第八章_疲劳裂纹扩展课件.PPT

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第八章 疲劳裂纹扩展,8.1,疲劳裂纹扩展速率,8.2,疲劳裂纹扩展寿命预测,8.3,影响疲劳裂纹扩展的若干因素,8.4,疲劳裂纹扩展速率试验,返回主目录,1,第八章 疲劳裂纹扩展,（,Fatigue crack growth),研究问题：含裂纹体的,疲劳裂纹扩展规律，,疲劳裂纹扩展寿命预测方法。,研究方法,裂纹尖端的应力应变场,LEFM：K,EPFM：,d,断裂力学法,初始条件：,初始裂纹尺寸,a,0,？,破坏条件：,临界裂纹尺寸,a,c,2,The fatigue life of component is made up of initiation and propagation stages.The size of the crack at transition from initiation to propagation is usually unknown and often depends on the point of view of the analyst and the size of the component being analyzed.,构件的疲劳寿命由起始和扩展二部分组成。,从起始到扩展转变时的裂纹尺寸通常未知且往往取决于分析的着眼点和被分析构件的尺寸。,3,For example,for a researcher equipped with microscopic equipment it may be on the order of a crystal imperfection,dislocation,（,位错）,or a 0.1 mm crack,while to the inspector in the field it may be the smallest crack that is readily detectable with nondestructive inspection equipment.,例如，对于有显微设备的研究者，上述尺寸可能是晶粒缺陷、位错或,0.1mm,的量级，,而对于现场,检验者，,则是,无损检测设备可检出最小的裂纹。,4,问题,:,有缺陷怎么办？发现裂纹，能否继续,使用？剩余寿命？如何控制检修？,均匀、无缺陷材料,循环载荷作用,S-N,曲线,e,-N,曲线,裂纹萌生寿命,理论基础：线弹性断裂力学,(1957),计算手段：计算机迅速发展；,实验手段：高倍电镜、电液伺服,疲劳机，电火花切割机等,研究可能,疲劳裂纹扩展研究需求,我们已经讨论过应力寿命方法和应变寿命方法，现在讨论用于疲劳裂纹扩展估计的断裂力学法。,5,给定,a,，,d,a,/dN,；,给定,a,d,a,/dN,。,8.1,疲劳裂纹扩展速率,讨论张开型,(I,型,),裂纹。,a,r,p,，,LEFM,力学可用。,一,.,a,N,曲线,二、疲劳裂纹扩展控制参量,a,N,曲线的斜率，就是裂纹扩展速率,da/dN,。,a(mm),a,0,N,CCT,CT,1,D,s,2,D,s,3,D,s,R=0,K,a,故,K,d,a,/dN,标准试样,预制疲劳裂纹,恒幅疲劳实验,记录,a,N,6,裂纹只有在张开的情况下才能扩展，,故控制参量,K,定义为：,K,=,K,max-,K,min R,0,K,=,K,max R,0,疲劳裂纹扩展速率,d,a,/dN,的控制参量,是,应力强度因子幅度,K,=f(,a,),，,即：,d,a,/dN=,(,K,R,),应力比,R=K,min,/K,max,=,min,/,max,=P,min,/P,max,；,与,K,相比，,R,的影响是第二位的。,7,三,.,疲劳裂纹扩展速率,FCGR,Fatigue Crack Growth Rate,R=0,时的,d,a,/dN-,K,曲线，是基本曲线。,实验,a,=,a,0,R=0,=const,a(mm),a,0,N,D,s,R=0,i,a,d,a,dN,a,N,曲线,a,i,(d,a,/dN),i,a,i,K,i,d,a,/dN-,K,曲线,lg da,/,dN,10,-5 -6,10,-9,lg,(K),D,8,lg da,/,dN,1 2 3,10,-5 -6,10,-9,lg,(K),D,1.da/dN-,K,曲线,低、中、高速率三个区域：,c,K,=(1-,R),K=(1-R)K,max,th,D,K,低速率区：,有下限或门槛值,K,th,K,K,th,裂纹不扩展,。