specimens under the same stress.18,27–31The number of specimens for fatigue test is relatively small,which cannot well reflect the fatigue life variation.

In this paper,a fatigue test of 22 pieces of DLD Ti-6.5Al-2Zr-1Mo-1V standard cylindrical specimens was conducted under Constant Amplitude(CA)stress.The specimens were extracted parallel to the deposition direction from a block fabricated by DLD.Through a fractographic analysis,the fatigue failure behavior was elucidated,and the effects of defects on fatigue life variation were discussed.Finally,a Bimodal Lognormal distribution(BLG)method to model the fatigue life variation was established.

2.Materials and experiments

2.1.DLD Ti-6.5Al-2Zr-1Mo-1V specimen

The Ti-6.5Al-2Zr-1Mo-1V titanium alloy rectangular plate was fabricated by the DLD process;the plate was then machined into standard smooth cylindrical specimens after duplex annealing(850 °C AC 1 h,650 °C FC 2 h).

As shown in Fig.1,the Ti-6.5Al-2Zr-1Mo-1V titanium alloy rectangular plate was deposited by short side reciprocating scanning strategy on a substrate.The XOY plane is the scanning plane;Z is the deposition direction.The substrate was made of wrought Ti-6.5Al-2Zr-1Mo-1V titanium alloy.The spherical powder,in the diameter range of 47–165 μm(-100/+325 mesh size),used for DLD Ti-6.5Al-2Zr-1Mo-1V,was prepared by Plasma Rotation Electrode Process(PREP)with details of the chemical composition provided in Table 1.The specific process parameters are shown in Table 2.

Fig.1 Schematic diagram for fabricating Ti-6.5Al-2Zr-1Mo-1V blank by DLD and cylindrical specimens’extraction.

The as-built Ti-6.5Al-2Zr-1Mo-1V titanium alloy blank was subjected to duplex annealing.Then the rectangular blank was machined into standard cylindrical specimens as shown in Fig.2,with a surface roughness Ra=0.32 μm.The minimum cross section of the specimen has a diameter of 5 mm and an accuracy of±0.02 mm.As shown in Fig.1,the specimen axis is perpendicular to the laser scanning plane(XOY)but parallel to the deposition direction(Z).

Fig.3 shows the microstructure of the material.As indicated in Fig.3(a),the material mainly consists of coarse columnar grains with the growth direction of the columnar as Z direction.The heat-affected zones parallel to each other can also be found in Fig.3(a).As shown in Fig.3(b),the columnar grain mainly consists of the basket-weave microstructure.Near the grain boundary,there is a large number of α colonies.However,it can be seen from Fig.3(b)that the microstructure of the material is inhomogeneous.Besides the fine basket-weave organization,α lamellar microstructure also existed in the material.

2.2.Fatigue test

The fatigue test was carried out on an INSTRON 8801-100 kN electrohydraulic servo fatigue test system in the atmospheric environment at room temperature under a sine-wave CA stress with a stress ratio R of 0.06 and a frequency f of 10 Hz.The specimen was fastened to the test machine by a pair of steel machined clamps(see Fig.4).The peak stress σmaxwas 800 MPa,and the peak-load Pmaxwas calculated by Pmax=σmaxA,where A presents the minimum cross-sectional area of the specimen and can be calculated according to the diameter(d)at the minimum cross section.As the surface of the specimen is relatively smooth,the nominal size of d(5 mm),rather than the measured value,was used in the calculation of peak load to prevent the vernier caliper scratches on the surface and additional surface defects.

2.3.Fractographic analysis

Fractographic analysis on fracture surface after fatigue tests was made by using Scanning Electron Microscope(SEM)to examine the crack initiations and identify the failure forms.Prior to the fractographic evaluation,the specimens were immersed in acetone and cleaned in an ultrasonic cleaner.

Table 1 Chemical composition of Ti-6.5Al-2Zr-1Mo-1V spherical powder.wt%

Table 2 DLD process parameters.

Fig.2 Schematic diagram of specimen’s dimensions.

Fig.3 Microstructure of DLD Ti-6.5Al-2Zr-1Mo-1V.

Fig.4 Component fatigue test setup.

3.Fatigue test results

A total of 22 specimens were tested.The fatigue life data are shown in Fig.5,and the fracture surfaces in Fig.6.Those specimens can be divided into two categories based on the locations where the cracks were initiated.

