亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        DAMAGE TOLERANCE AND FATIGUE LIFE ESTIMATION FOR PIPE/ROD BAR STRUCTURE

        2011-10-08 12:09:52DuraHariBahadurWuTieyingWuZhigong

        Dura Hari Bahadur,Wu Tieying,Wu Zhigong

        (College of Energy and Power Engineering,NU AA,29 Yudao Street,Nanjing,210016,P.R.China)

        INTRODUCTION

        Pipe structures are widely used in many engineering applications. Tension pipes are commonly found in engineering applications,such as in aircraft auxiliary power units (APUs)support system,reactor,rotorcraft,machine and machine components,etc. The structures are applied to the random loading spectrum. The cracks greatly reduce the load bearing capacity of pipes.Structure fracture leads airplane in danger.The primary techniques used in fracture mechanics are the finite element method and the line-spring element technique.As far as the crack propagation phase is concerned, the most dominant parameter is the near-crack-tip elastic stress intensity factor. The solutions for the external and internal circumferential cracks are of the same order.In engineering sense they show no significant difference[1].There are relatively few solutions for pipes containing partly elliptical circumferential surface flaws. Similar studies about the circumferential crack propagation in a pipe have been done in Refs.[1-4].

        The crack propagation phase in a pipe is studied in three phases show n in Fig.1.

        (1)PhaseⅠ:The shape of the crack front is nearly elliptical and the crack front only crosses the outer surface of pipe.

        (2)PhaseⅡ: Crack growth shape is near straight lineat the beginning and more complex at later phase.Crack front crosses both the inner and the outer surfaces of pipe.

        (3)PhaseⅢ:Crack growth shape is nearly elliptical and the crack front has just broken through in the opposite inner surface.Practically it cannot sustain any loading.It is very unstable.

        To estimate the crack propagation life under fatigue loading,the following information must be known:

        Fig.1 Crack propagation phases in pipe

        (1)Material properties such as d a/d N curve;

        (2)Fatigue loading spectrum;

        (3)Relations between K I vs crack size under specific loading.The finite element model(FEM)is used to find the relations.

        1 FINITE ELEMENT MODELING

        EFM is the most dominant technique for investigating these structures due to its flexibility in complex structure modeling[1,2,4,5].The crack configuration shown in Fig.2 is described by some non-dimensional parameters,i.e.,the inner to outer diameter ratio of the pipe(D in/D out)and the external crack propagation angle(θ).

        Fig.2 Circumferential cracked pipe under tension loading

        1.1 Crack tip element

        A significant advancement in the use of FEM for linear elastic fracture mechanic (LEFM)problems was simultaneous and independent development of ″quarter-point″e(cuò)lement[6-7].The quarter-point element achieves more accurate result. The singular elements were utilized around the crack front in order to induce a square root singularity of stress/strain field in the vicinity of crack front[8]. The twenty-node iso-parametric brick elements(Solid 95[9])were regarded as crack tip(Fig.3)and the other parts of the model were used with eight-node brick element(Solid 45[9])for the higher computational efficiency.The half-elliptical crack front consists of 20—60 crack tip elements depending on the crack propagation phase.The crack front uses the focused type of mesh with typically 5—10 elements to enclose each crack front element in radial direction as shown in Fig.4.In order to avoid the large number of required analyses and save time,the code in ANSYS Parametric Design Language (ANSYS-APDL) software is developed.

        Fig.3 Twenty-node crack tip element

        Fig.4 Focused type of mesh

        1.2 Boundary condition and loading

        The symmetry conditions in the longitudinal and lateral directions are exploited to reduce the computation and FEM efforts.FEM for a pipe containing the circumferential crack is shown in Fig.5.The loading condition includes the uniform pressure of p=1 MPa on the lower extreme surface of cylinder.Nodes A,B and C of the tip element in Fig.6 are constrained in z-direction to achieve the singularity in the strain[8]. Fig.6 shows the stress distribution on the crack tip,i.e.,ez=Ce/,and the displacement curve of the distorted element,i.e.,uz=Cu,where C e and Cu are constants[8].Moreover,Fig.6 shows the crack tip elements 1—6,where uz1/4 and uzare the crack tip opening displacements of the quarter chord node and the corner node,respectively.