,高速率区,:,有上限,K,max,=,K,c,，,扩展快，寿命可不计。,中速率区,:,有对数线性关系。,可表达为：,d,a,/dN=C(,K,),m,C,、,m,和,K,th,，,是描述疲劳裂纹扩展性能的,基本参数,。,微解理为主,微孔聚合为主,条纹为主,9,lg da,/,dN,1 2 3,10,-5 -6,10,-9,lg,(K),D,th,D,K,微解理为主,微孔聚合为主,条纹为主,三种破坏形式,:,微解理型,低速率,条纹型,稳定扩展,微孔聚合型,高速率,10,Paris,公式,：,d,a,/dN=C(,K,),m,2.,裂纹扩展速率公式,K,是疲劳裂纹扩展的主要控制参量；,疲劳裂纹扩展性能参数,C,、,m,由实验确定。,3.,扩展速率参数,C,m,的确定,实验,a,=,a,0,R=0,记录,a,i,、,N,i,(,K),i,=,f,(,a,i,),(d,a,/dN),i,=,(,a,i,+1,-,a,i,)/(N,i+1,-N,i,),a,i,=,(,a,i+,1,-,a,i,)/2,lg(,d,a,/dN)=lgC+mlg(,K,),最小二乘法,C,m?,11,8.2,疲劳裂纹扩展寿命预测,1.,基本公式,应力强度因子：,a,f,K,=,p,s,中心裂纹宽板,f=1,；,单边裂纹宽板,f=1.12,临界裂纹尺寸,a,C,：,有线弹性,断裂判据,：,或,疲劳裂纹扩展公式：,得到,裂纹扩展方程,：,(f,D,R,a,0,a,c,)=N,c,f,一般是裂纹尺寸的函数，通常需要数值积分。,12,得到,:,D,-,-,D,=,-,-,),ln(,),(,1,1,1,),1,5,.,0,(,),(,1,0,1,5,.,0,1,5,.,0,0,a,a,f,C,a,a,m,f,C,N,C,m,m,C,m,m,C,p,s,p,s,m=2,m,2,da/dN,用,Paris,公式表达时的裂纹扩展方程,对于无限大板，,f=const.,，,在,=const.,作用下，由,Paris,公式,da/dN=C(,K,),m,积分有：,13,已知,a,0,a,c,给定寿命,N,c,估算在使用工况,(R),下所允许使用的最大应力,Smax,。,2.,Paris,公式的应用,抗疲劳断裂设计计算,已知载荷条件,S,，,R,，,初始裂纹尺寸,a,0,估算临界裂纹尺寸,a,c,剩余寿命,N,c,.,已知载荷条件,S,，,R,给定寿命,N,c,确定,a,c,及可允许的初始裂纹尺寸,a,0,。,断裂判据,：,C,C,K,a,f,K,=,p,s,max,max,裂纹扩展方程,：,N,c,=,(,f,D,R,a,0,a,c,),基本方程,14,解：,1.,边裂纹宽板,K,的表达式：,K=1.12,s,(,p,a,),1/2,例,1,：,边裂纹板,a,0,=0.5mm,载荷为,s,max,=200Mpa,。,R=0,材料参数,s,ys,=630MPa,s,u,=670MPa,D,K,th,=5.5MPa,K,c,=104MPa,裂纹扩展速率为,d,a,/dN=6.910,-12,(,D,K),3,试估算其寿命。,4.,临界裂纹长度,a,c,？,由断裂判据有：,K,c,=1.12,s,max,(,p,a,c,),1/2,；,a,c,=,68mm,3.,长度为,a,0,的初始裂纹是否扩展？,D,K=1.12,s,(,p,a,),1/2,=9,MPa,D,K,th,=5.5,2.,D,K=K,max,-K,min,=1.12(,s,max,-,s,min,),=,1.12,s,15,5.,估算裂纹扩展寿命,N,c,：,由裂纹扩展速率方程得：,N,c,=189500,次循环,a,0,(mm),K,c,(MPa,m,),a,c,(mm,),N,c,(,千周）,%,0.5,104,68,189.5,100,1.5,104,68,101.9,53.8,2.5,104,68,74.9,39.5,0.5,208,272,198.4,105,0.5,52,17,171.7,90.6,讨论,1,：,a,0,和,K,c,对疲劳裂纹扩展寿命的影响,控制,a,0,，,可大大提高疲劳裂纹扩展寿命。,高强脆性材料,K,c,低,a,c,、,N,c,小，扩展寿命可不计。,16,“,若疲劳寿命完全由裂纹扩展所贡献，则,S-N,曲线可由,d,a,/dN-,K,关系获得且指数与,Paris,公式相同,”。