(1)Case I:Specimens with crack Initiated from the Surface or Subsurface(SISS)

Fig.5 Fatigue life data.

Fig.6 Fracture surfaces of SISS and SII.

There were a total of 15 specimens with crack initiated from the surface or subsurface with fatigue life shown in Fig.5.No significant defect was found at the crack initiation location(see Fig.6(a)).There was also one specimen with two crack sources,one of which locates at the surface and the other in the inner body of the specimen.However,the observation on the fracture surface shows that the growth region of the surface-initiated crack is obviously larger than that of the inner crack.Consequently,the crack initiated from the surface is considered to be the lead crack and this specimen was treated as SISS.

(2)Case II:Specimens with crack Initiated from the Inner(SII)

Fig.7 SISS and SII after fatigue test.

There were seven specimens with crack initiated from the inner as shown in Fig.6(b).The inner defects can be observed as the crack sources from the fracture surface.In this research,crack sources of all the 7 SII were not LOFs but pores.Their fatigue life data are shown in Fig.5.

All fatigue specimens are shown in Fig.7.The red dash line indicates the position of the minimum cross section of the specimen,where fatigue fracture most likely occurs(35 mm from the lower end of the specimen).The yellow dash line shows the range of the actual fracture position of the specimens in the fatigue test.The fracture positions for both SISS and SII were within±3 mm near the minimum cross section of the specimens.No significant differences were found in the fracture positions between SISS and SII.

3.1.Case I:SISS

The typical fractography of SISS is shown in Fig.8 and the fracture surface can be divided into three regions:(A)Crack Initiation Site(CIS),the location where cracks initiate from;(B)Crack Propagation Region(CPR),a flat plane vertical to the load direction formed as the result of the crack stabilized propagation;(C)Fast Fracture Region(FFR),the area produced by the fast crack propagation and fracture.

Typical CIS is shown in Fig.8(c).The cracks mainly initiated from the surface and subsurface of the specimen,which is similar to wrought and rolled materials.CIS consisted of many distinct cleavage faces,and cleavage feather-like features can be easily identified.

A typical CPR is shown in Fig.8(b).Radiation lines and fatigue striations(see Fig.9)could be found in CPR.Some secondary cracks indicated in the blue rectangle and unmelted particles in the green rectangle were observed.The location and shape of the secondary cracks were irregular,which may be related to the DLD parameters,the heat treatment processing and the stress state.Some powder sent synchronously failed to be completely melted,remaining as unmelted particles,which may exist in the spherical shape or partially melted irregularities.These particles also produced irregular voids inside the specimen that could in turn affect the fatigue properties of the specimen.

Fig.8 Typical fracture surface of SISS.

Fig.9 Typical fatigue striations and secondary cracks in CPR.

Fig.10 Typical dimple feature in FFR.

Fig.11 Fracture surface of specimen with both surface and inner cracks.

Obvious dimple features can be seen in the FFR(see Fig.10).As shown in Fig.8(a),FFR can be divided into two parts,denoted as FFR I and FFR II.FFR I is relatively flat and located in the same plane with CPR.FFR II is an inclined plane with an angle of about 45°to the plane of the CPR.The differences between the two FFR regions are mainly due to the different stress-strain state when the fracture occurs.FFR I is close to the ideal plane strain state due to the constraints inside the materials,while the FFR II is close to the plane stress state because of the small distance to the surface of the specimen.

One of the SISS has cracks initiated from both the surface and the inner of the specimen.As shown in Fig.11,the area inside the white dash line is the internal crack region with crack initiated from an inner pore,while the area inside the red dash line is the crack region which is initiated from the specimen surface.The size of the two CPRs shows that the area of the surface crack is larger than that of the inner crack,justifying the surface crack being the lead crack.Meanwhile,the internal crack is not located on the same plane as the lead crack.The fatigue life of this specimen is 49063 cycles,lower than those of most SISS and SII.This may be attributed to the presence of non-main crack(inner pore initiation)and the rapid crack growth induced by the inner-action of those two cracks reducing the crack growth life.However,it is still within the range of the SISS fatigue lives and the surface crack is the lead crack.Therefore,this specimen can be treated as SISS in the subsequent analysis.