        Fig.5 Finite element model

        Fig.6 Stress distribution on crack tip and element singularities

        2 FATIGUE CRACK PROPAGATION

        2.1 Iterative crack front propagation

        Most commonly used fatigue crack propagation model is the iterative crack front propagation[3-4].And it is also called the two parameter theoretical model[4]. The model uses the Paris-Erdogan law(Eq.(1))to assume the crack propagation.

        where d a/d N is the crack propagation rate expressed in m/cycle,ΔK I is expressed in Pa?m1/2,C and m are constants.The parameters influencing the crack shape change are[3]:

        (1)The relative crack size a/R(crack depth to radius)and a/L(crack aspect ratio).

        (2)The exponent m in the Paris-Erdogan law.

        (3)Type of loading.

        2.2 Iso-K I crack front propagation

        In FEM calculation of K I for pipe or rod bar,the crack front form is adjusted so that the parameters K I of nodes in the front are equal.Carpinteri[4]noted that the distribution of K I along the crack front is approximately constant for this particular value of the crack aspect ratio and the iso-K I criterion can be successfully applied only when the front of the initial surface defect is nearly circular-arc-shaped.

        According to the iso-K I criterion[4],the surface flaw grows by redistributing K I along the defect front in order to obtain a constant distribution of K I,i.e.,the initial flaw tends to a particular configuration during propagation to satisfy this assumption(constant K I along the crack front).

        For a given angle(θ),the crack tip nodes and their respective stress intensity factors are numbered by i=1,2,3,… and KI1,KI2,KI3,… ,respectively.The acceptable value of K I is

        In order to obtain K I within the acceptable value, an APDL program is created with geometry variables″a″and″b″as shown in Fig.7.Two″DO″loops are used to change the geometry of crack front and calculate K I within the acceptable limit.

        Fig.7 Crack front parameters

        Unlike the iterative crack front propagation geometry,the iso-K I crack front propagation is independent of the initial crack geometry.The iso-K I assumption avoids using the exponent m of Paris-Erdogan law in the calculation of KI,and the relation between K I vs crack size is generic and may be used in any material.

        3 FINITE ELEMENT RESULTS

        3.1 Crack propagation profile

        Once the crack propagates up to a certain relative depth, the subsequent stage is independent of the initial crack aspect ratio[2].FEM results show that the crack profile in the Phase I of any thickness pipe is nearly elliptical.When D in/D out is 0.6—0.9(thin pipe),the crack profile in the early PhaseⅡ is straight line,and withθin creasing the profile is more curved.As D in/D out goes on decreasing to 0.5—0.6(thick pipe),the crack propagation profile is near straight line in the early phase and has more curved in the later phase,so it is extremely difficult to determine.

        The crack propagation profiles in a pipe and a rod are simulated by the iso-KIcriterion,and their distinct difference is shown in Fig.8.Early and later phases of the PhaseⅡ in pipe and rod have distinct crack propagation fringes under fatigue.

        Fig.8 Iso-K I crack propagation profiles

        3.2 Stress intensity factor

        Ref.[10]proposed that the distorted elements are more accurate than the undistorted ones.Thus for obtaining the accurate result crack tip opening displacement(CTOD)is calculated with respect to the distorted element(element 6 in Fig.6).With distorted element different authors have used different nodes to calculate CTOD,the stress intensity factor and hence the fracture life.

        Ref. [7]used the quarter-point node displacement (uz1/4) and quarter-point node distance(r 1/4)to calculate K I.

        Ref.[8]used the corner-node displacement(uz)and the corner-node distance(r)to calculate the stress intensity.

        Under specific loading,KIincreases with the crack growth.For the iso-K I model,only one parameter is enough to describe the crack size.Here,the external crack propagation an gleθ(Fig.2)is used.Fig.9 shows FEM results in pipe and rod bars under specific loading for any material.

        Fig.9 Relation between K I vsθf(wàn)or different D in/D out

        The stress intensity factor curve is as expected.For the given pipe with fixed D out and different thickness,the thicker pipes are more resistant to the fracture. Fig.9 shows the transition from PhaseⅠ to PhaseⅡ where the increase of K I is significant,and also indicates that in the early phase of the PhaseⅡK I slowly increases,but in the later phase of PhaseⅡ K I exponentially increases.