,对于含有缺陷或裂纹的焊、铸件，是特别真实的,。,讨论,2,：,d,a,/dN-,K,曲线与,S-N,曲线之关系,上例中，若以,a,L,(,a,L,a,C,),定义寿命，,=const.,，,由,paris,公式：,m,a,W,a,f,C,dN,da,),(,p,s,D,=,L,积分有：,Const.,a,f,C,d a,N,L,a,a,m,m,=,=,D,0,p,s,此即,S-N,曲线：,17,讨论,3,：,Miner,理论用于裂纹扩展阶段,假设尺寸为,a,0,的裂纹，在,S,1,、,S,2,、,S,3,下,经,n,1,、,n,2,、,n,3,循环后，扩展到,a,L,。,S,1,下循环,n,1,次,从,a,0,扩展到,a,1,；,S,1,m,n,1,=,1,0,),(,a,a,a,d,a,j,S,2,下循环,n,2,次,从,a,1,扩展到,a,2,；,S,2,m,n,2,=,2,1,),(,a,a,a,d,a,j,S,3,下循环,n,3,次,从,a,2,扩展到,a,L,；,S,3,m,n,3,=,L,2,),(,a,a,a,d,a,j,S,1,m,N,1,=,L,0,),(,a,a,a,d,a,j,S,2,m,N,2,=,L,0,),(,a,a,a,d,a,j,S,3,m,N,3,=,L,0,),(,a,a,a,d,a,j,在,S,i,下从,a,0,到,a,L,的裂纹扩展,寿命为,N,1,、,N,2,、,N,3,。,18,此即,Miner,理论。,若不计加载次序影响，,Miner,理论也可用于裂纹扩展阶段,。,在,S,i,下循环,n,i,次的损伤为,n,i,/N,i,所以总损伤为：,n,1,/N,1,+n,2,/N,2,+n,3,/N,3,=(,+)/=1,1,0,),(,a,a,a,d,a,j,2,1,),(,a,a,a,d,a,j,L,2,),(,a,a,a,d,a,j,L,0,),(,a,a,a,d,a,j,若,a,0,=0.5,a,L,=30mm,，,每年载荷谱如表。,先算各,S,i,下的裂纹扩展寿命,N,i,，,再算,n,i,/N,i,。,S,i,(MPa),n,i,(10,3,)N,i,(10,3,)n,i,/N,i,150 30,426.6,0.0703,200 20,180.0,0.1111,250 10,92.1,0.1086,300 5,53.3,0.0938,设寿命为,年，则有：,n/N=1,，,=1/,n/N=2.6,年,19,例,2,中心裂纹宽板，作用应力,max,=200MPa,min,=20MPa,。,K,c,=104MPa,工作频率,0.1Hz,。,为保证安全，每,1000,小时进行一次无损检验。,试确定检查时所能允许的最大裂纹尺寸,a,i,。,d,a,/dN=410,-14,(,K),4,m/c,解：,1.,计算临界裂纹尺寸,a,c,：,对于中心裂纹宽板,f=1.0,有：,a,c,=,=0.086 m,2,max,),(,1,s,p,c,K,2.,检查期间的循环次数,:,N=0.136001000=3.610,5,次,20,3.,尺寸,a,i,的裂纹,在下一检查期内不应扩展至,a,c,。,本题,m=4,由裂纹扩展方程有：,-,-,D,=,-,-,1,1,),1,5,.,0,(,),(,1,1,5,.,0,1,5,.,0,0,a,a,m,f,C,N,m,C,m,m,C,p,s,注意,=,max,-,min,=180Mpa,，,有：,=160.8,得到：,a,i,=1/160.8=0.0062m=6.2mm,c,m,c,i,a,C,N,a,1,),(,1,+,D,=,p,s,讨论,：若检查发现,a,i,6.2mm,则不安全。,要继续使用，降低应力水平或缩短检查期。,21,如：检查时发现裂纹,a,i,=10mm,若不改变检查周期继续使用，则应满足：,注意，,改变，临界裂纹尺寸,a,c,不再为,0.086,m，,而应写为：,a,c,=,解得：,159MPa,max,=,/(1-R),176 Mpa,2,2,max,),),1,(,(,1,),(,1,s,p,s,p,D,-,=,c,c,K,R,K,如缩短检修周期，同样可求得由,a,i,=10mm,到,a,c,=86mm,的循环次数为：,N,213238,次，,检查期周为：,T,N/(0.13600)=592,小时。,22,4),计算任一时刻的裂纹长度,a,i,及其对应,K,i,。