3.2.Case II:SII

The causes of the internal defect formation are complex.Different scanning strategies and processing parameters,as well as differences in the quality and chemical composition of the powder,can all lead to inner defects occurring in the AM material.29Numerous studies have shown that internal defects are the major cause of the large fatigue scatters of AM materials.29,32In this investigation,the inner pores can be observed on the fracture surface of those 7 SII.Those pores mainly stem from the gas element in the powder itself,the gases adsorbed on the powder and the gases involved into the molten pool when the powder is delivering.33

Fig.12 Typical fracture surface of SII.

Fig.13 FDH of logarithmic lifetime.

Typical fractography of SII is shown in Fig.12.The fracture surface can also be divided into CIS,CPR,and FFR.In Fig.12(a),the region inside the white dash line is CPR,which is approximately circular.Like a fish eye,the center of the region close to the initiation of the crack is bright,while the surroundings are dark.Radiation lines can be found in CPR.Partial magnification of the initiation is shown in Fig.12(b).The crack is initiated from an inner pore.There are many cleavage faces around the pore.The other features of the CPR and FFR are almost the same as those of the SISS.

4.Statistical analysis of fatigue life

Of all the 22 specimens,the maximum fatigue life is about 17 times longer than the shortest,as shown in Fig.5.The fatigue life range of SII is 30293–544102 cycles and wider than that of SISS(30715–256709 cycles).However,the fatigue lives of the majority of the SII are within the range of SISS,and most parts of the fatigue life distribution band of SISS and SII are overlapped.As a result,we cannot treat fatigue life of SII and SISS as two sample groups from two independent parent populations.

To clarify the fatigue life variations,the fatigue lives of all 22 pieces of specimens were taken logarithmically and plotted as a Frequency Distribution Histogram(FDH)of logarithmic lifetime with an interval of 0.2(see Fig.13).Two peaks appear in the logarithmic lifetime frequency distribution histogram:the frequency between the logarithmic fatigue life range of 4.6–4.8 is the highest,followed by that at 5.2–5.4.This is different from the normally distributed logarithmic fatigue life of traditional metal materials.

4.1.Fatigue life distribution model

Fig.13 demonstrates that the right and left sides of both peaks are approximately symmetrical.Therefore,a BLG can be used to describe the fatigue life distribution of specimens.The fatigue life is denoted as the random variable Y.The Probability Density Function(PDF),fY（y）,and Cumulative Distribution Function(CDF),PY（y）,of Y are given by

where α represents the weight and 0 ≤ α ≤ 1.Y1and Y2,two independent random varieties,follow the lognormal distribution Y1~LG（μ1，σ21）,Y2~LG（μ2，σ22）.fY1,fY2,PY1,PY2represent the PDF and the CDF of Y1and Y2,respectively.When α=0 or α=1,Y degrades into a single-peak logarithmic normal distribution.

The PDF and the CDF of Y1and Y2are

Fig.14 FDH of logarithmic fatigue life and PDFs of BLG and LG.

Fig.15 Fatigue life data and CDFs of LG and BLG.

Table 3 Parameters of BLG.

The distribution of Y can be determined by five parameters,α，μ1，σ1，μ2，σ2.Thus,Y follows the BLG,which can be denoted as Y~BLG（α，μ1，σ21，μ2，σ22）.

4.2.Fatigue life distribution model

It is difficult to estimate all the five parameters’value of BLG due to the complicated forms of its PDF and CDF.A numeric method for estimating the BLG parameter is established in this paper via employing the Plotting Position Formula(PPF)and the Maximum Likelihood Method(MLM).The minimum Sum of Squares for Error(SSE)is used as the criterion for determining distribution parameters.In this method,the basic principle is using minimization of the SSE as a criterion for determining the distribution parameters.The details of the estimation method are shown as follows:

(1)Rank the fatigue lives in an ascending order.Denote the ranked fatigue lives as yi（i=1，2，...，n）,where i is the ordinal number,and n is the total number of specimens.In this paper,the value of n is 22.

(2)As Eq.(4),34calculate PR（yi）,the cumulative probability of yi,

(3)Classify the arranged fatigue life samples.Take the first n1samples as the first class,denoted as random variable Y1.Suppose that the residual n-n1samples are from another population as the second class,and are denoted as the random variable Y2.

