疲劳裂纹扩展规律Paris公式的一般修正及应用-倪向贵

疲劳裂纹扩展规律Paris公式的一般修正及应用,,(,230026):介绍了疲劳裂纹扩展规律Paris公式及其与传统应力疲劳S-N曲线的关系,分析了计算疲劳裂纹扩展寿命的一般过程阐述了当前Paris公式在工程中的一般修正,具体描述了不同的修正形式及其主要特征,简要介绍了Paris公式在弹塑性断裂力学和连续损伤力学中的修正及应用各种应用实践表明,对于不同要求的工程问题要采用相应的修正形式:疲劳裂纹;扩展速率;Paris公式:TQ05012:A:1001-4837(2006)12-0008-08GeneralModificationandApplicationoftheParisLawforFatigueCrackPropagationNIXiang-gui,LIXin-liang,WANGXiu-xi(CASKeyLaboratoryofMechanicalBehaviorandDesignofMaterials,UniversityofScience&TechnologyofChina,Hefei230026,China)Abstract:ThepaperhasreviewedtheParislawforfatiguecrackpropagation,therelationshipbetweentheParisequationandthetraditionalstressfatigueS-Ncurveofmaterial,andthecommonprocessofcalculatingthelifetimeforfatiguecrackpropagation.ThegeneralmodificationandapplicationoftheParislawinengineeringisdiscussed,andthedifferentformsandcharacteristicsofmodificationareanalyzedandexplicated.Themodifica-tionandapplicationintheelastoplasticfracturemechanicsandthecontinuumdamagemechanicsisbrieflyin-troduced.Ithasbeenshownthat,theappropriatemodificationformsshouldbeadoptedfordifferentproblemsinengineering.Keywords:fatiguecrack;propagationrate;theParislaw0-,(Ñ)(Ò)(Ó)(Ñ),[1],,,1963ParisErdogan,Paris[2],#8#,,:da/dN=C($K)m(1)a)))N)))da/dN)))Cm))),,$K)))$K=Kmax-Kmin=f$RPa(2)f)))KmaxKmin)))$R)))[3]Paris,,,,Paris,ParisParis,,,,[4];,,[5],,,Paris,,Paris,Ñ,Paris,Paris1ParisS-NS-N,S-NParis$R,Paris:da/dN=C($K)m=C[f(a,W,,)$RPa]m(3)[1]:$RmN=Qafa0daC[f(a,W,,)Pa]m(4)a0)))ac)));af(afac)W)))(4),,$R$S,:$SmN=C1SmaN=C2(5)Sa))),Sa=$S/2C1C2)))(5)S-N,,S-Nda/dN)$K,Paris,,ParisS-N,,[6]2ParisKda/dN$K,,,,,,,,1,[1,7]:1(1)Ñ(Ñ):#9#2312169$Kth,,$K[$Kth,,,,Ñ(2)Ò(Ò):(),$Kth,,da/dNParis,Paris(3)Ó(Ó):,da/dN,,KmaxKc,$K=(1-R)Kmax,1$K=(1-R)Kc(,Kc,R),Ò211计算临界裂纹扩展尺寸a0ac,Nc,,ac[1]:Kmax=fRmaxPac[Kcac=1P(KcfRmax)2(6)Rmax;(Wma),f=1;(Wma),f=1112212确定材料常数Cm[1],(ai,Ni),(da/dN)i:(da/dN)i=(ai+1-ai)/(Ni+1-Ni)(7)Paris(1):lg(da/dN)=lgC+mlg($K)(8),y=lg(da/dN)x=lg($K),lg($K)ilg(da/dN)i,,m,(8)C[8],a/c,ABParis:da/dN=CA($KA)mda/dN=CB($KB)m(9)$KA$KB)))CACB)))NewmanRaju[9]CB=019mCA[10],:CA=C,CB=019mCA(10)(CA+CB)/2=C,CB=019mCA(11),(10),(11)213疲劳裂纹扩展寿命基本方程,f=,,Paris:Qaca0daC(f$RPa)m=QNc0dN(12)Nc=1C(f$RP)m(015m-1)(1a015m-10-a015m-1c)(mX2)1C(f$RP)mln(a0ac)(m=2)(13)m=4,(13):Nc=ac-a0C(f$RPa0)4#a0ac(14)$K,(14):Nc=ac-a0C($K)4#a0ac(15),mX4,(15):N=aN-a0C($K)m#a0aN(16)(16)CVDA)1984[7],a0aNN,a0,#10#CPVTParisVol231No122006(RBI),,[11],,,,RBI,,[12],3Paris311考虑应力比R和断裂韧性Kc的影响,,FormanWalkerFormanKc[1,7]:dadN=C($K)m(1-R)Kc-$K(17)Forman,,KcR=Kmin/Kmax$K=Kmax-Kmin[13]:dadN=CKmax($K)m