：,a,i,=,a,o,+,a,i,(,i,=1,n),i,i,i,a,W,a,f,K,p,s,D,=,D,),(,L,3.,恒幅载荷下，裂纹扩展的数值计算方法,由,Paris,公式有：,d,a,/dN=C(,K),m,=C,m,(,a,),已知,a,0,，,，,参数,C,、,m,，,则数值计算方法为：,1),裂纹是否会扩展？,th,a,a,K,a,W,a,f,K,D,D,=,D,=,0,0,),(,0,p,s,L,2),临界裂纹尺寸,a,c,。,即：,2,max,),(,1,s,p,f,K,a,C,C,=,3),选取增量,a,i,。,如,a,i,=0.01,a,i,-1,；,a,i,越小精度越高,23,6),假定在,a,i,-1,-,a,i,内，,d,a,/dN,不变，且：,裂纹增长,a,i,的循环数：,与,a,i,对应的累计循环次数,N,i,为：,(,/,),(,),;,(,),/,da,dN,C,K,K,K,K,i,i,m,i,i,i,=,=,+,-,D,D,D,D,1,2,D,D,N,a,da,dN,i,i,i,=,/,(,/,),i,i,N,N,D,=,5),如,(,K,i,-,K,i,-1,)/,K,i,(=0.01),满足精度，继续。,否则,令,a,i,=,a,i,/2,返回,4,。,重复3)-6),直到,a,i,=,a,0,+,a,i,=,a,c,时，停止。,由算得的（,a,i,，,N,i,）,数据，可作,a,-N,曲线，,且从,a,i,扩展到,a,c,的寿命为：,N,c,=,N,i,24,Fracture mechanics approaches require that an initiation crack size be know or assumed.For components with imperfections or defects(such as welding porous,（,疏松,）,inclusions and casting defects,etc.),an initial crack size may be know.,断裂力学方法需要已知或假设一个初始裂纹尺寸。对于有缺陷（如焊接疏松、夹杂和铸造缺陷等）的构件，初始裂纹是可以知道的。,25,Alternatively,for an estimate of the total fatigue life of a detect-free material,fracture mechanics approaches can be used to determine propagation.Strain life(or stress life)approaches may then be used to determine initiation life,with the total life being the sum of these two estimates.,换言之，对于无缺陷材料疲劳总寿命的估计，断裂力学方法可用于确定裂纹扩展。应变寿命或应力寿命方法则用于确定起始寿命，总寿命是这二者之和。,26,At low strain amplitudes up to 90%0f the life may be taken up with initiation,while at high amplitudes the majority of the fatigue life may be spent propagation a crack.,Fracture mechanics approaches are used to estimate the propagation life.,在低应变幅时，裂纹起始可占到寿命的,90%,，而在高应变幅下，疲劳寿命的大部分在于裂纹扩展。断裂力学方法就是用于估算此扩展寿命的。