        4 CRACK PROPAGATION LIFE

        The fatigue crack growth analysis of a component subjected to a constant amplitude loading is rather simple because loading history can be ignored.Numerous fatigue crack growth models have existed which are capable of representing the fatigue rate data.Paris model,Walker model and For man model etc are some of the famous fatigue propagation models.

        4.1 For man model

        For man model improves the Walker model by considering the instability of crack growth when the stress intensity factor approaches its critical value[11].Moreover,it is capable of describing all the region of fatigue crack (i.e., early development of fatigue crack,intermediate crack propagation zone and high growth rate of fatigue crack)and the effect of stress ratio[11].

        For man model is expressed as follows

        whereΔKI=KImax- KImin,C and m are the material properties,K IC is the critical stress intensity factor depending on the material,N the cycle of applied loading,,e min and e max are the minimum and the maximum stress applied to the tensile pipe during the certain period.Stress in a pipe can be obtained in the experiment and the real loading situations.

        4.2 Cumulative damage law

        Two main approaches for cumulative damage are considered:One is the direct postulation of lifetime damage(such as the Miner rule[12]),the other is the residual strength.Miner rule is also called the Palmgren-Miner linear damage hypothesis and expressed as follows

        where nj is the number of cycles under the loading corresponding to the lifetime Nj.

        The linear cumulative damage (LCD)accumulates damage in a linearly additive manner independent of the sequence of the loading applications.Then,the total damage is used to predict the failure.So,the Miner equation(Eq.(6))is very useful and safer to use.However,it is well known that the fatigue life is dependent on the loading sequence. That is the non-linear cumulative damage.Since the loading is a random spectrum in the structures such as APU in airplanes, the loading sequence cannot be uniquely determined.In this case,Miner rule gives a conservative fatigue life[12], and can enforce the safety in airplanes.

        4.3 Visual C++

        The visual C++ code has been developed by using the finite element analysis(FEA)results.Miner rule is used to determine the cumulative damage life of the pipe.The input parameters in the program are D in,D out,θ,C,loading data and m.Fig.10 shows the flow chart of the program.For man model is used to calculate the crack growth life.

        Fig.10 Flow chart of program

        K IC is used for the crack propagation criterion.For the given crack geometry and loading condition, if K I> K IC, the crack propagates rapidly and fails.

        The geometric criterion is used for the failure of pipe.In the Life Est software program—GUI,the critical angle for pipe is set to 110°.For the rod, the equivalent crack depth to 110°circumferential crack angle is taken as the critical crack depth.Normally,in the aircraft structures the pipes are replaced once the crack is visible.From the view point of static design,the pipe with 110°circumferential crack cannot sustain any designed static loading.Finally,GUI is created in VC++ for the more convenience.Fig.11 shows the GUI window of Life Est software.The Life Est program is useful to design the fracture tolerant for the pipe/rod bar structure under tension-tension or tension-compression spectrum.

        Fig.11 GUI window of LifeEst software

        During the operation, APU pipes suffer random loading in which the peak sequence randomly occurs.Based on this kind of loading sequence,a block spectrum can be statistically formed by eliminating small peaks without considering the sequence.For each loading block in the spectrum,there are the maximum force F max and the minimum force F min in certain service time of the spectrum(h).Each loading block has ni cycles.The material properties are known from the experiments or the material handbooks and can be input through GUI.Users can also define the crack initial size and the failure size depending on applications.The software can give the estimated lifetime.

        A distribution example of the loading spectrum is given in Table 1.

        Table 1 Loading spectrum distribution

        Fig.12 shows the relation between life vs circumferential angle(θ)for the thick pipe with D in=20 mm,D out=30 mm and length(10 times of the outer diameter) under the tensile-compression loading spectrum in Table 1.It also shows that the crack propagation life of pipe exponentially decreases.

        Fig.12 Life estimation for thick pipe

        Fig.13 shows the influence of the critical angle on the fracture life of pipe structures containing circumferential crack angle 1°.It also shows that the assumed 110°as a critical crack geometry angle is quite safe.For the given pipe with circumferential crack angle 1°under the loading spectrum in Table 1,the total life beyond the critical crack angle 30°is constant and is safe to calculate the fracture life.