(4)Let n1take a value from 2 to n-2 in sequence.For the specified n1,the expectancy and the standard deviation of logarithmic fatigue life of Y1and Y2are estimated by the MLM,illustrated by Eq.(5)35

(5)Let αj，n1=0.001j（ j=0，1，...，1000）.For the specified n1and α = αj，n1,calculate the theoretical cumulative probability value for every yifollowing Eq.(1).Set the value aserror for specified n1and αj，n1,denoted as SSE（αj，n1，n1）,can be obtained,as shown in Eq.(6).

(6)Denote n1and αj，n1aswhen SSE（αj，n1，n1）take the minimum value.The estimated values of μ1，σ1，μ2，σ2forare recorded asFinally,the estimated values of the five parameters to be determined in Y~BLG（α）can be described as

4.3.Statistical analysis of fatigue life data

Five BLG parameters and some other typical parameters estimated from the fatigue life data are listed in Table 3.CDF and PDF are shown as Eqs.(8)and(9)respectively.It can be found that α is approximately equal to the ratio of n1and n.We can then consider that α is the proportion of the first class in the total population.

Blue curves in Figs.14 and 15 show the PDF and CDF of BLG.We can then conclude that PDF and FDH are good fits.Moreover,CDF is also consistent with the fatigue life data.

5.Discussion

5.1.Statistical analysis of fatigue life data

Conventionally,an LG can be used to describe the fatigue life distribution.Assume that the fatigue life follows the LG,and the parameters are estimated by using MLM based on 22 fatigue lives.Estimated parameters are listed in Table 4.

The PDF of BLG model and LG model are described in Fig.14.The blue curve is the PDF curve of BLG,typical of an obvious bimodal under the logarithmic coordinate.The two peaks appear at about lg N=4.7 and lg N=5.4 respectively with the former being higher.Compared with the PDFcurve of LG,red curve in Fig.14,the PDF curve of BLG is closer to the fatigue life distribution reflected by the FDH.

Table 4 Parameters of LG.

Fig.16 PDF of LGSISSand FDH of logarithmic fatigue lives of SISS.

As illustrated in Fig.14,the scatter of fatigue life can be significantly reduced under the BLG model.The red dash line shows the distribution band of LG between the quantiles μ +3σ and μ -3σ,corresponding to the cumulative probability range between 0.13%and 99.87%;the blue dash line shows the distribution of BLG corresponding to the same probability range.The distribution band width of the BLG is about two thirds of the LG.As indicated in Fig.15,CDF of BLG can better fit the fatigue life data than that of LG.SSEBLGis 0.032,far less than SSELG=0.107.

Therefore,BLG can better reflect the fatigue life distribution of DLD Ti-6.5Al-2Zr-1Mo-1V titanium alloy and thus significantly reduce the scatter.

5.2.Defects and fatigue behavior

Material defects caused by special processing techniques have significant effects on the fatigue life of DLD material,which is one of the main reasons for the excessive scatter of its fatigue life.

Given that fatigue life follows a lognormal distribution,the fatigue life data of 15 SISS were statistically counted,denoted as LGSISS.μSISSand σSISSwere estimated by MLM and the median life(N50,SISS)was calculated.The fatigue life scatter is still large even if the data of specimens with cracks initiated from inner pores are removed.The standard deviation of logarithmic fatigue life reaches 0.324.PDF and CDF are shown in Fig.16 and Fig.17 respectively.Obviously,LG is not suitable for describing fatigue life distribution of SISS.

Fig.18 PDF of LGSIIand FDH of logarithmic fatigue lives of SII.

The special process features of DLD depart the material from those made by forging and rolling.Previous investigations also confirmed that AM materials have some special features like inhomogeneity and anisotropy.These characteristics may affect the crack initiation and propagation.Therefore,for the DLD manufacturing of metal materials,even if cracks initiate only from the surface,the fatigue life may still have a great scatter.

The fatigue lives of SII are statistically processed by LG,denoted as LGSII. Logarithmic lifetime expectation(μSII=5.18)and logarithmic lifetime standard deviation(σSII=0.425)were estimated by MLM.The PDF is shown in Fig.18.The statistical analysis shows that the fatigue lives of SII have a greater scatter than SISS,and the median life(N50,SII)is longer than N50,SISS.