,27,再 见,习题：,8-3,，,8-5,第一次课完,请继续第二次课,返回主目录,28,第八章 疲劳裂纹扩展,8.1,疲劳裂纹扩展速率,8.2,疲劳裂纹扩展寿命预测,8.3,影响疲劳裂纹扩展的若干因素,8.4,疲劳裂纹扩展速率试验,返回主目录,29,前节回顾,:,The plot of log d,a,/dN versus log,D,K is a sigmoidal(S,形,),curve.,This curve may be divided into,three regions.,At low stress intensities,cracking,behavior is associated with threshold effects.,In the mid-region,the curve is essentially linear.,Finally,at high,D,K values,crack growth rates are extremely high and little fatigue life is involved.,lg da,/,dN,1 2 3,10,-5 -6,10,-9,lg,(K),D,c,K,=(1-,R),K=(1-R)K,max,th,D,K,30,Most of the current application of LEFM concepts to describe crack growth behavior are associated with region 2.In this region the log da/dN versus log,D,K curve is approximately linear and lies roughly between 10,-7,and 10,-4,mm/cycle.Many curve fits to this region have been suggested.The Paris equation,which was proposed in the early 1960s,is the most widely accepted.,大多数用线弹性断裂力学描述裂纹扩展的应用是与区域,2,相关的。在这一区域，,logda/dN-log,D,K,曲线,近似线性且在,10,-7,-10,-4,mm/c,间。,已有许多拟合曲线提出，,60,年代初的,Paris,公式是应用最广的。,31,8.3,影响疲劳裂纹扩展的若干因素,K,是控制,d,a,/dN,的最主要因素。,平均应力、加载频率、环境等的影响较次要，但有时也不可忽略。,同一材料,由不同形状、尺寸的试件所得到的,d,a,/dN-,K,曲线相同。,d,a,/dN-,K,曲线可以描述疲劳裂纹扩展性能。,K,Mpa.m,1/2,4 10 20 40,lgd,a,/dN,(m/c),-9,-8,-7,-6,碳钢,R=0.05,K Mpa.m,1/2,32,1.,平均应力或应力比的影响,注意到,a,=(1-R),max,/2,，,m,=(1+R),max,/2,；,有：,故,a,给定时，,R,，,m,。,讨论,应力比的影响，,就是,讨论,平均应力的影响。,a,m,R,R,s,s,),1,(,),1,(,-,+,=,R0,、,R0,时，,min,0,。,a,给定，,R,，,min,，,max,。,三个速率区域内，,da/dN,均增大。,d,a,/dN-,K,曲线整体向左移动。,Forman,公式：,K,K,R,K,C,dN,da,C,m,D,-,-,D,=,),1,(,),(,K=(1-,R,)K,max,K,max,K,c,，,分母,0,，,d,a,/dN,。,K,K,th,，,d,a,/dN,0,。,若考虑,K,th,的影响，有：,da,dN,C,K,K,R,K,K,m,th,m,c,=,-,-,-,(,),(,),(,),D,D,D,1,34,th,K,R=0.8,0,-1,lgda/dN,D,lg(K),D,低速率区,，,R,，,K,th,。,R,0,的情况：,负应力存在，,对,d,a,/dN,三区域的影响不同。,情况比,R0,时复杂得多。,0 .2 .4 .6 .8 1.0,87654321,低碳钢,低合金钢,不锈钢,A517-F,9301,A508C,A533B,不同钢材的,R-,K,th,关系,R,K,th,Mpa.m,1/2,有,经验关系为：,K,th,=,K,0,th,(1-,R),K,o,th,是,R=0,时的基本门槛应力强度因子幅度。,参数,、,由实验确定。