-1Kc-Kmax(18)(18)Forman,Walker,Kmax[1]:dadN=C[(1-R)mKmax]n(19)CmnWalkerR0R0,,,[13]:dadN=CKmmax($K)n(20)[14](20),$K,;Kmax,,W319A356312考虑有效应力强度因子幅$Keff的影响312111971,W1Elber-,,,Rop;,,Rcl;,Paris[1]:dadN=C($Keff)m(21)dadN=C(U$K)m=UmC($K)m(22)U)))U=$Keff/$K=$Reff/$R=(Rmax-Rop)/$R1(23)$ReffRmaxRop,[15]Ñ,(21),:$Keff=f$ReffPa$Reff=R1-Rtop(24)R1)))Rtop)))COD,rRop,,r=0Rtop31212Wheeler,,,[13],Wheeler,Willenberg,RresForman,#11#2312169[1]:dadN=C($Keff)m(1-Reff)Kc-$Keff(25):$Keff=f[(Rmax)eff-(Rmin)eff]Pa(26):Reff=(Rmin)eff/(Rmax)eff(27):(Rmax)eff=Rmax-Rres(Rmin)eff=Rmin-Rres(28),Rres,,Rres31213,,,,ÒÓ,,Ò,Ó[16],,$Keff,[17],Paris:da/dN=Cf1(KÒ0/KÑ0)($KV)mf2(KÒ0/KÑ0)(29)$KV=12$KÑ+12$K2Ñ+6$K2Ò$KÑ$KÒ)))Cm))),ÑKÑ0KÒ0)))f1(KÒ0/KÑ0)f2(KÒ0/KÑ0))))Ò,:f1(KÒ0KÑ0)=1+3192sin[tan-1(KÒ0KÑ0)]-0152{sin[tan-1(KÒ0KÑ0)]}2(30)f2(KÒ0KÑ0)=1-2109sin[tan-1(KÒ0KÑ0)]+1127{sin[tan-1(KÒ0KÑ0)]}2(31):$Keff=f1(KÒ0/KÑ0)-m@$KVf2(KÒ0/KÑ0)(32)(21),Paris[18],,:K2eff=(KÑ+B|KÓ|)2+2K2Ò(33),B=1Paris[19],Ñ-Ò,$Keff:$Keff=(K2Ñmax+$K2Ò)1/2(34),KÑmaxÑ,[19](21)(34),,,[20],:$a/$N=C($Keff)m(35)$Keff=12cosH02[$KÑ(1+cosH0)-3$KÒsinH0](36),H0,,,ÒÓÑ313考虑应力比和门槛应力强度因子幅$Kth的影响1972,Donahue[21]$Kth,Paris:da/dN=C($K-$Kth)m(37)1977,McEvilyGroeger[21],,m=2#12#CPVTParisVol231No122006dadN=C($K-$Kth)2(1+$KKc-Kmax)(38)[16]R1r2PrR1,,:da/dN=D($K-$Kth)2(39)D,,ParisC,Paris[1]:dadN=C[($K)m-($Kth)m](1-R)Kc-$K(40),(40)Forman[22],:dadN=C1(1-R)Kc-$K[2($K-$Kth)1-R]m(41),,LZ50,1999,McEvily[23]:da/dN=C($Keff-$Keffth)2(42)$Keffth(10-10m/cycle),,,ARMCO-ironD16CzTC4314从能量角度分析时的修正与应用2020,Griffith,,GGK[7],ÑÒ:G=K2/E()G=(1-L2)K2/E()(43)Ó:G=(1+L2)K2/E(44)E)))L)))$G,Paris[24]:da/dN=C($G)m(45)(45),4Paris411在弹塑性断裂力学中的修正及应用,,,,,,,$K,,[25]41111$JJ,Paris[7,26]:da/dN=CJ($J)mJ(46)CJmJ)))J[27],(46),JK,[25,28]Rice,,,JG[29];,,JG[30][31,32]/Ñ-Ó,,:da/dN=CÑ($JÑ)mÑda/dN=CÓ($JÓ)mÓ(47)ÑÓÑÓ,ÑÓ#13#2312169,da/dN:da/dN=CÑ($JÑ)mÑ+CÓ($JÓ)mÓ(48)(48),41112$D$E,,,$D,[7,26]:da/dN=CD($D)mD(49)CDmD)))CTOD,$D$Deff[33]$Deff=$K2eff2ERys(50)Rys)))COD,CODCOD,COD,J,,,J,JCOD,J[34,35]412在连续损伤力学中的修正及应用Paris,,dD/dN[30],D,,Paris[36],D,Paris:dL/dN=Cd($K)C(51)Cd=rc2Dc(1C22Prc)C(52)Dc)))rc)))C2C)))L))),[36],[37],(51),Paris5,Paris,,(1)Paris,,,Paris,Paris(2)Kf,,,(3)Paris,,J,,,(4),,Paris,,(51)Paris,Paris(5),Paris,2005,Taylor[38]#14#CPVTParisVol231No122006,[21],:[1].[M].:,20011[2]ParisP1,ErdoganF1.ACriticalAnalysisofCrackGrowthLaws[J].JournalofBasicEngineering,TransactionoftheASME,1963,85:528-5341[3],,,.Paris[J].,2003,3,35(2):171-175.[4],,,.CF-62[J].,2003,20(2):38-42.[5],,,.[J].,2001,18(5):43-53.[6].S-N[J].,2000,2,24