Although the defects induced cracks of SII were pores only,the location and size of the pores vary.The causes for a pore evolving into a crack are complex and can be largely affected by the size,shape,and position of an inner pore.The pore area and its minimum distance from the specimen surface were measured by using image process software,and the relation between pore area/distance and fatigue life is shown in Fig.19.In Fig.19(a),we can find that the fatigue lives of most specimens are negatively correlated with the pore area.The red and blue data points in the figure indicate the data points with similar distance to the specimen surface.It can be concluded that for the similar distance,the larger the pore area is,the shorter the fatigue life is.However,when the blue data points are compared with the red data points,we can see the differences in defect location and the fatigue life sensitivity to the size of the pore area.The farther it is away from the specimen surface,the greater the sensitivity is to the pore area.Likewise,when the area is similar,the farther the distance is,the shorter the fatigue life is,as shown in the green ellipses.

5.3.Effects on BLG of fatigue behavior

Fig.19 Influence of size and location of pore on fatigue life.

Fig.20 Comparison of PDFs under different distribution.

Although the bimodal distribution may be attributed to different failure behavior caused by the defects,it is not advisable to categorize all samples simply on the basis their different failure behavior.In Fig.20(a),the black curve is the PDF of BLGCFB(BLG calculated by the classification standard as different failure behavior).The blue and green curves are the PDF of LGSISSand LGSIImultiplied by the weights 15/22 and 7/22 respectively.Obviously,the black curve is the sum of the blue and green curve.The figure shows that the PDF of BLGCFBdoes not have obvious bimodal characteristics;therefore,it cannot fully reflect the distribution of FDH.Fig.20(b)shows no significant difference between the PDFs of LG and BLGCFB.The distribution band of BLGCFBbetween the probability range of 0.13%and 99.87%is still large,and much wider than that of the BLG.Fig.21 shows the CDF of the BLGCFB.The curve does not well fit the fatigue life data.Its SSE,reaching 0.093,is slightly smaller than the SSE of LG,but it is far greater than the BLG estimated in Section 4.3.

Such phenomena can be interpreted as follows:

(1)The difference in fatigue life between SISS and SII is not sufficiently significant to lead to an apparent bimodal characteristic of BLGCFB.The blue data points in Fig.21 represent the fatigue lives of SISS,while the red ones represent those of SII.The fatigue lives of two specimen types cannot be separated from each other as most parts of their fatigue life distribution bands are overlapped.It can also be found from Fig.20(a),although μSII=5.18 is larger than μSISS=4.91,the difference between them cannot be clearly identified,thus resulting in an unapparent bimodal characteristic of the BLGCFB.

Fig.21 CDF of BLGCFBand fatigue life data.

(2)The effects of the inner pores on fatigue life are complex.The sizes of pores are usually tiny(dpore＜ 100 μm).It is difficult to identify an inner defect of such small size by normal Non Destructive Testing(NDT)prior to the fatigue test.Moreover,it is impossible to determine whether the experimental data are valid simply based on whether or not a defect exists.The analysis shows that the location and area of the pores have different effects on the fatigue life of the specimens.The size,location,and quantity of the defects in the specimens are random.Consequently,it is not practical and efficient to classify the specimens based on the crack initiation location when the parameters of BLG are estimated.

6.Conclusions

Through the test and analysis,the following conclusions can be drawn:

(1)The fatigue failure of Z-direction DLD Ti-6.5Al-2Zr-1Mo-1V specimens after duplex annealing can be divided into two categories in accordance with the location of the lead crack initiation:surface or subsurface initiation and inner pores initiation.However,no significant difference can be identified in the fatigue lives of two categories of specimens.

(2)The presence of the defects may increase the scatter of the fatigue life.The fatigue lives of SII are related to the size and location of pores.When the pore positions are similar,the larger the area of the pore is,the shorter the fatigue life is;when the pore area is similar,the shorter the distance of the pore to the surface is,the longer the fatigue life is.

(3)Compared with the LG,the BLG can better describe the fatigue life distribution of DLD titanium alloy while the scatter is reduced.

Acknowledgements

The authors gratefully acknowledge the support from the National Key Research and Development Program of China(No.2017YFB1104003),the National Natural Science Foundation of China(No.11772027),and Aeronautical Science Foundation of China(No.28163701002).