,图中钢材的下限为：,K,th,=7.03(1-0.85R),35,Formans equation is often used to predict stress ratio effects.As R increases,the crack growth rate increases.This is consistent with test observations.Formans equation is valid only when R0.Generally,it is believed that when R0,no significant change in growth rate occurs compared with the R=0.Again this is material dependent,as some researchers have obtained data for certain materials which show higher growth rates for R0,时正确。一般认为与,R=0,相比，,R0,对,da/dN,没有显著影响。这仍与材料有关，对有些材料，也有研究者在,R0,时得到较高,da/dN,。,36,但是，在,高温或腐蚀环境下,，频率及波形对,d,a,/dN,的影响显著增大，是不容忽视的。,2.,加载频率的影响,30Cr,2,WmoV,钢,(30,万千瓦汽轮机高压转子钢,),频率影响实验。,低速区：加载频率对,d,a,/dN,基,本无影响。,中速率区：,f,，,d,a,/dN,。,有：,d,a,/dN=C(f)(,K),m,=(A-Blgf)(,K),m,lg(d,a,/dN),0.7,11,104,980,10000,30Cr WMoV,lg(K),2,D,f(,次,/,分,),在室温、无腐蚀环境中，,f=0.1,100Hz,时,对,da/dN,的影响可不考虑。循环波形影响是更次要的。,37,腐蚀介质作用下，裂纹可在低于,K,1C,时发生扩展。,试件加载到,K,1,，,置于腐蚀介质中。记录裂纹开始扩展的时间,t,f,。,腐蚀疲劳是,介质引起的,腐蚀破坏,过程,和,应力引起的,疲劳破坏,过程,的共同作用。,这二者的共同作用，比任何一种单独作用更有害。,1,）,应力腐蚀开裂,(Stress corrosion cracking),3.,腐蚀环境对,d,a,/dN,的影响,K,1,K,1scc,，,t,f,，,(,约,1000,小时,),。,K,1scc,是应力腐蚀开裂门槛值。,K,1,K,1scc,不发生应力腐蚀开裂。,K,1,K,1c,K,1scc,0,t,f,38,(d,a,/dN),CF,与,K,的关系如图，可分为三类：,2,）,腐蚀疲劳裂纹扩展速率,(d,a,/dt),CF,(1-R)K,c,thCF,D,d,a,/dN,K,K,A,A,类,；,(,K),thCF,K,th,腐蚀使,(d,a,/dN),CF,普遍加快,，,如铝合金在淡水中。,B,1scc,D,d,a,/dN,(1-R)K,K,(1-R)K,c,B,类：,K,max,K,1scc,腐蚀,使,d,a,/dN),CF,。,马氏体镍在干氢中,.,1scc,D,d,a,/dN,(1-R)K,K,C,(1-R)K,c,C,类：,AB,混合型 如高强钢在盐水中。,加载频率越低，腐蚀过程越充分,，,(d,a,/dN),CF,越快。,39,The fatigue crack growth rate can be greatly influenced by environmental effects.These effects are extremely complicated duo to the large number of mechanical,metallurgical,and chemical variables and the interaction between them.,环境效应对疲劳裂纹扩展速率的影响很大。由于有大量的机械、冶金和化学因素及其相互作用，环境效应极其复杂。,The environmental effect on fatigue crack growth rate is strongly dependent on the material-environment combination.Several additional factors that influence the environmental effect are frequency of loading,temperature,waveform of loading,and stress ratio.,环境对疲劳裂纹扩展速率的影响强烈地依赖于材料与环境的组合。影响环境效应的一些附加因素是加载频率、温度、加载波形和应力比。