        Fig.13 Total life estimation

        5 CONCLUSIONS

        (1)The iso-K I criterion is independent of the material property and is useful for the study of crack propagation in a pipe or a rod under simple loading.Using the iso-K I criterion,the profiles can present the fatigue crack fringe.

        (2)As the crack propagates from the PhaseⅠ to the PhaseⅡ,the stress intensity factor significantly increases.

        (3)The crack propagation profiles on a pipe and a rod are distinctly different in the early and later phases of the PhaseⅡ.

        (4)The developed software is useful if the loading spectrum is known.It is also easy to be modified for other types of crack and structure since it is implemented by object-oriented programming(OOP)language.

        [1] Bergman M. Stress intensity factors for circumferential surface cracks in pipes[J].Fatigue and Fracture of Engineering Materials and Structures,1995,18:1155-1172.

        [2] Potte C,Albaladejo S.Stress intensity factors and influence functions for circumferential surface cracks in pipes[J].Engineering Fracture Mechanics,1991,39:641-650.

        [3] Couroneau N,Royer J.Simplified model for the fatigue growth analysis of surface cracks in round bars under modeⅠ [J].International Journal of Fatigue,1998,20(10):711-718.

        [4] Carpinteri A,Brighenti R.Circumferential surface flaws in pipes under cyclic axial loading [J].Engineering Fracture Mechanics,1998,60(4):383-396.

        [5] Raju I S,Newman J C.Stress intensity factors for circumferential surface cracks in pipes and rods[J].Fracture Mechanics,1986,60(4):789-805.

        [6] Henshell R D,Shaw K G.Crack tip finite elements are unnecessary[J]. International Journal for Numerical Methods in Engineering,1975,9:495-507.

        [7] Barsoum R S.Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements[J].International Journal for Numerical Methods in Engineering,1977,11:85-98.

        [8] Wu T,Bathias C.Application of fracture mechanics concepts in ultrasonic fatigue[J]. Engineering Fracture Mechanics,1994,47(5):683-690.

        [9] ANSYS company.ANSYS12.0 user’s manual[M].USA:ANSYS Company,2010.

        [10]Shahani A R,Habibi SE.Stress intensity factor in a hollow cylinder containing a circumferential semi-elliptical crack subjected to combined loading[J].International Journal of Fatigue,2007,29(1):128-140.

        [11]Beden S M,Abdullah S,Ariffin A K.Review of fatigue crack propagation models for metallic components[J]. European Journal of Scientific Research,2009,28(3):364-397.

        [12]Christensen R M.An evaluation of linear cumulative damage(Miner′s law)using kinetic crack growth theory[J].Mechanics of Time-Dependent Materials,2002,6(4):363-377.

        久久久久亚洲av成人片| 国产伦精品一区二区三区在线| 国产精品综合女同人妖| 2018天天躁夜夜躁狠狠躁| 无码骚夜夜精品| 久久免费视亚洲无码视频| 精品国产车一区二区三区| 亚洲国产成人av二区| 男人靠女人免费视频网站| 亚洲AⅤ无码日韩AV中文AV伦| 亚洲国产成人av第一二三区| 人妻免费一区二区三区免费| 中国女人内谢69xxxx免费视频| 亚洲免费观看| 美女一区二区三区在线观看视频| 亚洲av日韩一卡二卡| 玩50岁四川熟女大白屁股直播| 欧美成aⅴ人高清免费| 亚洲午夜精品国产一区二区三区| 日本人妻免费在线播放| 免费人成再在线观看视频| 国产AV无码专区亚洲AV桃花庵| av大片网站在线观看| 精品无码人妻夜人多侵犯18 | 丰满岳乱妇久久久| 中文字幕乱码人妻无码久久久1| 亚洲一区二区三区成人网| 国产特黄级aaaaa片免| 色爱区综合激情五月综合小说 | 国产精品高潮呻吟av久久4虎| 无码一区二区三区网站| 蜜桃久久综合一区二区| 女人色熟女乱| 免费一区在线观看| 免费人妻精品区一区二区三| 99久久无码一区人妻| 日韩精品无码一区二区中文字幕 | 日本高清一区二区不卡| 国产超碰人人做人人爽av大片 | 成午夜福利人试看120秒| 久久久精品人妻一区二区三区四|