,40,In general,at low frequencies,crack growth rate increase as more time is allowed for environmental attack during the fatigue process.,一般地说，低频率时裂纹扩展速率增大，因为在疲劳过程中环境效应有更充分的时间作用。,Reduced fatigue life is usually observed with increasing temperature.,In addition,environmental effects are usually greater at elevated temperature,which is duo in part to oxide action.,温度增加，通常使疲劳寿命降低。同时，高温下环境的影响更大，这有一部分是氧化作用所致。,No effect of waveform on fatigue crack growth rate is usually observed in air.But in corrosion environment,higher da/dN generally occur if increasing tensile portion of the loading cycle occurs more slowly.,在空气中，一般观察不到波形对疲劳裂纹扩展速率的影响。但在腐蚀环境中，若载荷循环的拉伸部分作用慢，,da/dN,一般较高。,41,8.4,疲劳裂纹扩展速率试验,目的,：测定材料的,da/dN-,D,K,曲线,一、试验原理,：,Paris,公式,：,d,a,/dN=C(,K,),m,实验,a,=,a,0,R=0,记录,a,i,、,N,i,(,K),i,=,f,(,a,i,),(d,a,/dN),i,=,(,a,i,+1,-,a,i,)/(N,i+1,-N,i,),a,i,=,(,a,i+,1,+,a,i,)/2,lg(,d,a,/dN)=lgC+mlg(,K,),最小二乘法,C,m?,a(mm),a,0,N,D,s=,const.,R=0,D,a,i,DN,i,lgda/dN,lg(,D,K),42,二、试样,L=4W,W,a,D,P,三点弯曲,2孔,f,0.25W,D,P,D,P,a,W,1.25W,1.2W,0.55W,紧凑拉伸,中心裂纹,Ds,W,B,Ds,2a,建议厚度：,W/20,B,W/4,B,W,a,1,a,2,a,3,a,4,a,5,疲劳裂纹前缘,太厚,：疲劳裂纹前缘舌型大，表面读取的尺寸与内部相差大。若用,B=W/2,，,常需作尺寸修正。,43,三、试验方法,D,P,D,P,a,W,1.2W,紧凑拉伸试样,h,n,D,a,i,1,.,预制裂纹,要求,:(,CT,试样为例,),切口,尺寸：,a,n,0,.2W,(,保证,LEFM,的,K,解可用,),疲劳,预裂：,D,a,i,max0.1B,h,(,避开切口对裂尖的影响,),预裂,载荷,:R,与试验相同；,K,max,不大于开始试验时的,K,值。,(,保证裂纹足够尖锐，但所需时间长,),若用较大的,K,max,预裂,，,应按规定逐级降载。,44,2.K,增加试验法,da/dN-,D,K,曲线一般分为三个区域。不同的区域，试验方法不同。,K,增加试验法用于中高速率区。,名义,K,梯度,C,：,d,a,dK,K,C,1,=,K,随裂纹扩展的变化率,若应力比,R,不变有：,d,a,dK,K,1,d,a,dK,K,1,max,max,=,d,a,dK,K,1,min,min,=,d,a,d(,D,K),K,1,=,D,在恒幅载荷试验中，,D,P=const.,故有：,d(,D,K)0,C0,是,K,不断增加的试验方法。,45,3.K,减小试验法,K,减小试验法用于低速率区。,lg da,/,dN,1 2 3,10,-5 -6,10,-9,lg,(K),D,？,名义,K,梯度,C,：,d,a,dK,K,C,1,=,0,K,增大试验法,0,a,D,K,or,D,P,D,P,D,K,R,不变时有：,d,a,d(,D,K),K,1,=,D,C,将上式从,a,0,到,a,积分，得到：,D,K=,D,K,e,0,C(,a,-,a,0,),标准建议,C,-,0.08mm,-1,。,由此可计算不同,a,时的,D,K,、,D,P,。,46,小 结,1,）若,a,r,p,则线弹性断裂力学可用。,应力强度因子为：,K=f(,a,),；,中心裂纹：,f,(,a,)=1.0；,边裂纹：,f=1.12,。,2,）疲劳裂纹扩展速率的主要控制参量是,K,，,下限有,K,th,上限有,(1-R)K,c,。,K=K,max,-K,min,=f(,a,),R,0,min,0,=K,max,R,0,min,0,裂纹不扩展条件,K=f(,a,0,),K,th,临界裂纹尺寸,Kmax=K,c,a,c,=(1/,)(K,c,/f,max,),2,47,m=2,m,2,3,）,Paris,公式：,d,a,/dN=C(,K),m,在恒幅循环载荷作用下，积分后有,：,4,）初始裂纹尺寸,a,0,对寿命影响很大，要控制,a,0,。,5,）,R,，,d,a,/dN,；,频率 ，,d,a,/dN,；,腐蚀环境下,d,a,/dN,增高；,高温、腐蚀环境下，加载频率影响增大。,48,6,）基本疲劳分析方法的比较,应力疲劳法,应变疲劳法,断裂力学法,方,法,S,S,y,；,N,N,t,S,m,N=C;,S,a,/S,-1,+S,m,/S,u,=1,D=,n/N=1,相对,Miner,理论,N,A,=N,B,无限寿命设计,S,S,f,(n/N),B,(,n/N),A,S,S,y,；,N,N,t,e,a,=,s,a,/E+(,s,a,/K),1/n,De,=,Ds,/E,+2(,Ds,/2K),1/n,Neuber,曲线,:,DsDe,=K,t,2,D,S,D,e,e,e,e,a,ea,pa,=,+,=,s,e,f,b,f,c,E,N,N,+,(,),(,),2,2,S,S,y,;,r,p,a,裂纹不扩展,K,K,th,临界裂纹：,Kmax=Kc,Paris,公式：,d,a,/dN,=C(,K),m,49,应力疲劳法,应变疲劳法,断裂力学法,优,点,1、材料参数,少，易于,获取,。,2、分析方法,简单。,3、有大量的,数据积累,1,.,能描述循环应,力应变响应。,2.可考查载荷次,序影响。,3.利于缺口疲劳,分析。,4.利于疲劳,-,蠕变,混合分析。,1.,可考虑裂纹扩,展。利于控制,2.对扩展机理有,较好物理解释,3.可控制初始损,伤，检查周期,使用载荷等，,以保证安全。,50,应力疲劳法,应变疲劳法,断裂力学法,缺,点,1.经验性，不,考虑裂纹。,2.材料参数与,试件几何、,载荷形式有,关，通用性,较差。,3.缺口效应难,于分析,。,1,.,分析计算,较复杂。,2.只考虑裂,纹萌生。,3.缺口分析,过于偏保,守。,1.不研究裂纹起,始。,2.,a,0,往往难于估,计。,3.,构件几何复杂,时难算,K,。,4.LEFM,不满足,时要用,EPFM.,51,应力疲劳法,应变疲劳法,断裂力学法,应,用,1.,长寿命构件,如传动轴、,弹簧、齿轮,等。,2.,高强材料,S,S,y,a,c,小,3.,初步设计估,算。,4.,与,LEFM,一,起作全寿命,分析。,1.,构件,N,小，,塑性应变大,如低强结构,钢缺口件。,2.,高温、大应,变情况。,3.,高应力集中,情况。,4.,与,LEFM,一,起作全寿命,分析。,1.,大型，重要结,构件，如飞机,结构，核反应,堆，压力容器,2.,预先有裂纹存,在的结构，如,大型焊、铸件,3.,尖缺口寿命。,（近似裂纹）,52,summary,Fracture mechanics approaches provide an estimate of the crack propagation fatigue life.,The fatigue crack growth rate can be related to the stress intensity factor range.From this,cycles to failure may be calculated.,The fatigue life estimate is strongly dependent on the initial crack size,a,i,large changes in the estimate of the final crack size,a,c,result in only small changes in the life estimate.,53,问题,2,：变幅载荷作用次序，对,d,a,/dN,有,何影响；如何解释、预测其影响？,问题,1,：裂纹尖端的应力有奇异